text:
\section{Introduction}
\label{sec:intro}

The Moon, as well as other bodies in the solar system,
can be passive sources of high-energy gamma rays, resulting from inelastic collisions
of energetic cosmic-ray (CR) particles with their material~\cite{morris}.
A measurement of the lunar gamma-ray flux therefore represents a useful tool to
investigate the properties of CRs outside Earth's magnetic field.
Such a study does require accurate modeling of the interaction processes
of high-energy CRs with the lunar surface.

The emission of high-energy gamma rays from the Moon was first observed
by the EGRET experiment~\cite{egret}, which operated from 1991 to 2000
on the Compton Gamma Ray Observatory (CGRO). More precise results were
recently published by the Fermi LAT Collaboration using the data
collected by the Large Area Telescope (LAT) during its first $2$
years of operation~\cite{abdo2012}, which provided a measurement of the
gamma-ray flux above $100\units{MeV}$.

In the present work we have evaluated the gamma-ray flux from the
Moon using the data collected by the Fermi LAT in its first $7$ years of
operation, from August 2008 to June 2015.
Not only is the current data set much larger, but
the data were processed with the newest {\tt Pass 8} reconstruction
and event-level analysis ~\cite{atwood2012}, allowing  the useful energy range
to be extended well below $100\units{MeV}$. We have studied the
time evolution of the gamma-ray flux from the Moon, finding the
expected correlation with the solar activity.

Gamma rays from the Moon are mainly emitted with sub-$\units{GeV}$
energies and their flux depends on the fluxes of CRs impinging
on the Moon and on their inelastic interactions with the lunar regolith.
The chemical composition of the lunar surface
also plays a crucial role in determining the gamma-ray yield.
As will be discussed in sec.~\ref{sec:fluka}, the
energy spectrum of lunar gamma rays is sensitive
to the spectra of CR primaries in the range up to a few
tens of $\units{GeV/n}$, which are strongly affected by
the solar activity.

Therefore, the main ingredients of any model aiming to
provide an interpretation of the gamma-ray emission from the Moon are:
(a) the interactions of CRs with matter;
(b) the lunar surface composition;
(c) the CR energy spectra.
The models describing inelastic interactions of CRs with matter
are well validated against the data from accelerator experiments
and are quite reliable in the energy range of interest.
The predicted gamma-ray spectra will therefore depend on
the input CR spectra and on the lunar surface composition.

Simultaneous measurements of the lunar gamma-ray spectrum
and of the spectra of charged CRs near Earth can provide
the possibility to test the chemical composition of the
lunar surface. In fact, the CR energy spectra provided as input to
the models are usually evaluated from the data collected
in a different epoch and accounting for solar modulation.
The simultaneity allows eliminating uncertainties on
the CR spectra due to solar modulation.
The AMS-02 instrument is currently taking data simultaneously with
the Fermi LAT, and recently its measurements of the CR proton and
helium energy spectra near Earth have been published~\cite{ams02,amshe}.
This fact therefore offers the unprecedented possibility
to set severe constraints on the lunar gamma-ray emission models.

In this work we have implemented a full Monte Carlo simulation of the
CR interactions with the Moon surface based on the
FLUKA~\cite{battistoni2007,ferrari2005,flukaweb} code.
In our simulation we assumed a lunar surface
chemical composition derived from the samples of lunar rock
taken by the astronauts of the Apollo missions~\cite{apollo}.
We show that the simulation reproduces accurately the
Moon gamma-ray data taken by the LAT in the same epoch as the AMS-02
proton and helium data. Finally, starting from a model
of the local interstellar spectra (LIS) of CR protons and helium nuclei,
we have fitted the Moon gamma-ray data using the gamma-ray
yields predicted by our simulation to derive the CR proton and helium
spectra at $1 \units{A.U.}$ from the Sun
and to evaluate solar modulation potential.

\section{The lunar gamma-ray emission spectrum}
\label{sec:formulae}

As mentioned in sec.~\ref{sec:intro}, gamma rays emitted from the Moon
are produced after inelastic interactions of charged CRs with the
lunar surface. Hereafter we will make the assumption
that the CR flux on the lunar surface is spatially isotropic.

Indicating with $I_{i}(T)$ the intensity of CRs of the $i$-th species
(in units of $\units{particles~MeV^{-1}~cm^{-2}~sr^{-1}~s^{-1}}$) as a
function of kinetic energy $T$, the rate $\Gamma_{i}(T)$ of CRs of the $i$-th species
(in units of $\units{particles~MeV^{-1}~s^{-1}}$) impinging on the
lunar surface will be given by:

\begin{equation}
\Gamma_{i}(T) = 4 \pi R_{\leftmoon}^{2} I_{i}(T) \int \cos \theta_{M} d\Omega_{M} =
4 \pi^{2} R_{\leftmoon}^{2} I_{i}(T)
\label{eq:primrate}
\end{equation}
where $R_{\leftmoon}=1737.1\units{km}$ is the radius of the Moon.
In the previous equation we set $d\Omega_{M} = d \cos \theta_{M} d\phi_{M}$,
where $(\theta_{M}, \varphi_{M})$ are the zenith and azimuth
angles of CR particles with respect to the lunar surface
($0 < \cos \theta_{M} < 1$ and $0 < \phi_{M} < 2 \pi$).

The differential gamma-ray luminosity of the Moon $L_{\gamma}(E_{\gamma})$
(in units of $\units{photons~MeV^{-1}~s^{-1}}$) is given by:

\begin{eqnarray}
L_{\gamma}(E_{\gamma}) = \sum_{i} \int Y_{i}(E_{\gamma} | T) \Gamma_{i}(T) dT \nonumber \\
= 4 \pi^{2} R_{\leftmoon}^{2} \sum_{i} \int Y_{i}(E_{\gamma} | T) I_{i}(T)~dT
\label{eq:luminosity}
\end{eqnarray}
where $Y_{i}(E_{\gamma}|T)$ is the differential gamma-ray yield
(in units of $\units{photons~particle^{-1}~MeV^{-1}}$), i.e. the
number of photons per unit energy produced by a primary particle of the $i$-th species.
The yields $Y_{i}(E_{\gamma}|T)$ depend on the mechanisms of interactions
of primary CRs with the lunar surface (regolith) and on its composition.

The differential intensity of gamma rays (in units of
$\units{photons~MeV^{-1}~cm^{-2}~sr^{-1}~s^{-1}}$) emitted
from the Moon can be evaluated starting from the differential luminosity and
is given by:

\begin{equation}
I_{\gamma} (E_{\gamma}) = \cfrac{L_{\gamma}(E_{\gamma})}{4\pi^{2} R_{\leftmoon}^{2}}
= \sum_{i} \int Y_{i}(E_{\gamma} | T) I_{i}(T)~dT
\label{eq:gammaintensity}
\end{equation}

The gamma-ray flux observed by a detector at Earth
(in units of $\units{photons~MeV^{-1}~cm^{-2}~s^{-1}}$)
can also be evaluated from the differential luminosity and is given by:

\begin{eqnarray}
\label{eq:moonflux}
\phi_{\gamma}(E_{\gamma}) = \cfrac{L_{\gamma}(E_{\gamma})}{4\pi d^{2}}
= \cfrac{\pi R_{\leftmoon}^{2}}{d^{2}} I_{\gamma}(E_{\gamma}) \nonumber \\
= \cfrac{\pi R_{\leftmoon}^{2}}{d^{2}} \sum_{i} \int Y_{i}(E_{\gamma} | T) I_{i}(T)~dT
\end{eqnarray}
where $d$ is the distance between the center of the Moon and the detector.
In the case of the Fermi LAT, due to the orbital motions of
the Moon and of the Fermi satellite around the Earth,
$d$ ranges from about $3.4\times10^{5}\units{km}$ to
$4.1\times10^{5}\units{km}$ (i.e. from about $54 R_{\oplus}$
to $64 R_{\oplus}$, where $R_{\oplus}=6378\units{km}$ is the
mean equatorial Earth radius).

In particular, Eq.~\ref{eq:moonflux} shows that a $10\%$ change
of the distance $d$ corresponds to a $20\%$ change of the flux.
This effect cannot be eliminated from our data analysis because,
due to the limited photon statistics, in order to properly reconstruct
the fluxes, we need to analyze data samples collected in periods
of at least a few months, which are longer than the time scales
corresponding to the orbital periods of the Moon
($\sim 28 \units{days}$) and of the LAT ($\sim 1.5\units{hours}$).

\section{Data selection}
\label{sec:instrument}

The LAT is a pair conversion gamma-ray telescope,
sensitive in the energy range from $20 \units{MeV}$ to more than
$300 \units{GeV}$. Here a brief description of the instrument is
given, while full details can be found in ref.~\cite{atwood2009}.

The instrument is a $4 \times 4$ array of $16$ identical towers,
designed to convert incident gamma rays into $e^{+}e^{-}$ pairs, and
to detemine their arrival directions and energies. Each tower is
composed of a tracker module and a calorimeter module.
The tracker consists of $18$ $x-y$ planes of silicon strip detectors
interleaved with tungsten converter foils, for a total on-axis
thickness of $1.5$ radiation lengths.
The calorimeter consists of $96$ CsI (Tl) crystals, hodoscopically arranged
in $8$ layers.
The towers are surrounded by a segmented anticoincidence detector
consisting of plastic scintillators, which is used for rejecting
the charged cosmic-ray background.

The analysis presented in this paper has been performed using
the newest {\tt Pass 8} data~\cite{atwood2012}, specifically
P8\_SOURCE photon events starting from a minimum energy of
$30 \units{MeV}$.

A crucial point in the Moon gamma-ray data analysis is the
treatment of the background, which originates variously from the diffuse gamma-ray
emission, from the gamma-ray sources that the Moon drifts past along its path
in the sky, and from the tiny residual fraction of charged CRs that are
misclassified as photons. As the Moon is a moving source, the
use of a background template might lead to inaccurate results.
Hence, for our analysis we chose to evaluate the background
directly from the data, by using properly selected signal and background regions.

The signal region is defined as a cone centered on the Moon
position, with an energy dependent angular radius given by:

\begin{equation}
\label{eq:angrad}
\theta = \sqrt{
\left[ \theta_{0} ( E/E_{0} )^{-\delta} \right]^{2}
+ \theta_{min}^{2} }
\end{equation}
where $E$ is the photon energy, $E_{0}=100\units{MeV}$,
$\theta_{min}=1\hbox{${}^\circ$}$, $\theta_{0}=5\hbox{${}^\circ$}$
and $\delta=0.8$. The energy dependence of the angular radius follows
the behavior of the $68\%$ containment radius of the
LAT point-spread function (PSF)~\cite{psf}. This choice maximizes
the signal-to-noise ratio.
The value of $\theta_{min}$ in Eq.~\ref{eq:angrad}
has been chosen to account for the finite dimension
of the Moon, which is seen from the Earth as an extended source
of $0.25\hbox{${}^\circ$}$ angular radius.
The position of the Moon is obtained from its ephemeris using
software interfaced to the JPL libraries~\cite{ephem} and
correcting for Fermi orbital parallax.

The background region is a cone of the same angular radius
as the signal region, centered on a time-offset position of the Moon.
Since the Moon orbits around the Earth with a period of $\sim 28$ days,
we chose a time offset of $14$ days (i.e. at a given time,
the center of the background region is in the position that
the Moon will take $14$ days later).
We performed our analysis by splitting the data set in smaller subsamples,
each of one month duration.
This means that in a month of $30$ days, the center of the
background region will take $16$ days to reach the position
occupied by the Moon at the end of that month. When this
happens, the center of the background region will be brought
back to the position taken by the Moon at the beginning of the month
and, starting from this time, it will move along the path
described by the Moon during the first $14$ days of the month.
In this way the background region will span the same portion of sky
as the signal region and, since the orbital period of the Moon
is close to one month, the angular separation between the centers
of the signal and background regions will always be close
to $180\hbox{${}^\circ$}$.

For the analysis of the signal (and background) region we selected
the time intervals when the LAT was operating in its standard
science operation configuration and was outside the South Atlantic Anomaly
(SAA).
To avoid contamination from the bright limb of the Earth we discarded
the data taken during the times when the angular separation between
a cone of angular radius $\theta_{max}=15\hbox{${}^\circ$}$ centered on the
Moon\footnote{In the analysis of the background region the Moon position
is replaced with the position of the center of the background region.}
direction and the zenith direction exceeded $100\hbox{${}^\circ$}$.
We also discarded data taken during the times when the
Moon was observed with off-axis angles $\theta$ larger than $66.4\hbox{${}^\circ$}$
(i.e. $\cos \theta < 0.4$).
To mitigate the systematic uncertainties due to the bright diffuse gamma-ray
emission from the Galactic plane, in our analysis we selected only the
periods where the Moon was at a Galactic latitude
\mbox{$|b_{\leftmoon}|>20\hbox{${}^\circ$}$}.
We also required a minimum angular distance
of $20 \hbox{${}^\circ$}$ between the Moon and the Sun and between the Moon and any
bright\footnote{Here we define ``bright'' a source
whose gamma-ray flux above $100 \units{MeV}$ is larger
than $2\times 10^{-7} \units{photons~cm^{-2}~s^{-1}}$.}
celestial source in the 2FGL
Fermi LAT source catalog~\cite{nolan2012}.
Since the center of the background region spans the same portion of sky
as the Moon and the good time intervals for the two regions are chosen in the same way,
the exposures of the signal and of the background regions are nearly identical.

\begin{figure}[!t]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figure_01.eps}
\end{center}
\caption{Significance map of the Moon as a function of
right ascension and declination relative to the instantaneous Moon
position for
photons in the energy range from $30 \units{MeV}$ to $10 \units{GeV}$.
The map is built using a HEALPix~\cite{healpix} pixelization of
the sky with $N_{side}=256$ (each pixel corresponds to a solid
angle $\approx 1.6\times 10^{-5} \units{sr}$). The significance
is evaluated following the prescriptions of ref.~\cite{lima}.}
\label{fig:skymap}
\end{figure}

\section{Data analysis and results}
\label{sec:analysis}

Figure~\ref{fig:skymap} shows the significance map of the gamma-ray
signal from the Moon. The map has been built selecting photons
with energies from $30\units{MeV}$ to $10\units{GeV}$.
The significance of each pixel has been
evaluated according to the prescriptions of ref.~\cite{lima},
starting from the counts in the signal and in the background
regions and taking into account the livetime ratio between the
two regions. As expected, the significance map
exhibits a clear peak in its center, corresponding to
the gamma-ray emission from the Moon.
The angular size of the peak is broader than that of
the lunar disk ($0.25\hbox{${}^\circ$}$) due to the finite PSF
of the LAT and is comparable with the value of the PSF
at $200\units{MeV}$ ($2.9\hbox{${}^\circ$}$), where the peak of the
signal count spectrum is found.

Figure~\ref{fig:counts} shows the observed photon count spectra
in the signal and background regions, and the net signal count
spectrum. The latter was calculated by applying in each energy bin
the Bayesian procedure illustrated in ref.~\cite{loparco2011},
taking into account the livetimes of the signal and background
regions and assuming uniform priors for the net signal counts in
each energy bin. In particular, for each energy bin we evaluated
the posterior probability density function (PDF) for the signal
counts.
The central values of the net signal count spectrum shown in
Fig.~\ref{fig:counts} represent the average values of the corresponding
PDFs, while the error bars represent the corresponding RMSs.
In the energy bins where the significance of the net signal counts
is smaller than $2 \sigma$ upper limits at $95\%$ confidence level are shown.

To reconstruct the energy spectrum of gamma rays from the Moon
starting from the observed count spectra and taking energy dispersion
into account, we have implemented an
analysis method based on the software toolkit BAT~\cite{caldwell2009}.
The BAT package allows evaluating the full posterior probability
PDFs for the parameters of a model.
It is based on Bayes' theorem and is realized with the use of a
Markov Chain Monte Carlo (MCMC) analysis. In the present work we used BAT to extract,
starting from the observed count distributions in the signal and background
regions, the posterior PDFs for both the signal
and background gamma-ray fluxes.

\begin{figure}[!t]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figure_02.eps}
\end{center}
\caption{Count distributions as a function of
gamma-ray energy for the signal (black circles) and
background (red circles) regions. Blue symbols
represent the net signal count spectrum, evaluated by the
method described in ref.~\cite{loparco2011}.
Circles and associated error bars represent
the average values and the RMS values of the corresponding PDFs.
Arrows represent upper limits at $95\%$ confidence level.}
\label{fig:counts}
\end{figure}

Indicating with $\mu_{s}(E_{i})$ and $\mu_{b}(E_{i})$ the expected
counts in the $i$-th energy bin, respectively in the signal and in
the background region, it is possible to write the following equations:

\begin{equation}
\mu_{s}(E_{i}) = \sum_{j} P_{s}(E_{i}|E_{j})
\left[ \phi_{s}(E_{j}) + \phi_{b}(E_{j}) \right]
A ~ t_{s} ~ \Delta E_{j}
\label{eq:sigflux}
\end{equation}

\begin{equation}
\mu_{b}(E_{i}) = \sum_{j} P_{b}(E_{i}|E_{j})
\phi_{b}(E_{j}) ~ A ~ t_{b} ~ \Delta E_{j}.
\label{eq:bkgflux}
\end{equation}
In the previous equations $\phi_{s}(E_{j})$ and $\phi_{b}(E_{j})$
are the true signal and background fluxes in the $j$-th energy bin
($\phi_{s}(E)$ corresponds to $\phi_{\gamma}(E)$ in Eq.~\ref{eq:moonflux}),
that are treated as unknown parameters;
$P_{s}(E_{i}|E_{j})$ and $P_{b}(E_{i}|E_{j})$ are the smearing
matrices in the signal and background regions respectively,
i.e. the probabilities that a photon of energy $E_{j}$ is
observed with energy $E_{i}$, and are evaluated from a full
Monte Carlo simulation of the instrument, taking into account
the pointing histories of the two regions; $A=6\units{m^{2}}$ is the
cross sectional area of the spherical surface used for the generation
of the events in the Monte Carlo simulation; $t_{s}$ and $t_{b}$ are the live times
of the signal and background regions respectively.

If $n_{s}(E_{i})$ and $n_{b}(E_{i})$ are the actual
values of the counts in the $i$-th energy bin of the signal and of
the background regions, it is possible to define the likelihood
function as a product of Poisson PDFs:

\begin{eqnarray}
\label{eq:batlike}
\mathcal{L}(\vec{\phi}_{s} , \vec{\phi}_{b} ; \vec{n}_{s} , \vec{n}_{b}) =
\prod_{i} e^{-\mu_{s}(E_{i})} \frac{\mu_{s}(E_{i})^{n_{s}(E_{i})}}{n_{s}(E_{i})!} \times \nonumber \\
\prod_{i} e^{-\mu_{b}(E_{i})} \frac{\mu_{b}(E_{i})^{n_{b}(E_{i})}}{n_{b}(E_{i})!}
\end{eqnarray}
where we used the vector notation to denote sets of independent
quantities defined in the various energy bins (i.e.
$\vec{\phi_{s}}=(\phi_{s}(E_{1}),\phi_{s}(E_{2}),\ldots,)$ etc.).

\begin{figure}[!t]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figure_03.eps}
\end{center}
\caption{Gamma-ray energy spectrum of the Moon.
The flux values $\phi_{\gamma}(E)$ in each bin are multiplied by $E^{2}=E_{1}E_{2}$, where $E_{1}$
and $E_{2}$ are the lower and upper energy edges of each bin.
The results from the present analysis (black points) are compared
with those published in ref.~\cite{abdo2012}. Only statistical error bars are shown.
The central values of each bin represent the mean flux values, while the error bars
represent the RMSs of the corresponding PDFs.}
\label{fig:fluxes}
\end{figure}

As the starting point for the MCMC we assumed uniform prior PDFs for
the unknown parameters $\phi_{s}(E_{j})$ and $\phi_{b}(E_{j})$.
The posterior PDFs for $\phi_{s}(E_{j})$ and $\phi_{b}(E_{j})$ are
evaluated by BAT using the likelihood function in Eq.~\ref{eq:batlike}.

Figure~\ref{fig:fluxes} shows the reconstructed gamma-ray spectrum of the Moon.
The present results are compared with those published in
ref.~\cite{abdo2012}, obtained from the analysis of the first $2$ years
of data taken by the Fermi LAT. The points shown in the plot correspond
to the mean values of the PDFs on the signal fluxes in each bin, while the
error bars indicate the RMS values. The spectral energy distribution $E^{2}\phi_{\gamma}(E)$ is
peaked at about $150\units{MeV}$ and then drops with increasing energy as a power law
with spectral index of about $-2$.

The present results are consistent with those of ref.~\cite{abdo2012} at
energies above $150\units{MeV}$. The minor discrepancies in the range below
$150\units{MeV}$ can be ascribed to the solar modulation effect on CRs,
which affects the energy spectrum of gamma rays emitted from the Moon
(see also the discussion in sec.~\ref{sec:timeevolution}).
The 2-year interval analyzed in ref.~\cite{abdo2012}
corresponded to the minimum of solar activity at the
beginning of Solar Cycle 24. On the other hand,
the dataset used in this analysis spans a period of $7$ years,
covering more than half of Cycle 24. As a sanity check we applied the analysis
technique illustrated in this paper to the data taken by the LAT
in the first $2$ years, and the results were consistent with those
of ref.~\cite{abdo2012} in the whole energy range.

In Fig.~\ref{fig:fluxes} only statistical error bars on the fluxes are shown.
The systematic uncertainties, not shown in Fig.~\ref{fig:fluxes},
are primarily due to the uncertainties on the effective area of the instrument,
which propagate to the gamma-ray fluxes. The uncertainties on the effective area
were evaluated by the Fermi LAT Collaboration~\cite{systematics}: they drop from
$10\%$ to $3\%$ in the energy range from $30\units{MeV}$ to $100\units{MeV}$
and are $\sim 3\%$ at energies above $100 \units{MeV}$.
Systematic uncertainties are smaller than statistical ones in the whole
energy range: in fact the latter are of $\sim 25\%$ at $30\units{MeV}$,
drop to $\sim 5\%$ at $150\units{MeV}$ and increase again
to $\sim 25\%$ at $1.5\units{GeV}$.

To search for possible issues in the analysis, in addition to the approach discussed above
and based on BAT, we implemented two more analysis techniques, and we compared the
results.

In the first approach, we used the software toolkit MINUIT~\cite{minuit} to evaluate
the set of parameters $\vec{\phi_{s}}$ and  $\vec{\phi_{b}}$ that maximize the
likelihood function in Eq.~\ref{eq:batlike}. We find that the results from the MINUIT
analysis are consistent with those shown in Fig.~\ref{fig:fluxes} within
the statistical errors in the whole energy range.

In the second approach, we used an improved version of the bayesian unfolding technique
originally developed by the Fermi LAT Collaboration for the spectral
analysis of gamma-ray sources~\cite{mazziotta2009,loparco2009,dagostini1995,abdo2010a},
in which we implemented the prescriptions of ref.~\cite{dagostini2010}.
The starting point for the unfolding procedure is the set of posterior PDFs
for the signal counts in each energy bin, which are used to build a set of
random realizations of the signal count spectra. These count spectra are
then unfolded and the corresponding gamma-ray flux spectra are obtained.
Finally, starting from these spectra, the PDFs on the fluxes in the various
energy bins are evaluated.
The results from the unfolding analysis are also consistent within the
statistical errors with those shown in Fig.~\ref{fig:fluxes}.

\begin{figure}[!t]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figure_04_a.eps}
\includegraphics[width=0.98\columnwidth]{figure_04_b.eps}
\end{center}
\caption{(a) Time evolution of the gamma-ray intensity from the Moon.
The red, green, blue and purple symbols represent the intensites above
$56$, $75$, $100$ and $178\units{MeV}$ respectively.
The dashed lines indicate the average values
calculated over the whole data-taking period.
(b) Time evolution of the corrected count rates
registered by the neutron monitors of McMurdo (red), Newark (green),
South Pole (blue) and Thule (purple). The data of the neutron monitors
correspond to the good time intervals selected for the Moon data analysis.
Each point of the plot corresponds to an average value taken over a $6$-month period.}
\label{fig:fluxvstime}
\end{figure}

\section{Time evolution studies}
\label{sec:timeevolution}

To study the time evolution of the gamma-ray emission from the Moon, we
performed the same analysis described in section~\ref{sec:analysis}
on subsets of data corresponding to $6$-months intervals aligned with
the beginning of the solar years (i.e. January to June and July to December
except for the first one, starting in August $2008$).

Figure~\ref{fig:fluxvstime}.a shows the time evolution of the
gamma-ray intensities from the Moon above $56$, $75$, $100$ and $178\units{MeV}$.
The integral intensity is evaluated by integrating the differential
intensity in Eq.~\ref{eq:gammaintensity} over energy.
The latter is evaluated from the gamma-ray flux using Eq.~\ref{eq:moonflux}.
The error bars shown in the figure have been calculated taking
into account the statistical uncertainties on the fluxes
and the variations of the distance between the LAT
and the Moon during each data-taking period
(see the discussion in sec.~\ref{sec:formulae}).
The intensities in the different periods are compared with the
averages, which are calculated considering the whole data-taking period.

Figure~\ref{fig:fluxvstime}.b shows the time evolution of the
count rates registered by some neutron monitors of the Bartol
Research Institute~\cite{bartol} installed in various locations in the
northern (Thule and Newark) and southern (McMurdo and South Pole)
hemispheres. The count rates are corrected for differences in atmospheric pressure.
We selected only the neutron monitor data taken during the
good time intervals selected for the analysis of the Moon
(see the discussion in sec.~\ref{sec:instrument}).
The data from the South Pole neutron monitor do not cover
the whole LAT data-taking period because it was closed
from November 2005 until February 2010.

A comparison of the time evolution plots in Fig.~\ref{fig:fluxvstime} suggests that
the gamma-ray emission of the Moon is correlated to the counts
of the various neutron monitors.
In Fig.~\ref{fig:nmfluxcorr} we plot the gamma-ray intensities from the Moon
above $56$, $75$, $100$ and $178\units{MeV}$ against the count rates
registered by the McMurdo neutron monitor. The data indicate that the
lunar gamma-ray emission is indeed correlated with the neutron monitor
count rate. In particular, the correlation is stronger when
the gamma-ray energy threshold is lower and becomes weaker
as the threshold increases. Similar results are obtained when
comparing the lunar gamma-ray fluxes with the count rates
registered by other neutron monitors.
This result is expected, since gamma rays are produced in the
interactions of primary CRs with the surface of the Moon, and therefore
their flux must be affected by solar modulation. The correlation
is more evident at low energies, because the solar modulation affects mainly
the fluxes of low-energy CRs. In particular, in the case of CR protons,
the effect is relevant at kinetic energies $T \apprle 1-10 \units{GeV}$. Since
the typical energies of gamma rays produced in CR proton interactions are roughly
one order of magnitude less than those of primary protons, the solar modulation
effect is relevant for photons with energies $E_{\gamma} \apprle 0.1-1 \units{GeV}$.

\begin{figure}[!t]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figure_05.eps}
\end{center}
\caption{Comparison between the gamma-ray integral intensities from the Moon
above $56$ (red), $75$ (green), $100$ (blue) and $178 \units{MeV}$ (purple) and
the count rate registered by the McMurdo neutron monitor.
The dashed lines represent the linear regression curves of each series.
The values reported in brackets are the correlation coefficients.}
\label{fig:nmfluxcorr}
\end{figure}

\section{Monte Carlo simulation of CR interactions with the Moon}
\label{sec:fluka}

We have implemented a full Monte Carlo simulation of
the interactions of CRs with the surface of
the Moon based on the {\tt FLUKA}~\cite{battistoni2007,ferrari2005,flukaweb}
simulation code. This simulation has been used to evaluate the yields of
gamma rays produced in these interactions.

{\tt FLUKA} is a general-purpose Monte Carlo code for the simulation of hadronic
and electromagnetic interactions. It is used in many applications, and is continuously checked
using the available data from low-energy nuclear physics, high-energy
accelerator experiments and measurements of particle fluxes in the atmosphere.
Hadronic interactions are treated in {\tt FLUKA} following a theory-driven approach. The general phenomenology
is obtained from a microscopic description of the interactions between the fundamental constituents
(quarks and nucleons), appropriate for the different energy ranges.
Below an energy of a few $\units{GeV}$, the hadron-nucleon interactions model is based on resonance
production and decay, while for higher energies the Dual Parton Model (DPM) is used.
The extension from hadron-nucleon to hadron-nucleus interactions is done in the framework of
the Pre-Equilibrium Approach to Nuclear Thermalization (PEANUT) model~\cite{peanut1,peanut2},
including the Gribov-Glauber multi-collision mechanism
followed by the pre-equilibrium stage and eventually equilibrium
processes (evaporation, fission, Fermi break-up and gamma deexcitation).
In case of nucleus-nucleus interactions (in the present work involving
alpha projectiles) {\tt DPMJET-III}~\cite{dpmjet} and a modified version~\cite{ander2004}
of {\tt RQMD}~\cite{Sor89,Sor89a,Sor95} are used as external event generators,
depending on the projectile energy. More details
about the FLUKA package can be found in the manual~\cite{ferrari2005,flukaweb} and
a description of hadronic interaction models used in FLUKA can be found in ref.~\cite{ferrari1996}.

We have calculated the gamma-ray yields from the Moon assuming two different composition models
for the lunar surface. To test these models we have used the Moon gamma-ray
data taken in the same period as the AMS-02 proton and helium data~\cite{ams02,amshe}.
We have folded the CR proton and helium spectra measured by AMS-02 with the gamma-ray yields
predicted by the simulation, and we have compared the resulting predicted fluxes with the data.
Having found good agreement between the model and the data for one of the surface composition models,
we have assumed a model for the local interstellar spectra (LIS)
of CR protons and helium nuclei and, starting from the Moon gamma-ray data, we have evaluated
the solar modulation potential in the framework of the force field approximation.

\subsection{Evaluation of the gamma-ray yield from the Moon}
\label{sec:yield}

As mentioned in sec.~\ref{sec:intro}, in any calculation of the lunar
gamma-ray emission a Moon surface model must be assumed, which includes a
description of its geometry and its chemical composition.
Regarding the geometry, in our simulation we made the simplest assumption
that the Moon is a perfect sphere of radius $R_{\leftmoon}=1737.1 \units{km}$,
thus neglecting the roughness of the lunar surface (the top of the
highest mountain and the bottom of the deepest crater are within
$\pm 10\units{km}$ from the surface) and its eccentricity (the
difference between the equatorial radius and the polar radius is
$< 3 \units{km}$).

About the chemical composition, we note that the available data are
from actual samples of lunar rock taken by the
astronauts in the different landing sites of the Apollo missions and from
the low-energy gamma-ray, alpha and neutron spectroscopy data~\cite{apollo}. Over
the years, many models of the lunar surface have been proposed. In particular,
for the present work, we adopted the lunar surface models proposed by
Moskalenko and Porter in 2007~\cite{moskalenko2007} (which was also used
in ref.~\cite{abdo2012}) and by Turkevich in 1973~\cite{turk}
(hereafter these models will be indicated in the text as ``MP'' and ``TUR'').
The features of the MP and TUR models are summarized in tab.~\ref{tab:models}.
The main differences between the two
models can be found in the weight fractions of the different oxides and
in the density of the lunar surface. The differences
result in a lighter composition (lower average atomic and mass numbers)
of the TUR model with respect to the MP model.

\begin{table}[t]
  \begin{tabular}{L{2.0cm}  C{2.5cm}  C{2.5cm}}
  \hline
  Model & Moskalenko \& Porter, 2007 & Turkevich, 1973 \\
  \hline
  \hline
  SiO$_{2}$     & $45.0\%$ & $45.0\%$  \\
  FeO           & $22.0\%$ &  $7.6\%$  \\
  CaO           & $11.0\%$ & $15.5\%$  \\
  Al$_{2}$O$_{3}$ & $10.0\%$ & $22.2\%$ \\
  MgO           &  $9.0\%$ &  $8.0\%$  \\
  TiO$_{2}$     &  $3.0\%$ &  $1.1\%$  \\
  Na$_{2}$O     &      $-$ &  $0.6\%$  \\
\hline
  $\rho (\units{g/cm^{3}})$ & $1.80$ & $3.01$  \\
  $\langle Z \rangle$              	 &  $11.5$ &  $10.8$ \\
  $\langle A \rangle$ 			 &  $23.4$ &  $21.8$ \\
\hline
  $X_{0} (\units{g/cm^{2}})$             &  $22.4$ &  $24.4$ \\
  $\lambda_{el} (\units{g/cm^{2}})$      &  $84.5$ &  $82.1$ \\
  $\lambda_{inel} (\units{g/cm^{2}})$    & $150.4$ & $148.4$ \\
\hline
 \end{tabular}
\caption{Summary of the main features of the lunar surface composition models implemented
in the simulation. The first panel shows the weight fractions of the different oxides composing the lunar
surface. The second panel shows the value of mass density and the average values of the
atomic number and of the mass number. The last panel shows the values of the radiation length
and of the proton elastic and inelastic scattering lengths.}
  \label{tab:models}
\end{table}

For both models we have evaluated the gamma-ray yield from the Moon
by simulating protons and $^{4}$He nuclei with different kinetic energies impinging
isotropically on the lunar surface. The kinetic energies are
taken on a grid of $81$ equally spaced values in logarithmic scale from
$100\units{MeV/n}$ to $10\units{TeV/n}$.
The gamma-ray yield from the $i$-th species of CR primaries
(here $i$=p,$^{4}$He) $Y_{i}(E_{\gamma} | T)$ is calculated as:

\begin{equation}
Y_{i}(E_{\gamma} | T) = \frac{N_{\gamma,i}(E_{\gamma} | T)}
{N_{i}(T) \Delta E_{\gamma}}
\label{eq:yield}
\end{equation}
where $N_{i}(T)$ is the number of primaries of the $i$-th species generated
with kinetic energy $T$ and $N_{\gamma,i}(E_{\gamma}|T)$ is the
number of photons with energies between $E_{\gamma}$ and
$E_{\gamma} + \Delta E_{\gamma}$ produced by the primaries
of the type $i$ with
energy $T$ and escaping from the surface of the Moon.

\begin{figure}[!t]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figure_06_a.eps}
\includegraphics[width=0.98\columnwidth]{figure_06_b.eps}
\end{center}
\caption{Yields of gamma rays produced by the interactions
of protons (top) and $^{4}$He nuclei (bottom) on the Moon.
The yields have been evaluated assuming the MP composition model.}
\label{fig:protonyield}
\end{figure}

\begin{figure}[!t]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figure_07.eps}
\end{center}
\caption{Average number of gamma rays per primary particle (in units of $\units{photons/particle}$)
produced by primary protons (black) and $^{4}$He nuclei (red) as a function of the primary particle
kinetic energy per nucleon. The calculations have been performed for both the MP (continuous lines)
and the TUR (dashed lines) composition models.}
\label{fig:photperprim}
\end{figure}

Figure~\ref{fig:protonyield} shows the gamma-ray yields
from the interactions of primary protons and $^{4}$He nuclei
with the Moon calculated with the {\tt FLUKA} simulation as a function of
the kinetic energy per nucleon of the primary and of the gamma-ray energy
assuming the MP composition model.
From these plots it is evident that, for both
proton and $^{4}$He primaries, the gamma-ray yield is negligible
for $T/n \apprle 200~\units{MeV/n}$. This is because
most gamma rays originate from the decays of neutral pions, and the
process of $\pi^{0}$ production in $p$-nucleus and $^{4}$He-nucleus
interactions requires a threshold kinetic energy for the incident
particle.

\begin{figure}[!t]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figure_08_a.eps}
\includegraphics[width=0.98\columnwidth]{figure_08_b.eps}
\end{center}
\caption{Differential photon energy flux from the Moon
produced by the interactions of protons (top) and $^{4}$He nuclei (bottom) with the Moon surface.
The photon intensities have been evaluated by folding the gamma-ray yields with the CR proton
and helium intensity spectra measured by AMS-02~\cite{ams02,amshe}. The calculation has been
performed with the Moon surface composition model in ref.~\cite{moskalenko2007}.}
\label{fig:foldedyields}
\end{figure}

Figure~\ref{fig:photperprim} shows the average number of photons per primary
particle as a function of the projectile kinetic energy per nucleon produced
by protons and $^{4}$He nuclei, calculated assuming the MP and TUR composition models.
As can be seen in the figure, a $^{4}$He nucleus produces on average
about four times more gamma rays than a proton with the same kinetic energy per nucleon.
A simple interpretation of this fact can be given in terms
of the superposition model, according to which a $^{4}$He nucleus is equivalent to
four nucleons.

Another interesting result is that the gamma-ray yields predicted by the MP and
TUR models are quite similar. Indeed, a deeper inspection of the results shows
that the yields calculated with the TUR model are about $20\%$ higher than those
calculated with the MP model.
The differences could be
due either to the different compositions or to the different densities.
To test a possible dependence of the gamma-ray yield on
the density, we performed some simulations with the TUR and with
the MP models keeping the composition unchanged and changing
the density. The results showed that the
gamma-ray yield is almost independent of the density. We can therefore
conclude that the gamma-ray yield is mainly determined by the chemical
composition of the lunar surface. In particular, the results suggest that
higher values of $\langle Z \rangle$ and $\langle A \rangle$ correspond
to lower gamma-ray yields.

In both these models the lunar surface composition
is assumed to be independent of depth. Recently, another lunar surface model,
based on the neutron and gamma-ray data from the Lunar Prospector mission,
was proposed by Ota et al.~\cite{ota}, in which the regolith composition and
density are assumed to change with depth. In particular, in the Ota model,
the lunar surface is described as a stack of four different layers, each
with different thicknesses, compositions and densities (the details of this model
are given in table 1 of ref.~\cite{ota}).
The gamma-ray yields calculated with the Ota model, not shown in the figure, are
intermediate between those calculated with the MP and
TUR models. This result was expected, since the values of
$\langle Z \rangle$ and $\langle A \rangle$ for all the layers composing
the lunar surface are intermediate between those of the MP
and TUR models.

\begin{figure*}[!ht]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figure_09_a.eps}
\includegraphics[width=0.98\columnwidth]{figure_09_b.eps}
\end{center}
\caption{Gamma-ray flux from the Moon as a function of energy
in the period May 2011 - November 2013. The results from the LAT data analysis
(black points) are compared with the expected fluxes obtained
after folding the CR proton and helium spectra measured
by AMS-02 in 2011-13 with the gamma-ray yields evaluated in sec.~\ref{sec:yield}
with our simulation. The calculations were perfomed using the lunar surface
composition models in refs.~\cite{moskalenko2007} (left)
and~\cite{turk} (right). The continuous red lines indicate the total flux,
while the dashed blue and purple lines represent the
contributions to the lunar gamma-ray spectrum from protons and helium nuclei respectively.}
\label{fig:moondirect}
\end{figure*}

\subsection{Evaluation of the lunar gamma-ray spectrum}
\label{sec:spectrum}

To evaluate the lunar gamma-ray intensity spectrum we should fold the spectra of the various
species of CRs impinging on the lunar surface with the gamma-ray yields calculated from the
Monte Carlo simulation according to Eq.~\ref{eq:gammaintensity}.
In our calculation we will consider only the contributions from protons and $^{4}$He nuclei,
neglecting those from heavier nuclei. This approximation turns out to be reasonable when
taking into account the relative abundances of the various CR species.
Following the considerations in the previous section, we can roughly assume that the
gamma-ray yields from different nuclei are proportional to the number of their
constituent nucleons.
Hence, assuming that the relative abundance of CR $^{4}$He nuclei with respect to protons
is $\sim 10\%$, the contribution of $^{4}$He nuclei to the lunar gamma-ray emission is expected
to be $\sim 40\%$ of the proton contribution, and therefore cannot be neglected.
On the other hand, if we assume a relative abundance of carbon nuclei with respect to protons
of $\sim 0.1\%$, we expect their contribution to the lunar gamma-ray emission to be $\sim 1\%$ of
the proton contribution. Since other CR components are even less abundant than carbon,
we can conclude that the errors from neglecting heavier CR species
in the calculation of the lunar gamma-ray spectrum will be of the order of a few percent.

We also emphasize here that in the calculation of the lunar gamma-ray spectrum
the isotopic composition of primary CRs should be taken into account.
However, in the following we will assume that all
CRs with $Z=1$ are protons and all CRs with $Z=2$ are $^{4}$He nuclei.
Recent measurements~\cite{menn} performed by the
PAMELA experiment show that the $^{2}$H/$^{1}$H ratio decreases from $3.5\%$ to $1.8\%$
in the energy range from $0.1\units{GeV/n}$ up to $1 \units{GeV/n}$, while
the $^{3}$He/$^{4}$He ratio increases from about $8\%$ up to $18\%$ in the same
energy range. Since deuterons and $^{3}$He are secondaries produced in the
interactions of primary CRs with the interstellar medium, it is reasonable
to think that their abundances do not increase significantly at higher energies.
Therefore, assuming these values for the isotopic ratios, we expect that the error on the
lunar gamma-ray spectrum calculated neglecting the isotopic composition of primary
CRs will be of percent order.

The contribution to the differential gamma-ray intensity of the Moon
from the $i$-th species of CR projectiles (protons and $^{4}$He nuclei)
may be calculated as:

\begin{equation}
\frac{dI_{\gamma,i}(E_{\gamma} | T)}{dT} = Y_{i}(E_{\gamma} | T) I_{i}(T).
\end{equation}
The corresponding photon energy flux can be then evaluated as:

\begin{equation}
E_{\gamma}^{2} \frac{d\Phi_{\gamma,i}(E_{\gamma},T)}{dT} =
E_{\gamma}^{2} \frac{\pi R_{\leftmoon}}{d^{2}} \frac{dI_{\gamma,i}(E_{\gamma} | T)}{dT}
\end{equation}
Figure~\ref{fig:foldedyields} shows, for the MP lunar composition model,
the differential gamma-ray energy fluxes originated by proton and $^{4}$He primaries.
The calculations have been performed by folding the proton and helium
intensity spectra $I_{p}(T)$ and $I_{He}(T)$ measured by AMS-02~\cite{ams02,amshe}
with the gamma-ray yields calculated with our simulation\footnote{The AMS-02
helium spectrum includes both $^{4}$He and $^{3}$He nuclei. Once again it should
be emphasized that we are considering the He primaries as consisting entirely
of $^{4}$He.}.
The calculations show that, although the gamma-ray yield increases with
increasing primary energy, the contribution of high-energy primaries
($T>100\units{GeV}$ in the case of protons) to the lunar gamma-ray emission
is negligible, due to the shape of the primary intensity spectra
(at high energies $I_{p}(T) \sim T^{-2.7}$ and a similar behavior is
observed for helium primaries). On the other hand, the main contribution
to the lunar gamma-ray emission comes from primaries with energies
in the range from about $1\units{GeV/n}$ up to a few tens of $\units{GeV/n}$.

\subsection{Comparison of the Moon gamma-ray data with
the predictions from direct observations of the CR proton spectrum}
\label{sec:comparison}

As mentioned in sec.~\ref{sec:intro}, the dataset used for this analysis was
taken in a period of time overlapping with the data-taking period
of AMS-02~\cite{ams02,amshe}. This provides, for the first time, the possibility
to test our Monte Carlo simulation against the direct measurements of
the CR proton and helium spectra performed by AMS-02.
Our dataset is also partially overlapping with the data-taking period of
PAMELA. However, at present, a test of the simulation against the PAMELA data is not
possible. Although the PAMELA Collaboration has measured the
CR proton spectra in two different one-month time intervals
at the end of 2008 and 2009~\cite{pamela}, they did not provide a
measurement of the helium spectra in the same intervals.

To test our simulation against the AMS-02 data we selected a data sample
taken in the period from May 2011 to November 2013.
However, it is worthwhile to point out here that the time intervals selected for
our analysis of the gamma-ray emission from the Moon most likely do not match
those used for the AMS-02 data analysis in ref.~\cite{ams02}. In particular,
when applying the event selection described in sec.~\ref{sec:instrument},
we disregarded those time intervals corresponding to transient events,
such as solar flares, that might be included in the AMS data analysis.

We then folded the CR proton and helium reference spectra with the
gamma-ray yields obtained from our simulation with the MP and TUR models.
When evaluating the gamma-ray flux we assumed the LAT-Moon distance
equal to its average value during the data-taking period from
May 2011 to November 2013. In our calculations we did not take
into account the uncertainties on the proton and helium spectra
measured by AMS-02, which are of about $2\%$ on average~\cite{ams02,amshe}.

Figure~\ref{fig:moondirect} compares the measured gamma-ray fluxes
with the calculations from the Monte Carlo simulation for the two composition models.
As shown in the figure, the gamma-ray spectrum obtained from the
MP composition model reproduces quite well the data in the whole energy
range, with small discrepancies in the region around $1\units{GeV}$,
where the observed flux is smaller than predicted.
On the other hand, the spectrum obtained from the
TUR composition model seems to slightly overestimate the data
in the energy range above $200\units{MeV}$.
According to the discussion in sec.~\ref{sec:yield}, this result can
be attributed to the relatively lighter regolith
(lower $\langle Z \rangle$ and $\langle A \rangle$)
in the TUR model and the consequently greater gamma-ray yield.

We remark here that, when comparing the data
with the model predictions, one should also take into account
all the uncertainties, such as those originating from the fluctuations
on the LAT-Moon distance (see sec.~\ref{sec:formulae}), those on the
instrument effective area (see sec.~\ref{sec:analysis}), those on the
AMS proton and helium spectra (see discussion above) and those on the
hadronic interactions models. All these uncertainties are likely
of $10\%$ or less.

\begin{figure*}[!t]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figure_10_a.eps}
\includegraphics[width=0.98\columnwidth]{figure_10_b.eps}
\end{center}
\caption{Left panel: CR proton and helium spectra obtained from the best fit
of the Fermi LAT Moon gamma-ray data. The fit was performed using the
MP lunar surface model. The results of the fit (continuous black and red lines)
are compared with the proton measurements taken by PAMELA~\cite{pamela} in
2008 (blue points) and 2009 (purple points) and with the AMS-02~\cite{ams02}
proton (cyan points) and helium data (violet points). The plot shows also
the proton and helium LIS (dashed black and red lines)
and the Voyager 1 proton (light green points) and helium (dark green)
data~\cite{stone2013}. Right panel: Gamma-ray flux from the Moon as a function of energy.
The results from our analysis are compared with those of the fit. The
continuous red line represents the average gamma-ray spectrum obtained from the fit,
assuming that the Moon-LAT distance is equal to its average value during the whole
data-taking period.}
\label{fig:moonfluka}
\end{figure*}

On the basis of this result, in the following discussion we will adopt
the MP composition model for the lunar surface.
The small discrepancies between the simulation and the data could be ascribed
to inaccuracies in our model of CR interactions
with the Moon. In our model we assume that CR protons of all energies
are impinging isotropically on the whole Moon surface. However,
low-energy CRs could be affected by the Earth's magnetic field in their
journey to the Moon, in contrast with the hypothesis of an isotropic CR flux.
In addition, in our model we describe the lunar surface as a uniform sphere,
without accounting for the real morphology of the Moon. On the other hand,
the implementation of a more detailed model would require a huge effort
that is beyond the scope of the present work.

\subsection{Evaluation of the low-energy CR proton and $^{4}$He spectra
and of the solar modulation potential}
\label{sec:flukafit}

The data shown in sec.~\ref{sec:timeevolution} indicate that the lunar
gamma-ray spectrum is sensitive to the solar modulation effect.
This is because, as discussed in sec.~\ref{sec:yield},
the main contribution to the gamma-ray spectrum of the Moon is that
of CRs in the energy range up to $\sim 10\units{GeV/n}$.
In the present section we will illustrate an application of our Monte Carlo
simulation to the study of the solar modulation potential.

We start from a model for the CR proton and $^{4}$He LIS~\cite{noi,noipaper},
evaluated using a customized version of the CR propagation code
{\tt DRAGON}~\cite{evoli,gaggero}, in which we included a set of
cross sections for the production of secondary particles in CR
interactions calculated with {\tt FLUKA}.
Both the proton and $^{4}$He LIS of ref.~\cite{noi,noipaper}
were derived in a general framework and,
together with the LIS of other primary CR components, when propagated to
the solar system, allow to reproduce a wide set of observables.
In particular, these observables include the measurements of CR protons
performed by PAMELA~\cite{pamela} in 2008 and 2009, the measurements
of CR protons and He nuclei performed by AMS-02~\cite{ams02,amshe}
from 2011 to 2013, and those performed by Voyager 1~\cite{stone2013}
during its journey outside the Solar System.
The proton and $^{4}$He LIS are shown in the left panel of
Fig.~\ref{fig:moonfluka}, where they are also compared with the data
from direct measurements. We emphasize here that at high energies
the $^{4}$He LIS lies below the points measured by AMS-02 because,
as mentioned in sec.~\ref{sec:spectrum}, the AMS-02 data include
both the $^{4}$He and $^{3}$He component.

In the following analysis the intensity spectra $I_{i}(T)$ of the various
CR species (protons and $^{4}$He nuclei) in the Solar System
are evaluated starting from the LIS intensity spectra $I_{i}^{LIS}(T)$ using the
force field approximation~\cite{gleeson}:

\begin{eqnarray}
I_{i}(T) & = & I_{i}^{LIS}\left(T + e \Phi Z_{i} /A_{i}  \right) \times \nonumber \\
& & \cfrac{T \left( T + 2 m_{i}\right)}{\left( T + e \Phi Z_{i} /A_{i} \right) \left( T + e \Phi Z_{i} /A_{i} + 2 m_{i} \right)}
\end{eqnarray}
where $m_{i}$, $Z_{i}$ and $A_{i}$ are the mass, the charge and the number of nucleons
of the $i$-th primary component, $e$ is the absolute value of the electron charge, and $\Phi$ is
the solar modulation potential, which in the following discussion will be treated
as a free parameter.

\begin{figure}[!t]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figure_11.eps}
\end{center}
\caption{Time evolution of the solar modulation potential, evaluated from a fit
of the lunar gamma-ray emission. The central band corresponds to the average
value of the solar modulation potential during the whole data-taking period.}
\label{fig:solarmod}
\end{figure}

We used the proton and $^{4}$He LIS and the gamma-ray yields calculated
with the MP composition model for the lunar surface to perform a fit of the data.
The fit procedure is based on BAT, and is similar to the one described
in sec.~\ref{sec:analysis} for the reconstruction of the gamma-ray fluxes
from the Moon. In this case, the gamma-ray signal fluxes in the various
energy bins are correlated, and are calculated from the cosmic-ray proton
and helium intensities $I_{p}(T)$ and $I_{He}(T)$ using
eqs.~\ref{eq:luminosity} and~\ref{eq:moonflux}.
Here the parameters to be fitted are the background
photon fluxes $\vec{\phi}_{b}$ and the solar modulation potential $\Phi$.
In our calculations we assumed that the LAT-Moon distance $d$,
that appears in Eq.~\ref{eq:moonflux}, is constant and
equal to its average value during the whole data-taking period.

The fitting procedure, applied to the whole $7$ year data sample,
yields a solar modulation potential of $537 \pm 12 \units{MV}$.
The left panel of Fig.~\ref{fig:moonfluka} shows the fitted CR proton
and helium intensity spectra, compared with the results
of the direct measurements performed by PAMELA and by AMS-02.
As shown in the figure, the CR proton spectum
inferred from this analysis is consistent with the results from direct
measurements and lies between the PAMELA and the AMS-02 data.
The helium spectrum lies below the AMS-02 data because, as discussed
above, it includes only the $^{4}$He component.

The gamma-ray spectrum obtained from the fit is shown in the right panel
of Fig.~\ref{fig:moonfluka}, where it is compared with the results from
the data analysis discussed in section~\ref{sec:analysis}.
The fitted spectrum accurately reproduces
the data in the energy range up to $400\units{MeV}$, while at higher
energies it tends to overestimate the measured fluxes.

The fitting procedure discussed here was also applied to the $6$-month data
samples into which the original data set was divided, to study the time evolution
of the solar modulation potential. Fig.~\ref{fig:solarmod} shows the
time evolution of $\Phi$ obtained from the fit.
A comparison with the plots in Fig.~\ref{fig:fluxvstime} shows that, as expected,
the value of the solar modulation potential is
anticorrelated with the count rates of the various neutron monitors.
It is also worth noting that, starting in the second half of
2012, the solar modulation potential oscillates about the mean trend
from interval to interval. This feature
might be due to the major solar flare activity in recent years.

\section{Conclusions}

We measured the fluxes of gamma rays produced by the interactions
of charged CRs impinging on the surface of the Moon using
data collected by the Fermi LAT from August 2008 to June 2015.
Thanks to the high statistics of the data sample and to the newest
version of the Fermi LAT event-level analysis and
instrument response function, we have been able to measure the
gamma-ray fluxes in an energy range that extends from $30\units{MeV}$
up to a few $\units{GeV}$. The time evolution of the flux shows
that the gamma-ray emissivity of the Moon is correlated
with the solar activity.

We also developed a full Monte Carlo simulation of the
interactions of CR protons and helium nuclei with the Moon
using the {\tt FLUKA} simulation code to evaluate the gamma-ray yields.
We implemented two different composition models of the lunar surface
and we found that the gamma-ray emission from the Moon depends
on the elemental composition of its surface. In particular, we
observe that the MP composition model provides a good
agreement between the lunar gamma-ray data and the results of
direct measurements of the CR proton and helium spectra.

Starting from a custom model of the CR proton and helium LIS, we
then used the simulation to infer the local CR proton intensity
spectrum from the Moon gamma-ray spectrum in the framework of
the force field approximation. The CR spectra obtained
with this procedure are consistent with the results from direct measurements
performed by the PAMELA and AMS experiments. We applied this approach to evaluate the time
evolution of the solar modulation potential. The results
show that the potential is anticorrelated with the counts in
several neutron monitors.

\acknowledgments

The \textit{Fermi} LAT Collaboration acknowledges generous ongoing support
from a number of agencies and institutes that have supported both the
development and the operation of the LAT as well as scientific data analysis.
These include the National Aeronautics and Space Administration and the
Department of Energy in the United States, the Commissariat \`a l'Energie Atomique
and the Centre National de la Recherche Scientifique / Institut National de Physique
Nucl\'eaire et de Physique des Particules in France, the Agenzia Spaziale Italiana
and the Istituto Nazionale di Fisica Nucleare in Italy, the Ministry of Education,
Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research
Organization (KEK) and Japan Aerospace Exploration Agency (JAXA) in Japan, and
the K.~A.~Wallenberg Foundation, the Swedish Research Council and the
Swedish National Space Board in Sweden.

Additional support for science analysis during the operations phase is gratefully
acknowledged from the Istituto Nazionale di Astrofisica in Italy and the Centre
National d'\'Etudes Spatiales in France.

The authors acknowledge the use of HEALPix (\url{http://healpix.jpl.nasa.gov/})
described in ref.~\cite{healpix}.

redpajama_set_name: RedPajamaArXiv


Vickie! So excited that you've started a blog. This post makes me think of an audiobook I listened to a few years ago by Geoff Colvin– Talent is Overrated: What Really Separates World-Class Performers from Everybody Else. Colvin studied success stories like Mozart, Ben Franklin, and Tiger Woods and concluded that intentional practice is the key to success (along with having mentors, analyzing one's performance, and a supportive family). Most of the success stories he studied had 10 years of consistent practice under their belts before they made their first splash. Malcom Gladwell's Outliers, with its 10,000 hour rule, came out the same year as Talent is Overrated. I gotta say that True Grit has a better ring than Intentional Practice.
Chris–So glad to hear from you! Happy New Year and thanks for sharing your thoughts. I will get my hands on "Talent is Overrated" by Geoff Colvin. Miss you and Laura madly and never pass the old Borders Bookstore location without thinking of you and sending good thoughts your way. What will you create in this new, wondrous year? You are a Diva Extraordinaire! Much love, V.


text:
Christmas Broadcast 1956
Neither the long and troubled centuries that have passed since that child was born, nor the complex scientific developments of our age, have done anything to dim the simple joy and bright hope we all feel when we celebrate his birthday.
On Christmas Day in 1956 The Duke of Edinburgh was away from home on a voyage around the Commonwealth on BRITANNIA. Prince Philip spoke on the radio from the Royal yacht before The Queen made her broadcast live from her study in Sandringham, Norfolk.
Once again messages of Christmas greeting have been exchanged around the world.
From all parts of the Commonwealth, and from the remote and lonely spaces of Antarctica, words and thoughts, taking their inspiration from the birth of the child in Bethlehem long ago, have been carried between us upon the invisible wings of twentieth-century science.
Neither the long and troubled centuries that have passed since that child was born, nor the complex scientific developments of our age, have done anything to dim the simple joy and bright hope we all feel when we celebrate his birthday. That joy and hope find their most complete fulfilment within the loving circle of a united family.
You will understand me, therefore, when I tell you that of all the voices we have heard this afternoon none has given my children and myself greater joy than that of my husband.
To him I say: "From all the members of the family gathered here today our very best good wishes go out to you and to every one on board Britannia, as you voyage together in the far Southern seas. Happy Christmas from us all."
Of course it is sad for us to be separated on this day, and of course we look forward to the moment when we shall all again be together. Yet my husband's absence at this time has made me even more aware than I was before of my own good fortune in being one of a united family.
With that consciousness in mind, I would like to send a special message of hope and encouragement to all who are not so blessed, or for any reason cannot be with those they love today: to the sick who cannot be at home; to all who serve their country in foreign lands, or whose duty keeps them upon the oceans; and to every man or woman whose destiny it is to walk through life alone.
Particularly on this day of the family festival let us remember those who - like the Holy Family before them - have been driven from their homes by war or violence. We call them 'refugees': let us give them a true refuge: let us see that for them and their children there is room at the Inn.
If my husband cannot be at home on Christmas Day, I could not wish for a better reason than that he should be travelling in other parts of the Commonwealth. On his journey he has returned to many places that we have already visited together, and he has been to others that I have never seen.
On the voyage back to England he will call at some of the least accessible parts of the world, those islands of the South Atlantic separated from us by immense stretches of the ocean, yet linked to us with bonds of brotherhood and trust.
One idea above all others has been the mainspring of this journey. It is the wish to foster, and advance, concord and understanding within the Commonwealth.
No purpose comes nearer to my own desires, for I believe that the way in which our Commonwealth is developing represents one of the most hopeful and imaginative experiments in international affairs that the world has ever seen.
If, as its Head, I can make any real personal contribution towards its progress, it must surely be to promote its unity.
We talk of ourselves as a "family of nations", and perhaps our relations with one another are not so very different from those which exist between members of any family. We all know that these are not always easy, for there is no law within a family which binds its members to think, or act, or be alike.
And surely it is this very freedom of choice and decision which gives exceptional value to friendship in times of stress and disagreement. Such friendship is a gift for which we are truly and rightly grateful.
None the less, deep and acute differences, involving both intellect and emotion, are bound to arise between members of a family and also between friend and friend, and there is neither virtue nor value in pretending that they do not.
In all such differences, however, there comes a moment when, for the sake of ultimate harmony, the healing power of tolerance, comradeship and love must be allowed to play its part.
I speak of a tolerance that is not indifference, but is rather a willingness to recognise the possibility of right in others; of a comradeship that is not just a sentimental memory of good days past, but the certainty that the tried and staunch friends of yesterday are still in truth the same people today; of a love that can rise above anger and is ready to forgive.
That each one of us should give this power a chance to do its work is my heartfelt message to you all upon this Christmas Day. I can think of no better resolve to make, nor any better day on which to make it. Let us remember this during our festivities, for it is part of the Christmas message - "Goodwill toward men".
I wish you all a Happy Christmas and a Happy New Year.
A message from The Queen following the recent attacks in Barcelona and Cambrils
A message from The Queen following the landslides in Sierra Leone
A Message from The Queen at the opening of the 2017 IAAF World Championships at the Queen Elizabeth Stadium
The Queen and the Armed Forces
The Royal Family at Christmas
How The Queen and Members of The Royal Family celebrate
The Queen visits Canada House to celebrate 150th Anniversary of Confederation
Prince Harry delivers a message from The Queen at RAF Honnington
The Queen opens New Scotland Yard
This State Visit is an expression of the deep respect and friendship that describes relations between Spain and the United Kingdom
The Queen's speech at the Spanish State Banquet
The Spanish State Visit
The Queens Awards for Enterprise 2017
Announcement of next Governor General of Canada
Holyrood Week 2017
Published 6 July 2017
The Queen's Young Leaders 2017
The Queen and The Duke of Cambridge visit people affected by the Grenfell Tower fire
The Queen visits Tower Hamlets
A Message from Her Majesty The Queen on the opening of the 2017 Commonwealth Science Conference
The Queen's Official Birthday 2017
A message from The Queen following the fire in Grenfell Tower yesterday.
The Queen visits Manchester to meet victims of the Manchester Concert Attack
A message from Her Majesty The Queen to the Lord-Lieutenant of Greater Manchester
The Queen and Members of the Royal Family attend the Chelsea Flower Show
The Queen presents new colours to the Scots Guards
The Queen, along with members of The Royal Family, hosts the first Garden Party of 2017
Her Majesty The Queen and The Duke of Edinburgh visit Pangbourne College to celebrate the school's centenary.
The Queen hosts a ceremony at Windsor Castle to celebrate the 40th Anniversary of Motability.
Updated announcement of a State Visit by the King and Queen of Spain
The Queen visits Leicester Cathedral for Royal Maundy
The Queen opens a new Elephant Care Centre at Whipsnade Zoo
Nous avons le devoir de nous souvenir et d'honorer Ia mémoire de ceux qui ont servi vaillamment et qui ont tant donné ici, sur la crete de Vimy, et tout au long de la Premiere Guerre mondiale.
A message from The Queen on the 100th anniversary of the battle of Vimy Ridge (French)
It is our duty to remember and honour those who served so valiantly and who gave so much here at Vimy Ridge and throughout the First World War.
A message from The Queen on the 100th anniversary of the battle of Vimy Ridge
The Queen presents a Guidon to The Royal Lancers at Windsor Castle
Prince Philip and I were deeply saddened to learn of the devastating flooding and landslides in Mocoa this weekend.
The Queen's message to The President of Colombia, following the flooding and landslides in Mocoa
You have established yourselves as a unified Regiment and a force without match
The Queen addresses The Royal Lancers at Windsor Castle
My thoughts, prayers, and deepest sympathy are with all those who have been affected by yesterday's awful violence.
Message to Acting Commissioner of the Metropolitan Police Service Craig Mackey
The Queen reopens the National Army Museum
Prince Harry visits The Queen's Commonwealth Canopy Project at Epping Forest
Commonwealth Day Message by Her Majesty The Queen, Head of the Commonwealth
The Queen and members of the Royal Family mark Commonwealth Day 2017
The Winners: The Queen's Awards for Enterprise 2016
Find out more about some of the 2016 Queen's Awards for Enterprise winners...
The Queen and The Duke of Edinburgh visit the Charterhouse's new development in London
The Queen launches the 2017 UK-India Year of Culture
I hope that the new memorial will provide a place to remember, to grieve for what is lost, and to give thanks for what remains
A message from The Queen on the sixth anniversary of the Canterbury Earthquake in New Zealand
Celebrating The Queen's Official 90th Birthday
A snapshot of celebrations which happened all over the UK on the weekend of 10-12 June
The Queen and The Duke visit the National Cyber Security Centre
The Queen will unveil the Iraq Afghanistan Memorial
The Queen visits the Fiji Exhibition in Norwich
Our thoughts are with the families of the victims and the wounded, and with the Turkish people at this time.
The Queen's message of condolence to the President of Turkey

redpajama_set_name: RedPajamaCommonCrawl


This week I just returned from working in New Orleans during Essence Festival and with only a few days in-between to attempt to get some rest we'll be flying out in less than 8 hours to celebrate our official summer vacation trip. Needless to say that I am so exhausted but the mini conversations around the house of the kids chatting about their upcoming trip puts a smile on my face.
The fact that when we travel we are only allowed to take one backpack each and the kids run around stuffing their back pack puts a smile on my face.
Watching my youngest son set the alarm clocks all over the house including everyone's cell phone so that we don't over sleep puts a smile on my face.
Observing my youngest son watch the clock throughout the day in anticipation for the sun to finally set puts a smile on my face.
Watching my kids lay out their clothes for our flight in the morning puts a smile on my face.
Knowing that my kids are asleep in their beds at 10pm on a warm summer night because they don't want to over sleep for our flight puts a smile on my face.
Knowing that the house is quiet and I can finally get a few blog post completed and schedule my clients post because everyone is finally asleep early puts a smile on my face.
It's been a few years since the kids and I have gone on a vacation and they are so excited. I love the fact that since they have been traveling since birth they aren't upset if we're not able to get away like we've done in the past. A few years ago we went to Niagara Falls and another year we just grabbed a backpack and decided to backpack where ever we could hop a flight or drive which lead us to New York, New Jersey, Philadelphia, Florida and Georgia. I always teach my kids that it's all about the experience no matter where you go. It's the time to soak in the ambiance, have fun and create memories that will last a lifetime. It's almost midnight so I guess I better get in the bed to rest before our flight in the morning. We'll be sure to share our crazy adventures on my Instastory and Facebook throughout our stay. Until next time….BE BLESS!


Life Learning Journey: Contest Details for Computer Games Finally Up!
Contest Details for Computer Games Finally Up!
I finally got the information for the contest posted.
to give away to lucky people on the 26th of February.
So get your entry in before then!


Export Import Data Hindustan Law Book Company, is a premier company that exports and imports goods from countries including Bangladesh, Australia and host of other countries.
Hindustan Law Book Company, is a premier company that exports and imports goods from countries including Bangladesh, Australia and host of other countries.
Hindustan Law Book Company is a leading exporter of PRINTED LAWBOOK AS PER INV+PACKING LIST, having HS Codes 49011010. The company has its head office at 10/1/C, Rustomji Street,, Kolkata700019.
Hindustan Law Book Company is also a leading importer of LAW REPORTS (ENGLAND)1558 2003 AND INDEX(PRINTED MATTER IN BOOK FORM), LAW REPORTS (UK) AND INDEX (1865-2003)(PRINTED MATTER IN BOOK FORM), BOOKS (PRINTED LAW BOOKS), BLACKS LAW DICTIONARY 8TH (PRINTED LAW BOOKS FOR EDUCATIONAL PURPOSE ONLY), having HS Codes 49011010.
The company primarily imports products to India from Australia and mainly receives the consignments at Calcutta Air.


Description: Send warm wishes for the heart and soul. This Zen-inspired collection includes a Chai tea sampler: green tea chocolates. delicate biscuits, inspiring ginger sweets, and more in a ceramic planter complete with natural river stones.


Why are you and your brand interested in food and nutrition?
We ask this question because it is often all too easy to forget why you initially started your brand or what drew you to a specific area of nutrition in the first place. Most people/brands have one specific interest or brainwave that led to the creation of their brand so we encourage you to take a moment and reflect on that.


In addition, you'll find a link to the TripAdvisor Forum for Red DeerIf you have a question about your travel plans, post it on their Forum and see if others can give you an answer.
All of this can be found on the TripAdvisor's Tourism page for Red Deer.
Below is a list of those communities which have a TripAdvisor Tourism page and are relatively close to Red Deer - within 49 miles [78.9 km]<1>.
<1> Our distances are not driving distances, but are calculated as a 'straight-line' distance. A straight line distance ignores things like rivers, canyons, lakes, et cetera - it's truly a line from Point A (ie- Red Deer) to Point B.
Our distance measurements begin at a specific point in Red Deer. The point we use is located at these GPS coordinates - Latitude: 52.2691, Longitude: -113.8115 [Map].


All Android One Users this is your turn to enjoy the latest Android Operating System! Well, Google has made it perfect for you to enjoy the Android OS as the first user.
We are all aware that Google has finally roll out Android 7.0 Nougat and it is now available over-the-air update for Android One devices. Someone says the Cherry Mobile G1 is one of the many Android One phones that has the update on queue.
Just what happened with the former Android 6.0 Marshmallow, the Android One devices receive the latest software update the day after Google releases the Nexus factory images.
So we are happy to announce to you that if you have an Android One smartphone, you can update your device to Android 7!
Are you using Android One Phones then lets us know through the comment, if you have received the update?


text:
Career Services: Most Common Divisions, Names
August 16, 2017 | By NACE Staff
TAGS: operations, trends and predictions, surveys, benchmarks, spotlight
More than half of university career services operations are based in the student affairs division, according to results of NACE's 2016-17 Career Services Benchmark Report for Colleges and Universities.
Overall, nearly 52 percent of university career services operations are based in the student affairs division, followed by 24 percent in academic affairs.
Although the division that houses an institution's career services operation has remained relatively unchanged since last year, there has been gradual movement away from student affairs over the years, perhaps reflecting a desire by institutions to coordinate career services with other essential areas. (See Figure 1.) In 2006, 67 percent of career services operations were part of student affairs, while just 18 percent were in academic affairs.
In terms of names, "career services" was identified as the most commonly used title (44.4 percent), followed by "career center" (29.8 percent), and "career development" (28.7 percent). (See Figure 2.) The "other" category was identified by 19.1 percent of respondents and was comprised of dual-purpose titles such as "career and academic advising." Also, titles containing "career education" and "planning" occurred frequently (13.4 percent and 11.2 percent, respectively).
Data were collected for the 2016-17 Career Services Benchmark Survey Report for Colleges and Universities from September 30, 2016, to January 20, 2017, from NACE member institutions; there were 705 respondents, representing 35.3 percent of all eligible respondents. Highlights from the 2016-17 Career Services Benchmark Report for Colleges and Universities are available on NACEWeb. Participating members can access the full report through MyNACE.
Figure 1: Organizational Division, 2006-16
% of Respondents
Student Affairs 67.1% - 68.3% 63.1% 63.6% 59.4% 57.4% 59.0% 55.1% 54.6% 51.6%
Academic Affairs 17.7% - 19.6% 21.5% 24.0% 22.4% 21.7% 18.9% 20.2% 22.5% 23.5%
Other 15.2% - 7.5% 10.8% 3.4% 12.4% 9.8% 9.1% 11.0% 10.2% 9.9%
School(s) Within University - - - - - - 5.4% 6.5% 6.9% 5.6% 7.2%
Enrollment Management - - 2.8% 3.1% 6.0% 3.7% 3.0% 3.7% 4.1% 3.9% 4.3%
Institutional Development - - 1.8% 1.5% 3.0% 2.1% 2.5% 2.9% 2.7% 3.3% 3.6%
Source: 2016-17 Career Services Benchmark Survey Report for Colleges and Universities, National Association of Colleges and Employers
Figure 2: Naming Models Used in Office Title, by Carnegie Classification
A&S
Career center 40.4% 28.1% 38.9% 27.6% 21.7% 44.8% 22.7% 21.7% 31.1%
Career Development 24.2% 20.3% 27.8% 34.2% 31.9% 31.0% 40.0% 26.1% 14.8%
Career services 37.4% 48.4% 44.4% 38.8% 47.8% 58.6% 28.0% 63.0% 57.4%
Placement 1.0% 0.0% 0.0% 1.3% 0.0% 0.0% 0.0% 2.2% 4.9%
Professional development 5.1% 4.7% 2.8% 7.2% 5.8% 0.0% 8.0% 2.2% 0.0%
Other 13.1% 18.8% 16.7% 20.4% 20.3% 3.4% 26.7% 17.4% 23.0%


text:
Are you facing false criminal or civil charges? Call the US~Observer Today!
541-474-7885 editor@usobserver.com
— Main Menu —Home False Charges? Vindicated Stories Recent Editions	- Volume 2 – Edition 55 - Volume 2 – Edition 54 - Volume 2 – Edition 53 - Volume 2 – Edition 52 - Volume 2 – Edition 51 - Volume 2 – Edition 50 - Archived About Contact Subscription Search
False Charges?
Vindicated Stories
Volume 2 – Edition 55
Catfishing for Convictions: Florida Police Bend Entrapment Rules?
Wronged by the Justice System?
District Attorney Ron Brown "Most Evil Man in Clatsop County, Oregon"
Innocent Man Targeted by D.A. Ron Brown
Prosecutor and Police Chief Get Prison for Corruption
State Drops Williams' Case
By Edward Snook
GRANTS PASS, OR – The 4-year-old false and malicious prosecution case of Mack Williams was dismissed Thursday April 6, 2000, by Josephine County Circuit Court Judge Gerald Neufeld.
Disgraced Deputy District Attorney Mike Sanchez, after spending three days attempting to present his conspired case against Williams, bowed his head in shame and admitted the state didn't have enough evidence to convict Mr. Williams, a long-time resident of Grants Pass. In fact, the only evidence the state could present were out-right, conspired lies.
Williams was charged in 1996 of relocating Allen Creek in Southwest Grants Pass. He was also charged with removing riparian brush and polluting the creek. Over the years, the state had to postpone scheduled trials 16 times as they attempted to browbeat Williams and place liability belonging solely to the Oregon Department of Transportation (ODOT) on his shoulders. Deputy DA Scott Titzler, an easily provable liar, attempted to prosecute Williams until shortly before the April 4, 2000, trial; when the state turned the case over to another liar and master of "false prosecution," Mike Sanchez.
For four long years the state pursued charges against Williams, and for four years they forced this determined man to spend tens of thousands of hard-earned dollars defending himself.
The state had more than compelling evidence, which proved Williams' innocence, for years, yet they continued to pursue their false charges.
On several different occasions the state offered to drop the charges if Williams would plead guilty to a violation and pay a nominal fine. In fact, according to Williams, "they wanted me to plead guilty at one point and pay a small amount to the parks. I didn't do anything wrong and I wasn't about to admit to something I didn't do – no matter what the cost."
The State of Oregon had attacked Williams civilly in bogus hearings, where arbitrators ignored countless lies coming from Bob Brown of the Department of State Lands (DSL) and Mark Grinde, a supervisor with ODOT.
The state, admittedly, spent over 400-thousand-dollars attempting to prosecute Williams civilly and an estimated 100-thousand-dollars criminally. Williams spent well-over $100,000 fighting the convoluted and conspired case the state brought against him.
THE FALSE PROSECUTION TRIAL
On April 5, 2000, the second day of trial, DSL's Bob Brown admitted under oath that he had lied in previous hearings.
On the third day, as Williams' attorney Terry McCauley was readying to expose a dozen blatant lies Brown had told under oath, the state dropped the charges.
According to witnesses, Bob Brown made the comment to Williams in 1996, "You're [Williams] going to take responsibility for the job. It's embarrassing to me and to the state. You're going to take responsibility or I'm going to ruin you. I'll turn this over to the Attorney General. I'm going to fine you and you are going to restore the creek."
Williams then informed Brown, in front of witnesses, that ODOT had done the job and that he had sent Brown his incomplete application, along with a letter explaining that ODOT was looking into cleaning the creek, so he wouldn't be needing a permit. Brown has lied under oath on numerous occasions regarding this fact. Brown then reportedly continued, "You'll take responsibility for this or I will make a felon out of you." Brown's arrogant abuse didn't work and now the shoe is on the other foot.
WILLAMS FILES FEDERAL LAWSUIT
Attorney Terry McCauley filed a suit on Williams' behalf on February 3, 2000, in federal court against Bob Brown (DSL), Mark Grinde (ODOT), Mike Spaeth (ODOT Supervisor), Ulys Stapleton (Grants Pass City Attorney), and the City of Grants Pass.
Williams is currently amending the federal suit to include David Haight, from Oregon Department of Fish and Wildlife (ODFW), and Roy Lee Manning, with the U.S. Department of Agriculture. Both testified for the state and both allegedly lied under oath in their attempt to bolster the false prosecution case.
Barbara Hamilton, an adjacent landowner at Allen Creek is also expected to be named in Williams' federal suit, as is Larry Doe, a retired Oregon State Police Officer (OSP), who currently practices taxidermy in Josephine County.
Hamilton admitted under oath that she had logging done in or near the bed and banks of Allen Creek and she admitted that she allowed the Crawford family to live in an unauthorized trailer near Allen Creek for two years.
Had Williams been allowed to put on his defense, evidence would have shown that the Crawford's were dumping raw sewage into Allen Creek; that there was no permit for the trailer; and that Grants Pass City Attorney, Ulys Stapleton, knew so. It would have come out that numerous violations took place at Allen Creek, that trooper Doe knew about or should have known about, yet were ignored.
It's all too clear that Doe was intent on manufacturing a case against Williams, as is witnessed by the numerous lies contained in his reports. A prime example would be that Doe stated that the creek had been moved 150 yards. This would have placed the creek completely outside the basin. Bob Brown testified that Williams removed and or replaced a thousand cubic yards of material as he moved the creek channel and filled the old channel. These things never occurred according to the state's own witnesses, yet the false case continued.
Cat operator Jack Evans cleared the creek and ODOT's plugged grate – which was responsible for the problems. Riverside RediMix billed ODOT for the complete job and ODOT paid the bill in full.
ODOT's Mark Grinde claimed that he was a partner with Williams, and testified under oath at pre-trial hearings that he had seen Williams' application and that Williams had, "led him to believe that he had a permit."
It was anticipated that Grinde was going to confess on the third day of Williams' trial that he knew there was no permit before the job commenced and that he had never seen the application. Grinde, however, never got the opportunity to make his expected 12th-hour confession; even if he had, it still wouldn't have erased the four years of hell the state had put Williams, and his family, through.
Other evidence would have come out at trial had Williams been able to present his case, such as a topographic map with writing on it stating that it was submitted into the record by Ulys Stapleton and obtained through Barbara Hamilton. Realizing that water can't run up hill, Stapleton apparently had to show the elevation on Williams' property lower than it actually is. Barbara Hamilton testified that in May of 1994 she had Bob Montgomery contact Gene Leupold, a surveyor from Portland, to come clear to Grants Pass (3-4 hours South of Portland – a driving time of at least 7-8 hours) to survey her property near the creek. It appears that she actually did this even though the City of Grants Pass had a valid topographic map on file at the time, just as did the title companies in Grants Pass. Come on Barbara, I didn't just fall off the pumpkin truck! Doesn't make much sense, however the alarming issue is that Leupold's survey seems to have been altered. This evidence would have come out in Williams' trial had the charges not been dropped, but is now left for the federal suit. There is also a mountain of damning evidence against Ulys Stapleton and others waiting to be brought out in federal court.
Grants Pass City Manager Bill Peterson also lied about Williams' involvement in the Allen Creek job, and we certainly don't want him to think he is forgotten.
GRANTS PASS' DAILY COURIER CONTINUES PRACTICE OF LYING
When the state brings false charges against citizens, which happens all too frequently, they commonly turn over their lies to the local media to push to a believing public. This is exactly what occurred in the case of Mack Williams.
Back in 1996, the Daily Courier, without any investigation whatsoever, reported that the Allen Creek project was Mack Williams. This is a proven lie, which would have been revealed even by doing a brief investigation.
On April 6, 2000, the Daily Courier continued its practice of lying to the citizens of Josephine County when writer Shaun Hall reported, "In 1996, Williams got the financial help of the Oregon Department of Transportation to clear vegetation along the creek by telling ODOT he had a permit for the work from the Division of State Lands. ODOT never confirmed the existence of any permits." This is an absolute lie. It would be real newsworthy if the Courier could inform us as to why they needed to publish this lie and who prompted the lie. Mack Williams never "got the financial help of the Oregon Department of Transportation" and he certainly never told anyone that he had a permit.
The Courier continues, "After some $1,100 worth of stream work was done in 1996." How hard would it have been for Shaun Hall to contact Riverside RediMix to find out what they were paid for the work they did in the creek for ODOT? If Hall had taken the time before publishing this further lie, it would have been discovered that there was only $758 worth of work done. It would have also been discovered that Riverside billed ODOT this amount and ODOT paid the bill in full, a fact that Shaun Hall conveniently left out. I wonder why? Shaun Hall and the Daily Courier need to stop publishing lies and start presenting the Josephine County residents with the truth.
Isn't it newsworthy that a high ranking official such as Bob Brown with DSL admitted that he lied under oath? Isn't it important that Mark Grinde from ODOT lied under oath? Isn't it important that jurors felt Williams was innocent after the state's case was barely half over? Etc., etc., etc. All these facts are important to The Oregon Observer, Mack Williams and his family, and to thousands of concerned Josephine County residents, however they are apparently about as important to the Courier as ODFW employees clubbing and electrocuting thousands of supposedly endangered salmon to death. Get a life Shaun Hall, you're beginning to sound like Howard Huntington!
Would it possibly be of any importance to taxpayers that we are surely going to have to pay a few hundred thousand dollars in damages for the state's false prosecution? If the state didn't have a case half-way through their conspired trial, they didn't have a case two weeks prior to trial, they didn't have a case two months prior to trial and they certainly didn't have a case 4 years ago. But they continually attempted to extort from Mack Williams. This is a proven fact. Any prudent person must conclude that it is much more than disgusting for the Daily Courier and KAJO radio to keep this information from the public. Why in the world wouldn't these media inform citizens that Williams filed a major civil rights lawsuit some months ago, in which he charged public officials with conspiring against him, a fact that now has gained all the credibility in the world.
If local media would expose corruption, it would rarely raise its head and I would assume that Grants Pass, Oregon, wouldn't have picketers in front of the courthouse day after day, month after month. Maybe those celebrated and much needed picketers need to start splitting the valuable time they spend in front of the courthouse with the Daily Courier.
RESPONSIBILITY FOR THE FALSE PROSECUTION
All public officials and employees who have lied under oath (and now caught red-handed) are certainly responsible for damaging Mr. Williams, for putting his family through 4 years of tragic abuse and for costing him a portion of his life, however another is even more guilty than the rest.
Josephine County District Attorney Clay Johnson is that person. Although Mike Sanchez was the DA's scapegoat, or in other words, his "disposable assistant DA," Clay Johnson is responsible for the false charges and the unwarranted trial which Mr. Williams was forced to endure. Assistant DA Scott Titzler, until recently throwing the case to Sanchez, is also highly responsible. Former DA Tim Thompson was responsible for three-plus years of repeated attacks against Williams and for numerous extortion attempts directed at Williams, however Johnson has had the evidence of the lies and false charges at his disposal and still he chose to take Williams to trial.
You know folks, I have always been under the impression that perjury was a crime. I guess I have been sadly mistaken, or could it be that perjury just isn't a crime in Josephine County, Oregon, under the "special guidance" of District Attorney Clay Johnson? We'll soon find out because Johnson has in his possession perfect examples of perjury. Will he prosecute, or will he attempt to sweep criminal conduct under the carpet? Rest assured, Josephine County and the rest of the country will soon be informed!
A number of citizens have begun speaking of another recall. I am one such person and short of a public apology from Clay Johnson and a settlement for the great expense, both physical and monetarily, which his office has cost Mack Williams, a recall is certain to occur. If one is started I hope to be one of the petitioners and I can promise Clay Johnson that the effort will be well planned out and definitely successful.
The taxpayers of Josephine County also deserve an apology from Clay Johnson and his assistants for wasting tens of thousands in hard earned tax dollars. Rarely if ever do citizens receive the truth regarding the DA's office and the continual need for more funding. This article presents the reasons in a nutshell.
Out of arrogance we don't expect any apologies, however there is always room for surprises. Short of a surprise, I promise the Williams family that I will do everything in my power to get Clay Johnson and his "responsible assistants" out of Josephine County and I've had a great deal of practice at doing so with other "bad people in government."
Mack Williams and his family would not go along with calling anyone a liar, even after those certain "anyones" had attempted to wrongfully ruin their lives. This is unbelievable to me. I would just love to share their compassion but I don't. I'm not here doing what I do to seek the Williams' favor or anyone else's; I'm simply doing my level best to stop liars who are hurting others. When a person lies they haven't made a mistake, they have lied, like it or not!
Josephine County is currently asking its citizens, both the elderly and the young to continue supporting their gross waste and abuse with a new 18 million dollar levy against their homes and businesses to further false prosecutions. Vote NO on any new taxes until these abuses stop. It's the American thing to do!
UPDATE: WILLIAMS WINS FEDERAL SUIT!
Winning an undisclosed settlement due in part to the efforts of the US~Observer (then the Oregon Observer), Mack Williams has been vindicated and compensated. Another happy and vindicated US~Observer client win!
If you or anyone you know are facing unwarranted charges or being bullied by another party in court – contact us. We can help! Email: editor@usobserver.com – 541-474-7885.
Kevin Driscoll Raped by Prosecutor
Woman shows sign of trouble
Edward Snook Crushes Abuse – Celebrates 27th Anniversary
, By Ron Lee
IRS Capitulates – Moran's Jeep Returned
, By usob
State v. Keller Prineville, Oregon Man Escapes Criminal Charges (Part 2)
John Andrews is a Pedophile – US~Observer Aids in Case
State Drops Williams' Case
One Brave American Lady!
Walker Surveying Nightmare – Costs Approaching $500K – Dysfunctional Board of Surveyors
Prejudicial Judge John R. Stegner Applies for Idaho Supreme Court
Mack W. Multiple Felonies
Ella L. Assault & Resisting
James F. Murder
Angela F. Murder
Timothy T. Felony Sex Abuse
The Bluetears DHS / Child Custody
Kevin O. Assault
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