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the interest to electric dipole moments ( edm ) of elementary particles and more complex systems like nuclei and atoms exists since 1950 , when it was first suggested that there was no experimental evidence for symmetry of nuclear forces under parity transformation  @xcite .
the interest was renewed after 1964 when it was discovered that the invariance under cp transformation , which combines charge conjugation with parity , is violated in @xmath2-meson decays .
this provided a new incentive for edm searches . since the combined cpt transformation is expected to leave a system invariant , breakdown of cp invariance should be accompanied by t violation .
thus , there is a reason to expect that p and t violating edms should exist at some level .    the experimental upper limit on the neutron edm is @xcite @xmath3 the measured value for the proton edm is @xcite @xmath4 and is compatible with zero .
this corresponds to an upper limit which is three order of magnitude weaker than the one for the neutron .
the best upper limit on edm ever obtained was in an atomic experiment with @xmath0hg  @xcite .
the result for the dipole moment of this atom is @xmath5 unfortunately , the implications of this result are somewhat less impressive , due to the electrostatic screening of the nuclear edm in this essentially coulomb system .
the point is that in a stationary state of such a system , the total electric field acting on each particle must vanish .
thus , an internal rearrangement of the system s constituents gives rise to an internal field @xmath6 that exactly cancels @xmath7 at each charged particle ; the external field is effectively switched off , and an edm feels nothing @xcite .
still , some p and t odd component of the electrostatic potential survives due to final nuclear size .
it is created by the next moment in the nuclear electric dipole density distribution .
this is the schiff moment defined as @xcite @xmath8 the schiff moment generates a p and t odd electrostatic potential in the form @xmath9 interaction of atomic electrons with the potential given by eq .
( [ 2 ] ) produces an atomic dipole moment @xmath10 because of the contact origin of the potential , only the electrons in @xmath11 and @xmath12 atomic orbitals contribute to the dipole moment given by eq .
( [ 3 ] ) .
the eq.([1 ] ) is valid for any system of point - like charges @xmath13 .
let us split the sum in eq.([1 ] ) into the sum over coordinates of nucleons and the sum over coordinates of charges inside the nucleons : @xmath14 here @xmath15 is a nucleon position and @xmath16 is the position of the @xmath17th charge inside the nucleon .
combining the terms of the zeroth and first order in @xmath18 and using @xmath19 , @xmath20 , we obtain an expression for the schiff moment as a sum of two terms .
the first of them is similar to ( [ 1 ] ) @xmath21 where @xmath22 is equal to @xmath23 for a proton and zero for a neutron .
the mean value of this operator is nonzero only in the presence of the parity- and time - invariance violating nucleon - nucleon interaction    the second term in the operator ( [ 1.1 ] ) is related to the internal dipole moments of the nucleons @xmath24    the previous calculations of the schiff moment of a heavy nucleus @xcite were performed in a simplified manner , without taking into account the residual interaction between a valence nucleon and the core nucleons .
only recently more microscopic studies of the schiff moment of @xmath0hg @xcite and @xmath25ra @xcite appeared where effects of the core polarization with the effective forces for @xmath0hg and the octupole deformation for @xmath25ra based on skyrm - hartree - fock method were discussed . in this work
we would like to concentrate on the nucleon edm contribution to the schiff moment of the @xmath0hg nucleus . in the picture of independent particle model only an edm of a valence nucleon
contributes to the schiff moment . in case of @xmath0hg
it is a neutron edm .
however , when a residual quasiparticle interaction between the valence neutron and the protons in the core is taken into consideration , the proton edm contribution to the nuclear schiff moment becomes nonzero .
we calculated this contribution using a random phase appriximation with effective forces . from the relation between the schiff moment and the electric dipole moment of the hg atom @xcite
the new upper limit on the proton edm was obtained .
in our calculations we used full single - particle spectrum including continuum .
the single - particle basis was obtained using partially self - consistent mean - field potential of @xcite .
the potential includes four terms .
the isoscalar term is the standard woods - saxon potential @xmath26 with the parameters @xmath27 mev , @xmath28 fm , and @xmath29 fm .
two other terms @xmath30 , and @xmath31 were obtained in a self - consistent way using two - body landau - migdal - type interaction of @xcite for the spin - orbit and isovector parts of the potential .
the last term is the coulomb potential of a uniformly charged sphere with @xmath32 fm .
the mean field potential obtained in this way produces a good fit for single particle energies and r.m.s .
radii for nuclei in the region around @xmath33pb .
the effects of the core polarization for a single particle operator can be treated by introducing a renormalized operator @xmath34 satisfying the equation @xmath35 where @xmath36 is the bare schiff moment operator given by ( [ 1 ] ) , ( [ 1a ] ) or ( [ 1b ] ) . @xmath37 and @xmath38 are single particle occupation numbers and energies . for static moments the external frequency @xmath39 .
the value of the schiff moment is given by the diagonal matrix element of the z - component of the renormalized operator ( [ 11 ] ) between mean field states of the last unpaired nucleon with a maximal angular momentum projection .
@xmath40    for the residual interaction @xmath41 we use the phenomenological landau - migdal interaction that has the form @xmath42\delta({\bf
r}_1-{\bf r}_2),\ ] ] where @xmath43 300 mev @xmath44 .
the values of the empirical interaction constants @xmath45 and @xmath46 are crucial for our calculations .
the proton contribution is proportional to the proton - neutron interaction @xmath47 .
the constant @xmath46 is determined from magnetic properties of nuclei and positions of gamow - teller resonances .
its adopted value varies between @xmath48@xmath49 depending on details of the mean field potential used @xcite .
the constant @xmath45 is not so well defined .
the magnetic moments and m1 transitions are to large extent isovector and they do not fix @xmath45 .
an attempt to fix it from the structure of high spin states in @xmath33pb has been done in @xcite .
they found that @xmath50 had to be used in order to reproduce the excitation energies of the @xmath51 and @xmath52 states .
another value @xmath53 was quoted in the review paper @xcite .
the schiff moment operator can be presented in coordinate space in the form @xmath54 where we have introduced the set of linear independent tensor operators @xmath55 where @xmath56 is the vector spherical harmonic .
for @xmath57 we have @xmath58 , and @xmath59 .
for a spherical nucleus we can separate the angular variables and solve the obtained equations in coordinate space .
the equations are @xmath60 where @xmath61 and @xmath62 is the radial part of the schiff moment operator ( [ 1b ] ) multiplied by @xmath63 .
the kernel of the integral equation @xmath64 was calculated by means of the green functions of the radial schrdinger equation .
@xmath65 @xmath66 where @xmath67 , @xmath68 are the radial wave functions , and @xmath69 are the occupation numbers .    the solutions of eq .
( [ 11 ] ) for @xmath70 are shown in fig.1 and 2 .    ; the dashed curve is the bare operator @xmath71.,width=302 ]    ; the dashed curve is @xmath72.,width=302 ]    figure 1 demonstrates the magnitude of the core polarization effects .
repulsive residual interaction ( [ 15 ] ) leads to not very significant decrease of the mean value of the schiff moment .
figure 2 shows the radial dependence of the proton contributions induced by the core polarization .
note 1 order of magnitude difference in the scales in fig . 1 and 2 . the full curve in fig .
2 is the radial dependence at the first operator @xmath73 and the dashed curve is the radial dependence at the second operator @xmath74 .
@xmath75 changes sign inside the nucleus , therefore its mean value is smaller than the mean value of @xmath72 which is mostly negative inside the nucleus .
the value of the schiff moment of @xmath0hg can be presented as a sum of proton and neutron contributions @xmath76 in table i we list the values @xmath77 and @xmath78 calculated for different combinations of @xmath45 and @xmath46 .       from table [ tabr ]
one can see that the uncertainties in @xmath77 and @xmath78 due to uncertainties in @xmath45 and @xmath46 are @xmath79 the main contribution to @xmath77 and @xmath78 comes from the second term in eq .
( [ 1b ] ) .
the contribution of the first term is only -0.7 @xmath80 in @xmath78 and 0.006 @xmath80 in @xmath77 .
the constraint for the schiff moment of mercury nucleus from the experiment @xcite can be obtained using the results of ref .
they calculated edm of an atom created by the nuclear schiff moment .
for @xmath0hg they found @xmath81.\ ] ] from eq.([exp ] ) we obtain the following upper bound for the schiff moment @xmath82 from eq .
( [ sm ] ) we can give the following constraints for edm of nucleons : @xmath83 the constraint for the neutron edm is worse than the existing result @xmath84 @xcite , therefore , we shall not discuss it below . for proton edm the estimate ( [ an1 ] )
is 1 order of magnitude lower than the existing experiment @xmath85 e cm @xcite . in these circumstances
the question about a real theoretical accuracy of our approach becomes important .
it is clear that the value @xmath86 cited in eq.([spsn ] ) does not reflects the real accuracy of the theory .
it just came from the difference in adopted values of @xmath45 and @xmath46 .
the theoretical uncertainty appears from two sources .
first , it is an uncertainty in the atomic calculations that couple the nuclear schiff moment and edm of an atom .
we shall not discuss it here referring to the work @xcite .
second , it is an uncertainty in calculations of the core polarization effects using rpa with effective forces .
the latter can be estimated from the following considerations . using rpa with the effective forces we can fit different nuclear moments in one nucleus .
then , in neighbor nuclei the calculated moments will differ from the data .
this difference can be regarded as an uncertainty in the theory . in our experience
this difference is of the order of 20% on the average , reaching sometimes the value of 30% @xcite . to be safe ,
we can adopt a conservative 30% uncertainty in calculations of @xmath77 .
therefore , instead of ( [ spsn ] ) we would prefer to write for @xmath77 @xmath87 since the error in ( [ sp ] ) is not statistical , we can not give a probability distribution for @xmath77 .
if one takes @xmath88 as a minimal value of @xmath77 , then it gives the following value for the proton edm upper bound @xmath89    in summary , we calculated the contributions of the proton and neutron edm to the schiff moment of @xmath0hg .
the effects of core polarization were accounted for in the scope of rpa with the effective residual forces .
a new upper bound of the proton edm has been obtained from the upper bound on the atomic edm of @xmath0hg atom .
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we calculated the contribution of internal nucleon electric dipole moments to the schiff moment of @xmath0hg . 
 the contribution of the proton electric dipole moment was obtained via core polarization effects that were treated in the framework of random phase approximation with effective residual forces . 
 we derived a new upper bound @xmath1 cm of the proton electric dipole moment .