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one predicted result of a first order phase transition to a quark gluon plasma in heavy ion collisions is a long lived state due to the large latent heat and corresponding reduction in pressure gradients in the created system @xcite .
the primary method for measuring the space - time extent of heavy - ion collisions is two particle interferometry , which has been utilized in hadronic interactions from proton induced to nuclear collisions . for an incoherent source ( @xmath1 ) of identical bosons , the normalized probability of detecting two particles with relative momentum @xmath2 and average momentum @xmath3
is given by the correlation function ( @xmath4 ) :    @xmath5    where @xmath6 is the four - position , and the integral is taken over all space - time .
the direct utilization of this technique is hindered in principle because equation [ eq : c2 ] is uninvertible : the source has 7 independent variables while the measured correlation function has 6 .
furthermore , due to limited statistics most recent heavy ion experiments have chosen to plot and fit the correlation function in only three of the six dimensions versus the bertsch - pratt @xcite projection of @xmath7 in the out - side - long directions :    @xmath8    where @xmath9 is the momentum difference in the beam direction , @xmath10 , in the pair momentum direction , and @xmath11 , the corresponding orthogonal direction .
a benefit of such a fit is that , for a well - behaved , gaussian source with no position - momentum correlations or resonances , the lifetime is simply determined by the difference between @xmath12 and @xmath13 : @xmath14 @xcite . in such studies the k - dependence of the hbt radii is usually explored by repeating the fitting procedure with a subsample of the entire dataset of pairs .
the phenix experiment is described in detail elsewhere @xcite . for the analysis described in this article we use the data collected in the summer of 2000 .
after all offline analysis cuts , the data sample was approximately 1.5 million events .
this analysis used a subset of all of the detectors in the experiment . for vertex information and centrality definitions we rely on a pair of cerenkov beam counters and zero - degree calorimeters ; the beam counters also act as the start of the time of flight measurements .
the two drift chambers measure the deflection of particles through the magnetic field and , hence , their momentum , while the velocity is measured by either the time - of - flight wall ( tof ) or the electromagnetic calorimeter ( emc ) .
the tof timing resolution is approximately 115 ps @xcite , while the emc resolution is 700 ps . as a result
, the tof analysis provides @xmath15-@xmath16 separation to 1.5 gev / c ; the emc analysis , to 0.7 gev / c . due to geometric and acceptance effects
the tof analysis consists of @xmath17 ( @xmath18 ) pairs of identified @xmath19 ( @xmath20 ) while the emc analysis consists of approximately five times as many pairs .
the particle identification algorithm is similar in both analyses .
a pion is defined as being within 2@xmath21 of the pion mass - squared peak but 3@xmath21 away from the kaon peak .
backgrounds from long lived resonances , e.g. @xmath22 s , are reduced by intradetector association cuts .
energy deposition cuts in the tof slat or emc tower further reduce backgrounds due to accidental misassociations .
systematic studies have shown that the background contamination to the emc analysis is at least double that in the tof analysis leading to artificially lower @xmath23 values in the former .
ongoing studies of the backgrounds in the analyses aim to resolve these differences .
however , the introduction of background from accidental hits or electron contamination tend to only affect the resulting @xmath23 in the fits and do not change the measured radii .
a number of systematic studies have been performed to ensure that the resulting correlation function does not include any artificial , experimentally induced correlations from inefficiencies in either the detector or tracking algoithms . to remove these inefficiencies , pairs of particles within 2 cm of each other in the drift chamber
are removed .
further , pairs that share the same tof slat or emc cluster are also removed in both the signal and mixed background . for the coulomb correction ,
the source is parameterized as a gaussian in r@xmath24= @xmath25 , as determined by an iterative procedure @xcite .
.results of the bertsch - pratt fits to the identical pion pairs in the emc and tof analyses . errors shown represent statistical uncertainties only ; current systematic uncertainties are @xmath26 fm . [ cols="^,^,^,^,^",options="header " , ]     figure [ fig : memc ] shows the coulomb corrected correlation function for @xmath27 pairs measured in the emc analysis overlayed with the resulting fit . while the fit is performed in the full three dimensional space , we plot here projections of the correlation function into each of the standard momentum difference variables ( @xmath10 , @xmath11 , and @xmath9 ) .
the results of the fit are shown in table [ tab : results ] along with the results from the @xmath28 analysis from the emc and the @xmath19/@xmath20 analyses utilizing the tof .
the mean transverse momentum ( @xmath29 ) of the pairs is 350 mev / c in the tof analysis and 340 mev / c in the emc analysis while the rapidity coverage in both analyses is centered about mid - rapidity , @xmath30 .
the mean centrality of all pairs in the analysis is @xmath31% and is strongly biased towards central collisions .    within the current statistical and systematic error bars , the emc and tof analyses for both pion sets
are consistent with one another .
the results of the fits are moderately larger than identical measurements for au+au and pb+pb collisions at lower energies and comparable @xmath32 @xcite
. the results do not indicate an especially large source compared to measurements at lower energies and the resulting naively calculated lifetime deduced from these measurements is consistent with zero .
however , a stronger collective flow will shorten the effective source and lifetime measured by hbt .
plotted in fig .
[ fig : kt ] is the @xmath32 dependence of the radii in the emc @xmath19 ( squares ) and @xmath20 ( triangles ) analyses .
the sample is split into three approximately equal subsets of pairs and the correlation analysis is performed on each subset .
the @xmath0 bins are @xmath33 mev / c , @xmath34 mev / c and @xmath35 mev / c corresponding to @xmath36 mev / c , @xmath37 mev / c and @xmath38 mev / c respectively .
data points at identical @xmath32 are offset by @xmath39 mev / c for clarification .
the radii follow trends familiar from lower energy measurements at lower beam energies @xcite : @xmath12 has a mild , if any , dependence on the transverse momentum of the pair , while @xmath13 varies strongly with @xmath32 .
such dependencies have been described by collective motions , though temperature gradients and decays of short - lived resonances could also contribute to such dependencies @xcite .
we have shown first measurements of identical pion correlations measured by phenix at rhic .
the resulting bertsch - pratt radii are moderately larger than those measured at lower energies .
the @xmath0 dependence of the radii is consistent with the conjecture of a system with a large degree of collective motion .
an extension of these measurements over an wider range in @xmath0 with a larger data sample will be available following the upcoming 2001 data collection . during this second run the additional phenix acceptance and integrated luminosity should lead to approximately a factor of a hundred in pair statistics . the resulting data sample will lead to much stricter constraints on models of the collision and allow for comparisons to identical kaon and proton hbt analyses .
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first identical - pion correlations measured at rhic energies by phenix are presented . 
 two analyses with separate detectors , systematics , and statistics provide consistent results . 
 the resulting hbt radii are moderately larger than those measured at lower energies . 
 the @xmath0 dependence of the bertsch - pratt hbt radii is also similar to previous measures and is consistent with the conjecture of an expanding source .