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over the past decade , the analysis of particle multiplicities in heavy ion collions has shown overwhelming evidence for chemical equilibrium in the final state except for particles carrying strangeness which are mildly suppressed ; however , their relative yields fulfill statistical equilibrium . a summary as of 2006 , combining the results from many different groups  @xcite , is shown in fig . [ eovern ] .     us determined from heavy ion collisions at different beam energies . the lower ags points are based on a preliminary analysis of @xmath2 data.,width=226 ]    except for particle multiplicities at rhic energies , all data in fig . [ eovern ] use integrated particle yields , the very systematic change of thermal parameters over the full range of beam energies is one of the most impressive features of relativistic ion collisions to date . it is now possible to use the thermal model to make solid predictions for particle multiplicities at lhc energies  @xcite and to determine which beam energy will lead to the highest baryon density at freeze - out  @xcite . with chemical equilibrium for integrated yields thus firmly established , we focus on other properties , in particular , since the rapidity distributions of identified particles is now becoming available also at rhic energies  @xcite , it is now possible to determine the rapidity dependence of thermal parameters . a first analysis was done by stiles and murray  @xcite for the data obtained by the brahms collaboration at 200 gev  @xcite . this shows a clear dependence of the baryon chemical potential on rapidity in particular due to the changing @xmath3 ratio . subsequently it was shown by rhrich  @xcite that the particle ratios at large rapidities are consistent with those measured at the sps energies . this opens the possibility to compare measurements for e.g. the @xmath4 ratio at high rapidities and check them with the corresponding values measured in the energy scan at the sps , thus complementing the rapid variation of this ratio as a function of beam energy . a further analysis of the rapidity dependence was recently done in ref . a detailed report of our results will be presented elsewhere  @xcite . the general procedure is as follows : the rapidity axis is populated with fireballs following a gaussian distribution function given by @xmath5 where @xmath6 is the rapidity of the fireball . particles will appear when the fireball freezes out and will follow a thermal distribution centered around the position of the fireball @xmath7    the momentum distribution of hadron @xmath8 is then calculated from the distribution of fireballs as given by eq . [ [ eqrho ] ] along the rapidity axis as follows @xmath9 where @xmath10 is the the distribution of hadrons from a single fireball . the temperature @xmath0 and the baryon chemical potential @xmath1 will depend on the rapidity of the fireball and are not assumed to be constant . an important parameter is the width of the distribution . for the rhic data at 200 gev this was determined from the @xmath11 s as these are very sensitive to the value of @xmath12 and less to variations in the baryon chemical potential . the width of the distribution @xmath13 is compatible with the values quoted by the brahms collaborationi  @xcite , e.g. @xmath14 and @xmath15 . the hadrons described by eq .  [ [ eqdist ] ] are mainly resonances . only a fraction of these are stable under strong interactions . the majority of them will decay into stable hadrons at chemical freeze - out , hence the need to implement multi - particle decays . we assume that the temperature @xmath0 and the chemical potential @xmath1 are always related via the freeze - out curve as given in fig .  [ [ eovern ] ] ; if the temperature varies along the rapidity axis , then also the chemical potential will vary . thus a decrease in the temperature of the fireball will be accompanied by an increase in the baryon chemical potential . in other words , we assue a universality of the chemical freeze - out condition . this relationship between temperature and baryon chemical potential is very reasonable since all particle abundancies measured so far follow it . once the width of the distribution of fireballs has been fixed , we can go on with the dependence of the baryon chemical potential on the rapidity of the fireball ( units are in gev ) . @xmath16 the dependence of the @xmath3 ratio on the parameter @xmath17 is shown in figure [ [ fig : mub_y ] ] . the best value is @xmath18 gev . ratio as a function of rapidity . the curves show the dependence on the baryon chemical potential on the rapidity as discussed in the text.,width=226 ]    the variation of the temperature along the rapidity axis is shown in fig . [ fig : tmuy ] . the temperature is maximal at mid - rapidity and gradually decreases towards higher ( absolute ) values of the rapidity . the baryon chemical potential follows a different pattern : it has a minimum at mid - rapidity and increases quite substantially towards higher values of the rapidity . of particular interest are the largest values of the rapidity ( say @xmath19 ) . it can be seen that there is a region of overlap with the data obtained at the na49 experiment at cern - sps . particle yields measured in heavy ion collisions show an overwhelming evidence for chemical equilibrium at all beam energies . the rapidity dependence of the thermal parameters @xmath0 and @xmath1 can now be determined over a wide range of rapidities and show a systematic behavior towards an increase in @xmath1 as the rapidity is increased . this work was supported in part by the scientific and technological co - operation programme between italy and south africa , project number 16 . the help of d. cebra with the preliminary 4@xmath20 data at the lower ags beam energies is gratefully acknowledged , r. adams has helped in the analysis of these data in fig . [ 1 ] is acknowledged . 99 for references see e.g. j. cleymans , h.  oeschler , k. redlich , s. wheaton , phys . c73 ( 2006 ) 034905 . j. cleymans , i. kraus , h. oeschler , k. redlich , s. wheaton , phys . c74 ( 2006 ) 034903 . j.  randrup and j. cleymans , phys . c74 ( 2006 ) 047901 . stiles and m. murray , nucl - ex/0601039 , unpublished . d.  rhrich , proceedings of the talk given at the workshop on `` critical point and the onset of deconfinement '' , florence , italy , july 2006 . i.  arsene at al . , brahms collaboration , phys . 94 ( 2005 ) 162301 . bearden , brahms collaboration , contribution to the qm2006 conference , shanghai , china , november 2006 . b.  biedron , w.  broniowski , nucl - th/0610083 . f.  becattini and j.  cleymans ( in preparation ) . w. broniowski and f. florkowski , phys . c65 ( 2002 ) 064905 ; j. phys . g31 ( 2005 ) s1087 .
particle yields in heavy ion collisions show an overwhelming evidence for chemical or relative chemical equilibrium at all beam energies . the rapidity dependence of the thermal parameters @xmath0 and @xmath1 can now be determined over a wide range of rapidities and 
 show a systematic behavior towards an increase in @xmath1 away from mid - rapidity .