Results on the pion freeze-out phase-space density in sulphur-nucleus, Pb-Pb
and pion-proton collisions at CERN-SPS are presented. All heavy-ion reactions
are consistent with the thermal Bose-Einstein distrtibution f=1/(exp(E/T)-1) at
T~120 MeV, modified for expansion. Pion-proton data are also consistent with f,
but at T~180 MeV.Comment: 1 page, 1 figure; 98' report for GSI-Darmstad

Agababyan

Alber

Appelshäuser

B. Tomášik

Barrette

Bearden

Becattini

Beker

Bertsch

Chapman

D. Ferenc

Ferenc

J.G. Cramer

Schlei

Schnedermann

Stachel

Tomášik

U. Heinz

U.A. Wiedemann

Wiedemann

English

arXiv

Crossref

Nuclear Physics A

Universal pion freeze-out phase-space density

Results on the pion freeze-out phase-space density in sulphur-nucleus, Pb-Pb and pion-proton collisions at CERN-SPS are presented. All heavy-ion reactions are consistent with the thermal Bose-Einstein distrtibution f=1/(exp(E/T)-1) at T~120 MeV, modified for expansion. Pion-proton data are also consistent with f, but at T~180 MeV.Results on the pion freeze-out phase-space density in sulphur-nucleus, Pb-Pb and pion-proton collisions at CERN-SPS are presented. All heavy-ion reactions are consistent with the thermal Bose-Einstein distrtibution f=1/(exp(E/T)-1) at T~120 MeV, modified for expansion. Pion-proton data are also consistent with f, but at T~180 MeV.Results on the pion freeze-out phase-space density in sulphur-nucleus, Pb-Pb and pion-proton collisions at CERN-SPS are presented. All heavy-ion reactions are consistent with the thermal Bose-Einstein distrtibution f=1/(exp(E/T)-1) at T~120 MeV, modified for expansion. Pion-proton data are also consistent with f, but at T~180 MeV.Results on the pion phase-space density at freeze-out in sulphur-nucleus, Pb-Pb and π-p collisions at the CERN SPS are presented. All heavy-ion reactions are consistent with the thermal Bose-Einstein distribution ƒ = [exp( E/T ) − 1] −1 at T ∼ 120 MeV, modified for radial expansion. π-p data are also consistent with ƒ, but at T ∼ 180 MeV and without radial flow

Ferenc, D.

Heinz, Ulrich W.

Tomasik, B.

Wiedemann, U.A.

Cramer, J.G.

CERN Document Server

arXiv:hep-ph/9901230v1  6 Jan 1999Universal Pion Freeze-out Phase-Space DensityD. Ferenc, B. Toma´sˇik, U. Heinz, Inst. f. Theor. Physik, Universita¨t RegensburgG. Bertsch has indicated [1] a possibility to measure thepion freeze-out phase-space density and thereby test the lo-cal thermal equilibrium in a pion source. In case of thermalequilibrium at temperature T , identical pions of energy Ewould follow the Bose-Einstein distributionf =1eET − 1. (1)An average of this function over different phase-space re-gions is the quantity to be measured. When the pT -spectrum is parameterized by an exponential with Teff(y)being the inverse slope parameter, averaging over the spa-tial coordinates yields〈f〉(pT , y) =√pi2√λdir(pT ,y)Ep T2eff(y)exp(− pTTeff (y))dn−dy(y)Rs(pT , y)√R2o(pT , y)R2l (pT , y)− R4ol(pT , y).(2)This equation comprises information from essentially twodifferent classes of experimental results: the single parti-cle momentum spectra (dn−/dy, Teff), and the two pionBose-Einstein correlations (Rs, Ro, Rl, Rol, λdir). We havecalculated 〈f〉(pT , y) for the S-S, S-Cu, S-Ag, S-Au, S-Pband Pb-Pb data from the experiments NA35 [2], NA49 [3],NA44 [4], and for the pi-p data from the NA22 experi-ment [5] at CERN-SPS. From the results for 〈f〉 as a func-tion of pT , presented in Fig. 1, one may conclude:1. universal phase-space densityAll the nuclear collision data from the SPS in Fig. 1 areindistinguishably similar, in spite of a factor of ∼ 10 dif-ference in multiplicity density.2. agreement with Bose-Einstein distributionUsing simultaneously pion spectra and pion correlationsNA49 has disentangled thermal motion from collective ex-pansion [3]. Taking the NA49 result for the local freeze-out temperature T = 120 MeV as the only parameter inEq. (1) one indeed finds good agreement with the data.This is consistent with the thermal nature of the pionsource, and inconsistent with the presence of a hypotheticpion condensate.3. radial flowLooking in more detail, one finds that the data indicatea somewhat slower decrease with increasing pT than theBose-Einstein curve. This is most likely due to radial col-lective expansion which adds extra transverse momentumto particles, i.e. the local 〈f〉 values appear in the mea-surement at a pT that is higher than the local 〈pT 〉 in thesource reference frame. A detailed study is under way.4. rapidity dependenceA certain departure from the universal scaling is seen forthe data at rapidities close to the projectile rapidity, bothat AGS and SPS; moreover, the two results are consistent.Figure 1: Phase-space density as a function of pT fordifferent data sets. Heavy-ion data from SPS are indis-tinguishably similar, although they span over an order ofmagnitude range in multiplicity. A Bose-Einstein function(Eq. (1)) is superimposed with the three choices of thelocal freeze-out temperature: 80 MeV, 120 MeV and 180MeV.5. high temperature decoupling in pi − p collisionsIn contrast to freeze-out in nuclear collisions which takesplace in two steps (chemical at T ≃ 170-180 MeV andthermal at T ≃ 120 MeV), pion production in pi-p col-lisions [5] is essentially immediate, without the secondevolution stage, and therefore freeze-out temperatures ofaround 180 MeV should be expected. The data [5] areindeed consistent with this expectation, as seen in Fig. 1.References[1] G.F. Bertsch, Phys. Rev. Lett. 72 (1994) 2349, and77 (1996) 789e.[2] NA35, T. Alber et al., Z. Phys. C66 (1995) 77, Phys.Rev. Lett. 74 (1995) 1303.[3] NA49, H. Appelsha¨user, Ph.D. Thesis, Univ. Frank-furt, 1997. H. Appelsha¨user et al., Eur. Phys. J. C2(1998) 661.[4] NA44, H. Beker et al., Phys. Rev. Lett. 74 (1995)3340. I.G. Bearden et al., Phys. Rev. C58 (1998)1656.[5] N.M. Agababyan et al., Z. Phys. C71 (1996) 405.[6] E877, J. Barrette et al., Phys. Rev. Lett. 78 (1997)2961.

Universal Pion Freeze-out Phase-Space Density

Results on the pion phase-space density at freeze-out in sulphur- nucleus. Pb-Pb and pi -p collisions at the CERN SPS are presented. All heavy-ion reactions are consistent with the thermal Bose-Einstein distribution f=[exp(E/T)-1]/sup -1/ at T~120 MeV, modified for radial expansion. pi -p data are also consistent with f, but at T~180 MeV and without radial flow. (18 refs).Results on the pion phase-space density at freeze-out in sulphur-nucleus, Pb-Pb and pi-p collisions at the CERN SPS are presented. All heavy-ion reactions are consistent with the thermal Bose-Einstein distribution f=1/[exp(E/T)-1] at T ~ 120 MeV, modified for radial expansion. pi-p data are also consistent with f, but at T ~ 180 MeV and without radial flow.Results on the pion phase-space density at freeze-out in sulphur-nucleus, Pb-Pb and pi-p collisions at the CERN SPS are presented. All heavy-ion reactions are consistent with the thermal Bose-Einstein distribution f=1/[exp(E/T)-1] at T ~ 120 MeV, modified for radial expansion. pi-p data are also consistent with f, but at T ~ 180 MeV and without radial flow.Results on the pion phase-space density at freeze-out in sulphur-nucleus, Pb–Pb and π –p collisions at the CERN SPS are presented. All heavy-ion reactions are consistent with the thermal Bose–Einstein distribution f =[exp( E / T )−1] −1 at T ∼ 120 MeV, modified for radial expansion. π –p data are also consistent with f , but at T ∼ 180 MeV and without radial flow

Physics Letters B

Universal Pion Freeze-out Phase-Space Density

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