First results on systematic investigations of sub-threshold f meson production in heavy-ion reactions measured with the 4p detector system FOPI at GSI have been previously reported [1,2]. About N_ev = 4.7 ·10⁶ (6.8 ·10⁶) central events comprising about 9% (15%) of the total cross section have been analysed for the system Ni+Ni (Ru+Ru) at 1.93 (1.69) A·GeV. We select candidates of charged kaons measured with the subdetectors Helitron (Hel) and outer Plastic Wall (Pla) within the polar angle and velocity acceptance limits of Dq_K (15^o < q < 27^o) and Db_K (0.4 < b < 0.85), respectively. These limits confine a phase space sector located near the region of highest intensity, i.e. at mid-rapidity (b_cm ~ 0.7) and at low transverse momentum [1]. The efficiency-corrected f multiplicity is determined via P_f(Dq_K,Db_K) = [(N_f(Db_K, Dq_K))/(N_ev ·e²_det,K(Db_K, Dq_K))] with N_f(Db_K, Dq_K) being the number of f's reconstructed from their decay kaons and e_det,K(Db_K, Dq_K) representing the kaon detection efficiency (incorporating the matching efficiency of Hel tracks with Pla hits and the cut efficiency of kaon selection). The efficiency is taken from pseudo kaons, i.e. protons of similar angular and momentum range as kaons [1]. (This method does not work for the FOPI subdetectors CDC and Plastic Barrel, since the latter one alone does not allow for particle identification. There, all efficiencies are included in the f acceptance factor which is determined with the GEANT package simulating the detector response [2]. Since the acceptance depends strongly on the f phase space distribution which is generated as input, e.g. by using a thermal model with temperature T, any f yield extrapolated to 4p would depend on these assumptions, i.e. it would be model dependent.) For the Ni+Ni (Ru+Ru) system, the deduced f multiplicity per central event in the Hel/Pla acceptance given by Db_K and Dq_K amounts to P_f(Dq_K,Db_K)·10⁵ = 4.8±2.0   (3.1±1.2).
These numbers can be compared directly with the output of transport approaches when implementing the detector acceptance/geometry and the decay properties of both the f mesons and the daughter kaons. Appropriate transport model calculations have been performed recently [3]. Extending the IQMD transport model to f meson production a total of 3.5·10^-4 (2.2·10^-4) f mesons per central event has been calculated for the Ni+Ni (Ru+Ru) system. Filtering the decay kaons through the acceptance limits described by Db_K and Dq_K and taking into account the branching ratio of the decay f®K⁺K^- of 49.1% and the finite kaon lifetime (ct = 3.71 m) a f yield of 1.8·10^-6 (1.1·10^-6) is found for the Ni+Ni (Ru+Ru) system.
The ratio of the yields with/w.o. filtering gives a typical f acceptance of 0.5%. Since the total f rapidity and transverse momentum spectra of the transport approach can be well approximated by an isotropic thermal distribution with T = 60-70 MeV, quite similar acceptance factors (including the f® K⁺K^- branching) are calculated also within our Monte-Carlo simulations when adopting this effective temperature [1].
For both considered systems, the f yield predicted by the transport model is substantially smaller than the experimental values. Also, an earlier attempt to predict the f production in the Ni+Ni reaction within the framework of another transport approach [4] delivered deviations of similar size though the involved elementary cross sections (esp. pp® ppf) are quite different. The reason for this strong underestimation of f meson production in both central heavy-ion reactions investigated at beam energies below the nucleon-nucleon threshold (2.54 A·GeV) is not yet understood. Therefore, further theoretical work is advisable [5].

References

[1]  R. Kotte (FOPI collaboration), Proc. Int. Workshop XXVIII, Hirschegg, Austria, Jan. 2000, p. 112

[2]  N. Herrmann (FOPI collaboration), Nucl. Phys. A 610 (1996) 49c

[3]  C. Hartnack and J. Aichelin, private communication

[4]  W.S. Chung, G.Q. Li, and C.M. Ko, Nucl. Phys. A 625 (1997) 347

[5]  H.W. Barz, B. Kämpfer, G. Wolf, and M. Zétényi, this Report  IKH 05/31/01 © R. Kotte