Recently f meson production was measured in subthreshold Ni+Ni and Ru+Ru collisions by the FOPI collaboration at the heavy-ion synchrotron at GSI Darmstadt [1]. The f meson yield found in these experiments is considerably larger than the predictions of Boltzmann-Ühling-Uhlenbeck (BUU) calculations [2]. A possible explanation could be the existence of new f production channels that have not been considered so far in BUU calculations. Therefore, we study the f production cross sections in r-N and r-D collisions.
We calculate the isospin averaged cross sections in a one-boson exchange model. In this case a single pion exchange diagram contributes to both processes. The differential cross section can be written as

ds dW = 1 64p2 s |pout,CM| |pin,CM| |M |2.

(1)

The quantity |M |² represents the squared matrix elements summed over the final and averaged over the initial spin and isospin states. These expressions read for the r-N channel

|M|2 = 32 æ ç è ArN ® fN pp2-mp2 ö ÷ ø 2   mN2(pN ·pN¢ - mN2 )( (pr·pf)2 - mr2 mf2 )

(2)

and for the r-D channel

|M|2 = 16 9 æ ç è ArD® fN pp2-mp2 ö ÷ ø 2   (pD·pN + mDmN ) æ ç è ( pD·pN mD )2 - mN2 ö ÷ ø ( (pr·pf)2 - mr2 mf2 ). (3)

Here, the incoming four-momenta are denoted by p_r, p_D and p_N¢ while the p_N and p_f are the outgoing momenta. The factors A_i are given by A_{rN ® fN} = (f_{pN N}f_prf/m_pm_f)F_{pN N}(p_p²)F_prf(p_p²) and A_{rD® fN} = (f_{pN D}f_prf/m_pm_f)F_{pN D}(p_p²)F_prf(p_p²). Substituting the appropriate values for the coupling constants f_i and the cutoff parameters appearing in the form factors F_i(p_p²) and integrating Eq. (1) numerically over the angle we obtain the total cross sections. Their values are displayed in Fig. 1 as a function of the CM energy above threshold using the peak masses of the resonance states involved. For comparison we have included the cross section for the process p+N ® N+f [2]. The obtained cross sections for f meson production in r channels are much higher than that of the p-N channel, therefore the r-baryon channels can essentially contribute to f production in heavy-ion collisions despite their relative small abundances.

Fig. 1 Total cross section of f meson production in the reactions r+N ® N+f and r+D® N+f. For comparison the cross section for the process p+N ® N+f is also included. Note that the threshold for the r+D process lies in the incoming channel.

¹ KFKI Budapest, Research Institute for Particle and Nuclear Physics, H-1525 Budapest, POB 49,
Hungary

References

[1] R. Kotte (FOPI collaboration), Proc. Int. Workshop XXVIII, Hirschegg, Austria, 2000, p. 112
[2] W.S. Chung, G.Q. Li and C.M. Ko, Nucl. Phys. A 625 (1997) 347  IKH 05/31/01 © H.W. Barz