Factorization in high-energy nucleus-nucleus fragmentation cross sections
Physical Review C
It is shown that the basic quantity of the abrasion-ablation model of nucleus-nucleus collisions, namely the probability of extracting a nucleon from the projectile, is a quasi-universal quantity. It can be given a form which does not depend upon the target and which depends weakly upon the projectile. It is shown how this property is related to the weak factorization of the cross sections. NUCLEAR REACTIONS Fragmentation in relativistic heavy ion collisions. Factorization of the cross section.
... It has been observed for a few years" that the inclusive fragmentation cross sections in the relativistic nucleus-nucleus collisions can be factorized according to the formula o(F, P, T) = o~~y», where F, P, and T stand for the fragment, the projectile, and the target, respectively. Form (I) can be called weak factorization as opposed to the strong factorization form which reads o (F, P, T) = (ropy T . The present experimental data do not allow one to draw conclusions about the validity of relation (2). It has been shown recently' that the abrasionablation model' ' of relativistic heavy ion collisions predicts that weak factorization is approximately valid while strong factorization is violated. In this paper, our aim is to bring to light the exact relation between the abrasion-ablation model and the factorization and to comment about some properties of the model. I.et us call o'"(P, T) the abrasion cross section for removing n nucleons from the projectile. It is clear that the factorization of o"(P,T) implies the one of the abrasion-ablation cross section (see Ref. 5). One has the basic relations' v"(P, Y)= ) f d'b[) -Pp (b)]" S where the probability function P~T(b) is defined by cleon cross section and p is the nuclear density. (t, z) are cylindrical coordinates with z along the incident direction and b is the impact parameter. We recall that Eqs. (3)-(5) are obtained by using the nonrelativistic Glauber multiple scattering theory' as applied' " to a composite projectile and target. It is interesting to note that the trivial relativistic extension, namely the introduction of Lorentz contracted objects, does not change the value of P~T(b) since the function (t)( t) is not affected by a Lorentz contraction. We have computed the quantities o"(P,T} and P~T(b) for a large number of colliding pairs. Our results confirm those of Ref. 3. Moreover, we observed that the probability function P»(b) can be written TABLE I. The translation amplitude ( (in fm) of Eq. (6) for different projectiles (P) and targets (T). It appears that $ is a function of T only. where the function f~(x) only depends upon the projectile P. In other words, the quantity PrT(b) only depends on the target T by a translation of the coordinate. More remarkable perhaps is the fact that the amplitude $T of the translation does not depend upon the projectile (see Table I} . We show in Fig. I how the relation (6) is fulfilled for the "Al and ' 'Ag projectiles. The discrepancy for x=b -)T smaller than 5 fm which arises for light targets only can be disregarded in practice since P (b) Jd T( (t)exp[ -AT=a'""( ((+b)[ (4) 16O