Fragmentation reactions ofLi11

H. Esbensen, G. F. Bertsch
1992 Physical Review C  
We examine the effect of the spatial correlation between the valence neutrons in "Li on the cross section for ("Li, Li) reactions on different targets at 800 MeV/nucleon. The correlation suppresses the nuclear part of the cross section slightly but it strongly enhances the Coulomb part compared to an independent particle description. Agreement with measurement is significantly improved. PACS number(s): 25.70.Mn, 24. 10.i An important test of theoretical models of the extremely loosely bound
more » ... eus "Li is the fragmentation cross section, in particular, the breakup reaction "Lĩ Li+2n. The first measurements [1] revealed a surprisingly large cross section for reactions on a lead target, and a substantial part was attributed to Coulomb dissociation. This implies a large dipole strength at very low excitations, and a large theoretical effort has been devoted, in recent years, to explaining and accounting for the necessary strength. In previous publications we developed a semiquantitative three-body model for "Li, assuming it consists of two valence neutrons interacting with each other and with an inert Li core, to study the ground state [2] and the dipole response [3] . The model predicts a weak binding and a strong dipole response of the valence neutrons quite close to threshold. However, in order to make comparisons with fragmentation data, it is also necessary to determine the nuclear part of the reactions, preferably within the same model that is used to calculate the dipole response. In this Brief Report, we present calculations of the nuclear part of the fragmentation at 800 MeV/nucleon. The high beam energy is an advantage since the nuclear interaction with the target nucleus can be described in an eikonal approximation as an absorption, with a strength determined by the free nucleon-nucleon cross sections. We have previously applied such a model [4] to calculate the nuclear fragmentation of "Li, assuming that the two valence neutrons are independent particles. Here we use the same "diffractive" eikonal model that we used in Ref. [4] to describe the nuclear absorption, but we shall assume that the two valence neutrons are bound in the correlated ground state %,(r&,rz), which we determined in Ref. [2] from our three-body model. We showed there that the correlations enhance the Coulomb excitation cross section, but the nuclear fragmentation should be decreased by the correlations. The reason is that the nuclear mechanism is the absorption of the neutrons by the I target. A second neutron is less effective at producing additional absorption if it is in the immediate vicinity of the first one, since the areas of target interaction would overlap. Our calculation is based on the eikonal formula for the probability that the two valence neutrons remain in their ground state. The probability is calculated as a function of impact parameter b (with respect to a target nucleus) as where r, =(r;~,z, ), i =1, 2, are the positions of the two neutrons and y is the usual eikonal phase, y"(b)=f [o""p&(r)+o"~pr(r)]dz . (2) The eikonal distortion factor is expressed as e " = gF& (b, r)Y&"(r) . A, )M The probability amplitude is then given by (4) Here pz~are the target neutron and proton densities and r = b +z . We take nucleon-nucleon cross sections as in Ref. [4], 0""=0~~= 47 mb and 0"~= 38.5 mb. The target densities were obtained by a simple scaling of the charge distributions measured in elastic electron scattering [5] . We calculate the overlap in Eq. (1) using the LS representation of the two-neutron wave function (which has 1=0) and making a multipole expansion of the eikonal distortion factor. Thus we write the wave function 0, 1 Vs, (r&, r2)= g gP~( r&, r2)[[YI(r, )YI(rz)]I S)]J=o . L=S 1 0, 1 (%'g,~e " e "~% , ) = g g g A (LSl, 12') f dr, dr2$& (r, , r2)F~"(b, r, )F& "(b,rz)g~(r, , r2), L =S Il l~kP (5) 46 1552
doi:10.1103/physrevc.46.1552 pmid:9968268 fatcat:bvy2lxxnwjghldylfrb3z52wwi