Theoretical analysis of 8Li + 208Pb reaction and the critical angular momentum for complete fusion

Abstract

In a theoretical approach, the complete and incomplete fusions are investigated by considering the 8 Li + 208 Pb reaction. By decreasing the projectile ground-state binding energy ε b from its known experimental value, the complete fusion is shown to have insignificant dependence on such variations, whereas the incomplete fusion strongly depends on that. The complete and incomplete fusion cross sections are calculated by using a combination of both continuum-discretized coupled-channel and sum-rule models. To this end, an incident-energy dependent cut-off angular momentum L c is first obtained by using the available complete fusion experimental data, within an approach which is extended to model results obtained for other incident-energies. An approximated fitted expression linking L c to the well-known critical value L crit derived by Wilczyński [Nucl. Phys. A 216 (1973) 386] suggests a generalization of the corresponding sum-rule model to energies around and below the Coulomb barrier.

Analysis of Fusion Cross Sections in the 9Be Projectile Breakup on Different Target Nuclei

“…In Ref. [34], for 8 Li+ 208 Pb, the parameters C 0 and C 1 are 1.7 and 1.0 respectively. Therefore, by comparing these parameters with the ones obtained for 9 Be+ 208 Pb The critical angular quantum L crit and the coefficients γ pt (units MeV fm −2 ), were calculated using (16), with R p = 2.519 fm and R t (in fm) taken from Ref.…”

“…The cutoff angular momentum L c , which is an important ingredient to calculate the CF in the sum-rule model, was determined by following the same approach considered in Ref. [34], i.e., the partial total fusion cross sections σ (L) TF in (12), are summed up from L = 0 to a certain angular momentum L, until the sum fairly agrees with the CF experimental data, within about 5% tolerance. That is, σ th CF − σ exp CF ≤ 5%, where σ th CF is the theoretical CF cross section, and such angular momentum is L c .…”

“…In Ref. [34], by considering incident energies above the Coulomb barrier for the 8 Li+ 208 Pb reaction, the following analytical expression for L c in terms of E c.m. was found to fit well the computed data:…”

“…More recently we have the model proposed in [33], where fragment correlations have also being discussed. In order to study the dependence of CF and ICF cross sections on the projectile binding energy in the 8 Li+ 208 Pb reaction, an approach that combines the sum-rule (SR) model and the CDCC approach was recently introduced [34]. By varying the ground state binding energy of the 8 Li projectile, it was shown that, while the ICF suppression was found to be strongly dependent on the projectile breakup threshold, the CF cross section on the other hand, remained almost constant.…”

“…In this paper, we study the dependence of the TF, CF and ICF cross sections on the projectile ground state binding energy, in the breakup of the 9 Be nucleus on 124 Sn, 144 Sm and 208 Pb targets. One of our main goals is to investigate the extension of the approach presented in [34] to other reactions involving neutron-rich loosely bound projectiles. To this end, following the procedure of this reference, we vary the ground state binding energy within an arbitrarily selected interval, 0.5 MeV≤ ε b ≤ 3 MeV, covering binding energies below and above the experimental value.…”