Effective fusion barrier transmission model for heavy-ion fusion

Abstract

A new effective fusion barrier transmission model is developed. This gives a good description of the measured fusion cross sections both below and above the Coulomb barrier for a number of pairs of nuclei. The model uses only the surface region (r> RF-RB) of the heavy-ion optical potential describing the scattering data. The correlation of this approach with the direct reaction description of fusion is established. A physical interpretation for rF is indicated in terms of nucleon flux and neutron transfer time across the two nuclei.

Roles of survival probability and barrier reduction in heavy ion fusion induced by break up

“…In our calculation we set r F = 1.4 fm giving the fusion radius R F = 7.213 fm and T = ∆e = 0.75 MeV. In the application of EFB model in several cases elsewhere [9] we have found that at a given energy above V 0 B , σ F is minimum for R F ∼R B . Increasing or decreasing of R F from the optimum value gives higher values of σ F with sharper rise for values of R F >R B .…”

“…The expressions for transmission probability deduced within the framework EFB model and using the mathematical procedure of Farina [19] are used to analyze the heavy ion fusion cross section σ F of nucleus-nucleus collisions involving weakly bound unstable neutron rich projectiles namely 9 Be and 11 Li scattering on light as well as heavy stable targets. The influence of particle evaporation of the participants on the fusion process at low bombarding energies is investigated leading to the following observations: (i) When the neutron separation energy n < 5 MeV, it causes reduction in the survival probability SP of the participants and (ii) when n is very small , i.e., n < 1 MeV, along with the reduction of SP, there is reduction in the height of the potential barrier [3].…”

“…In the EFB transmission model for fusion elaborated in [9], the effective barrier for lth partial-wave is assumed to be…”

“…This model is found to be successful in the description of fusion around the Coulomb barrier in a number of HI cases. On the other hand, in the effective fusion barrier (EFB) transmission model [9] used by us a view point complementary to the DRM was adopted maintaining that fusion takes place when the interacting nuclei penetrate into the sphere r ≤ R F , i.e., once the colliding nuclei have center of mass separation r ≤ R F fusion takes place as a result of drastic attenuation of elastic scattering optical model wave function occuring due to the onset of large number of reaction channels competing with the elastic channel. In such a scenario EFB model assumes that fusion occurs as soon as the effective barrier present in the region r > R F is crossed leading to the penetration of nuclei into the region r ≤ R F .…”

“…It is found in general that weakly bound nuclei having small neutron separation energy n ( 1.67 MeV in 9 Be) lead to the reduction of σ F in sub-barrier region of energy due to lower survival probability (SP) of the participants [1,2]. Further, in fusion process there is additional feature of enhancement of σ F arising from a lower fusion barrier generated due to the evaporation and/or transfer of the neutrons from the neutron rich nuclei having very small n ( 0.2 MeV for two neutrons in 11 Li [3,10]).…”