Derivation of capture cross sections from quasi-elastic excitation functions

Abstract

The relationship between the quasielastic excitation function and the capture cross section is derived. The quasielastic data is shown to be a useful tool to extract the capture cross sections and the angular momenta of the captured systems for the reactions 16 O+ 144,154 Sm, 208 Pb, 20 Ne+ 208 Pb, and 32 S+ 90,96 Zr at near and above the Coulomb barrier energies.

Recent developments in fusion and direct reactions with weakly bound nuclei

“…At energies above the barrier, good agreement was found between the capture (fusion) cross sections obtained by this method and direct fusion cross section data for several tightly bound systems [62]. In collisions of weakly bound nuclei, the breakup process must be taken into account.…”

“…For the indirect determination of σ cap , through Eq. (64), Sargsyan et al [62] used the quasi-elastic and breakup data of Lin et al [70]. The agreement is good at near-barrier energies.…”

“…Recently it has been shown that quasi elastic scattering at backward angles can also be employed to derive fusion and reaction cross sections [62][63][64][65][66][67]. As quasi-elastic processes are much simpler to be measured than fusion, this is a very useful tool to, at least, estimate fusion cross sections.…”

“…Taking into account lowest order corrections to the J-dependent barrier radius and barrier height [68], Sargsyan et al [62] converted the sum over J into an integral over ε J ≡ ε and obtained the expression,…”

Energy-shifting formulae yield reliable reaction and capture probabilities

“…The key idea of the energy-shifting formula [8][9][10] consists in replacing the exact, reaction and capture probabilities for a nonzero partial wave J and a given incident energy E, P reac (E, J ) and P cap (E, J ), with the corresponding s-wave probabilities evaluated at a lower energy: * Corresponding author.…”