Analysis of heavy-ion fusion reactions at extreme sub-barrier energies using the proximity formalism

Abstract

The recent measured values of the fusion excitation functions of the heavy-ion colliding systems 28 Si+ 100 Mo, 58 Ni+ 54 Fe, and 64 Ni+ 64 Ni are investigated using the original version of the proximity formalism. The fusion cross sections are calculated based on the coupled-channels approach, including couplings to the low-lying 2 + and 3 − states in both target and projectile nuclei. The comparison between the calculated and the measured values of the fusion excitation functions indicates that the potential Prox.77 needs to be modified considerably at sub-barrier energies. In the present study, the role of the surface energy coefficient γ and also the temperature T of the compound nucleus in nuclear potential and fusion cross section has been explored for our colliding systems. Moreover, the mutual and the multiphonon excitations of the lowest 2 + and 3 − states are considered in the coupled-channels calculations. It is demonstrated that the potential Prox.77 with these corrective effects can reproduce the experimental data of the fusion cross section, the S factor and the logarithmic derivative for fusion reactions 28 Si+ 100 Mo, 58 Ni+ 54 Fe, and 64 Ni+ 64 Ni with good accuracy especially at below-barrier energies.

Exploring the fusion hindrance phenomenon: the case of 32,34S + 89Y

“…This phenomenon was observed initially in symmetric systems involving medium-heavy nuclei and was named as the fusion hindrance phenomenon [34,35]. One should keep in mind that to explain theoretically this phenomenon in heavy-ion fusion reactions, various approaches with different physical basis have been so far suggested [5,36,[37][38][39][40][41][42][43][44][45][46]. For example, the sudden approach proposed by Misicu and Esbensen [5,36], in which a repulsive core is included to take into account the incompressibility of nuclear matter as a consequence of the Pauli exclusion principle when the interacting partners overlap.…”

“…Ichikawa et al [37][38][39] proposed a model based on the adiabatic neck picture between the colliding nuclei in the overlap region, in which a damping factor is imposed on the coupling strength as a function of internuclear separation distance to take into account a gradual change from the sudden to the adiabatic formalism. In 2013 [45], we suggested that the deep sub-barrier fusion hindrance can be described by the proximity formalism. In connection with this formalism, it is necessary to mention that the proximity force theorem [55] enables us to give a realistic estimate of the nuclear contribution of the interaction potential between two heavy ions at the surface regions.…”

Describing the heavy-ion above-barrier fusion using the bare potentials resulting from Migdal and M3Y double-folding approaches

“…The proximity potential [7] used, e.g., in [8][9][10] seems to be much better founded. It includes a universal dimensionless function which does not depend upon the colliding nuclei.…”

Survey of deep sub-barrier heavy-ion fusion hindrance phenomenon for positive and negative Q-value systems using the proximity-type potential

“…The fully microscopic density-constrained time-dependent Hartree-Fock (DC-TDHF) approach also shows that to achieve a good description of the data at energies far below the Coulomb barrier, dynamical effects such as the surface properties due to neck formation, energy dependence of the fusion barriers, and mass transfer must be considered to modify the nucleus-nucleus potential in the inner region [23,24]. Inspired by the Pauli-blocking effects of -cluster decay in radioactive nuclei, a microscopic approach has been very recently introduced to explain the fusion hindrance at colliding energies far below the Coulomb barrier, see for example [25]. This approach is based on the -cluster α α structures in n nuclei, such as 12 C, 16 O, and 24 Mg. To construct the Pauli blocking potential in the n -nucleusinduced fusion reactions, a single folding procedure can be used.…”

“…The authors of Ref. [25] indicated that a shallow pocket is formed in the inner part of the potential barrier when the standard M3Y nuclear interaction accompanied by the Pauli blocking potential of two colliding nuclei is applied. Furthermore, it was shown that the fusion hindrance phenomenon in the colliding systems 12 C+ 198 Pt, 16 O+ 208 Pb, 12 C+ 30 Si, 24 Mg+ 30 Si, and 28 Si+ 30 Si can be described well by introducing the Pauli blocking potential.…”