Non-monotonic potential description of alpha–Zr refractive elastic scattering

Abstract

Experimental differential cross sections of α elastic scattering by 90Zr in the 15.0–141.7 MeV range of the bombarding energies have been analysed within the framework of an optical model using non-monotonic (NM) potentials. These potentials are generated from the energy-density functional theory using a realistic two-nucleon potential coupled with an appropriate consideration of the Pauli principle. The NM nature of the real part of the potential seems to be gradually diminishing at energies beyond 118.0 MeV. The Airy structure of the nuclear rainbow scattering data in the energy range of 79.5–141.7 MeV is for the first time well accounted for by the shallow NM potential. Two potential families, which are located in the real part, bear a linear variation of a volume integral in the energy range 25.0–141.7 MeV with a threshold anomaly at the lower energies. The potential contains an interior repulsive part that, with energy, shifts towards the surface and gradually weakens until it is almost lost in the nuclear surface. The requirement of a deep attractive real part of the nuclear potential seems to be generally non-stringent for describing the nuclear rainbow oscillations. Some discrete ambiguities in the potentials seem to persist even when the ‘exponential falloff’ in the angular distribution following the ‘rainbow angle’ is well reproduced in this investigation using the NM real part of the optical potentials.

Nature of potential families from elastic 16O + 16O rainbow scattering*

“…But, at higher energies, while trying to fit rainbow scattering data, the challenge has been to fit in the region of the Airy minima. At one point, the shift parameter D 1 of the repulsive barrier was tried by our group [20] for α + 90 Zr scattering. Intriguingly, this resulted in much improved fits.…”

“…The successes enjoyed by NM potentials [19][20][21] derived microscopically using energy density functional (EDF) theory [22][23][24][25] with the sudden-approximation [26,27] include alpha-elastic scattering [21,28], inelastic scattering [29], one- [30], two- [31,32] and three nucleon [33] stripping reactions and describing opposite signs of the vector analyzing powers of 6 Li and 7 Li [21] as well as the vector and tensors analyzing powers of the 6 Li + 12 C elastic scattering [34] without needing any renormalization factor. Furthermore, a novel method is applied using NM potentials [20] to determine the incompressibility modulus K [12,16] for cold nuclear matter. The various successes of the NM potentials can be attributed mainly to the consideration of the Pauli principle in the EDF theory.…”

Перерізи Пружного Розсіяння, Одержані На Основі Потенціалу Модифікованого Методу Томаса–Фермі З Урахуванням Кора

“…Note that the repulsion at small distances between the nuclei exists in the proximity potential [5] and in the microscopic approach [37,38]. Elastic scattering of light nuclei making allowance for the potential core was studied in works [13,14,19,22,[39][40][41]. The account for the repulsive component of the potential made it possible to describe the deep subbarrier hindrance of the fusion of heavy nuclei [42][43][44].…”

16O + 16O cluster states and their fusion to 32S: A non-monotonic potential description

“…However, nuclear scattering is intrinsically non-local, due to the Pauli exclusion principle (PEP) operating between constituent nucleons and in the coupling between elastic and inelastic channels. A non-monotonic (NM) nucleus-nucleus potential [10][11][12] arising out of the equation of state can be derived from the Pauli-compliant energy-density functional (EDF) theory of Brueckner [13] (BCD) using the sudden approximation [14,15]. PEP prevents the projectile nucleons from filling the quantum states already occupied by the target nucleons, leading to a repulsive core.…”

“…NM potentials with a repulsive core enjoy several successes. These include α elastic scattering [11,17]; inelastic scattering [18]; one- [19], two- [20,21] and threenucleon [22] stripping reactions; and the mixing of I π = 1 2 + and 3 2 + bands [23] in the Nilsson model. NM potentials are successful in reproducing the opposite signs of the vector analyzing power (VAP) of 6 Li and 7 Li elastic scattering and their cross-section (CS) data [12] in the simple optical model (OM) without renormalization.…”