Microscopic self-consistent study of neon halos with resonant contributions

Abstract

Recent reaction measurements have been interpreted as evidence of a halo structure in the exotic neutron-rich isotopes 29,31 Ne. While theoretical studies of 31 Ne generally agree on its halo nature, they differ significantly in their predictions of its properties and underlying cause (e.g., that 31 Ne has an inverted ordering of p-f orbitals). We have made a systematic theoretical analysis of possible Neon halo signatures -the first using a fully microscopic, relativistic mean field approach that properly treats positive energy orbitals (such as the valence neutron in 31 Ne) self-consistently with bound levels, as well as the pairing effect that keeps the nucleus loosely bound with negative Fermi energy. Our model is the analytical continuation of the coupling constant (ACCC) method based on a relativistic mean field (RMF) theory with Bardeen-Cooper-Schrieffer (BCS) pairing approximation. We calculate neutron-and matter-radii, one-neutron separation energies, p-and f -orbital energies and occupation probabilities, and neutron densities for single-particle resonant orbitals in 27-31 Ne. We analyze these results for evidence of neutron halo formation in 29,31 Ne. Our model predicts a p-orbit 1n halo structure for 31 Ne, based on a radius increase from 30 Ne that is 7-8 times larger than the increase from 29 Ne to 30 Ne, as well as a decrease in the neutron separation energy by a factor of ∼ 10 compared to that of 27-30 Ne. In contrast to some other studies, our inclusion of resonances yields an inverted ordering of p and f orbitals for spherical and slightly deformed nuclei. Furthermore, we find no evidence of an s-orbit 1n halo in 29 Ne as recently claimed in the literature.

Exploration of direct neutron capture with covariant density functional theory inputs

“…The positive energy single-particle resonant states play a critical role in the description of exotic nuclei with small binding energies, because valence nucleons can be readily scattered both into bound states above the Fermi surface and into resonant states in the continuum. It is known from previous studies [16,17] that consideration of the coupling and pairing correlations can, in some cases, significantly influence predictions of the location and properties of resonant levels and the neutron capture threshold (i.e., the one neutron separation energy). Therefore, they are crucial for determining the neutron capture cross sections needed for r-process simulations.…”

“…This RMF+ACCC+BCS approach [18,19], denoted by RAB for simplicity below, was recently used to describe s.p. levels in unstable nuclei including 131,133 Sn [12], and the p-wave halo nucleus 31 Ne [16]. In the BCS approximation, a constant pairing strength is determined for each nucleus by fitting the odd-even mass difference extracted from a three-point formula for neutron pairs in a procedure described in detail in Refs.…”

“…In the BCS approximation, a constant pairing strength is determined for each nucleus by fitting the odd-even mass difference extracted from a three-point formula for neutron pairs in a procedure described in detail in Refs. [16,19].…”

“…RMF models typically use only 10 interaction parameters that are determined by fits to finite nuclear properties. In this scheme, nuclear structure for nuclei both near and far from β stability can be reasonably well described [12,16,19,24,25].…”

“…We applied this microscopic covariant density functional approach to calculate the energies and properties of bound levels in three nuclei which have low level densities, few or no resonances above threshold, and existing experimental capture data: the double closed shell nuclei 16 O and 48 Ca, and the neutron-rich nucleus 36 S. We then used the information for these levels as inputs for the FRESCO reaction code [26] in which radiative capture (direct capture for E1 transition) cross sections are obtained by a one-step distorted-wave Born approximation (DWBA) using an energy-dependent optical model potential (OMP) for scattering states [27]. The s.p.…”