Nuclear Theory·nucl-th

Wednesday·April 7, 2021

12 papers—7 primary·5 cross-listed

01
Auxiliary Function Approach for Determining Symmetry Energy at Supra-saturation Densities
Bao-Jun Cai🇨🇳 · Bao-An Li🇺🇸
Nuclear symmetry energy $E_{sym} (ρ)$ at density $ρ$ is normally expanded or simply parameterized as a function of $χ = (ρ - ρ_{0}) /3 ρ_{0}$ in the form of $E_{sym} (ρ) \approx S + L χ + 2^{- 1} K_{sym} χ^{2} + 6^{- 1} J_{sym} χ^{3} + \dots$ using its magnitude $S$ , slope $L$ , curvature $K_{sym}$ and skewness $J_{sym}$ at the saturation density $ρ_{0}$ of nuclear matter. Much progress has been made in recent years in constraining especially the $S$ and $L$ parameters using various terrestrial experiments and astrophysical observations. However, such kind of expansions/parameterizations do not converge at supra-saturation densities where $χ$ is not small enough, hindering an accurate determination of high-density $E_{sym} (ρ)$ even if its characteristic parameters at $ρ_{0}$ are all well determined by experiments/observations. By expanding the $E_{sym} (ρ)$ in terms of a properly chosen auxiliary function $Π_{sym} (χ, Θ_{sym})$ with a parameter $Θ_{sym}$ fixed accurately by an experimental $E_{sym} (ρ_{r})$ value at a reference density $ρ_{r}$ , we show that the shortcomings of the $χ$ -expansion can be completely removed or significantly reduced in determining the high-density behavior of $E_{sym} (ρ)$ . In particular, using two significantly different auxiliary functions, we show that the new approach effectively incorporates higher $χ$ -order contributions and converges to the same $E_{sym} (ρ)$ much faster than the conventional $χ$ -expansion at densities $≲ 3 ρ_{0}$ . Several quantitative demonstrations using Monte Carlo simulations are given.
nucl-thastro-ph.HEnucl-exPRC(2021)·15 citations
02
$α$ -cluster structures above double shell closures via double-folding potentials from chiral effective field theory
Dong Bai🇨🇳 · Zhongzhou Ren🇨🇳
$α$ -cluster structures above double shell closures are among the cornerstones for nuclear $α$ -cluster physics. Semi-microscopic cluster models (SMCMs) are important theoretical models to study their properties. A crucial ingredient of SMCM is the effective potential between the alpha cluster and the doubly magic nucleus. We derive new double-folding potentials between $α$ clusters and doubly magic nuclei from soft local chiral nucleon-nucleon potentials given by chiral effective field theory ( $χ$ EFT) at the next-to-next-to-leading order. The $α$ -cluster structures in $^{8} Be$ , $^{20} Ne$ , $^{44, 52} Ti$ , and $^{212} Po$ are explored to validate these new double-folding potentials. The $α$ decay of $^{104} Te$ is also studied in the light of recent experimental results. Our study shows that double-folding potentials from $χ$ EFT are the new reliable effective potentials for the SMCM approach to $α$ -cluster structures above double shell closures, with both conceptual and phenomenological merits.
nucl-thPRC(2021)·12 citations
03
Nuclear matrix elements for Majoron emitting double- $β$ decay
Jenni Kotila🇫🇮 · Francesco Iachello🇺🇸
A complete calculation of the nuclear matrix elements (NME) for Majoron emitting neutrinoless double beta decay within the framework of IBM-2 for spectral indices $n = 1, 3, 7$ is presented. By combining the results of this calculation with previously calculated phase space factors (PSF) we give predictions for expected half-lives. By comparing with experimental limits on the half-lives we set limits on the coupling constants $⟨ g_{ee}^{M} ⟩$ of all proposed Majoron-emitting models.
nucl-thPRC(2021)·14 citations
04
Systematic analysis of inner crust composition using the extended Thomas-Fermi approximation with pairing correlations
Matthew Shelley🇬🇧 · Alessandro Pastore🇬🇧
We perform a systematic investigation of the chemical composition of the inner crust of a neutron star, using the extended Thomas-Fermi approximation, the Strutinsky integral correction for shell effects, and the BCS approximation for pairing. Fifteen Skyrme functionals were selected, which cover the range of values of important bulk properties of infinite nuclear matter, while also having pure neutron matter (PNM) equation of states (EoS) with varying degrees of stiffness. We find that a functional's low-density PNM EoS is correlated with the number of protons found in the inner crust's nuclear clusters and, in the lower-density region of the inner crust, with the pressure.
nucl-thPRC(2021)·17 citations
05
Nuclear pasta and symmetry energy in the relativistic point-coupling model
Fan Ji🇨🇳 · Jinniu Hu🇨🇳 · Hong Shen🇨🇳
Nonuniform structure of low-density nuclear matter, known as nuclear pasta, is expected to appear not only in the inner crust of neutron stars but also in core-collapse supernova explosions and neutron-star mergers. We perform fully three-dimensional calculations of inhomogeneous nuclear matter and neutron-star matter in the low-density region using the Thomas-Fermi approximation. The nuclear interaction is described in the relativistic mean-field approach with the point-coupling interaction, where the meson exchange in each channel is replaced by the contact interaction between nucleons. We investigate the influence of nuclear symmetry energy and its density dependence on pasta structures by introducing a coupling term between the isoscalar-vector and isovector-vector interactions. It is found that the properties of pasta phases in the neutron-rich matter are strongly dependent on the symmetry energy and its slope. In addition to typical shapes like droplets, rods, slabs, tubes, and bubbles, some intermediate pasta structures are also observed in cold stellar matter with a relatively large proton fraction. We find that nonspherical shapes are unlikely to be formed in neutron-star crusts, since the proton fraction obtained in $β$ equilibrium is rather small. The inner crust properties may lead to a visible difference in the neutron-star radius.
nucl-thastro-ph.HEPRC(2021)·16 citations
06
Forbidden electron capture on $^{24}$ Na and $^{27}$ Al in degenerate oxygen-neon cores
D. F. Strömberg🇩🇪 · G. Martínez-Pinedo🇩🇪 · F. Nowacki🇫🇷
Stars with an initial mass of $\sim 7$ -11 solar masses form degenerate oxygen-neon cores following carbon burning. Electron captures in such cores can trigger runaway oxygen burning, resulting in either a collapse or a thermonuclear explosion. We provide a detailed description of the formalism used in previous work and apply it to two further forbidden transitions that are relevant to degenerate oxygen-neon cores: the $4_{g.s.}^{+} \to 2_{1}^{+}$ transition in $^{24} Na (e^{-}, ν_{e})^{24} Ne$ and the $5/ 2_{g.s.}^{+} \to 1/ 2_{g.s.}^{+}$ transition in $^{27} Al (e^{-}, ν_{e})^{27} Mg$ . The relevant nuclear matrix elements are determined through shell model calculations and constraints from CVC theory. We then investigate the astrophysical impact using the stellar evolution code MESA and through timescale arguments. In the relevant temperature range, the forbidden transitions substantially reduce the threshold densities for $^{24} Na (e^{-}, ν_{e})^{24} Ne$ and $^{27} Al (e^{-}, ν_{e})^{27} Mg$ . In the MESA models, $^{24} Na (e^{-}, ν_{e})^{24} Ne$ now occurs immediately following the onset of $^{24} Mg (e^{-}, ν_{e})^{24} Na$ . The impact on the overall evolution is uncertain: this is due to known difficulties in accounting for convective instabilities triggered by the $A = 24$ electron captures. The transition between $^{27} Al$ and $^{27} Mg$ may have a minor effect on the early evolution but is unlikely to affect the outcome. The studied transitions should be included when calculating weak interaction rates between $^{24}$ Na and $^{24}$ Ne for temperatures $lo g_{10} (T [K]) ≲ 8.5$ and between $^{27}$ Al and $^{27}$ Mg for $lo g_{10} (T [K]) ≲ 8.8$ .
nucl-thastro-ph.SRPRC(2022)·7 citations
07
Spin/Parity Dependent Level Density
Richard B. Firestone🇺🇸
It is shown that the Constant Temperature (CT) model of nuclear level density is a direct consequence of a symmetrized Poisson distribution of nuclear level spacings. The standard CT model describing the total level density is shown to be fatally flawed due to discontinuities at the Yrast energies, the onset of new $J^{π}$ sequences, that disrupt the exponential formula and cause the back shift parameter to become nonphysically negative. A new CT-JPI level density model is proposed with a constant temperature and separate back shift parameters for each $J^{π}$ sequence. The CT-JPI model is also constrained to reproduce the spin distribution predicted by Ericson's spin distribution function at the neutron separation energy. A fitting procedure is described for determining the temperature $T$ , back shifts $E_{0} (J^{π})$ , and spin cutoff parameters $σ_{c}$ from nuclear structure and resonance data. The CT-JPI model is demonstrated to successfully predict the level densities for a wide range of spins and parities for 46 nuclear with Z=7-92. In variance with earlier predictions the spin cut-off parameters show no mass dependence and instead substantial variation at all mass regions.
nucl-thnucl-ex1 citation

Affiliations

first authorsco-authorsvia INSPIRE

Auxiliary Function Approach for Determining Symmetry Energy at Supra-saturation Densities

α-cluster structures above double shell closures via double-folding potentials from chiral effective field theory

Nuclear matrix elements for Majoron emitting double-β decay

Systematic analysis of inner crust composition using the extended Thomas-Fermi approximation with pairing correlations

Nuclear pasta and symmetry energy in the relativistic point-coupling model

Forbidden electron capture on 24Na and 27Al in degenerate oxygen-neon cores

Spin/Parity Dependent Level Density

Affiliations

$α$ -cluster structures above double shell closures via double-folding potentials from chiral effective field theory

Nuclear matrix elements for Majoron emitting double- $β$ decay

Forbidden electron capture on $^{24}$ Na and $^{27}$ Al in degenerate oxygen-neon cores