arXiv subjects

Wojciech Satula

Publications and source records attributed to Wojciech Satula.

15 recordsLinked to original sources

arXiv2024

Nucleonic Shells and Nuclear Masses

The binding energy of an isotope is a sensitive indicator of the underlying shell structure as it reflects the net energy content of a nucleus. Since magic nuclei are significantly lighter, or more bound, compared to their neighbors, the presence of nucleonic shell structure makes an imprint on nuclear masses. In this work, using a carefully designed binding-energy indicator, we catalog the appearance of spherical and deformed shell and subshell closures throughout the nuclear landscape. After presenting experimental evidence for shell and subshell closures as seen through the lens of nuclear masses, we study the ability of global nuclear mass models to predict local binding-energy variations related to shell effects.

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arXiv2017

Isospin-symmetry breaking in masses of $N\simeq Z$ nuclei

Effects of the isospin-symmetry breaking (ISB) beyond mean-field Coulomb terms are systematically studied in nuclear masses near the $N=Z$ line. The Coulomb exchange contributions are calculated exactly. We use extended Skyrme energy density functionals (EDFs) with proton-neutron-mixed densities, to which we add new terms breaking the isospin symmetry. Two parameters associated with the new terms are determined by fitting mirror and triplet displacement energies (MDEs and TDEs) of isospin multiplets. The new EDFs reproduce MDEs for the $T=\frac12$ doublets and $T=1$ triplets, and TDEs for the $T=1$ triplets. Relative strengths of the obtained isospin-symmetry-breaking terms {\em are not} consistent with the differences in the $NN$ scattering lengths, $a_{nn}$, $a_{pp}$, and $a_{np}$. Based on low-energy experimental data, it seems thus impossible to delineate the strong-force ISB effects from beyond-mean-field Coulomb-energy corrections.

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arXiv2016

Mirror and triplet displacement energies within nuclear DFT: numerical stability

Isospin-symmetry-violating class II and III contact terms are introduced into the Skyrme energy density functional to account for charge dependence of the strong nuclear interaction. The two new coupling constants are adjusted to available experimental data on triplet and mirror displacement energies, respectively. We present preliminary results of the fit, focusing on its numerical stability with respect to the basis size.

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arXiv2015

Strong-interaction isospin-symmetry breaking within the density functional theory

The conventional Skyrme interaction is generalized by adding zero-range charge-symmetry-breaking and charge-independence-breaking terms, and the corresponding energy density functional is derived. It is shown that the extended model accounts for experimental values of mirror and triplet displacement energies (MDEs and TDEs) in sd-shell isospin triplets with, on average, about 100~keV precision using only two additional adjustable coupling constants. Moreover, the model is able to reproduce, for the first time, the A=4n versus A=4n+2 staggering of the TDEs.

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arXiv2015

Isospin effects in N~Z nuclei in extended Density Functional Theory

This paper overviews various phenomena related to the concept of isospin symmetry. The focus is on N~Z nuclei, which are excellent laboratories of isospin physics. The theoretical framework applied is nuclear Density Functional Theory and its isospin- and angular-momentum projected extensions, as well as symmetry-projected multi-reference models. The topics covered include: isospin impurities, superallowed beta decays, beta-transitions in mirror nuclei, isospin breaking hadronic interactions, mirror and triplet binding energy differences, and isoscalar pairing.

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arXiv2014

Beta-decay Studies in N~Z Nuclei Using No-Core Configuration-Interaction Model

The no-core configuration-interaction model based on the isospin- and angular-momentum projected density functional formalism is introduced. Two applications of the model are presented: (i) determination of spectra of 0+ states in 62Zn and (ii) determination of isospin-symmetry-breaking corrections to superallowed beta-decay between isobaric-analogue 0+ states in 38Ca and 38K. It is shown that, without readjusting a single parameter of the underlying Skyrme interaction, in all three nuclei, the model reproduces the 0+ spectra surprisingly well.

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arXiv2014

Simple regularization scheme for multi-reference density functional theories

Background: Extensions of single-reference (SR) energy-density-functionals (EDFs) to multi-reference (MR) applications involve using the generalized Wick theorem (GWT), which leads to singular energy kernels that cannot be properly integrated to restore symmetries, unless the EDFs are generated by true interactions. Purpose: We propose a new method to regularize the MR EDFs, which is based on using auxiliary quantities obtained by multiplying the kernels with appropriate powers of overlaps. Methods: Regularized matrix elements of two-body interactions are obtained by integrating the auxiliary quantities and then solving simple linear equations. Results: We implement the new regularization method within the self-consistent Skyrme-Hartree-Fock approach and we perform a proof-of-principle angular-momentum projection (AMP) of states in odd-odd nucleus 26Al. We show that for EDFs generated by true interactions, our regularization method gives results identical to those obtained within the standard AMP procedure. We also show that for EDFs that do not correspond to true interactions, it gives stable and converging results that are different than unstable and non-converging standard AMP values. Conclusions: The new regularization method proposed in this work may provide us with a relatively inexpensive and efficient tool to generalize SR EDFs to MR applications, thus allowing for symmetry restoration and configuration mixing performed for typical nuclear EDFs, which most often do not correspond to true interactions.

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arXiv2006

Probing effective nucleon-nucleon interaction at band termination

Low-energy nuclear structure is not sensitive enough to resolve fine details of nucleon-nucleon (NN) interaction. Insensitivity of infrared physics to the details of short-range strong interaction allows for consistent, free of ultraviolet divergences, formulation of local theory at the level of local energy density functional (LEDF) including, on the same footing, both particle-hole as well as particle-particle channels. Major difficulty is related to parameterization of the nuclear LEDF and its density dependence. It is argued that structural simplicity of terminating or isomeric states offers invaluable source of informations that can be used for fine-tuning of the NN interaction in general and the nuclear LEDF parameters in particular. Practical applications of terminating states at the level of LEDF and nuclear shell-model are discussed.

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arXiv2005

Nuclear Symmetry Energy in Relativistic Mean Field Theory

The Physical origin of the nuclear symmetry energy is studied within the relativistic mean field (RMF) theory. Based on the nuclear binding energies calculated with and without mean isovector potential for several isobaric chains we conform earlier Skyrme-Hartree-Fock result that the nuclear symmetry energy strength depends on the mean level spacing $ε(A)$ and an effective mean isovector potential strength $κ(A)$. A detaied analysis of isospin dependence of the two components contributing to the nuclear symmetry energy reveals a quadratic dependence due to the mean-isoscalar potential, $\simεT^2$, and, completely unexpectedly, the presence of a strong linear component $\simκT(T+1+ε/κ)$ in the isovector potential. The latter generates a nuclear symmetry energy in RMF theory that is proportional to $E_{sym}\sim T(T+1)$ at variance to the non-relativistic calculation. The origin of the linear term in RMF theory needs to be further explored.

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arXiv2005

Pairing in Nuclei

Simple generic aspects of nuclear pairing in homogeneous medium as well as in finite nuclei are discussed. It is argued that low-energy nuclear structure is not sensitive enough to resolve fine details of nuclear nucleon-nucleon (NN) interaction in general and pairing NN interaction in particular what allows for regularization of the ultraviolet (high-momentum) divergences and a consistent formulation of effective superfluid local theory. Some aspects of (dis)entanglement of pairing with various other effects as well as forefront ideas concerning isoscalar pairing are also briefly discussed.

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arXiv2005

Global properties of the Skyrme-force-induced nuclear symmetry energy

Large scale calculations are performed to establish the global mass dependence of the nuclear symmetry energy, $a_{sym}(A)$, which in turn depends on two basic ingredients: the mean-level spacing, $ε(A)$, and the effective strength of the isovector mean-potential, $κ(A)$. Surprisingly, our results reveal that in modern parameterizations including SLy4, SkO, SkXc, and SkP these two basic ingredients of $a_{sym}$ are almost equal after rescaling them linearly by the isoscalar and the isovector effective masses, respectively. This result points toward a new fundamental property of the nuclear interaction that remains to be resolved. In addition, our analysis determines the ratio of the surface-to-volume contributions to $a_{sym}$ to be $\sim$1.6, consistent with hydrodynamical estimates for the static dipole polarizability as well as the neutron-skin.

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arXiv2004

Spin-orbit term and spin-fields: extension of Skyrme-force induced local energy density approach

A systematic study of terminating states in A$\sim$50 mass region using the self-consistent Skyrme-Hartree-Fock model is presented. The objective is to demonstrate that the terminating states, due to their intrinsic simplicity, offer unique and so far unexplored opportunities to study different aspects of the effective NN interaction or nuclear local energy density functional. In particular, we demonstrate that the agreement of the calculations to the data depend on the spin fields and the spin-orbit term which, in turn, allows to constrain the appropriate Landau parameters and the strength of the spin-orbit potential.

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arXiv2001

Cranking in isospace - towards a consistent mean-field description of N=Z nuclei

Excitation spectra of T=0,1,2 states in even-even (e-e) and odd-odd (o-o) N=Z nuclei are analyzed within a mean-field based model involving isovector and isoscalar pairing interactions and the iso-cranking formalism applied to restore approximately isospin symmetry. It is shown that T=0 states in o-o and T=1 states in e-e nuclei correspond to two-quasiparticle, time-reversal symmetry breaking excitations since their angular momenta are different than zero. On the other hand the lowest T=2 states in e-e and T=1 states in o-o nuclei, which both are similar in structure to their even-even isobaric analogue states, are described as e-e type vaccua excited (iso-cranked) in isospace. It appears that in all cases isoscalar pairing plays a crucial role in restoring the proper value of the inertia parameter in isospace.

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arXiv2000

Microscopic structure of fundamental excitations in N=Z nuclei

Excitation energies of the $T$=1 states in even-even as well as $T$=0 and $T$=1 states in odd-odd $N$=$Z$ nuclei are calculated within the mean-field approach. It is shown that the underlying structure of these states can be determined in a consistent manner only when both isoscalar and isovector pairing collectivity as well as isospin projection, treated within the iso-cranking approximation, are taken into account. In particular, in odd-odd $N$=$Z$ nuclei, the interplay between quasiparticle excitations (relevant for the case of $T$=0 states) and iso-rotations (relevant for the case of $T$=1 states) explains the near-degeneracy of these fundamental excitations.

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arXiv1998

Wigner energy, odd-even mass staggering and the time-odd mean-fields

Various properties of single-particle Hartree-Fock ground-state solutions in $N\sim Z$ nuclei are investigated. The emphasis is on a role of single-particle mean-field in odd-even mass staggering. It is shown that, unlike in traditional scenario originating from the Fermi gas or macroscopic models, the symmetry energy contribution to odd-even mass staggering is nearly cancelled by the contribution coming from the average level density. It allows to construct indicators probing both pairing as well as mean-field components to the odd-even mass staggering. The impact of the single-particle Hartree-Fock field on Wigner energy and residual $pn$ interaction in odd-odd nuclei is also discussed.

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