arXiv subjects

Jacek Dobaczewski

Publications and source records attributed to Jacek Dobaczewski.

At least 19 recordsLinked to original sources

arXiv2025

Moments of inertia of rare-earth nuclei and the nuclear time-odd mean fields within exact solutions of the adiabatic theory

We systematically analyse the nuclear moments of inertia determined within the Skyrme and Gogny density functional theories. The time-odd mean fields generated by collective rotation are self-consistently determined by a novel exact iterative solution of the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) equations. Although details of the results depend on the functional used, the calculated moments of inertia are in good overall agreement with the experimental data, with no adjustable parameters. To show the essential importance of the time-odd mean fields, we compared the ATDHFB moments of inertia with those obtained from the Inglis-Belyaev formula. For Skyrme density functionals, we find strong correlations between the effective mass and the impact of the time-odd mean fields on the rotational and vibrational collective inertia.

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arXiv2024

Iterative solutions of the ATDHFB equations to determine the nuclear collective inertia

An iterative adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) method is developed within the framework of Skyrme density functional theory. The ATDHFB equation is solved iteratively to avoid explicitly calculating the stability matrix. The contribution of the time-odd mean fields to the ATDHF(B) moment of inertia is incorporated self-consistently, and the results are verified by comparing them with the dynamical cranking predictions. The inertia mass tensor is calculated with the density-derivative term evaluated by numerical differentiation.

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arXiv2024

Two-center harmonic oscillator basis for Skyrme-DFT calculations (I): formalism and Proof of Principle

We present a new method to solve the nuclear density functional theory (DFT) equations using a two-center harmonic oscillator for Skyrme-like functionals, incorporating pairing and Coulomb interactions. The goal is to efficiently determine the fission and fusion configurations in nuclei. The Coulomb exchange term is evaluated exactly, allowing for a novel approach to neck formation without the Slater approximation, commonly used in space coordinate-based approaches. The new method has been implemented in the code {\sc hfodd}, enabling direct comparison with standard one-center solutions. This first paper focuses on deriving and implementing a methodology based on stable, precise, and exact applications of harmonic oscillator bases for the two fragments, which can either overlap or be separated by arbitrarily large distances. The implementation is tested on two proof-of-principle examples using light nuclei, specifically, $^8$Be and $^{24}$Mg.

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arXiv2023

Opportunities for Fundamental Physics Research with Radioactive Molecules

Molecules containing short-lived, radioactive nuclei are uniquely positioned to enable a wide range of scientific discoveries in the areas of fundamental symmetries, astrophysics, nuclear structure, and chemistry. Recent advances in the ability to create, cool, and control complex molecules down to the quantum level, along with recent and upcoming advances in radioactive species production at several facilities around the world, create a compelling opportunity to coordinate and combine these efforts to bring precision measurement and control to molecules containing extreme nuclei. In this manuscript, we review the scientific case for studying radioactive molecules, discuss recent atomic, molecular, nuclear, astrophysical, and chemical advances which provide the foundation for their study, describe the facilities where these species are and will be produced, and provide an outlook for the future of this nascent field.

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arXiv2021

Microscopic origin of reflection-asymmetric nuclear shapes

Background: The presence of nuclear ground states with stable reflection-asymmetric shapes is supported by rich experimental evidence. Theoretical surveys of odd-multipolarity deformations predict the existence of pear-shaped isotopes in several fairly localized regions of the nuclear landscape in the vicinity of near-lying single-particle shells with $Δ\ell=Δj=3$. Purpose: We analyze the role of isoscalar, isovector, neutron-proton, neutron-neutron, and proton-proton multipole interaction energies in inducing the onset of reflection-asymmetric ground-state deformations. Methods: The calculations are performed in the framework of axial reflection-asymmetric Hartree-Fock-Bogoliubov theory using two Skyrme energy density functionals and density-dependent pairing force. Results: We show that reflection-asymmetric ground-state shapes of atomic nuclei are driven by the odd-multipolarity neutron-proton (or isoscalar) part of the nuclear interaction energy. This result is consistent with the particle-vibration picture, in which the main driver of octupole instability is the isoscalar octupole-octupole interaction giving rise to large $E3$ polarizability.

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arXiv2020

Future of Nuclear Fission Theory

There has been much recent interest in nuclear fission, due in part to a new appreciation of its relevance to astrophysics, stability of superheavy elements, and fundamental theory of neutrino interactions. At the same time, there have been important developments on a conceptual and computational level for the theory. The promising new theoretical avenues were the subject of a workshop held at the University of York in October 2019; this report summarises its findings and recommendations.

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arXiv2020

Structure of Krypton Isotopes using the Generalised Bohr Hamiltonian Method

We investigate the properties of the excited spectra of the even-even isotopes of krypton using a Generalised Bohr Hamiltonian with three different Skyrme functionals. In particular, we investigate the evolution of the low-lying $2^{+}_{1}$ and $4^{+}_{1}$ states and their associated electromagnetic transitions. The model reproduces quite nicely the energy trends apart from ${}^{88}$Kr, where none of the interactions used here are able to grasp a sudden change in the energy spectrum. Additionally, we explore the neutron deficient region ${}^{72-76}$Kr which is a proposed region for shape coexistence. We observe that the model can reproduce the structure of the experimental spectrum of ${}^{72}$Kr exceedingly well.

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arXiv2018

Correlating Schiff moments in the light actinides with octupole moments

We show that the measured intrinsic octupole moments of $^{220}$Rn, $^{224}$Ra, and $^{226}$Ra constrain the intrinsic Schiff moments of $^{225}$Ra$^{221}$Rn, $^{223}$Rn, $^{223}$Fr, $^{225}$Ra, and $^{229}$Pa. The result is a dramatically reduced uncertainty in intrinsic Schiff moments. Direct measurements of octupole moments in odd nuclei will reduce the uncertainty even more. The only significant source of nuclear-physics error in the laboratory Schiff moments will then be the intrinsic matrix elements of the time-reversal non-invariant interaction produced by CP-violating fundamental physics. Those matrix elements are also correlated with octupole moments, but with a larger systematic uncertainty.

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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

Landau parameters for energy density functionals generated by local finite-range pseudopotentials

In Landau theory of Fermi liquids, the particle-hole interaction near the Fermi energy in different spin-isospin channels is probed in terms of an expansion over the Legendre polynomials. This provides a useful and efficient way to constrain properties of nuclear energy density functionals in symmetric nuclear matter and finite nuclei. In this study, we present general expressions for Landau parameters corresponding to a two-body central local regularized pseudopotential. We also show results obtained for two recently adjusted NLO and N$^2$LO parametrizations. Such pseudopotentials will be used to determine mean-field and beyond-mean-field properties of paired nuclei across the entire nuclear chart.

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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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arXiv2014

Mean-Field Calculation Based on Proton-Neutron Mixed Energy Density Functionals

We have performed calculations based on the Skyrme energy density functional (EDF) that includes arbitrary mixing between protons and neutrons. In this framework, single-particle states are generalized as mixtures of proton and neutron components. The model assumes that the Skyrme EDF is invariant under the rotation in isospin space and the Coulomb force is the only source of the isospin symmetry breaking. To control the isospin of the system, we employ the isocranking method, which is analogous to the standard cranking approach used for describing high-spin states. Here, we present results of the isocranking calculations performed for the isobaric analog states in $A = 40$ and $A = 54$ nuclei.

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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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arXiv2013

Energy-density-functional calculations including the proton-neutron mixing

We present results of calculations based on the Skyrme energy density functional including the arbitrary mixing between protons and neutrons. In this framework, single-particle states are superpositions of proton and neutron components and the energy density functional is fully invariant with respect to three-dimensional rotations in the isospin space. The isospin of the system is controlled by means of the isocranking method, which carries over the standard cranking approach to the isospin space. We show numerical results of the isocranking calculations performed for isobaric analogue states in the A=14 and $A=40-56$ nuclei. We also present such results obtained for high-isospin states in $^{48}$Cr, with constraints on the isospin implemented by using the augmented Lagrange method.

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arXiv2010

Fully self-consistent calculations of nuclear Schiff moments

We calculate the Schiff moments of the nuclei 199Hg and 211Ra in completely self-consistent odd-nucleus mean-field theory by modifying the Hartree-Fock-Bogoliubov code HFODD. We allow for arbitrary shape deformation, and include the effects of nucleon dipole moments alongside those of a CP-violating pion-exchange nucleon-nucleon interaction. The results for 199Hg differ significantly from those of previous calculations when the CP-violating interaction is of isovector character.

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arXiv2009

Lipkin translational-symmetry restoration in the mean-field and energy-density-functional methods

Based on the 1960 idea of Lipkin, the minimization of energy of a symmetry-restored mean-field state is equivalent to the minimization of a corrected energy of a symmetry-broken state with the Peierls-Yoccoz mass. It is interesting to note that the "unphysical" Peierls-Yoccoz mass, and not the true mass, appears in the Lipkin projected energy. The Peierls-Yoccoz mass can be easily calculated from the energy and overlap kernels, which allows for a systematic, albeit approximate, restoration of translational symmetry within the energy-density formalism. Analogous methods can also be implemented for all other broken symmetries.

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