Solution of the Skyrme–Hartree–Fock–Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.

We describe the new version (v2.38j) of the code hfodd which solves the nuclear SkyrmeHartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented: (i) projection on good angular momentum (for the Hartree-Fock states), (ii) calculation of the GCM kernels, (iii) calculation of matrix elements of the Yukawa interaction, (iv) the BCS solutions for statedependent pairing gaps, (v) the HFB solutions for broken simplex symmetry, (vi) calculation of Bohr deformation parameters, (vii) constraints on the Schiff moments and scalar multipole moments, (viii) the D T transformations and rotations of wave functio…

Global lifetime measurements of highly-deformed and other rotational structures in the a ∼135 light rare-earth region: probing the single-particle motion in a rotating potential

It has been possible, using GAMMASPHERE plus Microball,to extract differential lifetime measurements free from common systematic errors for over 15 different nuclei (various isotopes of Ce, Pr, Nd, Pm, and Sm) at high spin within a single experiment. This comprehensive study establishes the effective single-particle quadrupole moments in the A~135 light rare-earth region. Detailed comparisons are made with calculations using the self-consistent cranked mean-field theory.

Isospin-symmetry breaking in masses of ≃ 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=12 doublets and T=1 triplets, and TDEs for the T=1 triplets. Relative strengths of the obtained isospin-symmetry-breaking terms are not consistent with the d…

No-core configuration-interaction model for the isospin- and angular-momentum-projected states

[Background] Single-reference density functional theory is very successful in reproducing bulk nuclear properties like binding energies, radii, or quadrupole moments throughout the entire periodic table. Its extension to the multi-reference level allows for restoring symmetries and, in turn, for calculating transition rates. [Purpose] We propose a new no-core-configuration-interaction (NCCI) model treating properly isospin and rotational symmetries. The model is applicable to any nucleus irrespective of its mass and neutron- and proton-number parity. It properly includes polarization effects caused by an interplay between the long- and short-range forces acting in the atomic nucleus. [Metho…

Solution of universal nonrelativistic nuclear DFT equations in the Cartesian deformed harmonic-oscillator basis. (IX) HFODD (v3.06h) : a new version of the program

We describe the new version (v3.06h) of the code HFODD that solves the universal nonrelativistic nuclear DFT Hartree-Fock or Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we implemented the following new features: (i) zero-range three- and four-body central terms, (ii) zero-range three-body gradient terms, (iii) zero-range tensor terms, (iv) zero-range isospin-breaking terms, (v) finite-range higher-order regularized terms, (vi) finite-range separable terms, (vii) zero-range two-body pairing terms, (viii) multi-quasiparticle blocking, (ix) Pfaffian overlaps, (x) particle-number and parity symmetry restoration, (xi) axializatio…

Spin-orbit and tensor mean-field effects on spin-orbit splitting including self-consistent core polarizations

A new strategy of fitting the coupling constants of the nuclear energy density functional is proposed, which shifts attention from ground-state bulk to single-particle properties. The latter are analyzed in terms of the bare single-particle energies and mass, shape, and spin core-polarization effects. Fit of the isoscalar spin-orbit and both isoscalar and isovector tensor coupling constants directly to the f5/2-f7/2 spin-orbit splittings in 40Ca, 56Ni, and 48Ca is proposed as a practical realization of this new programme. It is shown that this fit requires drastic changes in the isoscalar spin-orbit strength and the tensor coupling constants as compared to the commonly accepted values but i…

Isobaric multiplet mass equation within nuclear density functional theory

We extend the nuclear Density Functional Theory (DFT) by including proton-neutron mixing and contact isospin-symmetry-breaking (ISB) terms up to next-to-leading order (NLO). Within this formalism, we perform systematic study of the nuclear mirror and triple displacement energies, or equivalently of the Isobaric Multiplet Mass Equation (IMME) coefficients. By comparing results with those obtained within the existing Green Function Monte Carlo (GFMC) calculations, we address the fundamental question of the physical origin of the ISB effects. This we achieve by analyzing separate contributions to IMME coefficients coming from the electromagnetic and nuclear ISB terms. We show that the ISB DFT …

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 m…

Solution of the Skyrme-Hartree–Fock–Bogolyubovequations in the Cartesian deformed harmonic-oscillator basis. (VIII) hfodd (v2.73y): A new version of the program

We describe the new version (v2.73y) of the code HFODD which solves the nuclear Skyrme Hartree-Fock or Skyrme Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following new features: (i) full proton-neutron mixing in the particle-hole channel for Skyrme functionals, (ii) the Gogny force in both particle-hole and particle-particle channels, (iii) linear multi-constraint method at finite temperature, (iv) fission toolkit including the constraint on the number of particles in the neck between two fragments, calculation of the interaction energy between fragments, and calculation of the nuclear and Coulomb ene…

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} co…

Microscopic calculations of isospin-breaking corrections to superallowed beta-decay

The superallowed beta-decay rates that provide stringent constraints on physics beyond the Standard Model of particle physics are affected by nuclear structure effects through isospin-breaking corrections. The self-consistent isospin- and angular-momentum-projected nuclear density functional theory is used for the first time to compute those corrections for a number of Fermi transitions in nuclei from A=10 to A=74. The resulting leading element of the CKM matrix, |V_{ud}|= 0.97447(23), agrees well with the recent result by Towner and Hardy [Phys. Rev. C {\bf 77}, 025501 (2008)].

Isospin-symmetry restoration within the nuclear density functional theory: formalism and applications

Isospin symmetry of atomic nuclei is explicitly broken by the charge-dependent interactions, primarily the Coulomb force. Within the nuclear density functional theory, isospin is also broken spontaneously. We propose a projection scheme rooted in a mean field theory, that allows the consistent treatment of isospin breaking in both ground and exited nuclear states. We demonstrate that this scheme is essentially free from spurious divergences plaguing particle-number and angular-momentum restoration approaches. Applications of the new technique include excited high-spin states in medium-mass N=Z nuclei, such as superdeformed bands and many-particle-many-hole terminating states.

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 …

Gamow-Teller response in the configuration space of a density-functional-theory–rooted no-core configuration-interaction model

Background: The atomic nucleus is a unique laboratory in which to study fundamental aspects of the electroweak interaction. This includes a question concerning in medium renormalization of the axial-vector current, which still lacks satisfactory explanation. Study of spin-isospin or Gamow-Teller (GT) response may provide valuable information on both the quenching of the axial-vector coupling constant as well as on nuclear structure and nuclear astrophysics.Purpose: We have performed a seminal calculation of the GT response by using the no-core configuration-interaction approach rooted in multireference density functional theory (DFT-NCCI). The model treats properly isospin and rotational sy…

ISOSPIN MIXING IN THE VICINITY OF THE N = Z LINE

We present the isospin- and angular-momentum-projected nuclear density functional theory (DFT) and its applications to the isospin-breaking corrections to the superallowed beta-decay rates in the vicinity of the N=Z line. A preliminary value obtained for the Cabbibo-Kobayashi-Maskawa matrix element, |V_{ud}|=0.97463(24), agrees well with the recent estimate by Towner and Hardy [Phys. Rev. C{\bf 77}, 025501 (2008)]. We also discuss new opportunities to study the symmetry energy by using the isospin-projected DFT.

Theoretical approaches that use one-body densities as dynamical variables, such as Hartree-Fock or the density functional theory (DFT), break isospin symmetry both explicitly, by virtue of charge-dependent interactions, and spontaneously. To restore the spontaneously broken isospin symmetry, we implemented the isospin-projection scheme on top of the Skyrme-DFT approach. This development allows for consistent treatment of isospin mixing in both ground and exited nuclear states. In this study, we apply this method to evaluate the isospin impurities in ground states of even-even and odd-odd N~Z nuclei. By including simultaneous isospin and angular-momentum projection, we compute the isospin-br…

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.

Isospin mixing in nuclei within the nuclear density functional theory.

We present the self-consistent, non-perturbative analysis of isospin mixing using the nuclear density functional approach and the rediagonalization of the Coulomb interaction in the good-isospin basis. The largest isospin-breaking effects are predicted for N = Z nuclei and they quickly fall with the neutron excess. The unphysical isospin violation on the mean-field level, caused by the neutron excess, is eliminated by the proposed method. We find a significant dependence of the magnitude of isospin breaking on the parametrization of the nuclear interaction term. A rough correlation has been found between the isospin mixing parameter and the difference of proton and neutron rms radii. The th…

Isospin Mixing Within the Symmetry Restored Density Functional Theory and Beyond

We present results of systematic calculations of the isospin-symmetry-breaking corrections to the superallowed I=$0+,T=1 --> I=0+,T=1 beta-decays, based on the self-consistent isospin- and angular-momentum-projected nuclear density functional theory (DFT). We discuss theoretical uncertainties of the formalism related to the basis truncation, parametrization of the underlying energy density functional, and ambiguities related to determination of Slater determinants in odd-odd nuclei. A generalization of the double-projected DFT model towards a no core shell-model-like configuration-mixing approach is formulated and implemented. We also discuss new opportunities in charge-symmetry- and cha…

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.