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…

Isospin-breaking corrections to superallowed Fermi beta-decay in isospin- and angular momentum-projected nuclear Density Functional Theory

Background: The superallowed beta-decay rates provide stringent constraints on physics beyond the Standard Model of particle physics. To extract crucial information about the electroweak force, small isospin-breaking corrections to the Fermi matrix element of superallowed transitions must be applied. Purpose: We perform systematic calculations of isospin-breaking corrections to superallowed beta-decays and estimate theoretical uncertainties related to the basis truncation, time-odd polarization effects related to the intrinsic symmetry of the underlying Slater determinants, and to the functional parametrization. Methods: We use the self-consistent isospin- and angular-momentum-projected nuc…

Kerman-Onishi conditions in self-consistent tilted-axis-cranking mean-field calculations

\item[Background] For cranked mean-field calculations with arbitrarily oriented rotational frequency vector $\boldsymbol{\omega}$ in the intrinsic frame, one has to employ constraints on average values of the quadrupole-moment tensor, so as to keep the nucleus in the principal-axis reference frame. Kerman and Onishi [Nucl. Phys. A {\bf 361}, 179 (1981)] have shown that the Lagrangian multipliers that correspond to the required constraints are proportional to $\boldsymbol{\omega} \times \boldsymbol{J}$, where $\boldsymbol{J}$ is the average angular momentum vector. \item[Purpose] We study the validity and consequences of the Kerman-Onishi conditions in the context of self-consistent tilted-a…

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.

Effective pseudopotential for energy density functionals with higher-order derivatives

We derive a zero-range pseudopotential that includes all possible terms up to sixth order in derivatives. Within the Hartree-Fock approximation, it gives the average energy that corresponds to a quasi-local nuclear Energy Density Functional (EDF) built of derivatives of the one-body density matrix up to sixth order. The direct reference of the EDF to the pseudopotential acts as a constraint that divides the number of independent coupling constants of the EDF by two. This allows, e.g., for expressing the isovector part of the functional in terms of the isoscalar part, or vice versa. We also derive the analogous set of constraints for the coupling constants of the EDF that is restricted by sp…

Spectroscopic Properties of Nuclear Skyrme Energy Density Functionals

We address the question of how to improve the agreement between theoretical nuclear single-particle energies (SPEs) and experiment. Empirically, in doubly magic nuclei, the SPEs can be deduced from spectroscopic properties of odd nuclei that have one more, or one less neutron or proton. Theoretically, bare SPEs, before being confronted with experiment, must be corrected for the effects of the particle-vibration-coupling (PVC). In the present work, we determine the PVC corrections in a fully self-consistent way. Then, we adjust the SPEs, with PVC corrections included, to empirical data. In this way, the agreement with experiment, on average, improves; nevertheless, large discrepancies still …

In-beam spectroscopic study of Cf244

The ground-state rotational band of the neutron-deficient californium (Z = 98) isotope 244Cf was identified for the first time and measured up to a tentative spin and parity of I I-pi = 20(+). The observation of the rotational band indicates that the nucleus is deformed. The kinematic and dynamic moments of inertia were deduced from the measured gamma-ray transition energies. The behavior of the dynamic moment of inertia revealed an up-bend due to a possible alignment of coupled nucleons in high-j orbitals starting at a rotational frequency of about (h) over bar (omega) = 0.20 MeV. The results were compared with the systematic behavior of the even-even N = 146 isotones as well as with avail…

Self-Consistent Tilted-Axis-Cranking Study of Triaxial Strongly Deformed Bands inEr158at Ultrahigh Spin

Stimulated by recent experimental discoveries, triaxial strongly deformed (TSD) states in $^{158}\mathrm{Er}$ at ultrahigh spins have been studied by means of the Skyrme-Hartree-Fock model and the tilted-axis-cranking method. Restricting the rotational axis to one of the principal axes---as done in previous cranking calculations---two well-defined TSD minima in the total Routhian surface are found for a given configuration: one with positive and another with negative triaxial deformation $\ensuremath{\gamma}$. By allowing the rotational axis to change direction, the higher-energy minimum is shown to be a saddle point. This resolves the long-standing question of the physical interpretation o…

Isospin-invariant Skyrme energy-density-functional approach with axial symmetry

We develop the isospin-invariant Skyrme-EDF method by considering local densities in all possible isospin channels and proton-neutron (p-n) mixing terms as mandated by the isospin symmetry. The EDF employed has the most general form that depends quadratically on the isoscalar and isovector densities. We test and benchmark the resulting p-n EDF approach, and study the general properties of the new scheme by means of the cranking in the isospin space. We extend the existing axial DFT solver HFBTHO to the case of isospin-invariant EDF approach with all possible p-n mixing terms. Explicit expressions have been derived for all the densities and potentials that appear in the isospin representatio…

Additivity of effective quadrupole moments and angular momentum alignments in the A~130 nuclei

The additivity principle of the extreme shell model stipulates that an average value of a one-body operator be equal to the sum of the core contribution and effective contributions of valence (particle or hole) nucleons. For quadrupole moment and angular momentum operators, we test this principle for highly and superdeformed rotational bands in the A~130 nuclei. Calculations are done in the self-consistent cranked non-relativistic Hartree-Fock and relativistic Hartree mean-field approaches. Results indicate that the additivity principle is a valid concept that justifies the use of an extreme single-particle model in an unpaired regime typical of high angular momenta.

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…

Recoil-α-fission and recoil-α–α-fission events observed in the reaction 48Ca + 243Am

Products of the fusion-evaporation reaction 48Ca + 243Am were studied with the TASISpec set-up at the gas-filled separator TASCA at the GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany. Amongst the detected thirty correlated α-decay chains associated with the production of element Z=115, two recoil-α-fission and five recoil-α-α-fission events were observed. The latter five chains are similar to four such events reported from experiments performed at the Dubna gas-filled separator, and three such events reported from an experiment at the Berkeley gas-filled separator. The four chains observed at the Dubna gas-filled separator were assigned to start from the 2n-evaporation ch…

Deformations and quasiparticle spectra of nuclei in the nobelium region

We have performed self-consistent Skyrme Hartree-Fock-Bogolyubov calculations for nuclei close to $^{254}$No. Self-consistent deformations, including $\beta_{2,4,6,8}$ as functions of the rotational frequency, were determined for even-even nuclei $^{246,248,250}$Fm, $^{252,254}$No, and $^{256}$Rf. The quasiparticle spectra for N=151 isotones and Z=99 isotopes were calculated and compared with experimental data and the results of Woods-Saxon calculations. We found that our calculations give high-order deformations similar to those obtained for the Woods-Saxon potential, and that the experimental quasiparticle energies are reasonably well reproduced.

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…

Nuclear moments put a new spin on the structure of 131In

Abstract In spite of the high-density and strongly correlated nature of the atomic nucleus, experimental and theoretical evidence suggests that around particular 'magic' numbers of nucleons, nuclear properties are governed by a single unpaired nucleon1,2. A microscopic understanding of the extent of this behaviour and its evolution in neutron-rich nuclei remains an open question in nuclear physics 3-5. A textbook example is the electromagnetic moments of indium (Z = 49) 6, which are dominated by a hole with respect to the proton magic number Z = 50 nucleus. They exhibit a remarkably constant behaviour over a large range of odd-mass isotopes, previously interpreted as pure "single-particle b…

Charged-current neutrino and antineutrino scattering off 116Cd described by Skyrme forces

We perform calculations of the cross sections for charged-current neutrino and antineutrino scattering off 116Cd using ten different Skyrme interactions, at energies typical of supernova neutrinos. We use the quasiparticle random-phase approximation in its charged-changing mode (pnQRPA) to construct the required nuclear wave functions for the participant initial and final states. We compare the results of these calculations with the results of calculations based on the Bonn one-boson-exchange potential. The response of 116Cd to supernova neutrinos is calculated by folding the obtained cross sections with suitably parametrized Fermi-Dirac distributions of the electron-neutrino and electron-a…

Solution of self-consistent equations for the N3LO nuclear energy density functional in spherical symmetry. The program hosphe (v1.02)

Abstract We present solution of self-consistent equations for the N 3 LO nuclear energy density functional. We derive general expressions for the mean fields expressed as differential operators depending on densities and for the densities expressed in terms of derivatives of wave functions. These expressions are then specified to the case of spherical symmetry. We also present the computer program hosphe (v1.02), which solves the self-consistent equations by using the expansion of single-particle wave functions on the spherical harmonic oscillator basis. Program summary Program title: HOSPHE (v1.02) Catalogue identifier: AEGK_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEGK_…

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…

Multidimensional Skyrme-density-functional Study of the Spontaneous Fission of 238U

We determined the spontaneous fission lifetime of 238U by a minimization of the action integral in a three-dimensional space of collective variables. Apart from the mass-distribution multipole moments Q20 (elongation) and Q30 (left–right asymmetry), we also considered the pairing- fluctuation parameter λ2 as a collective coordinate. The collective potential was obtained self-consistently using the Skyrme energy density functional SkM∗ . The inertia tensor was obtained within the nonperturbative cranking approximation to the adiabatic time-dependent Hartree–Fock– Bogoliubov approach. The pairing-fluctuation parameter λ2 allowed us to control the pairing gap along the fission path, which sign…

Rotational properties of nuclei aroundNo254investigated using a spectroscopic-quality Skyrme energy density functional

Background: Nuclei in the $Z\ensuremath{\approx}100$ mass region represent the heaviest systems where detailed spectroscopic information is experimentally available. Although microscopic-macroscopic and self-consistent models have achieved great success in describing the data in this mass region, a fully satisfying precise theoretical description is still missing.Purpose: By using fine-tuned parametrizations of the energy density functionals, the present work aims at an improved description of the single-particle properties and rotational bands in the nobelium region. Such locally optimized parametrizations may have better properties when extrapolating towards the superheavy region.Methods:…

Quadrupole collective inertia in nuclear fission: Cranking approximation

Collective mass tensor derived from the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) approach is compared with that obtained in the Gaussian Overlap Approximation (GOA) to the generator coordinate method. Illustrative calculations are carried out for one-dimensional quadrupole fission pathways in 256Fm. It is shown that the collective mass exhibits strong variations with the quadrupole collective coordinate. These variations are related to the changes in the intrinsic shell structure. The differences between collective inertia obtained in cranking and perturbative cranking approximations to ATDHFB, and within GOA, are discussed.

Self-consistent symmetries in the proton-neutron Hartree-Fock-Bogoliubov approach

Symmetry properties of densities and mean fields appearing in the nuclear Density Functional Theory with pairing are studied. We consider energy functionals that depend only on local densities and their derivatives. The most important self-consistent symmetries are discussed: spherical, axial, space-inversion, and mirror symmetries. In each case, the consequences of breaking or conserving the time-reversal and/or proton-neutron symmetries are discussed and summarized in a tabulated form, useful in practical applications.

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 …

Hartree-Fock-Bogoliubov theory of polarized Fermi systems

Condensed Fermi systems with an odd number of particles can be described by means of polarizing external fields having a time-odd character. We illustrate how this works for Fermi gases and atomic nuclei treated by density functional theory or Hartree-Fock-Bogoliubov (HFB) theory. We discuss the method based on introducing two chemical potentials for different superfluid components, whereby one may change the particle-number parity of the underlying quasiparticle vacuum. Formally, this method is a variant of non-collective cranking, and the procedure is equivalent to the so-called blocking. We present and exemplify relations between the two-chemical-potential method and the cranking approxi…

Convergence of density-matrix expansions for nuclear interactions

We extend density-matrix expansions in nuclei to higher orders in derivatives of densities and test their convergence properties. The expansions allow for converting the interaction energies characteristic to finite- and short-range nuclear effective forces into quasi-local density functionals. We also propose a new type of expansion that has excellent convergence properties when benchmarked against the binding energies obtained for the Gogny interaction.

Variation of fundamental constants and 229Th

The first excited state of the nucleus229Th has an exceptionally small excitation energy of7.8 eV, which is expected to be very sensitive to changes in the fine structure constant α.A small difference in the Coulomb energies of the two states, which both are of the order109eV, would amplify variations in α into large variations of the transition frequency.Hartree-Fock and Hartree-Fock-Bogoliubov calculations are performed to compute theCoulomb energies of the two states. The kinetic energies are also calculated which reflecta possible variation in the nucleon or quark masses or local Lorentz invariance violation. peerReviewed

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…

Propagation of uncertainties in the Skyrme energy-density-functional model

Parameters of nuclear energy-density-functionals (EDFs) are always derived by an optimization to experimental data. For the minima of appropriately defined penalty functions, a statistical sensitivity analysis provides the uncertainties of the EDF parameters. To quantify theoretical errors of observables given by the model, we studied the propagation of uncertainties within the UNEDF0 Skyrme-EDF approach. We found that typically the standard errors rapidly increase towards neutron rich nuclei. This can be linked to large uncertainties of the isovector coupling constants of the currently used EDFs.

Nonlocal energy density functionals for low-energy nuclear structure

We introduce a finite-range pseudopotential built as an expansion in derivatives up to next-to-next-to-next-to-leading order (N$^3$LO) and we calculate the corresponding nonlocal energy density functional (EDF). The coupling constants of the nonlocal EDF, for both finite nuclei and infinite nuclear matter, are expressed through the parameters of the pseudopotential. All central, spin-orbit, and tensor terms of the pseudopotential are derived both in the spherical-tensor and Cartesian representation. At next-to-leading order (NLO), we also derive relations between the nonlocal EDF expressed in the spherical-tensor and Cartesian formalism. Finally, a simplified version of the finite-range pse…

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…

Precision Mass Measurements beyond $^{132}$Sn: Anomalous behaviour of odd-even staggering of binding energies

Atomic masses of the neutron-rich isotopes $^{121-128}$Cd, $^{129,131}$In, $^{130-135}$Sn, $^{131-136}$Sb, and $^{132-140}$Te have been measured with high precision (10 ppb) using the Penning trap mass spectrometer JYFLTRAP. Among these, the masses of four r-process nuclei $^{135}$Sn, $^{136}$Sb, and $^{139,140}$Te were measured for the first time. The data reveals a strong $N$=82 shell gap at $Z$=50 but indicates the importance of correlations for $Z>50$. An empirical neutron pairing gap expressed as the odd-even staggering of isotopic masses shows a strong quenching across $N$=82 for Sn, with the $Z$-dependence that is unexplainable by the current theoretical models.

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…

Finite-range separable pairing interaction within the new N3LO DFT approach

For over four decades, the Skyrme functional within various parametrizations has been used to calculate nuclear properties. In the last few years there was a number of attempts to improve its performance and introduce generalized forms. In particular, the most general phenomenological quasi-local energy density functional, which contains all combinations of density, spin-density, and their derivatives up to the sixth order (N3LO), was proposed in [1]. Since in the phenomenological-functional approaches, the particle-particle (pp) channel is treated independently of the particle-hole (ph) channel, there remains a question of what pairing interaction is suitable to use within the N3LO energy …

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)].

Microscopic description of complex nuclear decay: multimodal fission

Our understanding of nuclear fission, a fundamental nuclear decay, is still incomplete due to the complexity of the process. In this paper, we describe a study of spontaneous fission using the symmetry-unrestricted nuclear density functional theory. Our results show that the observed bimodal fission can be explained in terms of pathways in multidimensional collective space corresponding to different geometries of fission products. We also predict a new phenomenon of trimodal spontaneous fission for some rutherfordium, seaborgium, and hassium isotopes.

Model nuclear energy density functionals derived from ab initio calculations

We present the first application of a new approach, proposed in [Journal of Physics G: Nuclear and Particle Physics, 43, 04LT01 (2016)] to derive coupling constants of the Skyrme energy density functional (EDF) from ab initio Hamiltonian. By perturbing the ab initio Hamiltonian with several functional generators defining the Skyrme EDF, we create a set of metadata that is then used to constrain the coupling constants of the functional. We use statistical analysis to obtain such an ab initio-equivalent Skyrme EDF. We find that the resulting functional describes properties of atomic nuclei and infinite nuclear matter quite poorly. This may point out to the necessity of building up the ab init…

The Negele-Vautherin density matrix expansion applied to the Gogny force

We use the Negele-Vautherin density matrix expansion to derive a quasi-local density functional for the description of systems of fermions interacting with short-ranged interactions composed of arbitrary finite-range central, spin-orbit, and tensor components. Terms that are absent in the original Negele-Vautherin approach owing to the angle averaging of the density matrix are fixed by employing a gauge invariance condition. We obtain the Kohn-Sham interaction energies in all spin-isospin channels, including the exchange terms, expressed as functions of the local densities and their derivatives up to second (next to leading) order. We illustrate the method by determining the coupling consta…

Spontaneous fission lifetimes from the minimization of self-consistent collective action

The spontaneous fission lifetime of 264Fm has been studied within nuclear density functional theory by minimizing the collective action integral for fission in a two-dimensional quadrupole collective space representing elongation and triaxiality. The collective potential and inertia tensor are obtained self-consistently using the Skyrme energy density functional and density-dependent pairing interaction. The resulting spontaneous fission lifetimes are compared with the static result obtained with the minimum-energy pathway. We show that fission pathways strongly depend on assumptions underlying collective inertia. With the non-perturbative mass parameters, the dynamic fission pathway become…

Charged-current neutrino and antineutrino scattering offCd116described by Skyrme forces

We perform calculations of the cross sections for charged-current neutrino and antineutrino scattering off Cd-116 using ten different Skyrme interactions, at energies typical of supernova neutrinos. We use the quasiparticle random-phase approximation in its charged-changing mode (pnQRPA) to construct the required nuclear wave functions for the participant initial and final states. We compare the results of these calculations with the results of calculations based on the Bonn one-boson-exchange potential. The response of Cd-116 to supernova neutrinos is calculated by folding the obtained cross sections with suitably parametrized Fermi-Dirac distributions of the electron-neutrino and electron…

New subshell closure atN=58emerging in neutron-rich nuclei beyondNi78

The structure of neutron-rich nuclei beyond $^{78}\mathrm{Ni}$ was studied using postaccelerated radioactive beams of $^{83,84,85}\mathrm{Ga}$ utilizing $\ensuremath{\beta} \ensuremath{\gamma}$ and $\ensuremath{\beta}\ensuremath{-}n \ensuremath{\gamma}$ spectroscopy. Our data, when combined with energy level systematics, suggests a possible new spherical subshell closure at $N=58$ is created by the nearly degenerated $\ensuremath{\nu}3{s}_{1/2}$ and $\ensuremath{\nu}2{d}_{5/2}$ orbitals being well separated from other orbitals above $N=50$. The near degeneracy of these states could be evidenced by isomerism in this region. The energies of the ${2}_{1}^{+}$ and proposed ${4}_{1}^{+}$ states …

Nonlocal energy density functionals for pairing and beyond-mean-field calculations

We propose to use two-body regularized finite-range pseudopotential to generate nuclear energy density functional (EDF) in both particle-hole and particle-particle channels, which makes it free from self-interaction and self-pairing, and also free from singularities when used beyond mean field. We derive a sequence of pseudopotentials regularized up to next-to-leading order (NLO) and next-to-next-to-leading order (N2LO), which fairly well describe infinite-nuclear-matter properties and finite open-shell paired and/or deformed nuclei. Since pure two-body pseudopotentials cannot generate sufficiently large effective mass, the obtained solutions constitute a preliminary step towards future imp…

Bootstrap Technique to Study Correlation Between Neutron Skin Thickness and the Slope of Symmetry Energy in Atomic Nuclei

We present a new statistical tool based on random sampling to assess the confidence interval of Pearson's and Spearman's correlation coefficients. These estimators are then used to quantify the statistical correlations among the neutron skin thickness of atomic nuclei and the slope of the symmetry energy in the infinite nuclear medium.

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 …

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 β-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. peerReviewed

Shape staggering of midshell mercury isotopes from in-source laser spectroscopy compared with density-functional-theory and Monte Carlo shell-model calculations

Neutron-deficient Hg177-185 isotopes were studied using in-source laser resonance-ionization spectroscopy at the CERN-ISOLDE radioactive ion-beam facility in an experiment combining different detection methods tailored to the studied isotopes. These include either α-decay tagging or multireflection time-of-flight gating for isotope identification. The endpoint of the odd-even nuclear shape staggering in mercury was observed directly by measuring for the first time the isotope shifts and hyperfine structures of Hg177-180. Changes in the mean-square charge radii for all mentioned isotopes, magnetic dipole, and electric quadrupole moments of the odd-A isotopes and arguments in favor of I=7/2 s…

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, mo…

Properties of spherical and deformed nuclei using regularized pseudopotentials in nuclear DFT

We developed new parameterizations of local regularized finite-range pseudopotentials up to next-to-next-to-next-to-leading order (N3LO), used as generators of nuclear density functionals. When supplemented with zero-range spin-orbit and density-dependent terms, they provide a correct single-reference description of binding energies and radii of spherical and deformed nuclei. We compared the obtained results to experimental data and discussed benchmarks against the standard well-established Gogny D1S functional.

Linear response strength functions with iterative Arnoldi diagonalization

We report on an implementation of a new method to calculate RPA strength functions with iterative non-hermitian Arnoldi diagonalization method, which does not explicitly calculate and store the RPA matrix. We discuss the treatment of spurious modes, numerical stability, and how the method scales as the used model space is enlarged. We perform the particle-hole RPA benchmark calculations for double magic nucleus 132Sn and compare the resulting electromagnetic strength functions against those obtained within the standard RPA.

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 $A = 54$ nuc…

Dependence of single-particle energies on coupling constants of the nuclear energy density functional

We show that single-particle energies in doubly magic nuclei depend almost linearly on the coupling constants of the nuclear energy density functional. Therefore, they can be very well characterized by the linear regression coefficients, which we calculate for the coupling constants of the standard Skyrme functional. We then use these regression coefficients to refit the coupling constants to experimental values of single-particle energies. We show that the obtained rms deviations from experimental data are still quite large, of the order of 1.1 MeV. This suggests that the current standard form of the Skyrme functional cannot ensure spectroscopic-quality description of single-particle energ…

Local nuclear energy density functional at next-to-next-to-next-to-leading order

We construct nuclear energy density functionals in terms of derivatives of densities up to sixth, next-to-next-to-next-to-leading order (N3LO). A phenomenological functional built in this way conforms to the ideas of the density matrix expansion and is rooted in the expansions characteristic to effective theories. It builds on the standard functionals related to the contact and Skyrme forces, which constitute the zero-order (LO) and second-order (NLO) expansions, respectively. At N3LO, the full functional with density-independent coupling constants, and with the isospin degree of freedom taken into account, contains 376 terms, while the functionals restricted by the Galilean and gauge symme…

Shell structure beyond the proton drip line studied via proton emission from deformed 141Ho

Abstract Fine structure in proton emission from the 7 / 2 − [ 523 ] ground state and from the 1 / 2 + [ 411 ] isomer in deformed nucleus 141Ho was studied by means of fusion-evaporation reactions and digital signal processing. Proton transitions to the first excited 2+ state in 140Dy, with the branching ratio of I p g s ( 2 + ) = 0.9 ± 0.2 % and I p m ( 2 + ) = 1.7 ± 0.5 % , were observed. The data are analyzed within the non-adiabatic weak coupling model assuming a large quadrupole deformation of the daughter nucleus 140Dy as predicted by the self-consistent theory. Implications of this result on coexistence effects around N = 74 are discussed. Significant modifications of the proton shell…

Giant Monopole Resonances and nuclear incompressibilities studied for the zero-range and separable pairing interactions

Background: Following the 2007 precise measurements of monopole strengths in tin isotopes, there has been a continuous theoretical effort to obtain a precise description of the experimental results. Up to now, there is no satisfactory explanation of why the tin nuclei appear to be significantly softer than 208Pb. Purpose: We determine the influence of finite-range and separable pairing interactions on monopole strength functions in semi-magic nuclei. Methods: We employ self-consistently the Quasiparticle Random Phase Approximation on top of spherical Hartree-Fock-Bogolyubov solutions. We use the Arnoldi method to solve the linear-response problem with pairing. Results: We found that the dif…

Effective theory for low-energy nuclear energy density functionals

We introduce a new class of effective interactions to be used within the energy-density-functional approaches. They are based on regularized zero-range interactions and constitute a consistent application of the effective-theory methodology to low-energy phenomena in nuclei. They allow for defining the order of expansion in terms of the order of derivatives acting on the finite-range potential. Numerical calculations show a rapid convergence of the expansion and independence of results of the regularization scale.

Polarization corrections to single-particle energies studied within the energy-density-functional and quasiparticle random-phase approximation approaches

Background: Models based on using perturbative polarization corrections and mean-field blocking approxima- tion give conflicting results for masses of odd nuclei. Purpose: We systematically investigate the polarization and mean-field models, implemented within self- consistent approaches that use identical interactions and model spaces, to find reasons for the conflicts between them. Methods: For density-dependent interactions and with pairing correlations included, we derive and study links between the mean-field and polarization results obtained for energies of odd nuclei. We also identify and discuss differences between the polarization-correction and full particle-vibration-coupling (PV…

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.

Neutron-proton pairing correlations in a single l-shell model

The long standing problem of neutron-proton pairing correlations is revisited by employing the Hartree-Fock-Bogoliubov formalism with neutron-proton mixing in both the particle-hole and particle-hole channels. We compare numerical calculations performed within this method with an exact pairing model based on the $SO(8)$ algebra. The neutron-proton mixing is included in our calculations by performing rotations in the isospin space using the isocranking technique.

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…

Yrast superdeformed band in59Cu

High-spin states in Cu-59 were populated using the fusion-evaporation reactions Si-28+ Ca-40 at a beam energy of 125 MeV and Ar-36+Si-28 at a beam energy of 143 MeV. The Gammasphere array in conjunction with ancillary detector systems allowed for the identification of a superdeformed rotational band in Cu-59, which was firmly linked to low-spin yrast states. Using directional correlations of oriented states, a spin-parity assignment of I-pi=25/2(+) to the band head was possible. The average quadrupole moment of the band is measured to be Q(t)=(2.24+/-0.40) e b. The characteristics of the band are compared to neighboring nuclei and predictions of different mean-field theories.

High-precision mass measurements and production of neutron-deficient isotopes using heavy-ion beams at IGISOL

An upgraded ion-guide system for the production of neutron-deficient isotopes with heavy-ion beams has been commissioned at the IGISOL facility with an $^{36}\mathrm{Ar}$ beam on a $^{\mathrm{nat}}\mathrm{Ni}$ target. It was used together with the JYFLTRAP double Penning trap to measure the masses of $^{82}\mathrm{Zr}, ^{84}\mathrm{Nb}, ^{86}\mathrm{Mo}, ^{88}\mathrm{Tc}$, and $^{89}\mathrm{Ru}$ ground states and the isomeric state $^{88}\mathrm{Tc}^{m}$. Of these, $^{89}\mathrm{Ru}$ and $^{88}\mathrm{Tc}^{m}$ were measured for the first time. The precision of measurements of $^{82}\mathrm{Zr}, ^{84}\mathrm{Nb}$, and $^{88}\mathrm{Tc}$ was significantly improved. The literature value for $^…

Lipkin method of particle-number restoration to higher orders

Background: On the mean-field level, pairing correlations are incorporated through the Bogoliubov-Valatin transformation, whereupon the particle degrees of freedom are replaced by quasiparticles. This approach leads to a spontaneous breaking of the particle-number symmetry and mixing of states with different particle numbers. In order to restore the particle number, various methods have been employed, which are based on projection approaches before or after variation. Approximate variation-after-projection (VAP) schemes, utilizing the Lipkin method, have mostly been used within the Lipkin-Nogami prescription. Purpose: Without recurring to the Lipkin-Nogami prescription, and using instead st…

Error analysis of nuclear mass fits

We discuss the least-square and linear-regression methods, which are relevant for a reliable determination of good nuclear-mass-model parameter sets and their errors. In this perspective, we define exact and inaccurate models and point out differences in using the standard error analyses for them. As an illustration, we use simple analytic models for nuclear binding energies and study the validity and errors of models' parameters, and uncertainties of its mass predictions. In particular, we show explicitly the influence of mass-number dependent weights on uncertainties of liquid-drop global parameters.

One-quasiparticle States in the Nuclear Energy Density Functional Theory

We study one-quasiproton excitations in the rare-earth region in the framework of the nuclear Density Functional Theory in the Skyrme-Hartree-Fock-Bogoliubov variant. The blocking prescription is implemented exactly, with the time-odd mean field fully taken into account. The equal filling approximation is compared with the exact blocking procedure. We show that both procedures are strictly equivalent when the time-odd channel is neglected, and discuss how nuclear alignment properties affect the time-odd fields. The impact of time-odd fields on calculated one-quasiproton bandhead energies is found to be rather small, of the order of 100-200 keV; hence, the equal filling approximation is suff…

Precision Mass Measurements beyondSn132: Anomalous Behavior of Odd-Even Staggering of Binding Energies

Atomic masses of the neutron-rich isotopes $^{121--128}\mathrm{Cd}$, $^{129,131}\mathrm{In}$, $^{130--135}\mathrm{Sn}$, $^{131--136}\mathrm{Sb}$, and $^{132--140}\mathrm{Te}$ have been measured with high precision (10 ppb) using the Penning-trap mass spectrometer JYFLTRAP. Among these, the masses of four $r$-process nuclei $^{135}\mathrm{Sn}$, $^{136}\mathrm{Sb}$, and $^{139,140}\mathrm{Te}$ were measured for the first time. An empirical neutron pairing gap expressed as the odd-even staggering of isotopic masses shows a strong quenching across $N=82$ for Sn, with a $Z$ dependence that is unexplainable by the current theoretical models.

Error Estimates of Theoretical Models: a Guide

This guide offers suggestions/insights on uncertainty quantification of nuclear structure models. We discuss a simple approach to statistical error estimates, strategies to assess systematic errors, and show how to uncover inter-dependencies by correlation analysis. The basic concepts are illustrated through simple examples. By providing theoretical error bars on predicted quantities and using statistical methods to study correlations between observables, theory can significantly enhance the feedback between experiment and nuclear modeling.

Global nuclear structure aspects of tensor interaction

A direct fit of the isoscalar spin-orbit and both isoscalar and isovector tensor coupling constants to the f5/2-f7/2 SO splittings in 40Ca, 56Ni, and 48Ca requires: (i) a significant reduction of the standard isoscalar spin-orbit strength and (ii) strong attractive tensor coupling constants. The aim of this paper is to address the consequences of these strong attractive tensor and weak spin-orbit fields on total binding energies, two-neutron separation energies and nuclear deformability.

Continuity equation and local gauge invariance for the N3LO nuclear energy density functionals

Background: The next-to-next-to-next-to-leading order (N3LO) nuclear energy density functional extends the standard Skyrme functional with new terms depending on higher-order derivatives of densities, introduced to gain better precision in the nuclear many-body calculations. A thorough study of the transformation properties of the functional with respect to different symmetries is required, as a step preliminary to the adjustment of the coupling constants. Purpose: Determine to which extent the presence of higher-order derivatives in the functional can be compatible with the continuity equation. In particular, to study the relations between the validity of the continuity equation and invari…

Polarization corrections to single-particle energies studied within the energy-density-functional and quasiparticle random-phase approximation approaches

Background: Models based on using perturbative polarization corrections and mean-field blocking approximation give conflicting results for masses of odd nuclei. Purpose: We systematically investigate the polarization and mean-field models, implemented within self-consistent approaches that use identical interactions and model spaces, to find reasons for the conflicts between them. Methods: For density-dependent interactions and with pairing correlations included, we derive and study links between the mean-field and polarization results obtained for energies of odd nuclei. We also identify and discuss differences between the polarization-correction and full particle-vibration-coupling (PVC) …

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.

Binding energies and pairing gaps in semi-magic nuclei obtained using new regularized higher-order EDF generators

We present results of the Hartree-Fock-Bogolyubov calculations performed using nuclear energy density functionals based on regularized functional generators at next-to-leading and next-to-next-to-leading order. We discuss properties of binding energies and pairing gaps determined in semi-magic spherical nuclei. The results are compared with benchmark calculations performed for the functional generator SLyMR0 and functional UNEDF0.

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…

Rotational properties of nuclei around 254 No investigated using a spectroscopic-quality Skyrme energy density functional

Abstract. Background: Nuclei in the Z≈100 mass region represent the heaviest systems where detailed spectroscopic information is experimentally available. Although microscopic-macroscopic and self-consistent models have achieved great success in describing the data in this mass region, a fully satisfying precise theoretical description is still missing. Purpose: By using fine-tuned parametrizations of the energy density functionals, the present work aims at an improved description of the single-particle properties and rotational bands in the nobelium region. Such locally optimized parametrizations may have better properties when extrapolating towards the superheavy region. Methods: Skyrme H…

Structure of superheavy nuclei along decay chains of element 115

[Introduction] A recent high-resolution α , X -ray, and γ -ray coincidence-spectroscopy experiment offered the first glimpse of excitation schemes of isotopes along α -decay chains of Z = 115. To understand these observations and to make predictions about shell structure of superheavy nuclei below 288 115, we employ two complementary mean-field models: the self-consistent Skyrme energy density functional approach and the macroscopic-microscopic Nilsson model. We discuss the spectroscopic information carried by the new data. In particular, candidates for the experimentally observed E 1 transitions in 276 Mt are proposed. We find that the presence and nature of low-energy E 1 transitions in w…

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 nucle…

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…

Angular momentum projection of cranked Hartree-Fock states: Application to terminating bands inA~44nuclei

We present the first systematic calculations based on the angular-momentum projection of cranked Slater determinants. We propose the Iy --> I scheme, by which one projects the angular momentum I from the 1D cranked state constrained to the average spin projection of =I. Calculations performed for the rotational band in 46Ti show that the AMP Iy --> I scheme offers a natural mechanism for correcting the cranking moment of inertia at low-spins and shifting the terminating state up by ~2 MeV, in accordance with data. We also apply this scheme to high-spin states near the band termination in A~44 nuclei, and compare results thereof with experimental data, shell-model calculations, and res…

Properties of nuclei in the nobelium region studied within the covariant, Skyrme, and Gogny energy density functionals

We calculate properties of the ground and excited states of nuclei in the nobelium region for proton and neutron numbers of 92 <= Z <= 104 and 144 <= N <= 156, respectively. We use three different energy-density-functional (EDF) approaches, based on covariant, Skyrme, and Gogny functionals, each within two different parameter sets. A comparative analysis of the results obtained for odd-even mass staggerings, quasiparticle spectra, and moments of inertia allows us to identify single-particle and shell effects that are characteristic to these different models and to illustrate possible systematic uncertainties related to using the EDF modelling

New density-independent interactions for nuclear structure calculations

We present a new two-body finite-range and momentum-dependent but density-independent effective interaction, which can be interpreted as a regularized zero-range force. We show that no three-body or density-dependent terms are needed for a correct description of saturation properties in infinite matter, that is, on the level of low-energy density functional, the physical three-body effects can be efficiently absorbed in effective two-body terms. The new interaction gives a very satisfying equation of state of nuclear matter and opens up extremely interesting perspectives for the mean-field and beyond-mean-field descriptions of atomic nuclei.

Characterization of the shape-staggering effect in mercury nuclei

In rare cases, the removal of a single proton (Z) or neutron (N) from an atomic nucleus leads to a dramatic shape change. These instances are crucial for understanding the components of the nuclear interactions that drive deformation. The mercury isotopes (Z = 80) are a striking example1,2: their close neighbours, the lead isotopes (Z = 82), are spherical and steadily shrink with decreasing N. The even-mass (A = N + Z) mercury isotopes follow this trend. The odd-mass mercury isotopes 181,183,185Hg, however, exhibit noticeably larger charge radii. Due to the experimental difficulties of probing extremely neutron-deficient systems, and the computational complexity of modelling such heavy nucl…

Hartree-Fock-Bogoliubov solution of the pairing Hamiltonian in finite nuclei

We present an overview of the Hartree-Fock-Bogoliubov (HFB) theory of nucleonic superfluidity for finite nuclei. After introducing basic concepts related to pairing correlations, we show how the correlated pairs are incorporated into the HFB wave function. Thereafter, we present derivation and structure of the HFB equations within the superfluid nuclear density functional formalism and discuss several aspects of the theory, including the unitarity of the Bogoliubov transformation in truncated single-particle and quasiparticle spaces, form of the pairing functional, structure of the HFB continuum, regularization and renormalization of pairing fields, and treatment of pairing in systems with …

Towards a novel energy density functional for beyond-mean-field calculations with pairing and deformation

We take an additional step towards the optimization of the novel finite-range pseudopotential at constrained Hartree-Fock-Bogolyubov level and implement an optimization procedure within an axial code using harmonic oscillator basis. We perform the optimization using three different numbers of the harmonic oscillator shells. We apply the new parameterizations in the O-Kr part of the nuclear chart and isotopic chain of Sn, and we compare the results with experimental values and those given by a parameterization obtained using a spherical code.

Pairing-induced speedup of nuclear spontaneous fission

Collective inertia is strongly influenced at the level crossing at which quantum system changes diabatically its microscopic configuration. Pairing correlations tend to make the large-amplitude nuclear collective motion more adiabatic by reducing the effect of those configuration changes. Competition between pairing and level crossing is thus expected to have a profound impact on spontaneous fission lifetimes. To elucidate the role of nucleonic pairing on spontaneous fission, we study the dynamic fission trajectories of $^{264}$Fm and $^{240}$Pu using the state-of-the-art self-consistent framework. We employ the superfluid nuclear density functional theory with the Skyrme energy density fun…

Regularized pseudopotential for mean-field calculations

We present preliminary results obtained with a finite-range two-body pseudopotential complemented with zero-range spin-orbit and density-dependent terms. After discussing the penalty function used to adjust parameters, we discuss predictions for binding energies of spherical nuclei calculated at the mean-field level, and we compare them with those obtained using the standard Gogny D1S finite-range effective interaction.

Dependence of direct neutron capture on nuclear-structure models

The prediction of cross sections for nuclei far off stability is crucial in the field of nuclear astrophysics. We calculate direct neutron capture on the even-even isotopes $^{124-145}$Sn and $^{208-238}$Pb with energy levels, masses, and nuclear density distributions taken from different nuclear-structure models. The utilized structure models are a Hartree-Fock-Bogoliubov model, a relativistic mean field theory, and a macroscopic-microscopic model based on the finite-range droplet model and a folded-Yukawa single-particle potential. Due to the differences in the resulting neutron separation and level energies, the investigated models yield capture cross sections sometimes differing by orde…

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.