Search Results (68 total)

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, whereas the functionals restricted by Galilean and gauge symmetries contain 100 and 42 terms, respectively. For functionals additionally restricted by the spherical, space-inversion, and time-reversal symmetries, the corresponding numbers of terms are equal to 100, 60, and 22, respectively.

We discuss the least-squares 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.

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 energies, and that extensions of this form are very much required.

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 f_5/2-f_7/2 spin-orbit splittings in ⁴⁰Ca, ⁵⁶Ni, and ⁴⁸Ca is proposed as a practical realization of this new program. 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 it considerably and systematically improves basic single-particle properties including spin-orbit splittings and magic-gap energies. Impact of these changes on nuclear binding energies is also discussed.

In the framework of the density functional theory for superconductors, we study the restoration of the particle-number symmetry by means of the projection technique. Conceptual problems are outlined and numerical difficulties are discussed. Both are related to the fact that neither the many-body Hamiltonian nor the wave function of the system appear explicitly in the density functional theory. Similar obstacles are encountered in self-consistent theories utilizing density-dependent effective interactions.

We present the first systematic calculations based on the angular momentum projection of cranked Slater determinants. We propose the I_y→I scheme, by which one projects the angular momentum I from the one-dimensional cranked state constrained to the average spin projection of 〈Î_y〉=I. Calculations performed for the rotational band in ⁴⁶Ti show that the AMP I_y→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 results of the approximate analytical symmetry-restoration method proposed previously.

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 deformed and superdeformed rotational bands in A~130 nuclei. Calculations are done in the self-consistent cranked nonrelativistic 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.

Variation after particle-number restoration is incorporated for the first time into the Hartree-Fock-Bogoliubov (HFB) framework employing the Skyrme energy density functional with zero-range pairing. The resulting projected HFB equations can be expressed in terms of the local gauge-angle-dependent densities. Results of projected calculations are compared with those obtained within the Lipkin-Nogami method in the standard version and with the Lipkin-Nogami method followed by exact particle-number projection.

Calculations using realistic mean-field methods suggest the existence of nuclear shapes with tetrahedral T_d and/or octahedral O_h symmetries sometimes at only a few hundreds of keV above the ground states in some rare earth nuclei around ¹⁵⁶Gd and ¹⁶⁰Yb. The underlying single-particle spectra manifest exotic fourfold rather than Kramers’s twofold degeneracies. The associated shell gaps are very strong, leading to a new form of shape coexistence in many rare earth nuclei. We present possible experimental evidence of the new symmetries based on the published experimental results—although an unambiguous confirmation will require dedicated experiments.

A search for self-consistent solutions for the chiral rotational bands in the N=75 isotones ¹³⁰Cs, ¹³²La, ¹³⁴Pr, and ¹³⁶Pm is performed within the Skyrme-Hartree-Fock cranking approach using SKM^* and SLy4 parametrizations. The dependence of the solutions on the time-odd contributions in the energy functional is studied. From among the four isotones considered, self-consistent chiral solutions are obtained only in ¹³²La. The microscopic calculations are compared with the ¹³²La experimental data and with results of a classical model that contains all the mechanisms underlying the chirality of the collective rotational motion. Strong similarities between the Hartree-Fock and classical model results are found. The suggestion formulated earlier by the authors that the chiral rotation cannot exist below a certain critical frequency is further illustrated and discussed, together with the microscopic origin of a transition from planar to chiral rotation in nuclei. We also formulate the separability rule by which the tilted-axis-cranking solutions can be inferred from three independent principal-axis-cranking solutions corresponding to three different axes of rotation.

We discuss methods used in mean-field theories to treat pairing correlations within the local density approximation. Pairing renormalization and regularization procedures are compared in spherical and deformed nuclei. Both prescriptions give fairly similar results, although the theoretical motivation, simplicity, and stability of the regularization procedure make it a method of choice for future applications.

We present a comprehensive mean-field calculation of the Schiff moment of the nucleus ²²⁵Ra, the quantity that determines the static electric-dipole moment of the corresponding atom if time-reversal (T) invariance is violated in the nucleus. The calculation breaks all possible intrinsic symmetries of the nuclear mean field and includes, in particular, both exchange and direct terms from the full finite-range T-violating nucleon-nucleon interaction, and the effects of short-range correlations. The resulting Schiff moment, which depends on three unknown T-violating pion-nucleon coupling constants, is much larger than in ¹⁹⁹Hg, the isotope with the best current experimental limit on its atomic electric-dipole moment.

We use the canonical Hartree-Fock-Bogoliubov basis to implement a self-consistent quasiparticle-random-phase approximation (QRPA) with arbitrary Skyrme energy density functionals and density-dependent pairing functionals. The point of the approach is to accurately describe multipole strength functions in spherical even-even nuclei, including weakly bound drip-line systems. We describe the method and carefully test its accuracy, particularly in handling spurious modes. To illustrate our approach, we calculate isoscalar and isovector monopole, dipole, and quadrupole strength functions in several Sn isotopes, both in the stable region and at the drip lines. We also investigate the consequences of neglecting the spin-orbit or Coulomb residual interactions in the QRPA.

Proton and neutron densities have been obtained for the even–even isotopes of Sn from ¹⁰⁰Sn to ¹⁷⁶Sn using a Hartree-Fock-Bogoliubov model with a Skyrme interaction. The matter densities so defined have been used with realistic nucleon–nucleon interactions in a folding model to specify optical potentials for the elastic scattering of protons with energies in the range 40–200  MeV. Those potentials have been used to make predictions of the differential cross sections and spin observables for proton scattering. As the target mass increases, the emergence of the neutron skin in the Sn isotopes is revealed by marked effects in the differential cross section. Comparisons with available data show how similar scattering data for the neutron-rich isotopes may provide constraints for the model structures.

Self-consistent solutions for the so-called planar and chiral rotational bands in ¹³²La are obtained for the first time within the Skyrme-Hartree-Fock cranking approach. It is suggested that the chiral rotation cannot exist below a certain critical frequency which under the approximations used is estimated as ℏω_crit≈0.5–0.6   MeV. However, the exact values of ℏω_crit may vary, to an extent, depending on the microscopic model used, in particular, through the pairing correlations and/or calculated equilibrium deformations. The existence of the critical frequency is explained in terms of a simple classical model of two gyroscopes coupled to a triaxial rigid body.

In the present study we generalize the self-consistent Hartree-Fock-Bogoliubov (HFB) theory formulated in the coordinate space to the case which incorporates an arbitrary mixing between protons and neutrons in the particle-hole (p-h) and particle-particle (p-p or pairing) channels. We define the HFB density matrices, discuss their spin-isospin structure, and construct the most general energy-density functional that is quadratic in local densities. The consequences of the local gauge invariance are discussed and the particular case of the Skyrme energy-density functional is studied. By varying the total energy with respect to the density matrices the self-consistent one-body HFB Hamiltonian is obtained and the structure of the resulting mean fields is shown. The consequences of the time-reversal symmetry, charge invariance, and proton-neutron symmetry are summarized. The complete list of expressions required to calculate total energy is presented.

An improved prescription for choosing a transformed harmonic-oscillator (THO) basis for use in configuration-space Hartree-Fock-Bogoliubov (HFB) calculations is presented. The new HFB+THO framework that follows accurately reproduces the results of coordinate-space HFB calculations for spherical nuclei, including those that are weakly bound. Furthermore, it is fully automated, facilitating its use in systematic investigations of large sets of nuclei throughout the periodic table. As a first application, we have carried out calculations using the Skyrme force SLy4 and volume pairing, with exact particle-number projection following application of the Lipkin-Nogami prescription. Calculations were performed for all even-even nuclei from the proton drip line to the neutron drip line having proton numbers Z=2,4,…,108 and neutron numbers N=2,4,…,188. We focus on nuclei near the neutron drip line and find that there exist numerous particle-bound even-even nuclei (i.e., nuclei with negative Fermi energies) that have at the same time negative two-neutron separation energies. This phenomenon, which was earlier noted for light nuclei, is attributed to bound shape isomers beyond the drip line.

We use the Skyrme-Hartree-Fock method, allowing all symmetries to be broken, to calculate the time-reversal-violating nuclear Schiff moment (which induces atomic electric dipole moments) in the octupole-deformed nucleus ²²⁵Ra. Our calculation includes several effects neglected in an earlier work, including self-consistency and polarization of the core by the last nucleon. We confirm that the Schiff moment is large compared to those of reflection-symmetric nuclei, though ours is generally a few times smaller than recent estimates.

The superdeformed bands in ⁵⁸Cu, ⁵⁹Cu, ⁶⁰Zn, and ⁶¹Zn are analyzed within the frameworks of the Skyrme-Hartree-Fock as well as Strutinsky-Woods-Saxon total Routhian surface methods with and without T=1 pairing correlations between like particles. It is shown that a consistent description within these standard approaches cannot be achieved. A T=0 neutron-proton pairing configuration mixing of signature-separated bands in ⁶⁰Zn is suggested as a possible solution to the problem.

We investigate the effects of the spin-isospin channel of the Skyrme energy functional on predictions for Gamow-Teller distributions and superdeformed rotational bands. We use the generalized Skyrme interaction SkO^′ to describe even-even ground states and then analyze the effects of time-odd spin-isospin couplings, first term by term and then together via linear regression. Some terms affect the strength and energy of the Gamow-Teller resonance in finite nuclei without altering the Landau parameter g₀^′ that to leading order determines spin-isospin properties of nuclear matter. Though the existing data are not sufficient to uniquely determine all the spin-isospin couplings, we are able to fit them locally. Altering these coupling constants does not change the quality with which the Skyrme functional describes rotational bands.

The latest generation γ-ray detection system, GAMMASPHERE, coupled with the Microball charged-particle detector, has made possible a new class of nuclear lifetime measurement. For the first time differential lifetime measurements free from common systematic errors for over 15 different nuclei ( >30 rotational bands in various isotopes of Ce, Pr, Nd, Pm, and Sm) have been extracted at high spin within a single experiment. This comprehensive study establishes the effective single-particle transition quadrupole moments in the A∼135 light rare-earth region. Detailed comparisons are made with theoretical calculations using the self-consistent cranked mean-field theory which convincingly demonstrates the validity of the additivity of single-particle quadrupole moments in this mass region.

Rotational bands have been found in ⁵⁷Co using the ²⁸Si(³²S,3p) reaction at 130 MeV. The bands, extending the mass 60 region of large deformation down to Z=27, are signature-partner sequences. Their quadrupole moments are similar to those of bands in the neighboring nuclei. The features of the new bands are described by Skyrme Hartree-Fock calculations favoring a configuration assignment with one neutron and one proton excited in the respective 1g_9/2 intruder orbital. An attempt to describe the magnetic (M1) properties of the signature-partner structure is also presented.

Odd-even staggering of binding energies is studied in finite fermion systems with pairing correlations. We discuss contributions of the pairing and mean field to the staggering, and we construct the binding-energy indicators which measure the magnitude of pairing correlations and the effective single-particle spacings in a given system. The analysis is based on studying several exactly solvable many-body Hamiltonians as well as on the analytical formulas that can be applied in the weak and strong pairing limits.

High-spin states in ⁵⁹Cu were populated using the fusion-evaporation reactions ²⁸Si+⁴⁰Ca at a beam energy of 125 MeV and ³⁶Ar+²⁸Si 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 ⁵⁹Cu, which was firmly linked to low-spin yrast states. Using directional correlations of oriented states, a spin-parity assignment of I^π=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.

Superdeformed and highly deformed rotational bands were established in ⁶⁵Zn using the ⁴⁰Ca(²⁹Si,4p)⁶⁵Zn reaction, and averaged quadrupole moments were measured for two of these bands. The configurations of these bands were assigned based on Hartree-Fock calculations. One of the three bands exhibits at low ħω a rise in the J⁽²⁾ dynamic moments of inertia that is similar to the alignment gain observed in ⁶⁰Zn. A comparison of the rotational band configurations and their J⁽²⁾ moments of inertia for light Zn isotopes suggests that the rise in J⁽²⁾ is most likely caused by np interactions associated with the valence protons and neutrons occupying the g_9/2 intruder orbits.