Application of the gradient method to Hartree-Fock-Bogoliubov theory

A computer code is presented for solving the equations of Hartree-Fock-Bogoliubov (HFB) theory by the gradient method, motivated by the need for efficient and robust codes to calculate the configurations required by extensions of HFB such as the generator coordinate method. The code is organized with a separation between the parts that are specific to the details of the Hamiltonian and the parts that are generic to the gradient method. This permits total flexibility in choosing the symmetries to be imposed on the HFB solutions. The code solves for both even and odd particle number ground states, the choice determined by the input data stream. Application is made to the nuclei in the $sd$-shell using the USDB shell-model Hamiltonian.Comment: 20 pages, 5 figures, 3 table

Systematics of quadrupolar correlation energies

We calculate correlation energies associated with the quadrupolar shape degrees of freedom with a view to improving the self-consistent mean-field theory of nuclear binding energies. The Generator Coordinate Method is employed using mean-field wave functions and the Skyrme SLy4 interaction. Systematic results are presented for 605 even-even nuclei of known binding energies, going from mass A=16 up to the heaviest known. The correlation energies range from 0.5 to 6.0 MeV in magnitude and are rather smooth except for large variations at magic numbers and in light nuclei. Inclusion of these correlation energies in the calculated binding energy is found to improve two deficiencies of the Skyrme mean field theory. The pure mean field theory has an exaggerated shell effect at neutron magic numbers and addition of the correlation energies reduce it. The correlations also explain the phenomenon of mutually enhanced magicity, an interaction between neutron and proton shell effects that is not explicable in mean field theory.Comment: 4 pages with 3 embedded figure

Electromagnetic transition strengths in soft deformed nuclei

Spectroscopic observables such as electromagnetic transitions strengths can be related to the properties of the intrinsic mean-field wave function when the latter are strongly deformed, but the standard rotational formulas break down when the deformation decreases. Nevertheless there is a well-defined, non-zero, spherical limit that can be evaluated in terms of overlaps of mean-field intrinsic deformed wave functions. We examine the transition between the spherical limit and strongly deformed one for a range of nuclei comparing the two limiting formulas with exact projection results. We find a simple criterion for the validity of the rotational formula depending on $$, the mean square fluctuation in the angular momentum of the intrinsic state. We also propose an interpolation formula which describes the transition strengths over the entire range of deformations, reducing to the two simple expressions in the appropriate limits.Comment: 16 pages, 5 figures, supplemental material include

The Spectral Line Shape of Exotic Nuclei

The quadrupole strength function of $^{28}O$ is calculated making use of the SIII interaction, within the framework of continuum-RPA and taking into account collisions among the nucleons (doorway coupling). The centroid of the giant resonance is predicted at $\approx 14$ MeV, that is much below the energy expected for both isoscalar and isovector quadrupole resonances in nuclei along the stability valley. About half of this width arises from the coupling of the resonance to the continuum and about half is due to doorway coupling. This result is similar to that obtained in the study of giant resonances in light, $\beta$-stable nuclei, and shows the lack of basis for the expectation, entertained until now in the literature, that continuum decay was the main damping mechanism of giant resonances in halo nuclei.Comment: LaTeX file, 7 pages, figures not included but available if requested at [email protected], accepted for publication in Phys. Rev.

Global study of quadrupole correlation effects

We discuss the systematics of ground-state quadrupole correlations of binding energies and mean-square charge radii for all even-even nuclei, from O16 up to the superheavies, for which data are available. To that aim we calculate their correlated J=0 ground state by means of the angular-momentum and particle-number projected generator coordinate method, using the axial mass quadrupole moment as the generator coordinate and self-consistent mean-field states only restricted by axial, parity, and time-reversal symmetries. The calculation is performed within the framework of a non-relativistic self-consistent mean-field model using the same non-relativistic Skyrme interaction SLy4 and a density-dependent pairing force to generate the mean-field configurations and mix them. (See the paper for the rest of the abstract).Comment: 28 pages revtex, 29 eps figures (2 of which in color), 10 tables. submitted to Phys. Rev.

Surface properties of nuclear pairing with the Gogny force in a simplified model

Surface properties of neutron-neutron (T=1) pairing in semi-infinite nuclear matter in a hard wall potential are investigated in BCS approximation using the Gogny force. Surface enhancement of the gap function, pairing tensor and correlation energy density is put into evidence.Comment: 16 pages; 4 figures ; submitted to Phys. Lett.

Comparison of Viscosities from the Chapman-Enskog and Relaxation Time Methods

A quantitative comparison between the results of shear viscosities from the Chapman-Enskog and relaxation time methods is performed for selected test cases with specified elastic differential cross sections: (i) the non-relativistic, relativistic and ultra-relativistic hard sphere gas with angle and energy independent differential cross section, (ii) the Maxwell gas, (iii) chiral pions and (iv) massive pions. Our quantitative results reveal that the extent of agreement (or disagreement) depends very sensitively on the energy dependence of the differential cross sections employed.Comment: Submitted to Cent. Eur. J.Phy

Hanbury-Brown--Twiss Analysis in a Solvable Model

The analysis of meson correlations by Hanbury-Brown--Twiss interferometry is tested with a simple model of meson production by resonance decay. We derive conditions which should be satisfied in order to relate the measured momentum correlation to the classical source size. The Bose correlation effects are apparent in both the ratio of meson pairs to singles and in the ratio of like to unlike pairs. With our parameter values, we find that the single particle distribution is too distorted by the correlation to allow a straightforward analysis using pair correlation normalized by the singles rates. An analysis comparing symmetrized to unsymmetrized pairs is more robust, but nonclassical off-shell effects are important at realistic temperatures.Comment: 21 pages + 9 figures (tarred etc. using uufiles, submitted separately), REVTeX 3.0, preprint number: DOE/ER/40561-112/INT93-00-3

Mean field and pairing properties in the crust of neutron stars

Properties of the matter in the inner crust of a neutron star are investigated in a Hartree-Fock plus BCS approximation employing schematic effective forces of the type of the Skyrme forces. Special attention is paid to differences between a homogenous and inhomogeneous description of the matter distribution. For that purpose self-consistent Hartree Fock calculations are performed in a spherical Wigner-Seitz cell. The results are compared to predictions of corresponding Thomas Fermi calculations. The influence of the shell structure on the formation of pairing correlations in inhomogeneous matter are discussed.Comment: 11 pages, 9 figure