We have explored the occurrence of the spherical shell closures for superheavy nuclei in the framework of the relativistic Hartree–Fock–Bogoliubov (RHFB) theory. Shell effects are characterized in ...terms of two-nucleon gaps δ2n(p). Although the results depend slightly on the effective Lagrangians used, the general set of magic numbers beyond 208Pb are predicted to be Z=120, 138 for protons and N=172, 184, 228 and 258 for neutrons, respectively. Specifically the RHFB calculations favor the nuclide 120304 as the next spherical doubly magic one beyond 208Pb. Shell effects are sensitive to various terms of the mean-field, such as the spin-orbit coupling, the scalar and effective masses.
We develop a new framework of the deformed quasiparticle-random-phase approximation (QRPA) where the Skyrme density functional and the density-dependent pairing functional are consistently treated. ...Numerical applications are carried out for the isovector dipole and the isoscalar quadrupole modes in the spherical {sup 20}O and in the deformed {sup 26}Ne nuclei, and the effect of the momentum-dependent terms of the Skyrme effective interaction for the energy-weighted sum rule is discussed. As a further application, we present for the first time the moments of inertia of {sup 34}Mg and {sup 36}Mg using the Thouless-Valatin procedure based on the self-consistent deformed QRPA, and we show the applicability of our new calculation scheme not only for the vibrational modes but also for the rotational modes in deformed neutron-rich nuclei.
Random Phase Approximation (RPA) calculations are nowadays an indispensable tool in nuclear physics studies. We present here a complete version implemented with Skyrme-type interactions, with the ...spherical symmetry assumption, that can be used in cases where the effects of pairing correlations and of deformation can be ignored. The full self-consistency between the Hartree–Fock mean field and the RPA excitations is enforced, and it is numerically controlled by comparison with energy-weighted sum rules. The main limitations are that charge-exchange excitations and transitions involving spin operators are not included in this version.
Program title: skyrme_rpa (v 1.00)
Catalogue identifier: AENF_v1_0
Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AENF_v1_0.html
Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 5531
No. of bytes in distributed program, including test data, etc.: 39435
Distribution format: tar.gz
Programming language: FORTRAN-90/95; easily downgradable to FORTRAN-77.
Computer: PC with Intel Celeron, Intel Pentium, AMD Athlon and Intel Core Duo processors.
Operating system: Linux, Windows.
RAM: From 4 MBytes to 150 MBytes, depending on the size of the nucleus and of the model space for RPA.
Word size: The code is written with a prevalent use of double precision or
REAL(8) variables; this assures 15 significant digits.
Classification: 17.24.
Nature of problem: Systematic observations of excitation properties in finite nuclear systems can lead to improved knowledge of the nuclear matter equation of state as well as a better understanding of the effective interaction in the medium. This is the case of the nuclear giant resonances and low-lying collective excitations, which can be described as small amplitude collective motions in the framework of the Random Phase Approximation (RPA). This work provides a tool where one starts from an assumed form of nuclear effective interaction (the Skyrme forces) and builds the self-consistent Hartree–Fock mean field of a given nucleus, and then the RPA multipole excitations of that nucleus.
Solution method: The Hartree–Fock (HF) equations are solved in a radial mesh, using a Numerov algorithm. The solutions are iterated until self-consistency is achieved (in practice, when the energy eigenvalues are stable within a desired accuracy). In the obtained mean field, unoccupied states necessary for the RPA calculations are found. For all single-particle states, box boundary conditions are assumed. To solve the RPA problem for a given value of total angular momentum and parity Jπ a coupled basis is constructed and the RPA matrix is diagonalized (protons and neutrons are treated explicitly, and no approximation related to the use of isospin formalism is introduced). The transition amplitudes and transition strengths associated to given external operators are calculated. The HF densities and RPA transition densities are also evaluated.
Restrictions: The main restrictions are related to the assumed spherical symmetry and absence of pairing correlations.
Running time: The typical running time depends strongly on the nucleus, on the multipolarity, on the choice of the model space and of course on the computer. It can vary from a few minutes to several hours.
A Skyrme-like effective interaction is built up from the equation of state of nuclear matter. The latter is calculated in the framework of the Brueckner-Hartree-Fock approximation with two- and ...three-body forces. A complete Skyrme parametrization requires a fit of the neutron and proton effective masses and the Landau parameters. The new parametrization is probed on the properties of a set of closed-shell and closed-subshell nuclei, including binding energies and charge radii.
Making use of the finite rank separable approach for the quasiparticle random phase approximation enables one to perform nuclear structure calculations in very large two-quasiparticle spaces. The ...approach is extended to take into account the residual particle-particle interaction. The calculations are performed by using Skyrme interactions in the particle-hole channel and density-dependent zero-range interactions in the particle-particle channel. To illustrate our approach, we study the properties of the lowest quadrupole states in the even-even nuclei {sup 128}Pd, {sup 130}Cd, {sup 124-134}Sn, {sup 128-136}Te, and {sup 136}Xe.
The formation of new shell gaps in intermediate mass neutron-rich nuclei is investigated within the relativistic Hartree–Fock–Bogoliubov theory, and the role of the Lorentz pseudo-vector and tensor ...interactions is analyzed. Based on the Foldy–Wouthuysen transformation, we discuss in detail the role played by the different terms of the Lorentz pseudo-vector and tensor interactions in the appearing of the N=16, 32 and 34 shell gaps. The nuclei 24O, 48Si and 52,54Ca are predicted with a large shell gap and zero (24O, 52Ca) or almost zero (48Si, 54Ca) pairing gap, making them candidates for new magic numbers in exotic nuclei. We find from our analysis that the Lorentz pseudo-vector and tensor interactions induce very specific evolutions of single-particle energies, which could clearly sign their presence and reveal the need for relativistic approaches with exchange interactions.
For the first time a fully self-consistent charge-exchange relativistic RPA based on the relativistic Hartree-Fock (RHF) approach is established. The self-consistency is verified by the so-called ...isobaric analog state (IAS) check. The excitation properties and the nonenergy weighted sum rules of two important charge-exchange excitation modes, the Gamow-Teller resonance (GTR) and the spin-dipole resonance (SDR), are well reproduced in the doubly magic nuclei 48Ca, 90Zr and 208Pb without readjustment of the particle-hole residual interaction. The dominant contribution of the exchange diagrams is demonstrated.
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