Spherical Hartree-Fock Calculations Research Articles

Delta Excitation in the Compressed Finite Nucleus <sup>90</sup>Zr

Constrained spherical Hartree-Fock (CSHF) calculations under radial compression are presented for 90Zr in a model space consisting of nine major oscillator shells. An effective baryon-baryon interaction which includes the Δ resonances is used. The nucleon-nucleon (N-N) interaction is Reid Soft Core (RSC) potential. The sensitivity of the results to the choice model space is examined. It is found that the nuclear system becomes more compressible when the model space is increased. The radial density and the number of Δs are decreased by increasing model space. The results suggest that the behavior of single particle energies is independent of the model space.

SHELL STRUCTURE IN NEUTRON-RICH Ca AND Ni NUCLEI

The shell structure of the neutron-rich Ca and Ni nuclei is investigated by the spherical Hartree-Fock calculations with the semi-realistic NN interactions. The tensor force plays a significant role in the Z dependence of the shell structure, as is exemplified by N = 32 and N = 40. Loose binding may lead to a submagic number N = 58 in 86 Ni , assisted by the weak pair coupling.

Shell structure in neutron-rich Ca and Ni nuclei under semi-realistic mean fields

Shell structure in the neutron-rich Ca and Ni nuclei is investigated by the spherical Hartree-Fock calculations with the semi-realistic $NN$ interactions. Specific ingredients of the effective interaction, particularly the tensor force, often play a key role in the $Z$ dependence of the neutron shell structure. Such examples are found in N=32 and N=40; N=32 becomes magic or submagic in $^{52}$Ca while its magicity is broken in $^{60}$Ni, and N=40 is submagic (though not magic) in $^{68}$Ni but not in $^{60}$Ca. Comments are given on the doubly magic nature of $^{78}$Ni. We point out that the loose binding can lead to a submagic number N=58 in $^{86}$Ni, assisted by the weak pair coupling.

Spherical Hartree-Fock calculations with linear-momentum projection before the variation

The hole spectral functions and from these the spectroscopic factors have been calculated in a Galilei-invariant way for the ground-state wave functions resulting from spherical Hartree-Fock calculations with projection onto zero total linear momentum before the variation for the nuclei 4He, 12C, 16O, 28Si, 32S and 40Ca. The results are compared to those of the conventional approach which uses the ground states resulting from usual spherical Hartree-Fock calculations subtracting the kinetic energy of the center-of-mass motion before the variation and to the results obtained analytically with oscillator occupations.

Spherical Hartree-Fock calculations with linear-momentum projection before the variation

Spherical Hartree--Fock calculations with projection onto zero total linear momentum before the variation are performed for the nuclei 4He, 12C, 16O, 28Si, 32S and 40Ca using a density--independent effective nucleon--nucleon interaction. The results are compared to those of usual spherical Hartree--Fock calculations subtracting the kinetic energy of the center of mass motion either before or after the variation and to the results obtained analytically with oscillator occupations. Total energies, hole--energies, elastic charge form factors and charge densities and the mathematical Coulomb sum rules are discussed.

Hartree-Fock calculations on unstable nuclei with several types of effective interactions

Spherical Hartree-Fock calculations are carried out using several types of effective interactions. As well as the Skyrme and the Gogny interactions, a new interaction with Yukawa form is developed by modifying the M3Y interaction. Effects of the effective interactions on the gap at N = 16 are investigated. It is confirmed that the (σ · σ) (τ · τ) interaction plays a certain role in the occurrence of the N = 16 magic number in the neutron-rich region. This study shows that the M3Y-type interaction is useful to properly take into account spin-isospin characters in the mean-field theories, and to make a correspondence between the mean-field theories and the shell model.

Delta excitations in compressed finite nuclei. II. Nucleon-nucleon interaction dependence.

Spherical Hartree-Fock calculations at equilibrium and under radial compression are presented for $^{40}\mathrm{Ca}$ and $^{90}\mathrm{Zr}$ in a model space of seven major oscillator shells. We employ an effective baryon-baryon interaction which includes the \ensuremath{\Delta}(1236) resonance explicitly. The nucleon-nucleon (N-N) interactions are based on the Nijmegen and Reid soft core potentials. The results indicate a significant dependence on the choice of the N-N interaction at large nuclear compression. We found mixing between nucleons and \ensuremath{\Delta}'s even at equilibrium in $^{90}\mathrm{Zr}$ with either choice of potentials, but not in $^{40}\mathrm{Ca}$. Substantial amounts of the excitation energy induced by compression goes to the creation of \ensuremath{\Delta} excitations. \textcopyright{} 1996 The American Physical Society.

Nuclear shell model with delta excitations

Working in an oscillator basis, we define the nuclear Hamiltonian in a no-core model space to consist of an effective nucleon-nucleon interaction obtained with Brueckner theory from the Reid Soft Core interaction, a Coulomb term, nucleondelza transition potentials, and delta-delta interaction terms. This Hamiltonian is suitable for direct diagonalization and will account for interaction effects usually attributed to three-body, four-body, etc., forces arising from the virtual excitation of deltas. A natural outcome of this approach is a nuclear shell-model involving single particle states which are primarily nucleon in character and others, at higher energies, which are primarily delta in character. By performing spherical Hartree Fock calculations with this “realistic baryon Hamiltonian” we have found that the ground states of 16O, 40Ca and 56Ni are nearly pure nucleonic states while 2 Sn has about 10% of one delta in the ground state. For an estimate of how the delta degree of freedom is excited as one goes away from the ground state, we have performed spherical Hartree-Fock calculations with a radial constraint to compress the nucleus. The delta degree of freedom is gradually populated as the nucleus is compressed. Our results suggest that inclusion of the delta in the nuclear dynamics could lead to a significant softening of the nuclear equation of state.

Mutual support of magicities and residual effective interactions near 208Pb

We summarize experimental evidence in the lead region on the increased stability associated with neutron magic number when the proton number is magic, and vice versa. The effect is interpreted in the framework of the nuclear shell model with empirical effective interactions. Its relation to spherical Hartree-Fock calculations is pointed out and used to test Skyrme-type forces. None of the considered Skyrme interactions reproduce the effect.

Hartree-Fock Charge Distributions for 1p-Shell Nuclei

Nuclear charge distributions based on spherical Hartree-Fock calculations are employed to study the elastic electron scattering on some (spherical as well as deformed) 1p-shell nuclei. Extension to the deformed nuclei is made using the quadrupole-scattering theory. The nuclei studied are (He'), Li6 , C 12 , N 14 and 0. Fair agreement with the experimental data is obtained for not-too-large momentum transfers. § l. Introduction The nuclear charge distributions based on Hartree-Fock or projected Hartree­ Fock calculations!) are some of the non-phenomenological charge distributions em­ ployed to analyse the elastic electron scattering data on light nuclei. Charge densities based on Brueckner-Hartree-Fock calculations have also been tested suc­ cessfully in this respect.') Recently a model-independent method of determination of charge radius of a spin-zero light nucleus has been proposed.3l The method is based on the hypothesis of analyticity of the form factor in the complex q 2 plane. In this paper we have employed charge distributions based on spherical Hartree-Fock (HF) calculations4l along with the quadrupole-scattering theory to study the elastic electron scattering on some (spherical as well as deformed) 1P-shell nuclei. These HF wave functions have as their basis the Yale effective interaction derived by Shakin et al., 5l using a unitary-model-operator approach and they take into account short-range central nucleon-nucleon correlations. The cor­ rections due to the Coulomb energy and the centre-of-mass motion of the nucleus are incorporated in these calculations in a self-consistent manner. The resulting HF single particle energy levels are in fair agreement with the experimental data. The agreement of the calculated binding energies and the rms radii, however, is not as good, because the second order terms in the K-matrix are not included self-consistently.

The determination of the nuclear charge distribution of 12C from elastic electron scattering

Using an iterative procedure previously applied to 208Pb, the static nuclear charge distribution for 12C and the error and error correlations in coordinate space implied by the experimental statistical errors are determined from experimental electron scattering data at three energies. Pseudodata generated from a known charge distribution and randomized according to the experimental errors are investigated extensively to demonstrate the validity of the method. Deformed and spherical Hartree-Fock calculations with phenomenological and realistic forces are compared with experiment, and the effect of dispersion corrections on the analysis is shown to be small. Various corrections to the experimental data are discussed, and the analysis is compared with other current approaches.

Bubbles and the odd-state force

We show that the formation of bubbles in spherical Hartree-Fock calculations on 36A depends sensitively on the odd-state effective interaction, being strongly favoured, like alpha clustering, when this is repulsive

On Spherical Hartree–Fock Calculations with Sussex Interaction

Spherical Hartree–Fock calculations for 4He, 12C, and 16O nuclei have been carried out with Sussex relative matrix elements of Elliott et al. It is observed that the calculated binding energies for all these nuclei are considerably smaller than the experimental values. However, the Sussex matrix elements give better results for the binding energies of these nuclei compared with the truncated results of other realistic interactions in most of the cases. The rest of the calculated properties are in fair agreement with experiments.

A Hartree-Fock calculation for the stability of super-heavy nuclei

Spherical Hartree-Fock calculations have been carried out in the super-heavy region with the Skyrme interaction. Shell effects are discussed and stability against alpha and beta-decay are investigated. A strong shell effect is found to occur at N = 228.