Some Extensions of the Schematic Model for Core Polarization of the Nuclear Effective Interaction

1972 ◽  
Vol 50 (22) ◽  
pp. 2768-2775 ◽  
Author(s):  
Donald W. L. Sprung ◽  
A. M. Jopko
Keyword(s):  
Shell Model ◽  
Effective Interaction ◽  
Higher Order ◽  
Schematic Model ◽  
Small Contribution ◽  
Core Polarization

A number of higher order core polarization processes recently considered by Kirson are here treated in the case of the soluble schematic model. We confirm the conclusion of Kirson that the sum of all the processes considered gives a very small contribution to the shell model effective interaction. In particular, the anomalously large results found in the RPA are disposed of.

Higher Order Core Polarization Contributions to the Effective Interaction in 42Ca – 42Sc

1973 ◽  
Vol 51 (21) ◽  
pp. 2275-2282 ◽  
Author(s):  
A. M. Jopko ◽  
Donald W. L. Sprung
Keyword(s):  
Numerical Calculation ◽  
Effective Interaction ◽  
Closed Shell ◽  
Higher Order ◽  
Core Polarization ◽  
Polarization Contribution ◽  
The Core ◽  
The One

A numerical calculation of the core polarization of the effective interaction between nucléons outside the 40Ca closed shell has been carried out, taking account of several higher order processes suggested by Kirson. These are a systematic inclusion of particle–hole scattering, self-screening of phonons, and modification of the one-particle to two-particle, one-hole vertex. These processes have the same effect as in the earlier calculation for 16O; namely, the final result is a very small net core polarization contribution to the effective interaction, which cannot explain the low-lying spectra.

scholarly journals Core-polarization effect in longitudinal electron scattering form factors of 65Cu nucleus

2019 ◽  
Vol 14 (31) ◽  
pp. 13-27
Author(s):  
Adie D. Salman
Keyword(s):  
Experimental Data ◽  
Shell Model ◽  
Electron Scattering ◽  
Transition Probabilities ◽  
Effective Interaction ◽  
Form Factors ◽  
Model Space ◽  
Inelastic Electron ◽  
Core Polarization ◽  
Reduced Transition Probabilities

Inelastic longitudinal electron scattering form factors to 2+ and 4+ states in 65Cu nucleus has been calculated in the (2p3/2 1f 5/2 2p1/2) shell model space with the F5PVH effective interaction. The harmonic oscillator potential has been applied to calculate the wave functions of radial single-particle matrix elements. Two shell model codes, CP and NUSHELL are used to obtain results. The form factor of inelastic electron scattering to 1/21−, 1/22−, 3/22−, 3/23−, 5/21−, 5/22− and 7/2- states and finding the transition probabilities B (C2) (in units of e2 fm4) for these transitions and B (C4) (in units of e2 fm8) for the transition 7/2-, and comparing them with experimental data. Both the form factors and reduced transition probabilities with core-polarization effects gave a reasonable description of the experimental data.

scholarly journals Effective interaction techniques for the Gamow shell model

2005 ◽  
Vol 71 (4) ◽  
Author(s):  
Gaute Hagen ◽  
M. Hjorth-Jensen ◽  
Jan S. Vaagen
Keyword(s):  
Shell Model ◽  
Effective Interaction ◽  
Interaction Techniques

scholarly journals Study of the Electric Quadrupole Moments for some Scandium Isotopes Using Shell Model Calculations with Different Interactions

2018 ◽  
Vol 15 (3) ◽  
pp. 304-309
Author(s):  
Baghdad Science Journal
Keyword(s):  
Shell Model ◽  
Theoretical Calculations ◽  
Microscopic Theory ◽  
Model Space ◽  
Electric Quadrupole ◽  
Quadrupole Moments ◽  
Core Polarization ◽  
Model Calculations ◽  
Major Shell ◽  
Experimental Values

The electric quadrupole moments for some scandium isotopes (41, 43, 44, 45, 46, 47Sc) have been calculated using the shell model in the proton-neutron formalism. Excitations out of major shell model space were taken into account through a microscopic theory which is called core polarization effectives. The set of effective charges adopted in the theoretical calculations emerging about the core polarization effect. NushellX@MSU code was used to calculate one body density matrix (OBDM). The simple harmonic oscillator potential has been used to generate the single particle matrix elements. Our theoretical calculations for the quadrupole moments used the two types of effective interactions to obtain the best interaction compared with the experimental data. The theoretical results of the quadrupole moments for some scandium isotopes performed with FPD6 interaction and Bohr-Mottelson effective charge agree with experimental values.

On the role of third- and higher-order contributions to the effective interaction for pf shell nuclei

1992 ◽  
Vol 541 (1) ◽  
pp. 105-130 ◽  
Author(s):  
M. Hjorth-Jensen ◽  
T. Engeland ◽  
A. Holt ◽  
E. Osnes
Keyword(s):  
Effective Interaction ◽  
Higher Order ◽  
Pf Shell

scholarly journals Lattice Dynamics of Simple Harmonic and Anharmonic Shell Models

1967 ◽  
Vol 20 (5) ◽  
pp. 495 ◽  
Author(s):  
J Oitmaa
Keyword(s):  
Dipole Moment ◽  
Shell Model ◽  
Lattice Dynamics ◽  
Higher Order ◽  
Force Constants ◽  
Dynamical Equations ◽  
Normal Coordinates ◽  
Shell Models ◽  
Rigid Ion Model ◽  
Explicit Expressions

The lattice dynamics of harmonic and anharmonic shell models are reviewed. It is shown that the various dynamical equations for the shell model can be expressed in the same form as those for the rigid ion model, but with modified force constants. The anharmonic shell model leads to higher order contributions to the dipole moment, quadratic and cubic in the normal coordinates, for which explicit expressions are obtained.

scholarly journals Shell-model calculations for upper pf-shell nuclei with an effective interaction

2018 ◽  
Vol 194 ◽  
pp. 01006
Author(s):  
Kalin Drumev
Keyword(s):  
Shell Model ◽  
Effective Interaction ◽  
Model Space ◽  
Model Calculations ◽  
Energy Eigenstates ◽  
Mixed Symmetry ◽  
Symmetry Approach ◽  
Oscillator Shell ◽  
Single Oscillator ◽  
Pf Shell

Results obtained for the energy spectra and the low-lying positive-parity energy eigenstates of the upper p f -shell nuclei 64Ge and 68Se with the use of the effective interaction JUN45 are reported. We address the question of how appropriate is the possibility to construct a symmetry-adapted shell model in a single oscillator shell using a Pairing-plus-Quadrupole Hamiltonian. Specifically, we study the goodness of the symmetries pseudo SU(3) and O(6) in the structure of the energy eigenstates. Finally, we relate our results to a proposed mixed-symmetry approach which is able to simultaneously account for the presence of both the pairing and the quadrupole modes as the most important ingredients in the effective interaction while using a restricted part of the full model space.

STRUCTURE OF ODD 79,81,83Se ISOTOPES WITH PROTON AND NEUTRON EXCITATIONS ACROSS Z = 28 AND N = 40

2013 ◽  
Vol 22 (12) ◽  
pp. 1350091 ◽  
Author(s):  
VIKAS KUMAR ◽  
P. C. SRIVASTAVA
Keyword(s):  
Experimental Data ◽  
Shell Model ◽  
Magnetic Moments ◽  
Effective Interaction ◽  
Quadrupole Moments ◽  
Excitation Energies ◽  
Valence Space

The recently measured experimental data of 79,81,83 Se isotopes have been interpreted in terms of shell model (SM) calculations. The calculations have been performed in f5/2pg9/2 space with the recently derived interactions, namely JUN45 and jj44b. To study the importance of the proton excitations across the Z = 28 shell in this region, we have also performed calculation in fpg9/2 valence space using an fpg effective interaction with 48 Ca core and imposing a truncation. Excitation energies, B(2) values, quadrupole moments and magnetic moments are compared with the experimental data available. Present study reveals the importance of proton excitations across the Z = 28 shell for predicting quadrupole and magnetic moments.

scholarly journals First signs of collectivity in N = 86 and 88 isotones above 132Sn

2018 ◽  
Vol 193 ◽  
pp. 01005 ◽  
Author(s):  
Houda NAÏDJA ◽  
Frédéric NOWACKI
Keyword(s):  
Field Theory ◽  
Shell Model ◽  
Effective Field Theory ◽  
Effective Interaction ◽  
Effective Field ◽  
Model Framework

Within the shell-model framework the low-lying states energies, E2 and M1 transitions of chains of nuclei 52 ≤ Z ≤ 60 with 82 ≤ N ≤ 88 are investigated. We use the N3LOP effective interaction derived from Effective Field Theory Potentials and phenomenologically constrained. We noticed clear collective features in N = 86 and 88 isotones, with signature of triaxial γ-bands.

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