A graphical procedure to evaluate the many-body shell-model equations

The shell model of Woods et al. has been modified to include the effect of the many-body interaction in the ionic crystals in a simple phenomenological way. This is based on the work of Lowdin, Lundqvist, and Verma and Dayal. In the new model which the authors refer to as the modified shell model, it is assumed that the volume-dependent potential is due to the interaction between the cores of the ions only. This introduces additional parameters in the model which have been derived from the elastic and dielectric properties of the crystal. The variation of the specific heat with temperature of potassium iodide has been studied by the original model of Woods et al. as well as by the new model. It is seen that the theoretical specific heats and dispersion curves given by both the models are in fair agreement with the experimental results. However, the shell model fails to account for the Cauchy discrepancy in this crystal, whereas the new model removes this difficulty.

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LATTICE DYNAMICS OF MgO USING THREE-BODY FORCE SHELL MODEL

Modern Physics Letters B ◽

10.1142/s0217984989001217 ◽

1989 ◽

Vol 03 (10) ◽

pp. 771-776 ◽

Cited By ~ 1

Author(s):

S. MOHAN ◽

T. RADJAKOUMAR

Keyword(s):

Shell Model ◽

Lattice Dynamics ◽

Spectroscopic Data ◽

Body Force ◽

Phonon Dispersion ◽

Many Body ◽

Body Interaction ◽

Lattice Potential ◽

The Many ◽

Three Body

A modified three-body force shell model is applied to evaluate the phonon dispersion values of MgO. The many-body interaction in the lattice potential is well accounted for by this theory. The values of the phonon frequencies evaluated by this method are in good confirmation with the neutron spectroscopic data.

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SYMPLECTIC NO-CORE SHELL MODEL

International Journal of Modern Physics E ◽

10.1142/s0218301308011811 ◽

2008 ◽

Vol 17 (supp01) ◽

pp. 133-145

Author(s):

JERRY P. DRAAYER ◽

TOMÁŠ DYTRYCH ◽

KRISTINA D. SVIRATCHEVA ◽

CHAIRUL BAHRI ◽

JAMES P. VARY

Keyword(s):

Shell Model ◽

Model Space ◽

Nucleon Nucleon ◽

Strength Parameter ◽

Core Shell ◽

Many Body ◽

Nucleon Interaction ◽

Atomic Nuclei ◽

Nucleon Nucleon Interaction ◽

The Many

The symplectic no-core shell model (Sp-NCSM) is described. The theory is applied to a study of the structure of 12 C and 16 O . Results from a full 6ħΩ NCSM calculation for low-lying states in these nuclei using a realistic nucleon-nucleon interaction are found to project at approximately the 90% level onto a few of the leading 0 p -0 h and 2 p -2 h symplectic representations. The results are nearly independent of the oscillator strength parameter and whether bare or renormalized effective interactions are used in the analysis. The Sp-NCSM model space is typically only a very small fraction (under 1%) of the NCSM space, and grows slowly with increasing ħΩ. The comparisons with NCSM results suggest either the effective nucleon-nucleon interaction possesses a heretofore unappreciated symmetry, namely Sp(3,R) and the complementary (spin-isospin) supermultiplet symmetry, or the nuclear many-body system acts as a filter that allows the symplectic symmetry to propagate in a coherent way into the many-body dynamics while tending to dampen out symplectic symmetry breaking terms. Also, since the Sp-NCSM is a multi-ħΩ generalization of the Elliott SU (3) model, the results obtained to date reaffirm the relevance of SU (3) to atomic nuclei.

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PROJECTED SHELL MODEL DESCRIPTION OF E2 TRANSITION PROBABILITIES AND g-FACTORS OF EVEN–EVEN NEUTRON-RICH NUCLEI FROM Xe TO Nd

International Journal of Modern Physics E ◽

10.1142/s0218301312500930 ◽

2012 ◽

Vol 21 (11) ◽

pp. 1250093

Author(s):

GOPAL KRISHAN ◽

RANI DEVI ◽

S. K. KHOSA

Keyword(s):

Shell Model ◽

Transition Probabilities ◽

Body Wave ◽

Energy Levels ◽

Neutron Number ◽

Model Description ◽

Many Body ◽

Projected Shell Model ◽

The Many ◽

G Factors

The systematics of E2 transition probabilities and g-factors of even–even N ≥ 86 Xe , Ba , Ce and Nd have been studied by using the projected shell model approach. The E2 transition probabilities and g-factors have been calculated by using the many-body wave functions that reproduce the low-lying ground state energy levels. The calculated B(E2) values show an increasing trend with spin and neutron number. The calculated g-factors reproduce the observed decreasing trend of [Formula: see text] with neutron number except Nd nuclei.

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