scholarly journals Neutrinoless double beta nuclear matrix elements around mass 80 in the nuclear shell-model

2015 ◽  
Vol 93 ◽  
pp. 01055
Author(s):  
N. Yoshinaga ◽  
K. Higashiyama ◽  
D. Taguchi ◽  
E. Teruya
Keyword(s):  
Shell Model ◽  
Nuclear Matrix ◽  
Nuclear Shell Model ◽  
Matrix Elements ◽  
Nuclear Shell

Collective motion in the nuclear shell model III. The calculation of spectra

1963 ◽  
Vol 272 (1351) ◽  
pp. 557-577 ◽  
Keyword(s):  
Shell Model ◽  
Collective Motion ◽  
Mass Region ◽  
Wave Functions ◽  
Nuclear Shell Model ◽  
Matrix Elements ◽  
One Dimensional ◽  
The One ◽  
Nuclear Shell ◽  
Main Pattern

A method is derived for calculating matrix elements of a two-body interaction in wave functions which were classified in part I interms of the group U 2- . For simplicity, a Cartesian basis of intrinsic functions is introduced in which the one-dimensional oscillators in x, y and z are separately diagonal. An application to 24 Mg in L-S coupling shows very little mixing of the quantum number K but an appreciable (10 to 20 %) mixing of U 3 representations (λμ). Overall agreement with experiment is quantitatively only tolerable but the main pattern of the spectrum is undoubtedly given by the lowest representation (84). On this basis, suggestions are made concerning the type of spectra to be expected for even and odd parity levels of the even-even nuclei in the mass region 16 < A < 40.

scholarly journals Nuclear Shell Model And Quantum Phase Transitions

2019 ◽  
Vol 26 ◽  
pp. 88
Author(s):  
S. Karampagia ◽  
V. Zelevinsky
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Shell Model ◽  
Quantum Phase Transitions ◽  
Mean Field ◽  
Nuclear Shell Model ◽  
Matrix Elements ◽  
Model Hamiltonian ◽  
Orbital Space ◽  
Nuclear Shell

The usual nuclear shell model defines nuclear properties through an effective mean-field plus a two-body interaction Hamiltonian in a finite orbital space. In this study we try to understand the correlation between the various parts of the shell model Hamiltonian and the nuclear observables and collectivity in nuclei. By varying specific groups of matrix elements we find signs of a phase transition in nuclei between a non-collective and a collective phase. In all cases studied the collective phase is attained when the single-particle transfer matrix elements are dominant in the shell model Hamiltonian, giving collective characteristics to nuclei.

CORRELATION BETWEEN EIGENVALUES AND SORTED DIAGONAL MATRIX ELEMENTS OF A LARGE DIMENSIONAL MATRIX

2008 ◽  
Vol 17 (supp01) ◽  
pp. 334-341
Author(s):  
AKITO ARIMA
Keyword(s):  
Shell Model ◽  
Uniform Distribution ◽  
Diagonal Matrix ◽  
Nuclear Shell Model ◽  
Matrix Elements ◽  
Extrapolation Methods ◽  
Dimensional Matrix ◽  
Nuclear Shell

Functional dependences of eigenvalues as functions of sorted diagonal elements are given for realistic nuclear shell model (NSM) hamiltonian, the uniform distribution hamiltonian and the GOE hamiltonian. In the NSM case, the dependence is found to be linear. We discuss extrapolation methods for more accurate predictions for low-lying states.

AN IDENTITY INVOLVING 9-j COEFFICIENTS

1964 ◽  
Vol 42 (6) ◽  
pp. 1081-1086 ◽  
Author(s):  
James D. Talman ◽  
William W. True
Keyword(s):  
Shell Model ◽  
Model Theory ◽  
The Other ◽  
Nuclear Shell Model ◽  
Matrix Elements ◽  
Nuclear Shell ◽  
Tensor Operators

An identity involving 9-j coefficients which may be of some value in spectroscopic calculations is obtained. Two proofs of the identity are described. In one proof the recoupling of matrix elements of tensor operators is considered; in the other the general methods of Yutsis, Levinsonas, and Vanagas are used. Two applications of the identity to nuclear shell-model theory are described.

scholarly journals TWO-BODY RANDOM ENSEMBLE FOR NUCLEI

2006 ◽  
Vol 15 (08) ◽  
pp. 1885-1895
Author(s):  
T. PAPENBROCK ◽  
H. A. WEIDENMÜLLER
Keyword(s):  
Shell Model ◽  
Ground States ◽  
Residual Interaction ◽  
Nuclear Shell Model ◽  
Matrix Elements ◽  
Generic Properties ◽  
Quantum Numbers ◽  
Nuclear Shell

The nuclear shell model exhibits dynamical and geometrical aspects. The former are determined by the two-body matrix elements of the residual interaction while the latter are due to the two-body operators that couple pairs of fermions to good quantum numbers of spin, isospin, and parity. We analyze the geometric aspects of the shell model and understand some of its generic properties regarding the generation of chaos in nuclear spectra and correlations between spectra with different quantum numbers. In particular, we address the preponderance of spin-0 ground states.

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