Reliability of Shell Model Calculations using the Dispersion Relation Approach

1971 ◽  
Vol 49 (11) ◽  
pp. 1401-1410 ◽  
Author(s):  
R. J. W. Hodgson
Keyword(s):  
Dispersion Relation ◽  
Phase Shift ◽  
Shell Model ◽  
Born Approximation ◽  
High Energy ◽  
Matrix Elements ◽  
Model Calculations ◽  
Phase Shift Data ◽  
Relation Approach ◽  
Shift Data

Two techniques for deriving the Born approximation from the two-nucleon phase shift data in states having l ≤ 4 are employed to study the influence of the high energy form of the phase shifts in deducing two-body matrix elements and shell model spectra. A comparison is made with results obtained by other approaches.

Solution of the Bethe–Goldstone Equation in Finite Nuclei from N–N Phase Shift Data

1972 ◽  
Vol 50 (9) ◽  
pp. 940-946
Author(s):  
R. J. W. Hodgson
Keyword(s):  
Wave Function ◽  
Phase Shift ◽  
Harmonic Oscillator ◽  
Shell Model ◽  
Phase Shifts ◽  
Matrix Elements ◽  
Pauli Operator ◽  
Phase Shift Data ◽  
Finite Nuclei ◽  
Shift Data

An approach is outlined wherein the Bethe–Goldstone wave function may be computed in a shell-model basis from a knowledge of the harmonic-oscillator matrix elements. These in turn may be derived from the N–N phase shifts by a number of different methods. The Pauli operator is treated exactly in the space of two-particle shell-model states. The method is applied to a calculation of the levels of 18O and 18F and results obtained using different two-body matrix elements are compared.

scholarly journals Large Scale Shell Model Calculations of the Negative-Parity States Structure in 24Mg Nucleus

2021 ◽  
Vol 66 (4) ◽  
pp. 293
Author(s):  
A.A. Al-Sammarraie ◽  
F.A. Ahmed ◽  
A.A. Okhunov
Keyword(s):  
Shell Model ◽  
Large Scale ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Energy Levels ◽  
Form Factors ◽  
Model Space ◽  
Negative Parity ◽  
Matrix Elements ◽  
Model Calculations

The negative-parity states of 24Mg nucleus are investigated within the shell model. We are based on the calculations of energy levels, total squared form factors, and transition probability using the p-sd-pf (PSDPF) Hamiltonian in a large model space (0 + 1) hW. The comparison between the experimental and theoretical states showed a good agreement within a truncated model space. The PSDPF-based calculations successfully reproduced the data on the total squared form factors and transition probabilities of the negative-parity states in 24Mg nucleus. These quantities depend on the one-body density matrix elements that are obtained from the PSDPF Hamiltonian. The wave functions of radial one-particle matrix elements calculated with the harmonic-oscillator potential are suitable to predict experimental data by changing the center-of-mass corrections.

scholarly journals ββ DECAY AND NUCLEAR STRUCTURE

2007 ◽  
Vol 16 (02) ◽  
pp. 552-560 ◽  
Author(s):  
E. CAURIER ◽  
F. NOWACKI ◽  
A. POVES
Keyword(s):  
Shell Model ◽  
Nuclear Matrix ◽  
Large Scale ◽  
Predictive Power ◽  
Strong Impact ◽  
Matrix Elements ◽  
Model Calculations ◽  
Mode Stability ◽  
Recent Developments

The determination of accurate nuclear matrix elements for ββ decay processes is a challenge for nuclear theory and can have a strong impact in neutrino physics. Large Scale Shell Model (LSSM) calculations are among the best tools for such determination and recent developments have allowed to extend its application domains. In particular, systematic studies of nuclear matrix elements calculations have been now undertaken in this framework for most of the ββ emitters. These calculations are crucial in the determination of the most favorable emitters in the forthcoming generation of ββ experiments. The present paper focuses on the recent advances and remaining difficulties of shell model calculations for the neutrinoless mode. Stability and predictive power of the results will be discussed.

EXOTIC ELECTROMAGNETIC TRANSITIONS IN NEUTRON-RICH CARBON ISOTOPES

2009 ◽  
Vol 18 (10) ◽  
pp. 1992-1996 ◽  
Author(s):  
TOSHIO SUZUKI ◽  
TAKAHARU OTSUKA
Keyword(s):  
Shell Model ◽  
Carbon Isotopes ◽  
Magnetic Dipole ◽  
Tensor Force ◽  
Electromagnetic Properties ◽  
Matrix Elements ◽  
Electromagnetic Transitions ◽  
Model Calculations ◽  
Shell Matrix ◽  
Model Hamiltonian

Structure and electromagnetic properties of exotic neutron-rich carbon isotopes are studied by shell model calculations. A p-sd shell model Hamiltonian is modified by enhancing the effects of the tensor force in the p-sd cross shell matrix elements as well as with corrections in the T=1 monopole terms. A considerable suppression of the magnetic dipole (M1) transition in 17 C from the [Formula: see text] state recently observed is found to be well explained by the modified Hamiltonian. The anomalous hindrance of the quadrupole (E2) transitions in 16 C and 18 C is also shown to be reproduced by our new Hamiltonian.

scholarly journals Shell model calculations in the A=80-100 mass region and study of double β transitions

2020 ◽  
Vol 1 ◽  
pp. 156
Author(s):  
J. Sinatkas ◽  
L. D. Skouras ◽  
D. Strottman ◽  
J. D. Vergados
Keyword(s):  
Shell Model ◽  
Satisfactory Agreement ◽  
Effective Interaction ◽  
Model Space ◽  
Mass Region ◽  
Least Square ◽  
Matrix Elements ◽  
Model Calculations ◽  
Least Square Fit ◽  
The One

The structure of the Ζ,Ν < 50 nuclei is examined in a model space consisting of the 0g9/2, 1p1/2, 1p3/2 and the 0f5/2 hole orbitals outside the doubly closed 100Sn core. The effective interaction for this model space is derived by introducing second order corrections to the Sussex matrix elements, while the one-hole energies are deduced by a least square fit to the observed levels. The results of the calculation are found to be in very satisfactory agreement with experiment for all nuclei with 38<Ζ<46 but for Ζ<38 this agreement begins to deteriorate. Such a feature possibly indicates the appearance of deformation and the breaking of the Ν=50 core. The wavefunctions of the calculation are used to determine double β matrix elements in the Ge, Se, Sr and Kr isotopes.

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