scholarly journals Reply to “Comment on ‘Pygmy dipole response of proton-rich argon nuclei in random-phase approximation and no-core shell model’”

2008 ◽  
Vol 78 (3) ◽  
Author(s):  
C. Barbieri ◽  
E. Caurier ◽  
K. Langanke ◽  
G. Martínez-Pinedo
Keyword(s):  
Shell Model ◽  
Random Phase Approximation ◽  
Random Phase ◽  
Core Shell ◽  
Phase Approximation ◽  
Dipole Response

scholarly journals Estimation of nuclear matrix elements of double-$$\varvec{\beta }$$ decay from shell model and quasiparticle random-phase approximation

2021 ◽  
Vol 136 (9) ◽  
Author(s):  
J. Terasaki ◽  
Y. Iwata
Keyword(s):  
Shell Model ◽  
Nuclear Matrix ◽  
Single Particle ◽  
Random Phase Approximation ◽  
Random Phase ◽  
Nuclear Matrix Element ◽  
Phase Approximation ◽  
Quasiparticle Random Phase Approximation ◽  
Calculation Results ◽  
The Many

AbstractThe nuclear matrix element (NME) of neutrinoless double-$$\beta $$ β ($$0\nu \beta \beta $$ 0 ν β β ) decay is an essential input for determining the neutrino effective mass, if the half-life of this decay is measured. Reliable calculation of this NME has been a long-standing problem because of the diversity of the predicted values of the NME, which depends on the calculation method. In this study, we focus on the shell model and the QRPA. The shell model has a rich amount of the many-particle many-hole correlations, and the quasiparticle random-phase approximation (QRPA) can obtain the convergence of the calculation results with respect to the extension of the single-particle space. It is difficult for the shell model to obtain the convergence of the $$0\nu \beta \beta $$ 0 ν β β NME with respect to the valence single-particle space. The many-body correlations of the QRPA may be insufficient, depending on the nuclei. We propose a new method to phenomenologically modify the results of the shell model and the QRPA compensating for the insufficiencies of each method using the information of other methods in a complementary manner. Extrapolations of the components of the $$0\nu \beta \beta $$ 0 ν β β NME of the shell model are made toward a very large valence single-particle space. We introduce a modification factor to the components of the $$0\nu \beta \beta $$ 0 ν β β NME of the QRPA. Our modification method yields similar values of the $$0\nu \beta \beta $$ 0 ν β β NME for the two methods with respect to $$^{48}$$ 48 Ca. The NME of the two-neutrino double-$$\beta $$ β decay is also modified in a similar but simpler manner, and the consistency of the two methods is improved.

scholarly journals SHORTCUTS TO NUCLEAR STRUCTURE: LESSONS IN HARTREE–FOCK, RPA, AND THE NO-CORE SHELL MODEL

2005 ◽  
Vol 14 (01) ◽  
pp. 57-65
Author(s):  
CALVIN W. JOHNSON ◽  
IONEL STETCU
Keyword(s):  
Shell Model ◽  
Nuclear Structure ◽  
Random Phase Approximation ◽  
Center Of Mass ◽  
Random Phase ◽  
Mass Motion ◽  
Core Shell ◽  
Microscopic Approach ◽  
Hartree Fock ◽  
Appropriate Treatment

While the no-core shell model is a state-of-the-art microscopic approach to low-energy nuclear structure, its intense computational requirements lead us to consider time-honored approximations such as the Hartree–Fock (HF) approximation and the random phase approximation (RPA). We review RPA and point out some common misunderstandings, then apply HF + RPA to the no-core shell model. Here the main issue is appropriate treatment of contamination by spurious center-of-mass motion.

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