Perturbative Approach to Effective Shell-Model Hamiltonians and Operators

Coraggio, L.; Itaco, N.

doi:10.3389/fphy.2020.00345

Cited by 25 publications

(17 citation statements)

References 116 publications

(240 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The V low-k matrix elements are then employed as interaction vertices of the perturbative expansion of H eff , and detailed surveys about this topic can be found in Refs. [57,59,61]. Here, we sketch briefly the procedure that has been followed to derive H eff and SM effective decay operators.…”

Section: Theoretical Framework a The Effective Sm Hamiltonianmentioning

confidence: 99%

“…The outset is the high-precision CD-Bonn N N potential [54], whose repulsive high-momentum components are renormalized using the V low-k procedure [55]. The low-momentum V low-k is amenable to a perturbative expansion of the shell-model effective Hamiltonian [56][57][58][59] and decay operators [60,61], so that single-particle (SP) energies, two-body matrix elements of the residual interaction (TBMEs), matrix elements of effective electromagnetic transitions and GT-decay operators, as well as twobody matrix elements of the effective 0νββ-decay operator are derived in terms of a microscopic approach, without adjusting SM parameters to reproduce data. This approach has been recently employed first to study twoneutrino double-β (2νββ) decay of 48 Ca, 76 Ge, 82 Se, 130 Te, and 136 Xe [62,63], and then to calculate M 0ν s of the same nuclides for their 0νββ decay [64].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Shell-model calculation of $^{100}$Mo double-$β$ decay

Coraggio,

Itaco,

De Gregorio

et al. 2022

Preprint

View full text Add to dashboard Cite

For the first time, the calculation of the nuclear matrix element of the double-β decay of 100 Mo, with and without the emission of two neutrinos, is performed in the framework of the nuclear shell model. This task is accomplished starting from a realistic nucleon-nucleon potential, then the effective shell-model Hamiltonian and decay operators are derived within the many-body perturbation theory. The exotic features which characterize the structure of Mo isotopes -such as shape coexistence and triaxiality softness -push the shell-model computational problem beyond its present limits, making it necessary to truncate the model space. This has been done with the goal to preserve as much as possible the role of the rejected degrees of freedom in an effective approach that has been introduced and tested in previous studies. This procedure is grounded on the analysis of the effective single-particle energies of a large-scale shell-model Hamiltonian, that leads to a truncation of the number of the orbitals belonging to the model space. Then, the original Hamiltonian generates a new one by way of a unitary transformation onto the reduced model space, to retain effectively the role of the excluded single-particle orbitals. The predictivity of our calculation of the nuclear matrix element for the neutrinoless double-β decay of 100 Mo is supported by the comparison with experiment of the calculated spectra, electromagnetic transition strengths, Gamow-Teller transition strengths and the two-neutrino double-β nuclear matrix elements.

show abstract

Section: Theoretical Framework a The Effective Sm Hamiltonianmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Shell-model calculation of $^{100}$Mo double-$β$ decay

Coraggio,

Itaco,

De Gregorio

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…For recent attempts of theoretically deriving the effective transition operators of this decay, see Refs. [38,39] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Estimation of nuclear matrix elements of double-$β$ decay from shell model and quasiparticle random-phase approximation

Terasaki,

Iwata

2021

Preprint

View full text Add to dashboard Cite

The nuclear matrix element (NME) of the neutrinoless double-β (0νββ) decay is an essential input for determining the neutrino effective mass, if the half-life of this decay is measured. The reliable calculation of this NME has been a long-standing problem because of the diversity of the predicted values of the NME depending on the calculation method. In this paper, we focus on the shell model and the QRPA. The shell model have a rich amount of the many-particle many-hole correlations, and the QRPA can obtain the convergence of the result of calculation with respect to the extension of the single-particle space. It is difficult for the shell model to obtain the convergence of the 0νββ NME with respect to the valence single-particle space. The many-body correlations of the QRPA are insufficient depending on nuclei. We propose a new method to modify phenomenologically the results of the shell model and the QRPA compensating the insufficient point of each method by using the information of other method complementarily. Extrapolations of the components of the 0νββ 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 0νββ NME of the QRPA. Our modification method gives similar values of the 0νββ NME of the two methods for 48 Ca. The discrepancy of the shell model and the QRPA for the NME of the two-neutrino double-β decay is much smaller than that for the 0νββ NME without major modifications.

show abstract

“…For recent attempts to theoretically derive the effective transition operators of this decay, see Refs. [38,39] and references therein.…”

Section: Introductionmentioning

confidence: 99%

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

Terasaki

Iwata

2021

Eur. Phys. J. Plus

View full text Add to dashboard Cite

The 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.

show abstract

Perturbative Approach to Effective Shell-Model Hamiltonians and Operators

Cited by 25 publications

References 116 publications

Shell-model calculation of $^{100}$Mo double-$β$ decay

Shell-model calculation of $^{100}$Mo double-$β$ decay

Estimation of nuclear matrix elements of double-$β$ decay from shell model and quasiparticle random-phase approximation

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

Contact Info

Product

Resources

About