Two- and Four-Quasiparticle States in Spherical Vibrational Nuclei

A new model, based on the BCS approach, is especially designed to describe nuclear phenomena (A, Z ) → (A, Z ± 2) of double-charge exchange (DCE). Although it was proposed and applied in the particle-hole limit, by one of the authors [Krmpotić, Fizika B 14, 139 (2005)], it has not yet been applied within the BCS mean-field framework, nor has its ability to describe DCE processes been thoroughly explored. It is a natural extension of the pn-QRPA model, developed by Halbleib and Sorensen [Nucl. Phys. A 98, 542 (1967)] to describe the single β decays (A, Z ) → (A, Z ± 1), to the DCE processes. As such, it exhibits several advantages over the pn-QRPA model when used in the evaluation of the double beta decay (DBD) rates. For instance, (i) the extreme sensitivity of the nuclear matrix elements (NMEs) on the model parametrization does not occur; (ii) it allows us to study the NMEs, not only for the ground state in daughter nuclei, as the pn-QRPA model does, but also for all final 0 + and 2 + states, accounting at the same time for their excitation energies and the corresponding DBD Q values; (iii) together with the DBD-NMEs it also provides the energy spectra of Fermi and Gamow-Teller DCE transition strengths, as well as the locations of the corresponding resonances and their sum rules; (iv) the latter are relevant for both the DBD and the DCE reactions, since the underlying nuclear structure is the same; this correlation does not exist within the pn-QRPA model. As an example, detailed numerical calculations are presented for the (A, Z ) → (A, Z + 2) process in 48 Ca → 48 Ti and the (A, Z ) → (A, Z − 2) process in 96 Ru → 96 Mo, involving all final 0 + states and 2 + states.

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“…Details on the evaluation of matrix elements of H 2 can be found in Refs. [25,26]. However, our final results are different.…”

Section: B (Pn 2p2n)-qtda Modelmentioning

confidence: 56%

“…where the functions G and F are defined in the standard way [25,26]. They differ from those of Baranger [27] by a factor of −2, as can be seen, for example, from the comparison of [ [27], Eq.…”

Section: B (Pn 2p2n)-qtda Modelmentioning

confidence: 99%

Nuclear structure model for double-charge-exchange processes

et al. 2020

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“…[12] (this QRPA solves two RPA equations to calculate the NME) and the FQTDA formalism (Four Quasiparticle Tamm-Damcoff) [2]. In particular, the FTQDA is a new formalism employed to evaluate the NME based on the well-known QTDA [14]. The main difference in comparison to the QRPA comes from the description of the final (N − 2, Z + 2) nucleus.…”

Section: Results and Final Remarksmentioning

confidence: 99%

Computer code for double beta decay QRPA based calculations

Barbero¹,

Krmpotić²,

Mariano³

et al. 2014

AIP Conference Proceedings

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“…The RPA equations (19) depend explicitly on the mean field occupations v i through the A and B matrices defined in (20) and (21). At the same time, the quasiparticle occupations v i depend on the RPA amplitudes X, Y , on which depend also |0 , through the renormalized gap equation (11) and number equations (10).…”

Section: Rqrpamentioning

confidence: 99%

Limitations of the number self-consistent random phase approximation

Mariano

Hirsch

2000

Phys. Rev. C

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The Quasiparticle Random Phase Approximation equations are solved taking into account the Pauli Principle at the expectation value level, and allowing changes in the mean field occupation numbers to minimize the energy while having the correct number of particles in the correlated vacuum. The study of Fermi pn excitations in 76 Ge using a realistic Hilbert space shows that the pairing energy gaps in the modified mean field are diminished up to one half of the experimental value when strong proton-neutron correlations are present. Additionally, the Ikeda sum rule for Fermi transitions is violated due to the lack of scattering terms in the phonon operators. These results call for a critical revision of the double beta decay half-lives estimated using the QRPA extensions when standard QRPA calculations collapse. PACS numbers: 21.60.Jz, 23.40.-s * Fellow of the CONICET, Argentina. On leave

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Two- and Four-Quasiparticle States in Spherical Vibrational Nuclei

Cited by 43 publications

References 6 publications

Nuclear structure model for double-charge-exchange processes

Nuclear structure model for double-charge-exchange processes

Computer code for double beta decay QRPA based calculations

Limitations of the number self-consistent random phase approximation

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