Higher-order isospin-symmetry breaking corrections to nuclear matrix elements of superallowed $0^+\to 0^+$ Fermi $\beta$ decay of $T=1$ nuclei
| hal.structure.identifier | Centre d'Etudes Nucléaires de Bordeaux Gradignan [CENBG] | |
| dc.contributor.author | XAYAVONG, Latsamy | |
| hal.structure.identifier | Centre d'Etudes Nucléaires de Bordeaux Gradignan [CENBG] | |
| dc.contributor.author | SMIRNOVA, Nadezda | |
| dc.description.abstractEn | We study the shell-model formalism to include the isospin-symmetry-breaking correction ($\delta_{C}$) to nuclear matrix element of superallowed $0^+\to 0^+$ Fermi $\beta$ decays of $T=1$ nuclei. Based on a perturbation expansion in a small quantity, such as the deviation of the overlap integral between proton and neutron radial wave functions from unity or of the transition density from its isospin-symmetry value, we derive that $\delta_C$ can be obtained as a sum of six terms, including two leading order (LO) terms, two next-to-leading order (NLO) terms, one next-to-next-to-leading order (NNLO) term and one next-to-next-to-next-to-leading order (NNNLO) term. The first two terms have been considered in a series of shell-model calculations of Towner and Hardy as well as in the recent calculation of the present authors, while the remaining four terms are usually neglected. A numerical calculation has been carried out for 13 transitions in the $p$, $sd$ and the lower part of $pf$ shells. Our results indicate that the magnitude of the sum of all higher order terms is of the order of $10^{-3}$%. This number is well below typical theoretical errors quantified within the shell model with Woods-Saxon radial wave functions. | |
| dc.language.iso | en | |
| dc.title.en | Higher-order isospin-symmetry breaking corrections to nuclear matrix elements of superallowed $0^+\to 0^+$ Fermi $\beta$ decay of $T=1$ nuclei | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Physique [physics]/Physique Nucléaire Théorique [nucl-th] | |
| dc.identifier.arxiv | 2201.01035 | |
| hal.identifier | hal-03531273 | |
| hal.version | 1 | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03531273v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=XAYAVONG,%20Latsamy&SMIRNOVA,%20Nadezda&rft.genre=preprint |
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