Simultaneous analysis of matter radii, transition probabilities, and excitation energies of Mg isotopes by angular-momentum-projected configuration-mixing calculations

Abstract

We perform simultaneous analysis of (1) matter radii, (2) $B(E2;0^{+}\to 2^{+})$ transition probabilities, and (3) excitation energies, $E(2^{+})$ and $E(4^{+})$, for ${}^{24-40}$Mg by using the beyond mean-field (BMF) framework with angular-momentum-projected configuration mixing with respect to the axially symmetric ${\beta }_2$ deformation with infinitesimal cranking. The BMF calculations successfully reproduce all of the data for $r_{\mathrm{m}}$, $B(E2)$, and $E(2^{+})$ and $E(4^{+})$, indicating that it is quite useful for data analysis, particularly for low-lying states. We also discuss the absolute value of the deformation parameter ${\beta }_2$ deduced from measured values of $B(E2)$ and $r_{\mathrm{m}}$. This framework makes it possible to investigate the effects of ${\beta }_2$ deformation, the change in ${\beta }_2$ due to restoration of rotational symmetry, ${\beta }_2$ configuration mixing, and the inclusion of time-odd components by infinitesimal cranking. Under the assumption of axial deformation and parity conservation, we clarify which effect is important for each of the three measurements, and propose the kinds of BMF calculations that are practical for each of the three kinds of observables.

arXiv comment11 pages, 12 figures

References in corpus (22)

• Nuclear magic numbers: new features far from stability
• Shape Coexistence and the Effective Nucleon-Nucleon Interaction
• Collapse of the N=28 shell closure in ${}^{42}$Si
• Correlations beyond the mean field in Magnesium isotopes: Angular momentum projection and configuration mixing
• The merging of the islands of inversion at N=20 and N=28
• Deformation of Nuclei Close to the Two-Neutron Drip Line in Mg Region
• Well-developed deformation in 42Si
• Configuration mixing of angular-momentum projected triaxial relativistic mean-field wave functions. II. Microscopic analysis of low-lying states in magnesium isotopes
• Determination of the structure of ${}^{31}$Ne by full-microscopic framework
• Ground-state properties of neutron-rich Mg isotopes
• Augmented Lagrangian Method for Constrained Nuclear Density Functional Theory
• Electromagnetic transition strengths in soft deformed nuclei
• Deformation of Ne isotopes in the island-of-inversion region
• Light Nuclei near Neutron and Proton Drip Lines in the Relativistic Mean-Field Theory
• Symmetry conserving configuration mixing method with cranked states
• Deformation effect on total reaction cross sections for neutron-rich Ne-isotopes
• "Safe" Coulomb Excitation of 30Mg
• Neutron shell structure and deformation in neutron-drip-line nuclei
• Efficient method to perform quantum number projection and configuration mixing for most general mean-field states
• Angular momentum projected multi-cranked configuration mixing for reliable calculation of high-spin rotational bands
• Infinitesimal cranking for triaxial angular-momentum-projected configuration-mixing calculation and its application to the gamma vibrational band
• Realistic description of the rotational bands in rare earth nuclei by angular-momentum-projected multi-cranked configuration-mixing method

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• Properties of exotic nuclei and their linkage to the nucleonic interaction
• Cranked Skyrme-Hartree-Fock-Bogoliubov approach for a mean-field description of nuclear rotations near the drip line
• Enhanced moments of inertia for rotation in neutron-rich nuclei