Magnetic quadrupole transitions in the relativistic energy density functional theory

Abstract

Magnetic quadrupole (M2) excitation represents a fundamental feature in atomic nucleus associated to nuclear magnetism induced by spin and orbital transition operator. Since it has only been investigated within the non-relativistic theoretical approaches, and available experimental data are rather limited, it is interesting to study the properties of M2 transitions using the framework of relativistic nuclear energy density functional. In this work the nuclear ground state is calculated with relativistic Hartree-Bogoliubov model, while the M2 excitations are described using the relativistic quasiparticle random phase approximation with the residual interaction extended with the isovector-pseudovector term. The M2 transition strength distributions are described and analyzed for closed shell nuclei $^{16}$O, $^{48}$Ca, $^{208}$Pb, open-shell $^{18} \mathrm O$, $^{42}$Ca, $^{56}$Fe, and semi-magic $^{90}$Zr. The evolution of M2 transition properties has been investigated within the $^{36-64} \mathrm Ca$ isotope chain. The main M2 transitions have rather rich underlying structure and detailed analysis shows that collectivity increases with the mass number due to larger number of contributing particle-hole configurations. Pairing correlations in open shell nuclei have strong effect, causing the reduction of M2 strength and shifts of the centroid energies to higher values. The analysis of M2 transition strengths indicate that considerable amount of experimental strength may be missing, mainly due to limitations to rather restricted energy ranges. The calculated M2 strengths for Ca isotopes, together with the future experimental data will allow constraining the quenching of the g factors in nuclear medium.

Appendix A: The analysis of contributing particle-hole transitions in M2 excited states

Here we display the components of M2 transitions for $^{16}$O, $^{48}$Ca, and $^{208}$Pb nuclei, on which discussions are presented in the main text.

See Tables 4, 5, 6, 7, 8.

Table 4 Partial contributions $b^{\nu }_{ph}$ (neutrons) and $b^{\pi }_{ph}$ (protons) to the dominant M2 transitions in the $^{16}$O nucleus. The $E^{th.}_{peak}$ denotes the peak energy corresponding to the RRPA eigenvalue, and $B_{M2}(E)$ is its overall transition strength

Table 5 The same as Table 4 but for $^{48} \mathrm Ca$

Table 6 Continuation of Table 5 for $^{48} \mathrm Ca$

Table 7 The same as Table 4 but for $^{208} \mathrm Pb$

Table 8 Continuation of Table 7 for $^{208} \mathrm Pb$