Magnetic hexadecapole gamma transitions and neutrino-nuclear responses in medium heavy nuclei

Neutrino-nuclear responses in the form of squares of nuclear matrix elements,NMEs, are crucial for studies of neutrino-induced processes in nuclei. In this work we investigate magnetic hexadecapole (M4) NMEs in medium-heavy nuclei. The experimentally derived NMEs, $M_{\rm EXP}$(M4), deduced from observed M4 $\gamma$ transition half-lives are compared with the single-quasiparticle (QP) NMEs, $M_{\rm QP}$(M4), and the microscopic quasiparticle-phonon model (MQPM) NMEs $M_{\rm MQPM}$(M4). The experimentally driven M4 NMEs are found to be reduced by a coefficient $k \approx 0.29$ with respect to $M_{\rm QP}$(M4) and by $k \approx 0.33$ with respect to $M_{\rm MQPM}$(M4). The M4 NMEs are reduced a little by the quasiparticle-phonon correlations of the MQPM wave functions but mainly by other nucleonic and non-nucleonic correlations which are not explicitly included in the MQPM. The found reduction rates are of the same order of magnitude as those for magnetic quadrupole $\gamma$ transitions and Gamow-Teller (GT) and spin-dipole (SD) $\beta$ transitions. The impact of the found reduction coefficients on the magnitudes of the NMEs involved in astroneutrino interactions and neutrinoless double beta decays are discussed.