Advances in High Energy Physics

Volume 2016 (2016), Article ID 8417598, 8 pages

http://dx.doi.org/10.1155/2016/8417598

## Magnetic Hexadecapole Transitions and Neutrino-Nuclear Responses in Medium-Heavy Nuclei

^{1}Department of Physics, University of Jyvaskyla, P.O. Box 35, 40014 Jyvaskyla, Finland^{2}Research Center for Nuclear Physics, Osaka University, Osaka 567-0047, Japan

Received 17 March 2016; Accepted 14 April 2016

Academic Editor: Enrico Lunghi

Copyright © 2016 Lotta Jokiniemi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

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, (M4), deduced from observed M4 transition half-lives are compared with the single-quasiparticle (QP) NMEs, (M4), and the microscopic quasiparticle-phonon model (MQPM) NMEs (M4). The experimentally derived M4 NMEs are found to be reduced by a coefficient with respect to (M4) and by with respect to (M4). The M4 NMEs are reduced a little by the quasiparticle-phonon correlations of the MQPM wave functions but mainly by other nucleonic and nonnucleonic 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 transitions and Gamow-Teller (GT) and spin-dipole (SD) transitions. The impacts of the found reduction coefficients on the magnitudes of the NMEs involved in astroneutrino interactions and neutrinoless double beta decays are discussed.

#### 1. Introduction

Neutrino interactions in nuclei are studied, for example, by investigating scatterings of astroneutrinos on nuclei and by the attempts to record the neutrinoless double beta () decays. Here the neutrino-nuclear responses can be condensed in the squares of nuclear matrix elements (NMEs) and it is necessary to study through them the neutrino properties and astroneutrino reactions that are of interest to particle physics and astrophysics, as discussed in review articles [1–4] and references therein.

The present work aims at investigating the magnetic hexadecapole (M4) NMEs, (M4), in medium-heavy nuclei to study higher-multipole axial-vector NMEs associated with higher-energy components of astroneutrino reactions and decays. Such components are shown to be important for, for example, the decays [5].

Neutrino-nuclear responses associated with neutral-current (NC) and charged-current (CC) interactions are studied by investigating the relevant and decay transitions or NC and CC scatterings on nuclei. The momenta involved in astroneutrino scatterings and decays are of the order of 50–100 MeV/c. Accordingly, depending on the involved momentum exchanges, the multipoles with angular momenta up to around 4-5 are involved (e.g., decays mediated by light Majorana neutrinos; see [5]), or even higher multipoles can be engaged ( decays mediated by heavy Majorana neutrinos; see [5]).

In some previous works, axial-vector CC resonances of GT(1^{+}) and SD(2^{−}) NMEs for allowed and first-forbidden transitions are shown to be reduced much in comparison with the quasiparticle (QP) and pnQRPA (proton-neutron quasiparticle random-phase approximation) NMEs [6–10] due to spin-isospin () nucleonic and nonnucleonic correlations and nuclear-medium effects. These studies show that exact theoretical evaluations for the astroneutrino and NMEs, including possible renormalization of the axial-vector coupling constant , are hard. The corresponding NC nuclear responses of magnetic dipole (M1) and quadrupole (M2) transitions are also known to be much reduced with respect to the QP NMEs [11]. Similar studies have been conducted in the case of the two-neutrino double beta decays in [12, 13] in the framework of the IBA-2 model. Also the derivation of effective operators has been proposed [14]. All these studies bear relevance to the previously mentioned Majorana-neutrino mediated decays, to high-energy astroneutrino reactions, but also to the lower-energy (up to 30 MeV) supernova-neutrino scatterings off nuclei, as shown, for example, in [15–18].

In the light of the above discussions it is of great interest to investigate the spin-hexadecapole (4^{−}) NMEs to see how the higher-multipole NMEs are reduced by the nucleonic and nonnucleonic spin-isospin correlations. Actually, there are almost no experimental CC hexadecapole NMEs in medium-heavy nuclei since the decays are very rare third-forbidden unique transitions. However, it turns out that there are few measurements of the half-lives and electron spectra of the more complex fourth-forbidden nonunique transitions and they can serve as potential testing grounds concerning the quenching effects of the weak vector () and axial-vector () coupling constants [19]. On the other hand, there are many experimental data on NC M4 NMEs, where the isovector component of the NME is related to the analogous NME on the basis of the isospin symmetry. Thus we discuss mainly the M4 transitions in the present report with the aim of helping evaluate/confirm, for example, the NMEs concerning their higher-multipole aspects.

#### 2. Experimental M4 NMEs

Here we discuss stretched M4 transitions with , where and are the initial and final state spins and . The M4 transition rate (per sec) is given in terms of the reduced M4 strength (M4) as [20] where is the ray energy in units of MeV and is the conversion-electron coefficient. The reduced strength is expressed in terms of the M4 NME in units of as

The M4 NME is expressed in terms of the M4 coupling constants (M4) and the M4 matrix element (M4) as where the first and the second terms are for the odd-proton () and odd-neutron () transition NMEs with being the isospin component ( for neutron and for proton). The coupling constant is written as where for proton and for neutron, and are the proton and neutron magnetic moments, and and are the proton and neutron orbital coefficients. The M4 matrix element is expressed as where is the nuclear radius and is the spherical harmonic for multipole .

The isotopes used for ongoing and/or future experiments are , , , , , , and [2]. They are in the mass regions of = 70–120 and = 130–150. The single-quasiparticle (single-QP) M4 transitions in these mass regions are uniquely tagged by the pairs and , respectively. Here the higher spin state is the intruder one from the higher major shell with opposite parity. The single-particle M4 NMEs corresponding to these tagging transitions are quite large because of the large radial and angular overlap integrals.

The single-quasiparticle M4 transitions in the mentioned two mass regions are analyzed in Tables 1 and 2. The M4 NMEs derived from the experimental half-lives are given in the third column of these tables.