Parity violating magnetization at neutrino pair emission using trivalent lanthanoid ions

A new detection method using magnetization generated at triggered radiative emission of neutrino pairs (RENP), $ |e \rangle \rightarrow | g \rangle + \gamma + \sum_{ij}\nu_i \bar{\nu}_j $ (atomic de-transition from state $|e \rangle $ to state $|g \rangle$ emitting sum of neutrino pairs $\sum_{ij}\nu_i\bar{\nu}_j$ accompanied by a photon $\gamma$), is investigated in order to determine unknown neutrino properties; absolute neutrino masses of $\nu_i$ and Majorana/Dirac distinction. Magnetization associated with RENP events has parity violating component intrinsic to weak interaction enforced by crystal field effect in solids, and greatly helps background rejection of quantum electrodynamic (QED) origin even when these backgrounds are amplified. In proposed experiments we prepare a coherently excited body of trivalent lanthanoid ions, Er$^{3+}$ (a best candidate ion so far found), doped in a transparent dielectric crystal. The magnetic moment $\mu \langle \vec{S}\cdot\vec{k} \rangle/k $ arising from generated electron spin $\vec{S}$ parallel to trigger photon direction $\vec{k}/k$ is parity odd, and is absent in QED processes. The generated magnetic field of order nano gauss is stored in crystals long after pair emission event till spin relaxation time. An improved calculation method of coherent rate and angular distribution of magnetization is developed in order to incorporate finite size effect of crystal target beyond the infinite size limit in previous calculations.