Radiative emission of neutrino pair (RENP) from atomic states is a new tool to experimentally investigate undetermined neutrino parameters such as the smallest neutrino mass, the nature of neutrino masses (Majorana vs Dirac), and their CP properties. We study effects of neutrino pair emission either from nucleus or from inner core electrons in which the zero-th component of quark or electron vector current gives rise to large coupling. Both the overall rate and the spectral shape of photon energy are given for a few cases of interesting target atoms. Calculated rates exceed those of previously considered target atoms by many orders of magnitudes.