Electromagnetic transitions from isobaric analog states to study nuclear matrix elements for neutrinoless <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>β</mml:mi><mml:mi>β</mml:mi></mml:mrow></mml:math> decays and astro-neutrino inverse <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math> decays

Experimental studies of nuclear matrix elements (NMEs) for neutrinoless double-$\ensuremath{\beta}$ decays (DBDs) and astro-neutrino $(\ensuremath{\nu})$ inverse $\ensuremath{\beta}$ (IBDs) are crucial $\ensuremath{\nu}$ beyond the standard model astro-$\ensuremath{\nu}$ since accurate theoretical calculations NMEs hard due to high sensitivity models parameters used models. Some important electromagnetic transition operators associated with DBD IBD, including effective weak couplings, found be experimentally obtained by measuring corresponding gamma (EM:$\ensuremath{\gamma})$ transitions from isobaric analog states (IASs) IBD nuclei. Then experimental couplings evaluating checking calculations. The EM-NMEs, cross sections, event rates IAS-$\ensuremath{\gamma}$ estimated nuclei show feasibility experiments.