Nuclear Structure properties significant to neutrinoless double beta decay of $^{124}$Sn

International audience; The decay rate of neutrinoless double beta process is expected to give the first direct measure of the neutrino mass, if the corresponding nuclear matrix element can be reliably calculated [1]. A major complication in extracting the neutrino mass from the half-life of this decay is the uncertainty in the nuclear matrix element. There are certain experimental observable that may be placed to constrain the calculations of the matrix element [2]. One of the main ingredients in calculating the nuclear matrix element is the wave functions of the initial and final states, which are usually calculated based on different nuclear models [1, 2]. Single-nucleon transfer reactions can be used to probe the occupancy and vacancy of valence orbitals which can help to characterize the ground-state wave functions. The precise measurement of both neutron addition and removal cross-sections can be used to determine the occupation of valence orbits relevant to 0ν2β-decay, following the Macfarlane and French sum rules [3]. The method consists of requiring a normalization such that for a given orbit characterized by total angular momentum j, the sum of the measured occupancy and vacancy on the same target add up to the degeneracy of the orbit 2j+1. It has been shown that such measurements allowed for a detailed description of the energy and vacancy of the valence orbitals of 76Ge and 76Se, where 76Ge is a candidate for 0ν2βdecay. The results indicated that the Fermi surface is much more diffuse than in theoretical calculations [4]. Similar measurements have been recently performed on 130Te and 130Xe [5]. Both 76Ge and 130Te are subject of research for 0ν2β-decay programs known as GERDA, Majorana (for 76Ge) and CUORE (for 130Te). The present work is aimed to study neutron pickup and stripping transfer cross-sections on one of the 0ν2β-decay candidate 124Sn and its daughter 124Te. This nucleus is the focus of neutrino-less double beta decay study, at the upcoming underground India based Neutrino Observatory (INO). This information will be useful for constraining calculations of the nuclear matrix element for the 0ν2β-decay of 124Sn.