Occupation probabilities of valence orbitals relevant to neutrinoless double $\beta$ decay of $^{124}$Sn

International audience; Neutron transfer reaction measurements, relevant to the neutrinoless double β decay candidate Sn124 and its daughter Te124, have been performed. Precise measurements of both neutron addition [(d,p),(He4,He3)] and removal [(p,d),(He3,He4)] cross sections have been used to determine the occupation of valence orbitals pertinent to neutrinoless double β decay in these two nuclei. This information could be used to constrain calculations of the nuclear matrix element for the neutrinoless double β decay of Sn124. The change in the ground-state neutron vacancies in proceeding from Sn124 to Te124 is mainly found in the d3/2,5/2 and h11/2 orbitals. The occupancies of states near the Fermi level are in reasonable agreement with shell model calculations.