Valence neutron properties relevant to the neutrinoless double-β decay of 130Te

The valence neutron composition of the 130Te and 130Xe ground states has been studied with a view to constraining calculations of the nuclear matrix element for the neutrinoless double-β decay of 130Te. Single-neutron adding and removing reactions on 128^,130Te and 130^,132Xe have been used to probe the vacancy of the 0g_7/2, 1d_5/2, 1d_3/2, 2s_1/2, and 0h_11/2 orbitals. The change in the vacancy of these orbitals, obtained through a self-consistent determination of spectroscopic factors utilizing the Macfarlane-French sum rules, for 130Te→130Xe is shared only between the d, s_1/2, and h_11/2 orbitals, with the g_7/2 playing no significant role. This is in disagreement with recent calculations within both the quasiparticle random-phase approximation and shell-model frameworks, which show a role for the g_7/2 orbital that should have been observable. The neutron pairing properties of 130Xe have also been explored through the 132Xe(p,t) reaction showing no evidence for pairing vibrations.