Robust upper limit on the neutron single-particle energy of the $i_{13/2}$ orbit

Abstract

The boundary of the neutron $i_{13/2}$ single-particle energy is investigated with exact shell-model calculations, where random two-body interactions are adopted to overcome the bias from effective interactions. Excitation energies of $3_1^{-}$ state in ${}^{134}$Te and ${}^{136}$Xe, as well as those of $13/2_1^{+}$ states in ${}^{135}$Te and ${}^{137}$Xe, are taken as touchstones of our samplings. A robust upper limit of ${\epsilon }_{i13/2}<3.1$ MeV emerges in our calculations, given the mixing of $i_{13/2}$ single-neutron configuration and $f_{7/2}\otimes 3^{-}$ configuration in $13/2_1^{+}$ states of $N=83$ isotones.

Comments: 4 pages, 3 figures, brief report