Odd-neutron and odd-proton spectroscopic strengths have been obtained for low-lying bound states in the $N,Z$ = 50–82 major shell, populated through $1n$- and $1p$-transfer reactions on the even-$A$ ${}^{112-124}\mathrm{Sn}$ isotopes. While most proton orbitals in the 50–82 shell exhibit predominantly pure single-particle character, the neutron states show significant fragmentation of strength. The unperturbed energies of the neutron and proton single-particle levels are determined and display systematic shifts across the isotopic chain. In the odd-neutron nuclei, the yrast states closely track the measured neutron single-particle energies, which are largely driven by pairing correlations in the Sn valence space. In contrast, the odd-proton energies exhibit a prominent orbital-dependence that aligns well with mean-field calculations incorporating the effect of the neutron-proton tensor force. Both the $1n$- and $1p$-transfer probabilities show a reduction with worsening $Q$-value matching.

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• Nuclear reactions
• Optical, coupled-channel & distorted wave models
• Transfer reactions