Existence and impact of a proton bubble in 34Si

Determine whether the nucleus 34Si exhibits a central proton-density depletion (a "proton bubble") and ascertain the magnitude of its effect on the neutron 1p3/2–1p1/2 spin–orbit splitting in this mass region, in order to clarify the origin of the observed evolution of spin–orbit splittings.

Background

A pronounced reduction of the neutron 1p3/2–1p1/2 spin–orbit splitting along the N=21 isotones was initially attributed to a proposed proton "bubble" in 34Si, inferred from a very low occupancy of the 1s1/2 proton orbital in 34Si relative to 36S. Subsequent analyses that accounted for strength fragmentation suggested a smooth reduction consistent with weak-binding effects of low-ℓ orbitals.

The present work measures single-particle energies in 33Si via the 32Si(d,p)33Si reaction and finds a smooth evolution of the spin–orbit splitting consistent with Woods–Saxon calculations without modifying the spin–orbit strength, and contradicting relativistic mean-field predictions that associate a sudden reduction with a central density depletion. Nonetheless, theoretical predictions regarding both the existence of a proton bubble in 34Si and its quantitative impact on spin–orbit splitting vary and remain unsettled, motivating a definitive determination.