Radii in the $sd$ shell and the $s_{1/2}$ "halo" orbit: A game changer

Abstract

Proton radii of nuclei in the $sd$ shell depart appreciably from the asymptotic law, ${\rho }_{\pi }={\rho }_0{A}^{1/3}$. The departure exhibits systematic trends fairly well described by a single phenomenological term in the Duflo-Zuker formulation, which also happens to explain the sudden increase in slope in the isotope shifts of several chains at neutron number $N=28$. It was recently shown that this term is associated with the abnormally large size of the $s_{1/2}$ and $p$ orbits in the $sd$ and $pf$ shells respectively. Further to explore the problem, we propose to calculate microscopically radii in the former. Since the (square) radius is basically a one body operator, its evolution is dictated by single particle occupancies determined by shell model calculations. Assuming that the departure from the asymptotic form is entirely due to the $s_{1/2}$ orbit, the expectation value $⟨s_{1/2}|r^2|s_{1/2}⟩$ is determined by demanding that its evolution be such as to describe well nuclear radii. It does, for an orbit that remains very large (about 1.6 fm bigger than its $d$ counterparts) up to $N,Z=14$ then drops abruptly but remains some 0.6 fm larger than the $d$ orbits. An unexpected behavior bound to challenge our understanding of shell formation.

arXiv comment4 pages 6(7) figures

References in corpus (10)

• The Shell Model as Unified View of Nuclear Structure
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Cited by in corpus (1)

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