Proton radii of nuclei in the sd shell depart appreciably from the
asymptotic law, ρπ=ρ0A1/3. 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 s1/2 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 s1/2 orbit, the expectation value ⟨s1/2∣r2∣s1/2⟩ 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.Comment: 4 pages 6(7) figure