Whittaker asymptotics of shell-model wave functions for excited states of 13C

Abstract

Halo and skin structure of 1/2+, 3/2+, 5/2+ excited states of 13C nucleus is under investigation. The modified radial
functions have been constructed basing on the shell model functions. The matching procedure was performed
while using the corresponding Whittaker exponential-like asymptotics. To find the matching radius via the
oscillator parameter r0 three options were examined related to the experimental and theoretical data on the mean
square radii, and uncertainty relation. The renormalization of the modified functions shows the input of the
asymptotic region near 15-20%. The most qualitative effect is the redistribution of the probability density both
at short and long-range distances. The obtained functions are given as parametrization by Gauss basis. It is
proposed to confirm the observed halo and skin states of 13C via the impulse distributions measured with different
probing projectile like high-energy protons or α-particles. The most probable halo effect the 2S-state reveals due
to the node behavior of the corresponding radial wave function.