Isotopic shifts in light Kr nuclei and evidence of N=36 magicity near the rp-process path

Neutron-deficient Kr isotopes play an important role in the rp- process nucleosynthesis.\footnote{H. Schatz et al., Phys. Rep. 294 (1998) 167.} The isotope $^{72}$Kr has been described variously as a waiting-point nucleus. We have examined the experimental data on isotopic shifts in light Kr nuclei close to the proton drip line within the framework of the relativistic mean-field theory. Using the Lagrangian model with the vector self-coupling of $\omega$ meson,\footnote{M.M. Sharma, A.R. Farhan, S. Mythili, Phys. Rev. C61 (2000) 054306.} it is shown that $^{72}$Kr is oblate in its ground-state, which exhibits a shape-coexistence with a prolate shape. It is shown that the negative isotopic shift for $^{72}$Kr provides an evidence for a neutron shell closure at $N=36$. This is affirmed by the presence of a shell gap in the single-particle spectrum in the deformed space. This lends credence to the isotope $^{72}$Kr as being a waiting-point nucleus in the rp-process path.