Double magicity of N=Z nuclei near the rp-process path discerned

We have investigated the experimental isotope shifts in Kr nuclei near the proton drip-line within the framework of the deformed relativistic Hartree-Bogoliubov theory. In this work, we have attempted to answer the question as to why the charge radius of $^{72}$Kr shrinks significantly as against its expected swelling in approaching the proton drip line. It is shown that it happens due to the shell closure observed at N=Z=36 in deformed space, which compactifies the charge radius of $^{72}$Kr. Consequently, we have discerned that N=Z rp-process nuclei $^{68}$Se, $^{72}$Kr, $^{76}$Sr and$^{ 80}$Zr exhibit shell closures both at the proton and neutron numbers in the deformed space with the consequence that pairing correlations for protons and neutrons vanish. This lends a double magicity to these nuclei. Thus, N=Z rp-process waiting-point nuclei are shown to exhibit a magic character similar to that shown by the r-process waiting-point nuclei in the neutron-rich region. A significant number of nuclei in rp-process region are also shown to exhibit neutron magicity at N= 34, 36, 38, and 40 in the deformed space.