  In rapid-proton capture (rp-process), N=Z nuclei above Ni are understood to
act as waiting-point nuclei. The N=Z nuclei 68Se, 72Kr, 76Sr and 80Zr among
others are known to give rise to a large-energy x-ray flux and peaks in
abundances of these nuclei synthesized in the astrophysical rp-process.
Investigating the experimental isotope shifts in Kr isotopes near the proton
drip-line within the framework of the deformed Relativistic Hartree-Bogoliubov
theory, we have discovered that N=Z rp-process nuclei 68Se, 72Kr, 76Sr and 80Zr
exhibit large shell gap 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 doubly magic character to these nuclei. A significant
number of nuclei in this region are also shown to exhibit neutron magicity at
N=34, 36, 38, and 40 in the deformed space. A unique case of concomitance of
the double magicity and the shape-coexistence is found for 68Se.
