  Isomeric states in the nuclei along the rapid proton capture process path are
studied by the projected shell model. Emphasis is given to two waiting point
nuclei Se-68 and Kr-72 that are characterized by shape coexistence. Energy
surface calculations indicate that the ground state of these nuclei corresponds
to an oblate-deformed minimum, while the lowest state at the prolate-deformed
minimum can be considered as a shape isomer. Due to occupation of the orbitals
with large K-components, states built upon two-quasiparticle excitations at the
oblate-deformed minimum may form high $K$-isomers. The impact of the isomer
states on isotopic abundance in X-ray bursts is studied in a multi-mass-zone
X-ray burst model by assuming an upper-lower limit approach.
