Single-Particle and Collective Motion for Proton-Rich Nuclei on the Astrophysical rp-Process Path

Based on available experimental data, a new set of Nilsson parameters is proposed for proton-rich nuclei with proton or neutron numbers $28\leq N\leq 40$. The resulting single-particle spectra are compared with those from relativistic and non-relativistic mean field theories. Collective excitations in some even--even proton-rich nuclei in the upper $pf$ shell are investigated using the Projected Shell Model with the new Nilsson basis. It is found that the regular bands are sharply disturbed by band crossings involving $1g_{9/2}$ neutrons and protons. Physical quantities for exploring the nature of the band disturbance and the role of the $1g_{9/2}$ single-particle are predicted, which may be tested by new experiments with radioactive beams.