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Nuclear shape transition and oblate-prolate coexistence in $N=Z$ nuclei areinvestigated within the configuration space ($2p_{3/2}$, $1f_{5/2}$,$2p_{1/2}$, and $1g_{9/2}$). We perform shell model calculations for $^{60}$Zn,$^{64}$Ge, and $^{68}$Se and constrained Hartree-Fock (CHF) calculations for$^{60}$Zn, $^{64}$Ge, $^{68}$Se, and $^{72}$Kr, employing an effective pairingplus quadrupole residual interaction with monopole interactions. The shellmodel calculations reproduce well the experimental energy levels of thesenuclei. From the analysis of potential energy surface in the CHF calculations,we found shape transition from prolate to oblate deformation in these $N=Z$nuclei and oblate-prolate coexistence at $^{68}$Se. The ground state of$^{68}$Se has oblate shape, while the shape of $^{60}$Zn and $^{64}$Ge areprolate. It is shown that the isovector matrix elements between $f_{5/2}$ and$p_{1/2}$ orbits cause the oblate deformation for $^{68}$Se, and four-particlefour-hole ($4p-4h$) excitations are important for the oblate configuration.Comment: 6 pages, 5 figures, accepted for publication in Phys. Rev.

physical review. c. nuclear physics/physical review. c, nuclear physics

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Shape transition and oblate-prolate coexistence inN=Zfpg-shell nuclei