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Application of the extended P+QQ force model to $N \approx Z$ fp shell nuclei

To study collective motion, the extended pairing plus $QQ$ force model proposed recently is applied to $A$=46, 48 and 50 nuclei in the $fp$ shell region. Exact shell model calculations in the truncated model space $(f_{7/2},p_{3/2},p_{1/2})$ prove the usefulness of the interaction. The simple model with the pairing plus quadrupole pairing plus $QQ$ force and $J$-independent isoscalar proton-neutron force reproduces unexpectedly well observed binding energies, energy levels of collective (yrast) states and reduced $E2$ transition probabilities in $^{46}$Ti, $^{46}$V, $^{48}$V, $^{48}$Cr, $^{50}$Cr and $^{50}$Mn. The correspondence between theory and experiment is almost comparable to that attained by the full $fp$ shell model calculations with realistic effective interactions. Some predictions are made for energy levels and variations of $B(E2)$ in the yrast bands, in these nuclei. Characteristics of the interaction are investigated by comparing with the realistic effective interactions.