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The effective interaction GXPF1 for shell-model calculations in the full $pf$shell is tested in detail from various viewpoints such as binding energies,electro-magnetic moments and transitions, and excitation spectra. Thesemi-magic structure is successfully described for $N$ or Z=28 nuclei,$^{53}$Mn, $^{54}$Fe, $^{55}$Co and $^{56,57,58,59}$Ni, suggesting theexistence of significant core-excitations in low-lying non-yrast states as wellas in high-spin yrast states. The results of $N=Z$ odd-odd nuclei, $^{54}$Coand $^{58}$Cu, also confirm the reliability of GXPF1 interaction in the isospindependent properties. Studies of shape coexistence suggest an advantage ofMonte Carlo Shell Model over conventional calculations in cases wherefull-space calculations still remain too large to be practical.Comment: 29pages, 26figures, to be published in Physical Review

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

New effective interaction for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mi>f</mml:mi></mml:mrow></mml:math>-shell nuclei and its implications for the stability of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>28</mml:mn></mml:mrow></mml:math>closed core

New effective interaction forpf-shell nuclei and its implications for the stability of theN=Z=28closed core