Selection Rules for $^{\mathrm{48}}$Cr

In the single j shell $^{\mathrm{48}}$Cr is the first even-even nucleus for which there are T$=$0 (isoscalar) J$=$1$^{\mathrm{+}}$ states and T$=$1 J$=$0$^{\mathrm{+}}$ states. These states are studied here. This nucleus, in the f$_{\mathrm{7/2}}$ model space, is mid-shell for both neutrons and protons and this leads to many selection rules. Even though seniority is a good quantum~number for identical particles in this shell this~is in~general not true for a system of both~neutrons and protons. Thus,~in $^{\mathrm{48}}$Cr neither the seniority of the neutrons, the protons or the total are good quantum numbers. However S$=$(-1)\textasciicircum ((v$_{\mathrm{p}}+$v$_{\mathrm{n}})$/2) is a good quantum number. Non-zero B(M1) require that S does not change, but for nonzero B(E2)'s~S must change sign. A scissors mode like excitation~involving both spin and orbit is identified.