Nuclear Structure ofCa40,42,44,48from Inelastic Alpha-Particle Scattering

The ($\alpha ,{\alpha }^{\prime }$) reaction has been studied on ${\mathrm{Ca}}^{40,42,44,48}$ at 31-MeV incident energy with approximately 90-keV resolution and high statistics. Spin and parity assignments have been made on the basis of systematics and comparison with the distorted-wave Born approximation. Levels of a given spin and parity show remarkably similar angular distributions, even though they vary widely in magnitude. This indicates experimentally that because of the strong absorption of $\alpha$ particles, the shape of the differential cross section implies the spin and parity of the excited level, and the magnitude indicates the transition strength. The energy levels, spin and parity assignments, and transition strengths found in this experiment are compared with previous experiments and with theoretical results. Two $4^{+}$ states, which may be core excitations, have been found in ${\mathrm{Ca}}^{40,42,48}$ between 6- and 8.5-MeV excitation energy with an equivalent electromagnetic strength of approximately 0.5 to 3 single-particle units. Three octupole states have been found in ${\mathrm{Ca}}^{40,48}$, six octupole states in ${\mathrm{Ca}}^{42,44}$, a $5^{-}$ state in ${\mathrm{Ca}}^{40,42,48}$, and two $5^{-}$ states in ${\mathrm{Ca}}^{44}$. The fractionization of the $3^{-}$ strength and the rapid and similar drop of the $3^{-}$ and $5^{-}$ strength in going from ${\mathrm{Ca}}^{40}$ to ${\mathrm{Ca}}^{44}$ appear to be a challenge to current ideas about the nature of these states.