The ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$(p,n${)}^{40}$Sc reaction was studied at 134 MeV. Neutron energy spectra were measured by the time-of-flight technique with resolutions of 220 keV at angles from 0° to 41° and 415 keV out to 62°. The $2^{\mathrm{-}}$,$3^{\mathrm{-}}$,$4^{\mathrm{-}}$,$5^{\mathrm{-}}$ band of states based on the ($f_{7/2}$,$d_{3/2}^{\mathrm{-}1}$) 1p1h structure was observed at low excitation energies, in good agreement with known analog states in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{K}$. The shapes of the cross-section and analyzing-power angular distributions are in good agreement with distorted-wave impulse-approximation calculations using simple 1p1h (Tamm-Dancoff approximation) shell-model wave functions. A relatively strong transition to a state at $E_x$=2.3 MeV with L=3 is identified tentatively as a $4^{\mathrm{-}}$ state with the predominant 1p1h structure (1$f_{7/2}$,2$s_{1/2}^{\mathrm{-}1}$).

The excitation of the (T=1) $6^{\mathrm{-}}$ ($f_{7/2}$,$d_{5/2}^{\mathrm{-}1}$) stretched state is observed near $E_x$=7 MeV, fragmented over approximately 3 MeV. The normalization factor required to make a distorted-wave impulse-approximation calculation agree in magnitude with the $6^{\mathrm{-}}$ excitation is 0.35, which is larger than the normalization factor for this excitation in mass 28, analyzed in a similar manner. The L=1 giant resonance is observed to be centered near $E_x$=10 MeV with a width (full width at half maximum) of about 5 MeV, and a distorted-wave impulse-approximation normalization factor of 0.16. Two $1^{+}$ excitations are observed at $E_x$=2.7 and 4.3 MeV which indicate directly the presence of ground-state correlations in the ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ target. The fact that the analog of the higher $1^{+}$ excitation is not seen in inelastic electron scattering indicates strong interference between spin and orbital current contributions. The effect of ground-state correlations on the 1p1h wave functions was investigated by performing calculations which allowed multiparticle-multihole correlations in the $d_{3/2}$ and $f_{7/2}$ orbitals. The distorted-wave impulse-approximation normalization factors obtained with these wave functions were found to increase by a factor of about 2 relative to those obtained with ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ assumed to be a closed core.

• Received 11 February 1986

DOI:https://doi.org/10.1103/PhysRevC.34.80