The α${+}^{40}$Ca elastic scattering cross sections in the energy range from 29.0 to 61.0 MeV are shown to be well reproduced by the resonating-group method by introducing a phenomenological imaginary potential. The local potential equivalent to the nonlocal potential of the resonating-group method is found to be very close to the optical potential of Delbar et al. which fits the scattering data well in a wide energy range. Since the optical potential of Delbar et al. is the so-called unique optical potential which is free from the discrete ambiguity, this result means that the resonating-group method is powerful and reliable for the study of the internucleus interaction. By calculating the bound and quasibound level spectra by the same α${+}^{40}$Ca resonating-group method, it is found that the lowest positive parity rotational band is located near the observed ground rotational band of ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ti}$. In addition, when we use other effective two-nucleon forces so as to locate the calculated lowest $0^{+}$ state near the observed excited $0^{+}$ state with the excitation energy 8.54 or 11.2 MeV, which has large α strength, the fitting of the elastic scattering data by the resonating-group method is found to be very bad. These results force us to regard that the structure of the ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ti}$ ground band as containing a large amount of α${+}^{40}$Ca clustering component. However our present resonating-group method predicts the appearance of the negative parity rotational band with its bandhead $1^{\mathrm{-}}$ state below the excitation energy 10 MeV although there have been reported no such experimental indications at all of this.

• Received 2 May 1988

DOI:https://doi.org/10.1103/PhysRevC.38.2063