Nuclear structure of calcium isotopes from inelasticαscattering

Angular distributions were measured for elastic and inelastic $\alpha$ scattering from ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ at 24.0, 28.5, and 31.0 MeV, from ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$ at 24.0 MeV and from ${}_{}{}^{43,44}{}_{}{}^{}\mathrm{Ca}$ at 25.5 MeV. Analyses in terms of distorted-wave Born-approximation and coupled-channel theory, employing a vibrational collective model form factor, yield inelastic transition strengths, and many new spin and parity assignments or restrictions for levels in ${}_{}{}^{40,41,43,44}{}_{}{}^{}\mathrm{Ca}$. The inelastic multipole transition strengths are in excellent agreement with known electromagnetic strengths. Quadrupole strengths are interpreted in terms of the coexistence model. The data imply that the ground-state excited-core admixtures to ${\left(fp\right)}^n$ spherical configurations are 4% in ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$, 10% in ${}_{}{}^{40,41}{}_{}{}^{}\mathrm{Ca}$, 14% in ${}_{}{}^{43}{}_{}{}^{}\mathrm{Ca}$, and 30% in ${}_{}{}^{42,44}{}_{}{}^{}\mathrm{Ca}$. The octupole inelastic strength is strong and mainly localized in the lowest $3^{-}$ state in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, but becomes more fractionated and weaker with addition of neutrons and exhibits in ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$ characteristic weak-coupling fragmentation of the lowest $3^{-}$ state in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. These results are consistent with previous observations that the structure of the ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$ ground state is with high purity a $1f_{\frac{7}{2}}$ neutron coupled to the ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ ground state.