Independent-Particle Model of the Nucleus. III. The Calcium Isotopes

Abstract

The isotopes of calcium of mass number 41, 42, and 43 are analyzed using the methods given in papers I and II of this series. It is found that the experimental data on ${\mathrm{Ca}}^{41}$ and ${\mathrm{Ca}}^{42}$ is sufficient to predict the low-lying odd-parity levels of ${\mathrm{Ca}}^{43}$ as well as the magnetic moment. Detailed agreement between theory and experiment is obtained for the levels of ${\mathrm{Ca}}^{43}$ of spin and parity $\frac{7}{{2}^{\ensuremath{-}}}$, $\frac{5}{{2}^{\ensuremath{-}}}$, $\frac{3}{{2}^{\ensuremath{-}}}$, and $\frac{9}{{2}^{\ensuremath{-}}}$ and the experimental Schmidt line magnetic moment deviation of 0.595 nm is in agreement with a predicted deviation of 0.60 nm. The relative importance of particle forces and surface forces due to collective motion is investigated and it is concluded that for the isotopes investigated the surface forces are so weak as to have a negligible effect on the level spacings. As a measure of the upper limit of the strength of the surface forces the magnitude of $\ensuremath{\hbar}\ensuremath{\omega}$ (the surfon energy) is set at \ensuremath{\gtrsim}15 Mev. An effective two-particle interaction potential is derived which differs to some extent from the two-particle scattering potential in that it has a longer range and is more shallow.