J=0+States inCa40andCa42

Abstract

An attempt has been made to understand the low-lying spectra of $0^{+}$ states in ${\mathrm{Ca}}^{40}$ and ${\mathrm{Ca}}^{42}$, without having to introduce configurations with a very high number of holes. The analysis of ${\mathrm{Ca}}^{40}$ includes 0p-0h, 2p-2h, and 4p-4h configurations, with the particles and holes restricted to the $1f_{\frac{7}{2}}$ and $1d_{\frac{3}{2}}$ orbitals, respectively. The effects of higher orbitals are simulated by lowering the $1f_{\frac{7}{2}}-1\mathrm{}{d}_{\frac{3}{2}}$ single-particle splitting. The model reproduces all the known $0^{+}$ levels in ${\mathrm{Ca}}^{40}$ with remarkable accuracy. The calculation in ${\mathrm{Ca}}^{42}$ includes only the 2p-0h and 4p-2h configurations, and the same matrix elements used in the analysis of ${\mathrm{Ca}}^{40}$. Again all the known $0^{+}$ states are reproduced, including the group between 5.85 and 6.70 MeV. These states are predominantly of 4p-2h nature, with the four particles coupled to their maximum possible isospin.