Studies on the Shapes ofSi28,S32, andAr36via Deuteron Scattering

Deuteron elastic and inelastic scattering on ${}_{14}{}^{}{}_{}{}^{}\mathrm{Si}_{14}^{28}{}_{}{}^{}$, ${}_{16}{}^{}{}_{}{}^{}\mathrm{S}_{16}^{32}{}_{}{}^{}$, and ${}_{18}{}^{}{}_{}{}^{}\mathrm{Ar}_{18}^{36}{}_{}{}^{}$ was studied with an 18-MeV deuteron beam from the Yale MP tandem Van de Graaff accelerator. Optical-model and distorted-wave Born-approximation analyses of the experimental angular distributions were performed. The deformation parameters $\left|{\beta }_2\right|$ and $\left|{\beta }_3\right|$, extracted in this manner, are in accord with the corresponding parameters extracted from electromagnetic deexcitation lifetimes in those cases where the electromagnetic lifetimes of the states involved in the inelastic scattering have been measured. The experimental angular distributions were also analyzed through a coupled-channel approach. This method of analysis permitted extraction of more complete spectroscopic information concerning the nuclei under study, namely, the even-even $N=Z$ nuclei in the second half of the $2s-1d$ shell. The conclusions drawn regarding ${\mathrm{Si}}^{28}$ from the present work are not definite; however, the indications are that ${\mathrm{Si}}^{28}$ has an oblate static deformation, with excited states comprising a $K=0\mathrm{}$ rotational band based on the ground state. The strong octupole vibration (the 6.88-MeV $3^{-}$ level) in ${\mathrm{Si}}^{28}$ is to some degree in contradiction with this conclusion. In the case of ${\mathrm{S}}^{32}$, the results of the coupled-channel calculations indicate that the levels of ${\mathrm{S}}^{32}$ up to an excitation energy of 5 MeV are well explained on the assumption that ${\mathrm{S}}^{32}$ is an almost spherical vibrational nucleus. The results for ${\mathrm{Ar}}^{36}$ are quite similar to those for ${\mathrm{S}}^{32}$; however, the data are unfortunately less clear, since a number of the most important levels appear in the experimental spectrum as unresolved doublets. Spherical shell-model calculations have been found to be in excellent accord with the spectroscopic factors measured in this laboratory for deuteron-induced stripping and pickup reactions on these nuclei. These data, together with extensive spectroscopic measurements here and elsewhere on lighter-mass nuclei in the $s-d$ shell, suggest that in moving into the shell from ${\mathrm{O}}^{16}$ a pronounced static prolate deformation develops rapidly, reaching its maximum in the vicinity of $A=21-23\mathrm{}$; subsequently, this deformation is reduced, and in the vicinity of $A=28\mathrm{}$ it reverses sign to yield a weak, poorly stabilized oblate shape, which by $A=32\mathrm{}$ has returned to a spherical equilibrium configuration which is retained to the end of the shell. These experimental findings are not reproduced by the simplest Hartree-Fock calculations, which predict a more pronounced oblate deformation in the upper half of the shell.