Measurements of Static Quadrupole Moment of the First Excited $2^{+}$ States of the Nuclei ${\mathrm{Pd}}^{106}$ and ${\mathrm{Pd}}^{110}$ by Heavy-Ion Coulomb Excitation

The static quadrupole moments of the 511.7-keV $2^{+}$ state in ${\mathrm{Pd}}^{106}$ and the 373.8-keV $2^{+}$ state in ${\mathrm{Pd}}^{110}$ have been determined by employing Coulomb-excitation techniques. Foils (∼175 μg/${\mathrm{cm}}^2$) of separated Pd isotopes were bombarded with 25- and 30-MeV ${\mathrm{O}}^{16}$ ions and 55- and 56-MeV ${\mathrm{S}}^{32}$ ions from the Purdue University and Argonne National Laboratory tandem accelerators. The angular distributions of the inelastically scattered ions were measured in coincidence with the deexcitation $\gamma$ rays to determine the relative excitation probabilities. The experimental data were fitted using the Winther-de Boer multiple-Coulomb-excitation program so that the sign and magnitude of the static quadrupole moment could be extracted. The effect of higher excited states on the excitation probability of the $2^{+}$ state has been calculated using the matrix elements determined by Robinson et al. and the Winther-de Boer program. Self-consistency of the oxygen and sulfur data suggests that the excitation via the second $2^{+}$ state interferes constructively so as to increase the excitation probability. With this choice for the interference via the second $2^{+}$ state, the values of the static quadrupole moments are $Q_{22}=-0.458\mathrm{}\pm 0.059$ b for ${\mathrm{Pd}}^{106}$ and $Q_{22}=-0.483\mathrm{}\pm 0.049$ b for ${\mathrm{Pd}}^{110}$. If the excitation via the second $2^{+}$ state interferes destructively, the values of the static quadrupole moments are $Q_{22}=-0.282\mathrm{}\pm 0.059$ b for ${\mathrm{Pd}}^{106}$ and $Q_{22}=-0.266\mathrm{}\pm 0.049$ b for ${\mathrm{Pd}}^{110}$.