Systematics of ground-state quadrupole moments of odd-Adeformed nuclei determined with muonicMx rays

Abstract

The ground-state quadrupole moments of $^{151}\mathrm{Eu}$, $^{153}\mathrm{Eu}$, $^{159}\mathrm{Tb}$, $^{163}\mathrm{Dy}$, $^{167}\mathrm{Er}$, $^{177}\mathrm{Hf}$, $^{179}\mathrm{Hf}$, $^{191}\mathrm{Ir}$, and $^{193}\mathrm{Ir}$ were determined by measuring the quadrupole hyperfine-splitting energies of muonic $M$ x rays. The results are $Q=0.903(10)e$ b for $^{151}\mathrm{Eu}$, $Q=2.412(21) e$ b for $^{153}\mathrm{Eu}$, $Q=1.432(8) e$ b for $^{159}\mathrm{Tb}$, $Q=2.648(21) e$ b for $^{163}\mathrm{Dy}$, $Q=3,565(29) e$ b for $^{167}\mathrm{Er}$, $Q=3.365(29) e$ b for $^{177}\mathrm{Hf}$, $Q=3.793(33) e$ b for $^{179}\mathrm{Hf}$, $Q=0.816(9) e$ b for $^{191}\mathrm{Ir}$, and $Q=0.751(9) e$ b for $^{193}\mathrm{Ir}$. The present quadrupole moments, compared with values obtained from electronic-atom hyperfine measurements, show that the Sternheimer correction factors used in the rare-earth electronic-atom analysis are unreliable. Systematics of deformation parameters ${\ensuremath{\beta}}_{2}$ calculated from the present quadrupole moments for odd-$A$ nuclei, and from $B(E2)$ values of Coulomb excitation measurements for even-$A$ nuclei, also indicate that the largest deformation change so far known exists between $^{151}\mathrm{Eu}$ and $^{153}\mathrm{Eu}$. Except at the onset of nuclear deformation, the deformation parameters of the odd-$A$ nuclei are quite consistent with those of the even-$A$ neighbors.