Angular Distribution of Gamma Rays from Coulomb Excitation

The angular distributions of gamma rays with respect to the incident proton beam on a thick target have been measured for gamma rays following Coulomb excitation in ${\mathrm{Pt}}^{194,196}$, ${\mathrm{Au}}^{197}$, ${\mathrm{Ta}}^{181}$, ${\mathrm{Ag}}^{107,109}$, ${\mathrm{Pd}}^{106}$, ${\mathrm{Pd}}^{108}$, ${\mathrm{Pd}}^{110}$, and ${\mathrm{Rh}}^{103}$. The observed angular distributions deviate considerably from the semiclassical theory of angular distributions of gamma rays following Coulomb excitation given by Alder and Winther. Empirical curves of energy-dependent coefficients $a_{\nu }\left(\xi \right)$ for a thick target are obtained from the results for ${\mathrm{Pt}}^{194,196}$ and ${\mathrm{Pd}}^{106}$. With these empirical coefficients, information on the spin sequences and the character of the gamma transitions are deduced from the angular distribution measurements in the odd mass nuclei. The spin sequences are as follows: $\frac{7}{2}\mathrm{}\left(E2\mathrm{}\right)\mathrm{}\frac{3}{2}$ and $\frac{5}{2}\mathrm{}(E2+M1\mathrm{})\mathrm{}\frac{3}{2}$ with ${\delta }_{\gamma }=-0.75\mathrm{}$ (where ${{\delta }_{\gamma }}^2=\frac{E2\mathrm{}}{M1\mathrm{}}$) for the 550- and 277-kev transitions, respectively, in ${\mathrm{Au}}^{197}$; $\frac{11}{2}\mathrm{}\left(E2\mathrm{}\right)\mathrm{}\frac{7}{2}$ and $\frac{11}{2}\mathrm{}(E2+M1\mathrm{})\mathrm{}\frac{9}{2}$ with ${\delta }_{\gamma }=0.51\mathrm{}$ for the 303- and 166-kev transitions, respectively, in ${\mathrm{Ta}}^{181}$; $\frac{5}{2}\mathrm{}\left(E2\mathrm{}\right)\mathrm{}\frac{1}{2}$ and $\frac{3}{2}\mathrm{}(E2+M1\mathrm{})\mathrm{}\frac{1}{2}$ with ${\delta }_{\gamma }=-0.19\mathrm{} or -1.14\mathrm{}$ for the 427- and 325-kev transitions, respectively, in ${\mathrm{Ag}}^{107,109}$; and $\frac{5}{2}\mathrm{}\left(E2\mathrm{}\right)\mathrm{}\frac{1}{2}$ and $\frac{3}{2}\mathrm{}(E2+M1\mathrm{})\mathrm{}\frac{1}{2}$ with ${\delta }_{\gamma }=-0.18\mathrm{} or -1.17\mathrm{}$ for the 365- and 305-kev transitions, respectively, in ${\mathrm{Rh}}^{103}$.