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Alpha-Gamma Angular Correlation in Bi 212 (ThC)

1956; American Institute of Physics; Volume: 101; Issue: 2 Linguagem: Inglês

10.1103/physrev.101.717

1536-6065

John Wesley Horton,

Atomic and Subatomic Physics Research

The $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\gamma}$ angular correlation function, $W(\ensuremath{\theta})$, of the cascade ${\mathrm{Bi}}^{212}(\mathrm{ThC})\stackrel{\ensuremath{\alpha}(6.04 \mathrm{Mev})}{\ensuremath{\rightarrow}}{\mathrm{Tl}}^{208*}\stackrel{\ensuremath{\gamma}(40 \mathrm{kev})}{\ensuremath{\rightarrow}}{\mathrm{Tl}}^{208}(\mathrm{Th}{\mathrm{C}}^{\ensuremath{'}\ensuremath{'}})$ was determined by experiment to be consistent with a predicted law of the form $W(\ensuremath{\theta})=1+A{cos}^{2}\ensuremath{\theta}$. The ratio $\frac{W(90\ifmmode^\circ\else\textdegree\fi{})}{W(180\ifmmode^\circ\else\textdegree\fi{})}$ was measured to be 1.2993, \ifmmode\pm\else\textpm\fi{}0.0095 due to statistics, and \ifmmode\pm\else\textpm\fi{}0.010 due to experimental corrections. Comparison of this result with predictions of $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\gamma}$ angular correlation theory shows that ${\mathrm{Bi}}^{212}$ cannot have zero spin. Of fifty-four possibilities considered, it is shown that the following spin and parity assignments are most consistent with presently available experimental and theoretical evidence from several sources: the ground state of ${\mathrm{Bi}}^{212}$ is 1(-), the 40-kev state of ${\mathrm{Tl}}^{208}$ is 4(+), and the ground state of ${\mathrm{Tl}}^{208}$ is 5(+). These assignments determine the orbital momenta of $\ensuremath{\alpha}$ particles emitted in the decay of ${\mathrm{Bi}}^{212}$ to be a mixture of 3 and 5 units for the transition to the 40-kev state of ${\mathrm{Tl}}^{208}$ and to be 5 units for the transition to the ground state of ${\mathrm{Tl}}^{208}$. Using these values of orbital momenta in the Gamow theory, and in the Weisskopf-Devaney theory of $\ensuremath{\alpha}$ fine-structure, the theoretical ratios of decay probabilities for the two groups, $\frac{\ensuremath{\lambda}(40 \mathrm{kev})}{\ensuremath{\lambda}(0,)}$ are found to be in good agreement (10 to 50%) with the observed value. This agreement affords, in the case of ${\mathrm{Bi}}^{212}$, an explanation for the prohibited decay to the ground state relative to the first excited state found for many non-even-even nuclei by Perlman, Ghiorso, and ${\mathrm{Seaborg}.}^{1}$ Since the emission of the $\ensuremath{\alpha}$ particle with five units of orbital momentum hinders the decay ${\mathrm{Bi}}^{212}$ \ensuremath{\rightarrow} ${\mathrm{Tl}}^{208}$ (ground state) by a factor of 16, this helps to explain the unusual size of the "departure factor" (1000) given to this decay by Perlman et al.