Internal conversion coefficients in ${}^{134}\mathrm{Cs}$, ${}^{137}\mathrm{Ba}$, and ${}^{139}\mathrm{La}$: A precise test of theory

Recently we measured the ratio of $K$-shell internal conversion coefficients, ${\alpha }_K$, for the 127.5-keV $E3$ transition in ${}^{134}\mathrm{Cs}$ and the 661.7-keV $M4$ transition in ${}^{137}\mathrm{Ba}$. We here report a measurement of the 165.9-keV $M1$ transition in ${}^{139}\mathrm{La}$, based on which we convert our earlier ratio measurement into individual ${\alpha }_K$ values for the transitions in ${}^{134}\mathrm{Cs}$ and ${}^{137}\mathrm{Ba}$. These results continue to confirm the Dirac-Fock calculations of internal conversion coefficients that incorporate the atomic $K$-shell vacancy.

Figure 1

Percentage differences between the measured and calculated ICCs for two Dirac-Fock calculations: one (top) is without the atomic vacancy and the other (bottom) is with it included in the “frozen orbital” approximation. The points shown as solid diamonds in both plots correspond to the 20 cases listed by Raman et al. [3] that have better than 2% precision; as indicated at the bottom, five are for $E2$ tranditions, three for $E3$, and the remainder are for $M4$ transitions. The points shown as open circles correspond to the more recently measured ${\alpha }_K$ value for ${}^{193}\mathrm{Ir}$ [5, 6].

Figure 2

Abbreviated decay scheme for the β decay of ${}^{139}\mathrm{Ba}$. The information is taken from Ref. [13]. Note that all known γ-ray transitions from the 15 excited states populated in β decay go directly to the ground or first-excited state of ${}^{139}\mathrm{La}$.

Figure 3

Spectra for the two energy regions of interest in the determination of the ${\alpha }_K$ ratio for the 165.9-keV transition in ${}^{139}\mathrm{La}$: (a) the lanthanum $K$ x rays and (b) the 165.9-keV γ ray.

Figure 4

Portion of the γ-ray energy spectrum T1.1, measured soon after the activation of source T1. Peaks are identified by their β-decay parent.

Figure 5

Decay rates for the lanthanum $K$ x rays and the 165.9-keV γ rays from both sources. The squares refer to source T1 and the triangles to T2; open symbols are for the γ ray, and solid ones for the x rays. The lines through the points are best fits to the data as described in the text. The zero of the time axis corresponds to the end of the neutron activation period. Note that the results from spectra taken at later times were consistent with zero and were not included in the plot area.

Figure 6

Same as Fig. 1, except that the two results from the present work, for ${}^{134}\mathrm{Cs}$ and ${}^{137}\mathrm{Ba}$, have been added as open circles. They both are seen to agree with the calculation that includes the atomic vacancy in the “frozen orbital” approximation. The previous values that were listed by Raman et al. [3] are shown in grey, slightly displaced.