γ-ray multipolarimetry between low-spin states of ${}^{136}\mathrm{Ce}$: Search for the $2_{1,\mathrm{ms}}^{+}$ one-phonon mixed-symmetry state

An experiment was performed on ${}^{136}\mathrm{Ce}$ to measure $E2/M1$ multipole mixing ratios using the method of $\gamma \gamma$ angular correlations. The low-spin states of interest were populated by β decay from the $2^{+}$ ground state of ${}^{136}\mathrm{Pr}$ that has a half-life of 13.1 min. Emitted γ rays were detected with the Stony Brook cube germanium detector array. Five $E2/M1$ multipole mixing ratios were measured for the first time and two spin and parity quantum numbers were assigned. Candidates for the $2_{1,\mathrm{ms}}^{+}$ state of ${}^{136}\mathrm{Ce}$ were identified from large $M1$ fractions in the $E2/M1$ multipole mixing ratios. The $2_{1,\mathrm{ms}}^{+}$ state is suggested to be fragmented between the closely lying $2_3^{+}$ and $2_4^{+}$ states. A two state mixing scenario is employed for deducing an $F$-spin mixing matrix element of 43(5) keV.

Figure 1

The γ-ray spectrum observed from the ${}^{136}\mathrm{Pr}$ β decay. Displayed is the lower energy portion of the $\gamma \gamma$ coincidence matrix projection observed with Ge detectors at a relative angle of ${90}^{°}$ (Group 1).

Figure 2

The γ-ray spectrum observed from the ${}^{136}\mathrm{Pr}$ β decay. Displayed is one energy region of interest in the coincidence spectrum gated on the 552-keV ($2_1^{+}\to 0_1^{+}$) transition for Ge detectors at a relative angle of ${90}^{°}$ (Group 1).

Figure 3

Partial level scheme for ${}^{136}\mathrm{Ce}$ showing relevant low-spin states populated by β decay and the transitions for which angular correlation analysis could be done.

Figure 4

Angular correlation functions fitted to data for 3-2-0, 2-2-0, and 1-2-0 spin hypotheses with the $E2/M1$ multipole mixing ratio for the preceding transition, ${\delta }_1$, treated as a free parameter in each case.

Figure 5

The theoretical ellipses for the $a_2$ and $a_4$ angular correlation coefficients plotted parametrically as functions of ${\delta }_1$ for quadrupole-dipole mixing are shown along with the data (filled circles) for the (552–540)-, (552–1515)-, (552–1603)-, (461–1092)-, and (1001–552)-keV cascades. Values of ${\delta }_1$ on the ellipses are denoted with open circles.

Figure 6

Comparison of energy levels in Ce isotopes. The larger lines represent the candidates for the fragmented $2_{1,\mathrm{ms}}^{+}$ state in ${}^{136}\mathrm{Ce}$ and the fragmented $2_{1,\mathrm{ms}}^{+}$ state in ${}^{138}\mathrm{Ce}$.

Figure 7

Comparison of the low-energy level schemes of the $N=78$ isotones, ${}^{134}\mathrm{Ba}$ and ${}^{136}\mathrm{Ce}$. The larger lines represent the fragmented $2_{1,\mathrm{ms}}^{+}$ state of ${}^{134}\mathrm{Ba}$ and the proposed candidates for the fragmented $2_{1,\mathrm{ms}}^{+}$ state of ${}^{136}\mathrm{Ce}$.

Figure 8

Schematic of a two-state mixing scenario for the $2_{1,\mathrm{ms}}^{+}$ mixed-symmetry state and a $2_f^{+}$ fully-symmetric state.