Detailed spectroscopy of ${}^{110}$Cd: Evidence for weak mixing and the emergence of $\gamma$-soft behavior

A study of the ${\beta }^{+}$-electron capture decay of ${}^{110}$In into levels of ${}^{110}$Cd is combined with a reanalysis of data from a previous study of ${}^{110}$Cd with the $(n,n^{\prime }\gamma )$ reaction with monoenergetic neutrons. The $\gamma \gamma$ coincidences from the ${}^{110}$In decay leads to many new assignments of $\gamma$ rays observed in the $(n,n^{\prime }\gamma )$ reaction, permitting the observation of weak low-energy transitions, and setting stringent upper limits on unobserved decay branches. The uncertainties on many of the lifetimes from the $(n,n^{\prime }\gamma )$ reaction are significantly reduced, and limits are established for the lifetimes of levels too long for a direct measurement. The absence of enhanced transitions between the previously assigned phonon states and the deformed intruder states strongly suggests that mixing between the configurations is generally weak, refuting the strong-mixing scenario as an explanation of the decay pattern of the excited $0^{+}$ states in ${}^{110}$Cd. The decay pattern of the nonintruder states is suggestive of a $\gamma$-soft rotor, or O(6) nucleus, rather than a vibrational, or U(5), pattern. The existence of a four-particle–six-hole proton excitation in ${}^{110}$Cd is also suggested.

Figure 1

Portion of the level schemes for ${}^{110,112,114,116}$Cd showing the decays from the low-lying $0^{+}$ states. The observed transitions between levels are indicated by arrows with widths proportional to the $B\left(E2\right)$ values and are labeled with the absolute $B\left(E2\right)$ values or limits, with the uncertainties in parentheses. Data are taken from Ref. [8] and the present results for ${}^{110}$Cd.

Figure 2

Portion of the low-lying level scheme for ${}^{110}$Cd. The observed transitions between levels are indicated by arrows with widths proportional to $B\left(E2\right)$ values. The levels on the right side of the figure are assigned as members of the deformed intruder band based on a 2p-4h proton excitation [5, 6, 23, 24]. The 1731-, 1475-, and 1542-keV levels were previously assigned as the $0^{+}$, $2^{+}$, and $4^{+}$ two-phonon triplet and the 2079-keV ($0_4^{+}$), 2356-keV ($2_5^{+}$), 2163-keV ($3_1^{+}$), 2220-keV ($4_2^{+}$), and 2480-keV ($6_1^{+}$) levels as members of the three-phonon quintuplet [3, 18, 19, 24, 25].

Figure 3

Portions of the $\gamma$-ray spectrum obtained by summing the excitation function spectra obtained with the $(n,n^{\prime }\gamma )$ reaction for neutron energies from 2.5 to 2.8 MeV and subtracting a 2.4-MeV spectrum normalized to the total number of neutrons for the 2.5–2.8 MeV data. The peaks of interest are labeled by their energies in keV. The top panel (a) displays the region around the newly placed 880-keV $2_5^{+}\to 2_2^{+}$ $\gamma$ ray, whereas the bottom panel (b) displays the 624-keV $2_5^{+}\to 0_3^{+}$ $\gamma$ ray and the position of a hypothetical peak corresponding to a 572-keV $2_5^{+}\to 2_3^{+}\left(i\right)$ transition.

Figure 4

Portion of the $\gamma$-ray coincidence spectrum from the ${}^{110}$In decay obtained by placing a gate on the 641-keV $\gamma$ ray that feeds the 2480-keV $6_1^{+}$ state. The peaks are labeled by their energies in keV. The inset shows the expanded region near the 229-keV $6_1^{+}\to 4_3^{+}\left(i\right)$ $\gamma$ ray that leads to its firm assignment with a branching fraction of $5.1\left(3\right)\times {10}^{-4}$.

Figure 5

Portion of the spectrum of $\gamma$ rays in coincidence with the 815-keV $0_2^{+}\left(i\right)\to 2_1^{+}$ $\gamma$ ray, and the angular distribution data from the $(n,n^{\prime }\gamma )$ reaction at $E_n=2.6$ MeV. The top panel (a) displays the coincidence of the 310.5-keV $2_3^{+}\left(i\right)\to 0_2^{+}\left(i\right)$ $\gamma$ ray, leading to a measured branching fraction of $0.0037\pm 0.0004$, confirming the 1783-keV level as the $2^{+}$ rotational band member of the deformed intruder band based on the 1473-keV $0_2^{+}\left(i\right)$ state. (b) Singles spectrum obtained by the summation of spectra taken at 12 angles from ${30}^{\circ }$ to ${152}^{\circ }$. The 310.5-keV $\gamma$ ray is clearly visible, with only weak evidence of a peak at the location of a 307.8-keV $\gamma$ ray. This location corresponds to that of a transition from the 1783-keV level feeding the 1475-keV $2_2^{+}$ level; an upper limit for the branching fraction of $<9\times {10}^{-4}$ is established.

Figure 6

Portion of the $\gamma$-ray spectrum in coincidence with the 1397-keV $\gamma$ ray decaying from a $I=1$ level at 3475 keV to the 2079-keV $0_4^{+}$ level. The $\gamma$ rays are labeled by their energies in keV. Of note are the relative intensities of the 295- and 1421-keV $\gamma$ rays. The position of a hypothetical 603-keV $0_4^{+}\to 2_2^{+}$ $\gamma$ ray is indicated.