Deformation of the proton emitter ${}^{113}\mathbf{Cs}$ from electromagnetic transition and proton-emission rates

The lifetime of the $\left(11/2^{+}\right)$ state in the band above the proton-emitting $\left(3/2^{+}\right)$ state in ${}^{113}\mathrm{Cs}$ has been measured to be $\tau =24\left(6\right)$ ps from a recoil-decay-tagged differential-plunger experiment. The measured lifetime was used to deduce the deformation of the states using wave functions from a nonadiabatic quasiparticle model to independently calculate both proton-emission and electromagnetic $\gamma$-ray transition rates as a function of deformation. The only quadrupole deformation, which was able to reproduce the experimental excitation energies of the states, the electromagnetic decay rate of the $\left(11/2^{+}\right)$ state and the proton-emission rate of the $\left(3/2^{+}\right)$ state, was found to be ${\beta }_2=0.22\left(6\right)$. This deformation is in agreement with the earlier proton emission studies which concluded that ${}^{113}\mathrm{Cs}$ was best described as a deformed proton emitter, however, it is now more firmly supported by the present measurement of the electromagnetic transition rate.

Figure 1

(a) Two-dimensional histogram of DSSD energy versus time for decay events in anticoincidence with an MWPC signal. The area contained within the red line in (a) was used as the two-dimensional RDT gate for ${}^{113}\mathrm{Cs}$ in this work. (b) The one-dimensional total energy projection of the two-dimensional histogram. Proton decays are identified from ${}^{113}\mathrm{Cs}$ [11], ${}^{109}\mathrm{I}$ (813(4)-keV, $T_{1/2}\sim 100\mu \mathrm{s}$ [31]), ${}^{112}\mathrm{Cs}$ (807(7)-keV, $T_{1/2}\sim 500\mu \mathrm{s}$ [30]) and internal conversion electrons from the $T_{1/2}=6.9\left(3\right)-\mu \mathrm{s}$ isomer decay in ${}^{113}\mathrm{Xe}$ [32]. The inset to (b) shows the number of events within the ${}^{113}\mathrm{Cs}$ two-dimensional RDT gate as a function of time, demonstrating the 16.9(1) $\mu \mathrm{s}{}^{113}\mathrm{Cs}$ proton-decay half-life.

Figure 2

A partial level scheme of ${}^{113}\mathrm{Cs}$ showing the lower energy states of rotational bands 1 and 2 [11]. The width of each $\gamma$-ray transition arrow represents its relative intensity with the white part representing the internal-conversion component. The RDDS analysis was performed using the 384-keV, $(11/2^{+})$ to $(7/2^{+})$ transition in band 1.

Figure 3

${}^{113}\mathrm{Cs}$ proton-tagged fully Doppler-corrected Ring $2 \left(\theta ={134}^{\circ }\right)$ JUROGAM-II spectra. (a) A summed spectrum containing events from measurements made at all the distances. The inset is focused on the 384- and 389-keV peaks corresponding to the respective fully shifted and degraded components of the transition from the $\left(11/2^{+}\right)$ state. (b)–(g) Spectra corresponding to individual target-to-degrader distances, focused on the 384-keV [(b)–(e)] and 596-keV [(f) and (g)] $\gamma$-ray transitions from the $\left(11/2^{+}\right)$ and $\left(15/2^{+}\right)$ states in band 1. Gaussian fits to the fully shifted (red or purple) components and degraded (green or cyan) components are shown as well as the fully shifted component of the 610-keV transition from band 2 (orange).

Figure 4

Lifetime analysis for the $\left(11/2^{+}\right)$ state in ${}^{113}\mathrm{Cs}$ based on the DDCM. (a) shows the 24(6)-ps lifetime of the $\left(11/2^{+}\right)$ state. This lifetime was calculated from a weighted average of the individual ${\tau }_i\left(x\right)$, corresponding to distances, $x$, of 135, 210, and $300 \mu \mathrm{m}$ in the region of sensitivity. (b) shows the variation of the normalized intensity, $Q_{ij}^s$, of the fully shifted component of the 384-keV transition which depopulates the $\left(11/2^{+}\right)$ state as a function of distance. (c) shows the difference in fully shifted intensity as a function of distance between the $\left(11/2^{+}\right)$ component and the $\left(15/2^{+}\right)$ component multiplied by the side feeding parameter $\alpha$. In (b) and (c), the piece-wise polynomial fit used to extract the lifetime in the DDCM are shown by the solid lines, as discussed in the text.

Figure 5

Relative excitation energy of the states in Band 1 of ${}^{113}\mathrm{Cs}$ as a function of quadrupole deformation. Solid lines represent the experimental values and dashed lines the theoretical predictions.

Figure 6

Predicted excited-state lifetimes (a) $\left(11/2^{+}\right)$ and (b) $\left(15/2^{+}\right)$ as a function of quadrupole deformation in ${}^{113}\mathrm{Cs}$ employing the quasiparticle wave functions that have been used to calculate the proton-emission half-life in Fig. 7 (see later). The experimental lifetime of the $\left(11/2^{+}\right)$ state and its uncertainty are denoted by the red and dashed lines in (a). The $\tau <5$ ps limit for the $\left(15/2^{+}\right)$ state is denoted by the dashed line in (b), as discussed in the text. At deformations ${\beta }_2>0.25$ in the calculation, Band 1 is crossed by another configuration based on the $\left[404\right]9/2$ level, beyond which the lifetime is no longer reflective of the underlying configuration of Band 1.

Figure 7

Theoretical proton emission half-life as a function of quadrupole deformation for the low-spin states in ${}^{113}\mathrm{Cs}$ using the non-adiabatic quasiparticle wave functions [17]. Also shown is the 16.9(1)-$\mu \mathrm{s}$ experimental value from this work which only overlaps with the calculated half-life of the $\left(3/2^{+}\right)$ state.