Evidence of nonstatistical neutron emission following $\beta$ decay near doubly magic ${}^{132}\mathrm{Sn}$

Models of the $\beta$-delayed neutron emission ($\beta n$) assume that neutrons are emitted statistically via an intermediate compound nucleus post $\beta$ decay. Evidence to the contrary was found in an ${}^{134}\mathrm{In}\beta$-decay experiment carried out at ISOLDE CERN. Neutron emission probabilities from the unbound states in ${}^{134}\mathrm{Sn}$ to known low-lying, single-particle states in ${}^{133}\mathrm{Sn}$ were measured. The neutron energies were determined using the time-of-flight technique, and the subsequent decay of excited states in ${}^{133}\mathrm{Sn}$ was studied using $\gamma$-ray detectors. Individual $\beta n$ probabilities were determined by correlating the relative intensities and energies of neutrons and $\gamma$ rays. The experimental data disagree with the predictions of representative statistical models which are based upon the compound nucleus postulate. Our results suggest that violation of the compound nucleus assumption may occur in $\beta$-delayed neutron emission. This impacts the neutron-emission probabilities and other properties of nuclei participating in the $r$-process. A model of neutron emission, which links the observed neutron emission probabilities to nuclear shell effects, is proposed.

Figure 1

Schematic of ${}^{134}\mathrm{In}\beta n$ emission representing the $\beta$ decay to neutron unbound states in ${}^{134}\mathrm{Sn}$ and subsequent neutron emission to single-particle states in ${}^{133}\mathrm{Sn}$. As an example, the schematic is labeled assuming an initial ${}^{134}\mathrm{In}{J}^{\pi }=7^{-}$. Two different scenarios for neutron emission, statistical neutron emission, and direct neutron emission, are represented by boxes 2.a and 2.b, respectively.

Figure 2

Full TOF spectrum with analytical deconvolution given by red line with the underlying $\gamma$-ray background represented by the dashed black line. Individual neutron transitions are represented by the underlying curves. Color and dash schemes are related to the analysis process. The ground state neutron-emissions are marked with dark blue. Components of the ${}^{133}\mathrm{Sn}$ excited states are plotted in magenta. Additional responses are marked in light blue. See text for additional details.

Figure 3

$\gamma$-ray energies observed following a $\beta$ decay event (top). Neutron time-of-flight distribution in coincidence with the 854- (middle) and 1561-keV (bottom) $\gamma$ rays, which correspond to the de-excitations from the $3/2^{-}$ and $9/2^{-}$ excited states to the $7/2^{-}$ ground state in ${}^{133}\mathrm{Sn}$, respectively.

Figure 4

(a): Theoretical $B$(GT) values from LSSM calculations for $J^{\pi }=6^{-},7^{-}{}^{134}\mathrm{In}$ ground state spin and parity. B: Measured feeding intensities to excited states in ${}^{133}\mathrm{Sn}$, $I_{\beta }$, where the largest intensity has been normalized to unity. Column shading represents $I_{\beta n_i}$. The red rectangles reflect the uncertainty in intensity and energy for each point. (c), (d), (e): BeoH calculations of the relative neutron branching ratios to the $7/2^{-}$ (c), $3/2^{-}$ (d), and the $9/2^{-}$ (e) states in ${}^{133}\mathrm{Sn}$. Black data points in each panel are the experimentally determined neutron branching ratios.

Figure 5

A cumulative plot of calculated neutron branching ratios of $J^{\pi }=5^{-},6^{-},7^{-},8^{-}{}^{134}\mathrm{Sn}$ states as a function of excitation energy with the doorway interpretation using neutron $L=6$ emission from $0i_{13/2}$. The predictions of the Hauser-Feshbach model for a given spin are shown for comparison: solid blue line represents feeding to $7/2^{-}$ state and dashed blue line to $3/2^{-}$. The last two plots show average cumulative branching ratios expected in the Gamow-Teller decay for the ${}^{134}\mathrm{In}$ ground state spins of $J^{\pi }=6^{-}$ and $J^{\pi }=7^{-}$, respectively.

Figure 6

Same as Fig. 5, except that the doorway interpretation uses $L=4$ neutron emission from $1g_{9/2}$.