$\beta$-delayed neutron emissions from $N>50$ gallium isotopes

$\beta$-delayed $\gamma$-neutron spectroscopy has been performed on the decay of $A=84$ to 87 gallium isotopes at the RI-beam Factory at the RIKEN Nishina Center using a high-efficiency array of ${}^3\mathrm{He}$ neutron counters (BRIKEN). $\beta \text{−}2n\text{−}\gamma$ events were measured in the decays of all of the four isotopes for the first time, which is direct evidence for populating the excited states of two-neutron daughter nuclei. Detailed decay schemes with the $\gamma$ branching ratios were obtained for these isotopes, and the neutron emission probabilities ($P_{xn}$) were updated from the previous study. Hauser-Feshbach statistical model calculations were performed to understand the experimental branching ratios. We found that the $P_{1n}$ and $P_{2n}$ values are sensitive to the nuclear level densities of $1n$ daughter nuclei and showed that the statistical model reproduced the $P_{2n}/P_{1n}$ ratio better when experimental levels plus shell-model level densities fit by the Gilbert-Cameron formula were used as the level-density input. We also showed the neutron and $\gamma$ branching ratios are sensitive to the ground-state spin of the parent nucleus. Our statistical model analysis suggested $J\le 3$ for the unknown ground-state spin of the odd-odd nucleus ${}^{86}\mathrm{Ga}$, from the $I_{\gamma }(4^{+}\to 2^{+})/I_{\gamma }(2^{+}\to 0^{+})$ ratio of ${}^{84}\mathrm{Ga}$ and the $P_{2n}/P_{1n}$ ratio. These results show the necessity of detailed understanding of the decay scheme, including data from neutron spectroscopy, in addition to $\gamma$ measurements of the multineutron emitters.

Figure 1

Particle identification plot of the secondary beam at BigRIPS. The red ellipses indicate the gates applied to select each Ga ion. This plot shows the sum of the two different runs (see the text).

Figure 2

Comparison of the $\gamma$-ray intensities between this work ($I_{\gamma }$) and previous studies ($I_{\gamma \text{-ref}}$). The red circle shows the $\gamma$ rays in the decay of ${}^{77}\mathrm{Cu}$ previously reported by Sahin et al. [47] and the blue triangles are the ones from ${}^{85}\mathrm{Ga}$ decay by Miernik et al. [36].

Figure 3

The decay curves gated by neutron multiplicity 0, 1, and 2 for (a) ${}^{84}\mathrm{Ga}$ and (b) ${}^{85}\mathrm{Ga}$. The solid blue curves represent the fitting functions. The dashed red curves show the decay components of the precursor nuclei. The dashed-dotted green curves are the sums of the daughter decays, including neutron emission branches. The plots at the top right corners of each spectrum are the residuals of the decay spectra from the fitting function.

Figure 4

Neutron energy spectra expected in the decay of ${}^{86}\mathrm{Ga}$ predicted from the statistical model calculation using $B\left(\text{GT}\right)$ predicted by the shell model [34]. The red and blue histograms show the single-neutron energy spectra for $1n$ and $2n$ channels, respectively. The dashed orange curve shows the simulated neutron detection efficiency of the BRIKEN array [30] whose axis is on the right-hand side of the plot.

Figure 5

$\gamma$-ray energy spectra of ${}^{84}\mathrm{Ga}$ gated by neutron multiplicities. Green, red, and blue histograms show $\gamma$ rays observed with the neutron multiplicity equal to 0, 1, and 2, respectively. Histograms with a time window from 0 to 100 ms are drawn in lighter colors while the ones from 200 to 300 ms are drawn in darker colors and hatched in order to distinguish if the peaks originate in the parent ${}^{84}\mathrm{Ga}$ decay or from the decay of the descendant nuclei. Peaks that are distinct only in the lighter colors are regarded as the $\gamma$ rays from the decay of ${}^{84}\mathrm{Ga}$.

Figure 6

Level scheme of ${}^{82\text{–}84}\mathrm{Ge}$ populated in the $\beta$ decays of ${}^{84}\mathrm{Ga}$. Spin-parity assignments are from Refs. [56, 57, 58]. Intensities of the $\gamma$ transitions in square brackets are given per 100 ${}^{84}\mathrm{Ga}$ decays.

Figure 7

$\gamma$-ray energy spectra of ${}^{85}\mathrm{Ga}$ gated by neutron multiplicities. See the caption of Fig. 5 for details. A part of the $\gamma \text{−}\gamma$ coincidence spectrum gated by the 858-keV peak is shown in the $1n$ spectrum in the upper panel.

Figure 8

Level scheme of ${}^{83\text{–}85}\mathrm{Ge}$ populated in the $\beta$ decays of ${}^{85}\mathrm{Ga}$. Spin-parity assignments are from Refs. [56, 57, 60]. Intensities of the $\gamma$ transitions in square brackets are given per 100 ${}^{85}\mathrm{Ga}$ decays.

Figure 9

$\gamma$-ray energy spectra of ${}^{86}\mathrm{Ga}$ gated by neutron multiplicities.

Figure 10

Level scheme of ${}^{84\text{–}86}\mathrm{Ge}$ populated in the $\beta$ decays of ${}^{86}\mathrm{Ga}$. Spin-parity assignments are from Refs. [56, 60, 61]. Intensities of the $\gamma$ transitions in square brackets are given per 100 ${}^{86}\mathrm{Ga}$ decays.

Figure 11

$\gamma$-ray energy spectra of ${}^{87}\mathrm{Ga}$ gated by neutron multiplicities.

Figure 12

Delayed $\gamma$-ray energy spectrum from 600 ns to 3 $\mu \mathrm{s}$ after implantation of the ${}^{86}\mathrm{Ga}$ ion. The plot at the top right corner shows the decay curve of the 97.8 = keV $\gamma$ line.

Figure 13

$P_{0n}$ versus $T_{1/2}$ plot for the shell-model calculations on ${}^{86,87}\mathrm{Ga}$. The hatched areas in the plots represent the experimental error bars on those values.

Figure 14

Comparison of the default Gilbert-Cameron level densities in the statistical model and those from the shell-model calculation for ${}^{85}\mathrm{Ge}$.

Figure 15

Populations of the states excited by particle emission after the decay of ${}^{86}\mathrm{Ga}$ simulated by the statistical model. $J^{\pi }=2^{-}$ was assumed for the ground state of ${}^{86}\mathrm{Ga}$.

Figure 16

$P_{2n}/P_{1n}$ ratio in the decay of Ga isotopes. The red circle shows the experimental value while the blue-dashed and orange-solid lines show the shell-model predictions by using default and shell-model based parameters for the Gilbert-Cameron level densities, respectively.

Figure 17

Comparison of branching ratios calculated by the statistical model with the modified level densities with different assumptions on the unknown $J^{\pi }$ of the parent nucleus in the decay of ${}^{86}\mathrm{Ga}$. Only odd spins for positive and even spins for negative parity states are presented for the sake of clarity. The blue circles and red open circles show negative and positive parity states, respectively. (a) $\gamma$-ray intensity ratio between $4^{+}\to 2^{+}$ (805 keV) and $2^{+}\to 0^{+}$ (624 keV) transitions of the ${}^{84}\mathrm{Ge}$ nuclei in the $2n$ decay of ${}^{86}\mathrm{Ga}$. Since the $4^{+}$ decay $\gamma$ line was not observed, the experimental upper limit (see text for detail) is indicated by the red horizontal line. (b) $P_{2n}/P_{1n}$ ratio. The red line shows the experimental value with a grey error band.