Measurement of the isomer production ratio for the ${}^{112}\mathbf{Cd}(n,\gamma ){}^{113}\mathbf{Cd}$ reaction using neutron beams at J-PARC

The astrophysical origin of a rare isotope ${}^{115}\mathrm{Sn}$ remains an open question. An isomer ($T_{1/2}=14.1\mathrm{y}$) in ${}^{113}\mathrm{Cd}$ is an $s$-process branching point from which a nucleosynthesis flow reaches ${}^{115}\mathrm{Sn}$. The $s$-process abundance of ${}^{115}\mathrm{Sn}$ depends on the isomer production ratio in the ${}^{112}\mathrm{Cd}(n,\gamma ){}^{113}\mathrm{Cd}$ reaction. However, the ratio has not been measured in an energy region higher than the thermal energy. We have measured $\gamma$ rays following neutron capture reactions on ${}^{112}\mathrm{Cd}$ using two cluster high-purity germanium (HPGe) detectors in conjunction with a time-of-flight method at J-PARC. We have obtained the result that the relative $\gamma$-ray intensity ratio of the isomer is almost constant in an energy region of up to 5 keV. This result suggests that the $s$-process contribution to the solar abundance of ${}^{115}\mathrm{Sn}$ is minor. We have found that the ratio of a resonance at 737 eV is about 1.5 times higher than other ratios. This enhancement can be explained by a $p$-wave neutron capture. This result suggests measurements of decay $\gamma$ rays to isomers are effective to assign the spin and parity for neutron capture resonances.

Figure 1

Partial nuclear chart and nucleosynthesis flows around ${}^{113}\mathrm{Cd}$ and ${}^{115}\mathrm{Sn}$. Most isotopes are synthesized by the $s$ and $r$ processes. Neutron deficient isotopes are also produced by the $\gamma$ process. The isotopes of ${}^{112,114,115}\mathrm{Sn}$ locate outside of the main $s$-process flow and shielded against ${\beta }^{-}$ decay after the freeze-out of the $r$ process. The dashed line shows a weak path of the $s$ process from the ${}^{113}\mathrm{Cd}$ isomer to ${}^{115}\mathrm{Sn}$.

Figure 2

Schematic view of the ${}^{112}\mathrm{Cd}(n,\gamma ){}^{113}\mathrm{Cd}$ reaction. Low spin excited states in ${}^{113}\mathrm{Cd}$ are populated by neutron capture reactions on the $0^{+}$ ground state of ${}^{112}\mathrm{Cd}$. Each populated state decays away to the ground state or the isomer. The energy difference between the maximum $\gamma$ ray and the $\gamma$ ray decaying to the isomer is only 264 keV.

Figure 3

TOF spectra in the thermal energy region (a) and the energy region from eV to keV (b). The large peak at the thermal energy originate from the contamination of ${}^{113}\mathrm{Cd}$ to the enriched ${}^{112}\mathrm{Cd}$ target. The neutron capture resonance on ${}^{113}\mathrm{Cd}$ at 0.18 eV is also observed. In an energy region higher than the thermal energy, the resonances on ${}^{112}\mathrm{Cd}$ are clearly observed.

Figure 4

The $\gamma$-ray energy spectra measured by the two cluster type of HPGe detectors. (a) Gated spectrum by neutron energy of 66.8 eV. (b) Gated spectrum by neutron energy of 737 eV. The $\gamma$ rays decaying to the ground state of ${}^{112}\mathrm{Cd}$ are observed at 299 and 316 keV. The $\gamma$ ray to the isomer is also observed at 259 keV.

Figure 5

Partial level scheme of ${}^{113}\mathrm{Cd}$. There is the ground state with $J^{\pi }=1/2^{+}$ and the isomer with $J^{\pi }=11/2^{-}$. The branching ratio to the isomer depends on the spin and parity of states populated by neutron capture reactions. The solid arrows are the $\gamma$ transitions observed in the present experiment. The dashed arrows indicate unobserved $\gamma$ rays.

Figure 6

Measured $\gamma$-ray intensity ratios of 259 keV to the sum of 299 and 259 keV. These ratios are expected to be approximately proportional to the isomer production ratios. The ratios for the measured resonances are almost constant except the ratio at 737 eV. These resonances are assigned to the $s$-wave neutron capture resonances.

Figure 7

Calculated isomer production ratios following the ${}^{112}\mathrm{Cd}(n,\gamma ){}^{113}\mathrm{Cd}$ reaction. The ratio is almost constant in an energy region of $E<100$ eV. On the other hand, in an energy region of $E>100$ eV, the ratio increases with increasing neutron energy.

Figure 8

Calculated production ratio of 259 keV decay $\gamma$ ray to the summation of 259 and 299 keV from states with $J^{\pi }=1/2^{+}, 1/2^{-}, 3/2^{+}, 3/2^{-}$, and $5/2^{+}$ following the ${}^{112}\mathrm{Cd}(n,\gamma ){}^{113}\mathrm{Cd}$ reaction. The ratio from the state with $J^{\pi }=3/2^{-}$ is about 1.6 times larger than that with $J^{\pi }=1/2^{+}$.