Gamma Decay of Unbound Neutron-Hole States in ${}^{133}\mathrm{Sn}$

Excited states in the nucleus ${}^{133}\mathrm{Sn}$, with one neutron outside the double magic ${}^{132}\mathrm{Sn}$ core, were populated following one-neutron knockout from a ${}^{134}\mathrm{Sn}$ beam on a carbon target at relativistic energies at the Radioactive Isotope Beam Factory at RIKEN. Besides the $\gamma$ rays emitted in the decay of the known neutron single-particle states in ${}^{133}\mathrm{Sn}$ additional $\gamma$ strength in the energy range 3.5–5.5 MeV was observed for the first time. Since the neutron-separation energy of ${}^{133}\mathrm{Sn}$ is low, $S_n=2.402(4)\mathrm{MeV}$, this observation provides direct evidence for the radiative decay of neutron-unbound states in this nucleus. The ability of electromagnetic decay to compete successfully with neutron emission at energies as high as 3 MeV above threshold is attributed to a mismatch between the wave functions of the initial and final states in the latter case. These findings suggest that in the region southeast of ${}^{132}\mathrm{Sn}$ nuclear structure effects may play a significant role in the neutron versus $\gamma$ competition in the decay of unbound states. As a consequence, the common neglect of such effects in the evaluation of the neutron-emission probabilities in calculations of global $\beta$-decay properties for astrophysical simulations may have to be reconsidered.

Figure 1

Doppler-corrected $\gamma$-ray spectrum (for $\gamma$-ray multiplicity $M_{\gamma }=1$ after add back) of ${}^{133}\mathrm{Sn}$ populated via one-neutron knockout from ${}^{134}\mathrm{Sn}$. The response function fit to the experimental spectrum is shown by the thick red line while the individual components are shown as thin black lines. The background is indicated as the gray area. The inset shows the high-energy region of the spectrum on a linear scale.

Figure 2

Comparison between the experimental shape of the 854-keV line observed in the DALI2 detectors at polar angles (a) $<67°$ and (b) $>67°$ and simulations assuming lifetimes of $\tau =0$ (blue) and $\tau =30\mathrm{ps}$ (red) for the 854-keV state.

Figure 3

(a) Schematic of the neutron orbital occupancies after the knockout of a $0h_{11/2}$ neutron from the ${}^{134}\mathrm{Sn}$ projectile, followed by $\gamma$ decay or neutron emission; (b) Illustration of the population of bound (gray regions) and unbound (blue region) excited states in ${}^{132,133}\mathrm{Sn}$ following one-neutron knockout (KO) from either the valence space ($N>82$) or the $N=50–82$ core ($N\le 82$). Energies are quoted in MeV.

Figure 4

Total experimental cross sections for the removal of $x$ neutrons, ${\sigma }_{xn}$, from ${}^{133}\mathrm{Sn}$ (open squares) and ${}^{134}\mathrm{Sn}$ (filled circles) projectiles. Lines are drawn to guide the eye. The vertical bars for $x=1$ indicate the cross sections for knockout from the $N>82$ valence space (black) and from the $N=50–82$ core (gray) as calculated using eikonal reaction theory. The contribution from the $0h_{11/2}$ orbital to the latter amounts to 67 and 56 mb, respectively.