Informing direct neutron capture on tin isotopes near the $N=82$ shell closure

Half of the elements heavier than iron are believed to be produced through the rapid neutron-capture process ($r$ process). The astrophysical environment(s) where the $r$ process occurs remains an open question, even after recent observations of neutron-star mergers and the associated kilonova. Features in the abundance pattern of $r$-process ashes may provide critical insight for distinguishing contributions from different possible sites, including neutron-star mergers and core-collapse supernovae. In particular, the largely unknown neutron-capture reaction rates on neutron-rich unstable nuclei near ${}^{132}\mathrm{Sn}$ could have a significant impact on the final $r$-process abundances. To better determine these neutron-capture rates, the $(d,p)$ reaction has been measured in inverse kinematics using radioactive ion beams of ${}^{126}\mathrm{Sn}$ and ${}^{128}\mathrm{Sn}$ and a stable beam of ${}^{124}\mathrm{Sn}$ interacting with a ${\left({\mathrm{CD}}_2\right)}_n$ target. An array of position-sensitive silicon strip detectors, including the Super Oak Ridge Rutgers University Barrel Array, was used to detect light reaction products. In addition to the present measurements, previous measurements of ${}^{130,132}\mathrm{Sn}(d,p)$ were reanalyzed using state-of-the-art reaction theory to extract a consistent set of spectroscopic factors for $(d,p)$ reactions on even tin nuclei between the heaviest stable isotope ${}^{124}\mathrm{Sn}$ and doubly magic ${}^{132}\mathrm{Sn}$. The spectroscopic information was used to calculate direct-semidirect $(n,\gamma )$ cross sections, which will serve as important input for $r$-process abundance calculations.

Figure 1

$Q$-value spectra of (a) ${}^{126}\mathrm{Sn}(d,p)$ and (b) ${}^{128}\mathrm{Sn}(d,p)$ reaction measurements in inverse kinematics, summed over all angles. The uncertainties on the data are purely statistical. Colored curves represent the fits to each state and the background. A solid black line represents the sum of all of the fits and the background. The centroids extracted from the individual fits for panel (a) are $Q_A=0.62\pm 0.04, Q_B=0.01\pm 0.05$, and $Q_C=-0.56\pm 0.05\mathrm{MeV}$ and for panel (b) are $Q_A=0.40\pm 0.05, Q_B=-0.21\pm 0.05$, and $Q_C=-0.81\pm 0.06\mathrm{MeV}$. The uncertainties on the centroids are determined from the error in the fit.

Figure 2

Typical pairs of $\ell =3$ and $\ell =1$ absolute differential cross sections from the ${}^{126}\mathrm{Sn}(d,p)$ [panels (a) and (b)] and ${}^{128}\mathrm{Sn}(d,p)$ [panels (c) and (d)] reactions with purely statistical uncertainties. Panels (a) and (c) are for states $A$ in Fig. 1 in ${}^{127}\mathrm{Sn}$ and ${}^{129}\mathrm{Sn}$, respectively, panels (b) and (d) are for states $B$ in Fig. 1 in ${}^{127}\mathrm{Sn}$ and ${}^{129}\mathrm{Sn}$, respectively. The data are compared to Finite Range ADiabatic Wave Approximation calculations for an angular momentum transfer of $\ell =3$ (red curves) and $\ell =1$ (blue curves). Adopted orbital angular momentum transfer calculations were performed using the Chapel-Hill parametrization (solid curve) and the Koning-Delaroche (KD) parametrization (dot-dashed curves). The alternate orbital angular momentum transfers $[\ell =1$ in (a) and (c) and $\ell =3$ in (b) and (d)] were calculated with the Chapel-Hill 89 parametrization (dashed line). In panel (d), the best fit for state $B$ was for only $\ell =1$ transfer. A state at 3394 keV with a (1/2,3/2) assignment was previously observed in $\beta$ decay [28].

Figure 3

Calculation of direct-semidirect neutron capture on ${}^{128}\mathrm{Sn}$. Similar results for capture on ${}^{124,126,130,132}\mathrm{Sn}$ were obtained and agree with the previous study of ${}^{130}\mathrm{Sn}$ [20]. The band (teal) represents the uncertainty in the cross section due to the uncertainties in $S$. $s$-wave direct capture to $\ell =1$ states dominates the capture at low neutron energies.

Figure 4

Comparison of calculated neutron-capture cross sections for tin isotopes at 30 keV. Present DSD calculations with experimental energies and spectroscopic factors (black diamonds), Hauser-Feshbach model calculations [44] (green squares), ${}^{132}\mathrm{Sn}$ direct capture using the theoretical spectroscopic factor [26] (black “$\times$”), ${}^{124}\mathrm{Sn}$ DSD calculations using spectroscopic factors of Ref. [27] for all $\ell =1$ levels having $\mathrm{S}>0.01$ (blue “$+$”), and DSD calculations with theoretical excitation energies and spectroscopic factors (red circles) [44].