Background: Modern nuclear structure models suggest that the shell structure near the valley of stability, with well-established shell closures at $N=50$, for example, changes in very neutron-rich nuclei far from stability. Single-particle properties of nuclei away from stability can be probed in single-neutron $(d,p)$ transfer reactions with beams of rare isotopes. The interpretation of these data requires reaction theories with various effective interactions. Often, approximations made to the final bound-state potential introduce a large uncertainty in the extracted single-particle properties, in particular the spectroscopic factor.

Purpose: Mitigate this uncertainty using a combined measurement method to constrain the shape of the bound-state potential and to reliably extract the spectroscopic factor.

Methods: The ${}^2\mathrm{H}({}^{86}\mathrm{Kr},p){}^{87}\mathrm{Kr}$ reaction was measured at 33 MeV/u at the National Superconducting Cyclotron Laboratory (NSCL) as a test of the combined method. The reaction protons were detected with the Oak Ridge Rutgers University Barrel Array (ORRUBA) of position sensitive silicon strip detectors, the first implementation of ORRUBA coupled to the S800 spectrograph with fast beams at NSCL.

Results: These measurements at 33 MeV/u are combined with previous studies of the ${}^{86}\mathrm{Kr}(d,p)$ reaction at 5.5 MeV/u to demonstrate a successful case of the combined method to constrain the shape of the single-particle potential and deduce asymptotic normalization coefficients and spectroscopic factors. In particular, the single-particle asymptotic normalization coefficient for the ground state of ${}^{87}\mathrm{Kr}$ was constrained to $b_{d5/2}=6.{46}_{-0.57}^{+1.12}{\mathrm{fm}}^{-1/2}$, and therefore the deduced spectroscopic factor is $S=0.{44}_{-0.13}^{+0.09}$ with uncertainties dominated by experimental statistics.

Conclusions: By combining measurements at two very different beam energies, single-particle asymptotic normalization coefficients, at least for low angular momentum transfers, can be constrained. Therefore, spectroscopic factors can be deduced with uncertainties dominated by experimental uncertainties, rather than limited knowledge of bound-state potential parameters.

• Received 2 June 2017
• Revised 30 January 2019

DOI:https://doi.org/10.1103/PhysRevC.99.054625