Constraining optical potentials with charge exchange to isobaric analogue states*

Recent work has produced global optical potentials using Bayesian calibration to (n,n) and (p,p) elastic scattering data [Pruitt et al., 2023].  When these uncertainties are propagated into calculations of differential cross sections for (p,n) charge exchange to Isobaric Analog States (IAS), the uncertainties are large, and, in some cases, agreement is poor [Smith et al., 2024]. The optical potential, in Lane-consistent form [Lane, 1962], is intimately related to the nuclear matter symmetry energy and its density slope, through isovector and neutron skins [Danielewicz et al., 2017, Loc et al., 2014, Khoa et al., 2007], and through the Hugenholtz-Van-Hove theorem [Xu et al., 2010]. Historic efforts to calibrate a global optical potential to (n, n), (p, p) and (n, p) simultaneously have to date never been done with full Bayesian uncertainty quantification, and have at times met difficulty describing all three reactions simultaneously with a global model [Lovas, 1976].

In this work, we develop the first uncertainty quantified Lane-consistent global optical potential with a Bayesian calibration, simultaneously using differential cross sections of (n, n), (p, p), and quasielastic (p, n) to the IAS. We demonstrate the effects of the choice of form of the posterior likelihood on the resulting agreement. We test the predictive power of models built with this approach by comparing the agreement between predictions of models fit two only two of (n, n), (p, p) and (p, n)IAS to experimental cross sections for the corresponding observable not used in fitting. Finally, we discuss the prospect of extracting new constraints on the nuclear symmetry energy and its density slope from our approach.

- Danielewicz, P., Singh, P., and Lee, J. (2017). Nuclear Physics A, 958:147–186.

- Khoa, D. T., Than, H. S., and Cuong, D. C. (2007). PRC, 76:014603.

- Lane, A. (1962). Nuclear Physics, 35:676–685.

- Loc, B. M., Khoa, D. T., and Zegers, R. G. T. (2014). PRC, 89:024317.

- Lovas, R. (1976). Nucl Phys A, 262(2):356–364.

- Pruitt, C., Escher, J., and Rahman, R. (2023). PRC, 107(1):014602.

- Smith, A., Hebborn, C., Nunes, F., and Zegers, R. (2024). arXiv:2403.18629.

- Xu, C., Li, B.-A., and Chen, L.-W. (2010). PRC, 82:054607