The East Lansing Model: a Bayesian uncertainty quantified optical potential for rare isotopes

Abstract

The East Lansing Model is a global, uncertainty-quantified optical potential for neutron and proton projectiles, with a novel form for the neutron-proton asymmetry component, with the goal to improve extrapolations away from stability. Our Bayesian calibration relies on (n,n), (p,p) and (p,n) experimental data for angular distributions on spherical targets with mass $A\geq 40$, and beam energies in the range $E = 10-100$ MeV. When considering the stable nuclei for which data is available, our results demonstrate that the inclusion of the $(p,n)$ data alone does not significantly change the parameterization. The additional information contained in (p,n) only becomes evident by introducing a new parameterization, one that gives the flexibility to encode neutron skins in the optical potential through an asymmetry dependent term. Finally, extrapolations of ELM toward the limits of stability (namely toward the proton and neutron driplines) leads to reduced uncertainties when compared to other global optical potentials in use.

Figures (7)

• Figure 1: Corner plot of a subset of the model parameters, including isoscalar depth, radii parameters and difuseness ($V_0,r_0,r^{(0}_0, a_0$), and isovector real and imaginary ($V_t,W_{st}$). The ELM (purple), ELM0 (orange) and ELM0el (blue) are compared with the prior distributions used (grey). See supplemental material for detailed definitions.
• Figure 2: Corner plot for the isovector geometry parameters $r_1,r^{(0}_1, a_1$ unique to ELM (purple), compared to the prior (grey).
• Figure 3: Corner plot for the fractional uncertainty parameters $\beta_l$ in the model discrepancy for each observable class $l$ {$(p,p)$, $(n,n)$ or $(p,n)$} expressed as a percentage, for ELM (purple), ELM0 (orange), ELM0el (blue). Note that ELM0el was not fit to $(p,n)$, and therefore has no model discrepancy for it.
• Figure 4: 68% credible intervals for the predictive posterior of the latent truth for $^{120}$Sn(p,n)$^{120}$Sb(IAS) from each model calibration, with experimental data in black: ELM (purple), ELM0 (orange), ELM0el (blue). Each successive energy is offset by a factor of 30 for visibility.
• Figure 5: Nominal versus empirical coverage of the $(p,n)$ experimental data used for calibration: ELM (purple), ELM0 (orange), ELM0el (blue), compared with ideal coverage (grey).