Uncertainty quantification for optical model parameters

Abstract

Background: Although uncertainty quantification has been making its way into nuclear theory, these methods have yet to be explored in the context of reaction theory. For example, it is well known that different parameterizations of the optical potential can result in different cross sections, but these differences have not been systematically studied and quantified.Purpose: The purpose of this work is to investigate the uncertainties in nuclear reactions that result from fitting a given model to elastic-scattering data, as well as to study how these uncertainties propagate to the inelastic and transfer channels.Method: We use statistical methods to determine a best fit and create corresponding 95% confidence bands. A simple model of the process is fit to elastic-scattering data and used to predict either inelastic or transfer cross sections. In this initial work, we assume that our model is correct, and the only uncertainties come from the variation of the fit parameters.Results: We study a number of reactions involving neutron and deuteron projectiles with energies in the range of 5-25 MeV/u, on targets with mass A=12-208. We investigate the correlations between the parameters in the fit. The case of deuterons on 12 C is discussed in detail: the elastic-scattering fit and the prediction of 12 C(d,p) 13 C transfer angular distributions, using both uncorrelated and correlated χ 2 minimization functions. The general features for all cases are compiled in a systematic manner to identify trends.Conclusions: Our work shows that, in many cases, the correlated χ 2 functions (in comparison to the uncorrelated χ 2 functions) provide a more natural parameterization of the process. These correlated functions do, however, produce broader confidence bands. Further optimization may require improvement in the models themselves and/or more information included in the fit.

Two-Nucleon Emitters Within a Pseudostate Approach

“…The computed width is consistent with the results in Ref. [6] from the three-body eigenphases within the hyperspherical R-matrix method to solve the actual three-body scattering problem. This is an indication that the method here presented provides a reasonable description of three-body resonances in a discrete basis.…”

“…We apply the method to study 16 Be(0 + ) states in a three-body ( 14 Be+ n+ n) model using the potentials in Refs. [6,7]. Calculations are performed within the hyperspherical formalism [9], where the relevant parameters are the maximum hypermomentum K max (which determines the number of angular components in the wave-function expansion), the number of basis functions N , and the scale parameter γ controlling the radial extension of the basis [10].…”

“…These are typically discussed in terms of different possible paths: The so-called sequential, direct and democratic decays [5]. From the theoretical point of view, a proper description of three-body resonances can help in understanding these correlations [6,7]. The description of few-body resonant states, however, is not an easy task.…”

Identifying structures in the continuum: Application to Be16

“…Moreover, resonant states in unbound nuclei can be populated in transfer or knockout reactions induced by exotic projectiles [12][13][14]. In this context, two-nucleon decays have attracted renewed * casal@pd.infn.it attention [12,[15][16][17][18]. The description of few-body resonances, however, is not an easy task.…”

Propagation of statistical uncertainties in covariant density functional theory: Ground state observables and single-particle properties

“…The need for such estimates has been clearly recognized by nuclear theory community as illustrated by a substantial number of the studies aiming at the quantification of theoretical uncertainties in nuclear structure, nuclear reactions and nuclear astrophysics (see Refs. [3][4][5][6][7][8][9][10] and references quoted therein).…”