Statistical error analysis for phenomenological nucleon-nucleon potentials

Abstract

Nucleon-Nucleon potentials are commonplace in nuclear physics and are determined from a finite number of experimental data with limited precision sampling the scattering process. We study the statistical assumptions implicit in the standard least squares χ 2 fitting procedure and apply, along with more conventional tests, a tail sensitive quantile-quantile test as a simple and confident tool to verify the normality of residuals. We show that the fulfillment of normality tests is linked to a judicious and consistent selection of a nucleon-nucleon database. These considerations prove crucial to a proper statistical error analysis and uncertainty propagation. We illustrate these issues by analyzing about 8000 proton-proton and neutron-proton scattering published data. This enables the construction of potentials meeting all statistical requirements necessary for statistical uncertainty estimates in nuclear structure calculations.

Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange includingΔresonances

“…In any case, the results of Ref. [11] show also that the long range part of the next-to-next-to-leading order (N2LO or Q 3 ) chiral potential can indeed fit the delta-shells+OPE selected data satisfactorily with a χ 2 /datum of 1.07, when the potential is taken to be valid for inter-nucleon distances ranging from 1.8 fm outwards.…”

“…Within the coarse grained framework the impact of chiral interactions on the selection of the database has also been studied in Ref. [11]. The result was that a larger number of data were rejected but at the same time the number of parameters was reduced.…”

“…[2] for an early review) and, after many years, culminated in the admirable Nijmegen partial wave analysis (PWA) of 1993 [3], based on the crucial observations that charge-dependent one-pion-exchange (CD-OPE), tiny but essential electromagnetic and relativistic effects, and a judicious selection of the scattering database could actually provide a satisfactory fit with χ 2 /datum ∼ 1 for a total number of data consisting, as of 1993, of 1787 pp and 2514 np (normalizations included) at the 3 σ level. These criteria have set the standard for PWA's and the design of high quality phenomenological potentials [4][5][6][7][8][9][10][11][12]. The inference point of view is mainly phenomenological and requires a balanced interplay between which data qualify as constraints and which models provide the most likely description of the data.…”

“…[12] for updated pp and np abundance plots in the (E lab , θ cm ) plane. However, not all of these data are mutually compatible and a decision has to be made as to which are more likely to be correct.…”

“…The chiral TPE potential [24] was also used within the coarse grained framework to determine the chiral constants in Ref. [11] with a global χ 2 /datum of 1.07, based on 6713 pp and np scattering data.…”