Error analysis of nuclear forces and effective interactions

Abstract

The Nucleon-Nucleon interaction is the starting point for ab initio Nuclear Structure and Nuclear reactions calculations. Those are effectively carried out via effective interactions fitting scattering data up to a maximal center of mass momentum. However, NN interactions are subjected to statistical and systematic uncertainties which are expected to propagate and have some impact on the predictive power and accuracy of theoretical calculations, regardless on the numerical accuracy of the method used to solve the many body problem. We stress the necessary conditions required for a correct and self-consistent statistical interpretation of the discrepancies between theory and experiment which enable a subsequent statistical error propagation and correlation analysis. We comprehensively discuss an stringent and recently proposed tail-sensitive normality test and provide a simple recipe to implement it. As an application, we analyze the deduced uncertainties and correlations of effective interactions in terms of Moshinsky-Skyrme parameters and effective field theory counterterms as derived from the bare NN potential containing One-Pion-Exchange and Chiral Two-Pion-Exchange interactions inferred from scattering data.

17 pages, 4 figures, 4 tables. Remarks added and typos corrected. Submitted to JPhysG Focus issue "Enhancing the interaction between nuclear experiment and theory through information and statistics" (ISNET)

References in corpus (28)

• An accurate nucleon-nucleon potential with charge-independence breaking
• The high-precision, charge-dependent Bonn nucleon-nucleon potential (CD-Bonn)
• Chiral effective field theory and nuclear forces
• Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory
• Construction of high-quality Nucleon-Nucleon potential models
• The two-nucleon system at next-to-next-to-next-to-leading order
• Nuclear Energy Density Optimization
• From low-momentum interactions to nuclear structure
• Peripheral Nucleon-Nucleon Phase Shifts and Chiral Symmetry
• An optimized chiral nucleon-nucleon interaction at next-to-next-to-leading order
• Error Estimates of Theoretical Models: a Guide
• Chiral two-pion exchange and proton-proton partial-wave analysis
• Covariant spectator theory of np scattering: Phase shifts obtained from precision fits to data below 350 MeV
• Coarse grained Potential analysis of neutron-proton and proton-proton scattering below pion production threshold
• The Nucleon-Nucleon Potential in the 1/N_c Expansion
• Towards a Model-Independent Low Momentum Nucleon-Nucleon Interaction
• Statistical Error analysis of Nucleon-Nucleon phenomenological potentials
• Coarse grained NN potential with Chiral Two Pion Exchange
• Block Diagonalization using SRG Flow Equations
• Error analysis of nuclear mass fits
• Hadron interactions in lattice QCD
• The Nucleon-Nucleon Interaction and Large N_c QCD
• Serber symmetry, Large Nc and Yukawa-like One Boson Exchange Potentials
• Coarse graining Nuclear Interactions
• Implicit vs Explicit Renormalization and Effective Interactions
• Effective interactions in the delta-shells potential
• Error Analysis of Nuclear Matrix Elements
• Van der Waals forces and Photon-less Effective Field Theories

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• Ab initio nuclear response functions for dark matter searches
• Self-consistent statistical error analysis of $\pi \pi$ scattering
• An introduction to Bootstrap for nuclear physics
• Uncertainty quantification of an empirical shell-model interaction using principal component analysis
• Three pion nucleon coupling constants
• Large-$N_c$ Relationships Among Two-Derivative Pionless Effective Field Theory Couplings
• Is the unusual near-threshold potential behavior in elastic scattering of weakly bound nuclei a precision error?
• Systematic Nuclear Uncertainties in the Hypertriton System
• The falsification of Chiral Nuclear Forces
• The Falsification of Nuclear Forces