Uncertainty quantification in nuclear shell model

Abstract

The uncertainty quantifications of theoretical results are of great importance to make meaningful comparisons of those results with experimental data and to make predictions in experimentally unknown regions. By quantifying uncertainties, one can make more solid statements about, e.g., origins of discrepancy in some quantities between theory and experiment. We propose a novel method for uncertainty quantification for the effective interactions of nuclear shell-model calculations as an example. The effective interaction is specified by a set of parameters, and its probability distribution in the multi-dimensional parameter space is considered. This enables us to quantify the agreement with experimental data in a statistical manner and the resulting confidence intervals show unexpectedly large variations. Moreover, we point out that a large deviation of the confidence interval for the energy in shell-model calculations from the corresponding experimental data can be used as an indicator of some exotic property, e.g. alpha clustering, etc. Other possible applications and impacts are also discussed.

arXiv comment6 pages, 2 figures, 1 table, accepted as a Rapid Communication in Phys. Rev. C

References in corpus (28)

• MCMC using Hamiltonian dynamics
• Modern Theory of Nuclear Forces
• Chiral effective field theory and nuclear forces
• The Shell Model as Unified View of Nuclear Structure
• Quantum Monte Carlo methods for nuclear physics
• Properties of ${}^{12}$C in the {\it ab initio} nuclear shell-model
• Ab initio calculation of the Hoyle state
• The information content of a new observable: the case of the nuclear neutron skin
• Error Estimates of Theoretical Models: a Guide
• A nucleus-dependent valence-space approach to nuclear structure
• Global performance of covariant energy density functionals: ground state observables of even-even nuclei and the estimate of theoretical uncertainties
• Structure of ground and excited states of ${}^{12}$C
• Nonperturbative shell-model interactions from the in-medium similarity renormalization group
• Ab initio no-core full configuration calculations of light nuclei
• Ab-initio coupled-cluster effective interactions for the shell model: Application to neutron-rich oxygen and carbon isotopes
• Uncertainty analysis and order-by-order optimization of chiral nuclear interactions
• Coarse grained Potential analysis of neutron-proton and proton-proton scattering below pion production threshold
• Uncertainty Quantification for Nuclear Density Functional Theory and Information Content of New Measurements
• Ground and excited states of doubly open-shell nuclei from ab initio valence-space Hamiltonians
• Statistical Error analysis of Nucleon-Nucleon phenomenological potentials
• Propagation of uncertainties in the Skyrme energy-density-functional model
• Accurate calibration of relativistic mean-field models: correlating observables and providing meaningful theoretical uncertainties
• Open $sd$-shell nuclei from first principles
• Neutron skin uncertainties of Skyrme energy density functionals
• Shell-model coupled-cluster method for open-shell nuclei
• Statistical uncertainties of a chiral interaction at next-to-next-to leading order
• Nuclear Structure from the In-Medium Similarity Renormalization Group
• Shell-model interactions from chiral effective field theory

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