Abstract
Eigenvector continuation (EC) has been shown to accurately and efficiently reproduce ground states for targeted sets of Hamiltonian parameters. It uses as variational basis vectors the corresponding ground-state eigensolutions from selected other sets of parameters. Here we extend the EC approach to scattering using the Kohn variational principle. We first test it using a model for S-wave nucleon-nucleon scattering and then demonstrate that it also works to give accurate predictions for non-local potentials, charged-particle scattering, complex optical potentials, and higher partial waves. These proofs-of-principle validate EC as an accurate emulator for applying Bayesian inference to parameter estimation constrained by scattering observables. The efficiency of such emulators is because the accuracy is achieved with a small number of variational basis elements and the central computations are just linear algebra calculations in the space spanned by this basis.
Highlights
Eigenvector continuation (EC) has been shown to accurately and efficiently reproduce ground states for targeted sets of Hamiltonian parameters
Bayesian parameter estimation generally requires Monte Carlo sampling of the parameter space, with many evaluations of the likelihood with different parameters
We merge EC and the Kohn variational principle and explore how well it works using a series of model calculations, starting with two-body scattering in partial waves
Summary
Bayesian inference is increasingly favored for uncertainty quantification in nuclear physics calculations (e.g., see [1,2,3,4,5]), but the computational requirements can be substantial. Bayesian parameter estimation generally requires Monte Carlo sampling of the parameter space, with many evaluations of the likelihood with different parameters. Efficient and effective EC emulators for nuclear bound-state properties and transitions have been demonstrated for many-body calculations using chiral effective field theory (χEFT) Hamiltonians [8, 9]. We would like to have fast EC emulators for scattering, e.g., for treating reactions and for few-body scattering used to constrain χEFT low-energy constants [10]. We merge EC and the Kohn variational principle and explore how well it works using a series of model calculations, starting with two-body scattering in partial waves.
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