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EMULATORS FOR UNBOUND NUCLEI

Nuwan Yapa�Kévin Fossez�Sebastian König�

STREAMLINE symposium (9^th and 10^th of May 2024)

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RESONANCES

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GAMOW STATES

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RIGGED HILBERT SPACE & COMPLEX–SCALING METHOD

Can be thought of as “trading” a section of the upper half-plane for a section of the lower half–plane

section of the RHS exposed via CSM

Hilbert space

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DETERMINING RESONANCES

Techniques

Complex scaling

Berggren basis

Avoided crossings

Few–body constructions

Finite volume

No–core shell model

Faddev–Yakubowski

This project

Gamow shell model

FV w/ CSM

NCSM w/ CSM

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FINITE VOLUME WITH COMPLEX SCALING

H. Yu, N. Yapa, and S. König, Phys. Rev. C 109, 014316 (2024).

“Periodic” boundary

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REDUCED BASIS METHOD 1

training points

“Periodic” boundary

N. Yapa and S. König, Volume Extrapolation via Eigenvector Continuation, Phys. Rev. C 106, 014309 (2022).

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REDUCED BASIS METHOD 2

Approach 2

Also known as Eigenvector Continuation (EC)

Tune the strength of the potential to train the emulator
Then extrapolate to the desired region

Can be utilized in two ways:

Narrow–to–broad extrapolation
Bound–to–resonant extrapolation

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REDUCED BASIS METHOD 2: NARROW–TO–BROAD

N. Yapa, K. Fossez, and S. König, Phys. Rev. C 107, 064316 (2023).

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REDUCED BASIS METHOD 2: NARROW–TO–BROAD

PRELIMINARY

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REDUCED BASIS METHOD 2: BOUND–TO–RESONANT

Naïve EC does not work
Needs Conjugate–Augmented Eigenvector Continuation (CA–EC)
Basic idea: Augment the emulator with proper asymptotics

N. Yapa, K. Fossez, and S. König, Phys. Rev. C 107, 064316 (2023).

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REDUCED BASIS METHOD 2: BOUND–TO–RESONANT

PRELIMINARY

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BERGGREN BASIS

Deform the contour below the resonance poles, picking up the poles
Use this basis to construct Slater determinants of the few–body system

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BERGGREN BASIS: DEMONSTRATION

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THANK YOU

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EMULATORS FOR CALIBRATING COVARIANT ENERGY DENSITY FUNCTIONALS

Nuwan Yapa�Marc Salinas�Amy Anderson�Jorge Piekarewicz�

STREAMLINE symposium (9^th and 10^th of May 2024)

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RELATIVISTIC MEAN FIELD THEORY

Predictions for neutron star properties from two different models

M. Salinas and J. Piekarewicz, Building an Equation of State Density Ladder, Symmetry 15, 5 (2023).

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REDUCED BASIS METHODS

Can be solved via iteration
Too expensive to solve simultaneously
RBMs facilitate this
Galerkin projection is used to to construct RB expansion

Klein–Gordon equation for , , and

Dirac equation for

P. Giuliani, K. Godbey, E. Bonilla, F. Viens, and J. Piekarewicz, Bayes Goes Fast: Uncertainty Quantification for a Covariant Energy Density Functional Emulated by the Reduced Basis Method, Frontiers in Physics 10, (2023).

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EMPIRICAL INTERPOLATION METHOD (EIM)

A. L. Anderson, G. L. O’Donnell, and J. Piekarewicz, Applications of Reduced-Basis Methods to the Nuclear Single-Particle Spectrum, Phys. Rev. C 106, L031302 (2022).

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