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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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All atomic particles possess an intrinsic angular momentum, or 'spin'. Electrons, protons, and neutrons each have a spin value of ½, although protons and neutrons in nuclei may have higher half-integer spins owing to energetic factors.
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Solving the nuclear pairing model with neural network quantum states.

Mauro Rigo1, Benjamin Hall2,3, Morten Hjorth-Jensen2,4

  • 1Physics Department, University of Trento, via Sommarive 14, I-38123 Trento, Italy.

Physical Review. E
|March 18, 2023
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Summary
This summary is machine-generated.

We developed a new variational Monte Carlo method using artificial neural networks to solve the nuclear many-body problem. This approach accurately predicts nuclear energies, outperforming traditional methods like coupled-cluster.

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Area of Science:

  • Computational Physics
  • Nuclear Physics
  • Quantum Many-Body Theory

Background:

  • The nuclear many-body problem is computationally intensive.
  • Accurate solutions are crucial for understanding nuclear structure and interactions.
  • Existing methods like coupled-cluster have limitations.

Purpose of the Study:

  • To develop a novel variational Monte Carlo (VMC) method for the nuclear many-body problem.
  • To utilize artificial neural networks (ANNs) for representing the ground-state wave function.
  • To train the ANN efficiently using a memory-efficient stochastic reconfiguration algorithm.

Main Methods:

  • Variational Monte Carlo (VMC) method.
  • Occupation number formalism.
  • Artificial neural network (ANN) representation of the ground-state wave function.
  • Stochastic reconfiguration algorithm for network training.

Main Results:

  • The VMC-ANN method was benchmarked against established nuclear many-body techniques.
  • It accurately described nuclear pairing phenomena for various interactions and strengths.
  • The method demonstrated polynomial computational cost.
  • Energies obtained were in excellent agreement with full configuration-interaction (FCI) values.
  • Performance surpassed coupled-cluster methods.

Conclusions:

  • The proposed VMC-ANN method offers a powerful and efficient approach to solving the nuclear many-body problem.
  • It provides highly accurate ground-state energies.
  • This method shows significant promise for future nuclear structure calculations.