Hypernuclei with neural network quantum states

Leveraging complementary machine-learning-based approaches, we compute properties of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>s</a:mi> </a:math> - and <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>p</b:mi> </b:math> -shell <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi mathvariant="normal">Λ</c:mi> </c:math> hypernuclei—including binding energies, single-particle densities, and radii—starting from the individual interactions among their constituents. These interactions are modeled based on a leading-order finite-cutoff pionless effective field theory expansion. The couplings and the range of the three-nucleon and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mi mathvariant="normal">Λ</e:mi> </e:math> -nucleon-nucleon potentials are determined via a Gaussian process framework anchored on virtually exact few-body techniques. We solve the many-body Schrödinger equation using a variational Monte Carlo method based on neural network quantum states, extending it for the first time to include <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mi mathvariant="normal">Λ</g:mi> </g:math> particles alongside protons and neutrons. The predicted binding energies show remarkably good agreement with experimental results, given the simplicity of the input Hamiltonian. We also confirm the experimentally observed shrinkage of the proton radius in <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mmultiscripts> <i:mi>Li</i:mi> <i:mprescripts/> <i:mi mathvariant="normal">Λ</i:mi> <i:mn>7</i:mn> </i:mmultiscripts> </i:math> compared to its parent nucleus, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:mmultiscripts> <k:mi>Li</k:mi> <k:mprescripts/> <k:none/> <k:mn>6</k:mn> </k:mmultiscripts> </k:math> . This work paves the way for an description of medium-mass and heavy hypernuclei, which is critical for understanding the onset of strange degrees of freedom in the core of neutron stars.