# Similarity renormalization group evolution of hypernuclear Hamiltonians

## TL;DR

This paper develops a method to compute induced three-body hyperon-nucleon-nucleon interactions during SRG evolution and applies it to hypernuclear systems, revealing sensitivities and structural insights.

## Contribution

It introduces a detailed procedure for including induced three-body hyperon interactions in SRG-evolved hypernuclear Hamiltonians and demonstrates its application to various hypernuclei.

## Key findings

- Hypernuclear states are sensitive to the nucleonic Hamiltonian.
- The method accurately captures induced three-body interactions.
- Structural properties of hypernuclei with neutron-proton asymmetry are explored.

## Abstract

Unitary transformations of a Hamiltonian generally induce interaction terms beyond the particle rank present in the untransformed Hamiltonian that have to be captured and included in a many-body calculation. In systems with strangeness such as hypernuclei, the three-body terms induced by the hyperon-nucleon interaction are strong, so their inclusion is crucial. We present in detail a procedure for computing hyperon-nucleon-nucleon interaction terms that are induced during a similarity renormalization group (SRG) flow. The SRG is carried out in a basis spanned by antisymmetric harmonic-oscillator states with respect to three-body Jacobi coordinates. We discuss basis construction, antisymmetrization, numerical evaluation of the flow equations, and separation of the genuine three-body terms. We then use the hypernuclear no-core shell model with SRG-evolved Hamiltonians, addressing the sensitivity of hypernuclear states and hyperon separation energies to changes in the nucleonic Hamiltonian by example of $^7_\Lambda$Li, $^9_\Lambda$Be, $^{11}_\Lambda$B, $^{13}_\Lambda$C, and the hyper-helium chain. We also present a survey of the hyper-hydrogen chain, exploring the structure of hypernuclei with extreme neutron-proton asymmetries.