Similarity renormalization group evolution of hypernuclear Hamiltonians

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 ${}_{\Lambda }^7$Li, ${}_{\Lambda }^9$Be, ${}_{\Lambda }^{11}$B, ${}_{\Lambda }^{13}$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.

arXiv comment13 pages, 6 figures; accepted version

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• Thermal behavior as indicator for hyperons in binary neutron star merger remnants
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• Nuclear physics uncertainties in light hypernuclei
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• Ab initio calculation of charge symmetry breaking in $A=7$ and $8$ $\Lambda$-hypernuclei
• Hyperon-Nucleon Interaction Constrained by Light Hypernuclei
• Quenched Λ spin-orbit splitting by relativistic Fock diagram in single-Λ hypernuclei
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• Calculation of harmonic oscillator brackets in SU(3) basis