Abstract
We compute the Bertsch parameter for neutron matter by using nucleon-nucleon interactions that are fully diagonal in momentum space. We analyze the on-shell limit with the similarity renormalization group and compare the results for a simple separable toy model to realistic calculations with high precision NN potentials.
Highlights
About fifteen years ago George Bertsch proposed the following problem [1]: what would be the ground state properties of a many-body system composed of spin-1 2 fermions interacting via a short-range contact interaction with an infinitely large scattering length?The two-body scattering amplitude can be written asT2(k, k) ∝ [k cot δ − ik], (1)and at low energies, k cot δ can be described by the effective range expansion k cot δ = 1 − α0 + r0
On-shell interactions from the SRG and the Bertsch parameter In this work we want to study neutron matter at the unitary limit with on-shell interactions obtained by evolving the nuclear force with the similarity renormalization group (SRG) towards the infrared region of the similarity cutoff λ
We have developed techniques in nuclear physics in order to study the infrared fixed-point of the SRG by pushing the evolution towards the on-shell limit λ → 0 [6, 7, 8] and have found an elegant an simple way to determine phase shifts from fully diagonal interactions in momentum space complying with isospectrality and Levinson’s theorem [9]
Summary
If the scattering length is large and negative, the interaction is strongly attractive and the system is in the BEC limit where the fermions form deeply bound pairs [2] (see Fig. 1). Monte Carlo simulations of a superfluid Fermi gas with an attractive short-range two-body interaction in the unitary limit (infinite scattering length and zero effective range) estimate the energy per particle of neutron matter in 44% of the energy of the free Fermi gas and the pairing gap to be about twice the energy per particle [4].
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