Unitarity potentials and neutron matter at the unitary limit

作者：Dong Huan^*; Siu L W; Kuo T T S; Machleidt R

来源：Physical Review C, 2010, 81(3): 034003.

DOI：10.1103/PhysRevC.81.034003

We study the equation of state of neutron matter using a family of unitarity potentials, all of which are constructed to have infinite S-1(0) scattering lengths a(s). For such a system, a quantity of much interest is the ratio xi = E-0/E-0(free), where E-0 is the true ground-state energy of the system and E-0(free) is that for the noninteracting system. In the limit of a(s) -> +/-infinity, often referred to as the unitary limit, this ratio is expected to approach a universal constant, namely. xi similar to 0.44(1). In the present work we calculate this ratio xi using a family of hard-core square-well potentials whose a(s) can be exactly obtained, thus enabling us to have many potentials of different ranges and strengths, all with infinite a(s). We have also calculated xi using a unitarity CDBonn potential obtained by slightly scaling its meson parameters. The ratios xi given by these different unitarity potentials are all close to each other and also remarkably close to 0.44, suggesting that the above ratio xi is indifferent to the details of the underlying interactions as long as they have infinite scattering length. A sum-rule and scaling constraint for the renormalized low-momentum interaction in neutron matter at the unitary limit is studied. The importance of pairing in our all-order ring diagram and model-space HF calculations of neutron matter is discussed.

• 出版日期2010-3