Resummation of fermionic in-medium ladder diagrams to all orders

✍ Scribed by N. Kaiser

• Book ID: 103868083
• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 225 KB
• Volume: 860
• Category: Article
• ISSN: 0375-9474
• DOI: 10.1016/j.nuclphysa.2011.05.005

✦ Synopsis

A system of fermions with a short-range interaction proportional to the scattering length a is studied at finite density. At any order a n , we evaluate the complete contributions to the energy per particle Ē(k f ) arising from combined (multiple) particle-particle and hole-hole rescatterings in the medium. This novel result is achieved by simply decomposing the particle-hole propagator into the vacuum propagator plus a medium-insertion and correcting for certain symmetry factors in the (n -1)-th power of the in-medium loop. Known results for the low-density expansion up to and including order a 4 are accurately reproduced. The emerging series in ak f can be summed to all orders in the form of a double-integral over an arctangent function. In that representation the unitary limit a → ∞ can be taken and one obtains the value ξ = 0.5067 for the universal Bertsch parameter. We discuss also applications to the equation of state of neutron matter at low densities and mention further extensions of the resummation method.