TY - JOUR

T1 - Resummation of fermionic in-medium ladder diagrams to all orders

AU - Kaiser, N.

N1 - Funding Information:
I thank J.W. Holt, L. Platter, A. Schwenk and W. Weise for many useful discussions. I thank H.W. Hammer for communicating to me results from own unpublished work which have been very valuable. This work is partially supported by the DFG Excellence Cluster “Origin and Structure of the Universe”.

PY - 2011/6/15

Y1 - 2011/6/15

N2 - A system of fermions with a short-range interaction proportional to the scattering length a is studied at finite density. At any order an, we evaluate the complete contributions to the energy per particle E-(kf) 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 a4 are accurately reproduced. The emerging series in akf 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.

AB - A system of fermions with a short-range interaction proportional to the scattering length a is studied at finite density. At any order an, we evaluate the complete contributions to the energy per particle E-(kf) 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 a4 are accurately reproduced. The emerging series in akf 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.

KW - Bertsch parameter

KW - Many-body theory

KW - Resummation of ladder diagrams

UR - http://www.scopus.com/inward/record.url?scp=79957696809&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysa.2011.05.005

DO - 10.1016/j.nuclphysa.2011.05.005

M3 - Article

AN - SCOPUS:79957696809

SN - 0375-9474

VL - 860

SP - 41

EP - 55

JO - Nuclear Physics, Section A

JF - Nuclear Physics, Section A

IS - 1

ER -