Is the σ field in the σ − ω model related to a pion pair coherent state ?

Abstract

A two pion pair coherent state is proposed as an alternative to the σ field in the σ −ω model. Based on a phenomenological Hamiltonian for interacting pions with nonrelativistic coupling to nucleons and deltas we arrive at an expression for the binding energy of nuclear matter whose minimum is at ϱ/ ϱ o = 1 and yields E A = −16 MeV . These values were achieved with one single parameter k c , the cut-off momentum. An important ingredient of our model is the density dependence of the Landau parameter g′. The possibly accidental character of our results as well as their relevance for saturation mechanisms due to long range p − h and Δ − h screening effects are pointed out.