Why does the Walecka model not include pions?

Question

The Walecka or $\sigma$/$\omega$-model is an effective theory describing nucleon-nucleon interaction by an exchange of $\sigma$/$\omega$-mesons. Why does it not include interactions by pions?

Answer 1

I want to cite the original paper of Walecka where he answers your question.

From Annals of Physics 83/2 (1974) p. 491 "A theory of highly condensed matter":

"The reader might object to the fact that there is no one-pion exchange tail in this interaction; however, the strong spin and isospin dependence of the potential arising from the exchange of an isovector, pseudoscalar pion implies that the contribution of the one-pion exchange potential to the bulk properties of nuclear matter largely averages to zero"

Hope this helps.

Answer 2

The answer given in Walecka's 1974 paper is mostly correct. The one pion exchange contribution to the Hartree energy vanishes in balanced nuclear matter. The same point was made in the 1972 paper of Miller and Green (Phys Rev C5 241) where the same type model was used for doubly magic (finite) nuclei. If exchange is included (Hartree Fock as opposed to Hartree) then the pion would contribute.