Functional approach to the electromagnetic response function: The longitudinal channel

Abstract

In this paper we address the (charge) longitudinal electromagnetic response for a homogeneous system of nucleons interacting via meson exchanges in the functional framework. This approach warrants consistency if the calculation is carried on order-by-order in the mesonic loop expansion with RPA-dressed mesonic propagators. At the 1-loop order and considering π, ρ and ω exchanges we obtain a quenching of the response, in line with the experimental results. 21.65

The longitudinal and transverse responses in the inclusive electron scattering A functional approach

“…Having shortly revisited the experimental and theoretical situation, let us spend a few words about the philosophy underlying our approach [1,19].…”

“…The derivation of the response at the one loop level is given in detail in ref. [1] and will not be repeated here. We only remind the reader that a Hubbard-Stratonovitch transformation [26,27,28] bosonizes a potential theory, leading to an effective action coincident with (3) up to a redefinition of the symbols: D −1 0 is replaced by the inverse potential in the given p-h channel and the field φ is reinterpreted as an auxiliary field.…”

“…The results were qualitatively unsatisfactory, but they went in the right direction. A more sophisticated approach was pursued in [1]: the formalism is the same, but other channels are considered. We focused there our attention on the pion channel, the ρ channel and the transverse ω channel.…”

“…We neglected the scalar channels following the indications of Speth et al [29] that suggest there a weak or vanishing effective interaction. Of course this outcome is questionable and was adopted in [1] only for sake of simplicity. The statement of ref.…”

The nuclear response in the isoscalar channel

“…The dynamics considered in [2] was the exchange of π, ρ and the transverse component of the ω plus a residual interaction in the two first cases.…”