In order to correct the Landau-Migdal interaction to account for the finite range of the NN interaction the contribution due to meson exchange can be included explicitly. This correction would seem to be especially important in the spin-isospin channel because of the contribution of the lightest meson, the pion. If the meson is also included as the other isovector meson which could contribute the p-h force will take the form [Ost92]
where is a phenomenological constant related to the Landau-Migdal parameter . The and exchange terms do not describe well the short range behavior of the interaction so it is necessary to keep the contact term, which accounts for heavy meson and QCD effects. This is the so-called model for the isovector p-h interaction.
In momentum space the particle-hole potential for the model is given by [ETB85]
where is the meson-nucleon coupling constant , is the energy loss, q is the momentum transfer, is the meson mass, and is the monopole vertex form factor which takes the form [OTW82]
The cut-off mass, , is inversely related to the range of the meson-nucleon vertex and must be determined phenomenologically from the short range behavior. It is obvious from equation that, because of its pseudoscalar nature, the pion is primarily responsible for the spin-longitudinal response while the part dominates the spin-transverse response.
Through use of the identity we can separate equation into the spin-longitudinal and spin-transverse parts [McC92]:
Figure: The momentum transfer dependence of the residual particle-hole interaction due to and meson exchange. The dashed line shows the dependence and the dotted line shows the dependence of the interaction. [Pro91]
The separate spin-longitudinal and spin-transverse parts of the particle-hole force are plotted in figure with , GeV, GeV, and . Both components of the force are repulsive at short range, but, due to the small pion mass, the spin-longitudinal part becomes attractive at around 1 while the transverse part remains repulsive until . Therefore, using the model for the residual particle-hole interaction in their RPA calculations, Alberico et al. [AEM82] predicted the transverse response would be quenched and hardened while the longitudinal response is softened and enhanced, particularly between to . This means that the ratio of the longitudinal to the transverse responses should be larger at small energy loss in nA collisions than in nn collisions, as shown in figure .