Effect Of Ghost Pole On Response Function

In intermediate energy nuclear physics the key elementfor understanding the structure and dynamics of nuclei is itsresponse to an external probe as the function of transferredenergy and momentum. Experiments in the past forty yearsgave evidence that electron scattering is the best tool forinvestigating hadron systems such as atomic nuclei and theirconstituents. The electromagnetic interaction is very weakcomparing to the strength of the interaction between hadrons.Thus electron-hadron scattering can be treated adequately byassuming the validity of the Born Approximation, i.e. theone-photon exchange mechanism between electron andnuclei, and to date it has achieved much successful result.The large flexibility of the electron probe is reflected in thecross section, of which large number of structure functionsappear, relevant to the different ways of the targetsabsorbing the virtual photons correspondingly. Thus 50separation of the longitudinal and transverse components ofthe transition matrix elements is possible, and this assertionhas been confirmed by experiments. The model taken in this paper is the Waleckamodel(σ ?ω model). This model is a relativistic quantumfield theory describing nucleons interaction via the neutralscalar and vector mesons. The model was quite successful inreproducing many properties of nuclear matter and closedshell nuclei. Addition to Hartree approximation we introducethe effect of the Dirac sea i.e. the effect of the vacuumpolarization (RHA). But the RHA induces diverges and thusthe propagator must be renormalized. So we should use RPAto sum all the rings to infinite order. The unphysical pole may appear during solving the Dysonequation, known as the Landau ghost in QED. It has nomeaning in physics, so it should be eliminated. Redmondhad given the method of solving the Landau ghost in zerodensity. And Tanaka etc. have extended this method to finitedensity case. In this paper, we use Tanaka's method in finite 51density to give the interpretation of propagator. In contrast toTanaka's general vector meson dominance (GVMD)approximation we use another way to give the expression ofthe response function. Furthermore we prove that themethod we use is more rigorous simple and convenient thanTanaka's. Then we apply it to the response function andcompared the result with Tanaka's. At last we list thenumerical result to illustrate the position of ghost pole andits contribution to response function. From the figure we cansee the result is depressed by RPA. But the Fermi gas modeloverestimated the response function about 20％, this provedthat RPA without ghost pole is a good method forcalculation.