Quasielastic scattering with the relativistic Green’s function approach

Abstract

Abstract. A relativistic model for quasielastic (QE) lepton-nucleus scattering is presented. The effects of final-state interactions (FSI) between the ejected nucleon and the residual nucleus are described in the relativistic Green's function (RGF) model where FSI are consistently described with exclusive scattering using a complex optical potential. The results of the model are compared with experimental results of electron and neutrino scattering.Keywords: Relativistic models, Electron scattering, Neutrino scattering PACS: 25.30.Pt; 25.30.Fj; 13.15.+g; 24.10.Jv FINAL-STATE INTERACTIONS IN LEPTON-NUCLEUS SCATTERINGIn the QE region the nuclear response to an electroweak probe is dominated by one-nucleon knockout processes, where the scattering occurs with only one nucleon while the remaining nucleons of the target behave as simple spectators. The reaction can adequately be described in the relativistic impulse approximation (IA) by the sum of incoherent processes involving only one nucleon scattering and the components of the hadron tensor are obtained from the sum, over all the single-particle (s.p.) shell-model states, of the squared absolute value of the transition matrix elements of the single-nucleon current. A reliable description of FSI is an essential ingredient for the comparison with data. The relevance of FSI has been clearly stated for the exclusive (e, e ′ p) reaction, where the use of complex optical potentials (OP) in the distorted-wave impulse approximation (DWIA) is required [1,2,3,4,5,6,7,8]. The imaginary part of the OP produces an absorption that reduces the cross section and accounts for the fact that, if other channels are open besides the elastic one, part of the incident flux is lost in the elastically scattered beam and goes to the other (inelastic) channels which are open. In the inclusive scattering only the emitted lepton is detected, the final nuclear state is not determined and all elastic and inelastic channels contribute. This requires a different treatment of FSI where all final-state channels should be retained and the total flux, although redistributed among all possible channels, must be conserved. Different approaches have been used to describe FSI in relativistic calculations for the inclusive QE electron-and neutrino-nucleus scattering. In the relativistic plane-wave impulse approximation (RPWIA), FSI are simply neglected. In another approach, FSI are accounted for in relativistic DWIA (RDWIA) calculations by including only the real part of the relativistic optical potential (rROP).In the RGF techniques [9,10,11,12,13,14,15,16,17,18,19], FSI are described in the inclusive scattering by the same complex OP as in the exclusive scattering, but the imaginary part is used in the two cases in a different way and in the inclusive reaction the flux, although is redistributed in all the channels, is conserved. In the RGF model with suitable approximations, which are mainly related to the impulse approximation, the components of the hadron tensor are written in terms of the s.p. ...