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Register a new userGreens Function Approach to Inclusive Electron Scattering
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A Greens function approach to the inclusive quasielastic ($e,e$) scattering is presented. The components of the nuclear response are written in terms of the single-particle optical model Greens function. The explicit calculation of the Greens function can be avoided by its spectral representation, which is based on a biorthogonal expansion in terms of the eigenfunctions of the non-Hermitian optical potential and of its Hermitian conjugate. This allows one to treat final state interactions consistently in the inclusive ($e,e$) and in the exclusive ($e,eN$) reactions. Numerical results for the longitudinal and transverse response functions obtained in a nonrelativistic and in a relativistic framework are presented and discussed also in comparison with data.
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We compute inclusive electron-nucleus cross sections using ab initio spectral functions of $^4$He and $^{16}$O obtained within the Self Consistent Greens Function approach. The formalism adopted is based on the factorization of the spectral function and the nuclear transition matrix elements. This allows to provide an accurate description of nuclear dynamics and to account for relativistic effects in the interaction vertex. Our calculations use a saturating chiral Hamiltonian in order reproduce the correct nuclear sizes. When final state interactions for the struck particle are accounted for, we find nice agreement between the data and the theory for the inclusive electron-$^{16}$O cross section. The results lay the foundations for future applications of the Self Consistent Greens Function method, in both closed and open shell nuclei, to neutrino data analysis. This work also presents results for the point-proton, charge and single-nucleon momentum distribution of the same two nuclei. The center of mass can affect these quantities for light nuclei and cannot be separated cleanly in most ab initio post-Hartree-Fock methods. In order to address this, we developed a Metropolis Monte Carlo calculation in which the center of mass coordinate can be subtracted exactly from the trial wave function and the expectation values. We gauged this effect for $^4$He by removing the center of mass effect from the Optimal Reference State wave function that is generated during the Self Consistent Greens Function calculations. Our findings clearly indicate that the residual center of mass contribution strongly modifies calculated matter distributions with respect to those obtained in the intrinsic frame. Hence, its subtraction is crucial for a correct description of light nuclei.
We compare the results of the relativistic Greens function model with the experimental data of the charged-current inclusive differential neutrino-nucleus cross sections published by the T2K Collaboration. The model, which is able to describe both MINER$ u$A and MiniBooNE charged-current quasielastic scattering data, underpredicts the inclusive T2K cross sections.
The production of slow nucleons in semi-inclusive deep inelastic electron scattering off the deuteron is investigated in the region $x gsim 0.3$. It is shown that within the spectator mechanism the semi-inclusive cross section exhibits a scaling property even at moderate values of $Q^2$ ($sim$ few $(GeV/c)^2$) accessible at present facilities, like $CEBAF$. Such a scaling property can be used as a model-independent test of the dominance of the spectator mechanism itself and provides an interesting tool to investigate the neutron structure function. The possibility of extracting model-independent information on the neutron to proton structure function ratio from semi-inclusive experiments is illustrated. The application of the spectator scaling to semi-inclusive processes off complex nuclei is outlined.
We have studied the scaling properties of the electromagnetic response functions of $^4$He and $^{12}$C nuclei computed by the Greens Function Monte Carlo approach, retaining only the one-body current contribution. Longitudinal and transverse scaling functions have been obtained in the relativistic and non relativistic cases and compared to experiment for various kinematics. The characteristic asymmetric shape of the scaling function exhibited by data emerges in the calculations in spite of the non relativistic nature of the model. The results are consistent with scaling of zeroth, first and second kinds. Our analysis reveals a direct correspondence between the scaling and the nucleon-density response functions.
The production of slow nucleons in semi-inclusive deep inelastic electron scattering off the deuteron is investigated in the region $x gsim 0.3$ for kinematical conditions accessible at $HERA$. Within the spectator mechanism the semi-inclusive cross section exhibits a scaling property, which can be used as a model-independent test of the dominance of the spectator mechanism itself, providing in this way an interesting tool to investigate the neutron structure function. The possibility of extracting model-independent information on the neutron to proton structure function ratio from semi-inclusive experiments is also illustrated.
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