The 4^4He(e,e′p)3(e,e^\prime p)^3H Reaction with Full Final--State Interaction

An {\it ab initio} calculation of the $^4$He$(e,e^\prime p)^3$H longitudinal response is presented. The use of the integral transform method with a Lorentz kernel has allowed to take into account the full four--body final state interaction (FSI). The semirealistic nucleon-nucleon potential MTI--III and the Coulomb force are the only ingredients of the calculation. The reliability of the direct knock--out hypothesis is discussed both in parallel and in non parallel kinematics. In the former case it is found that lower missing momenta and higher momentum transfers are preferable to minimize effects beyond the plane wave impulse approximation (PWIA). Also for non parallel kinematics the role of antisymmetrization and final state interaction become very important with increasing missing momentum, raising doubts about the possibility of extracting momentum distributions and spectroscopic factors. The comparison with experimental results in parallel kinematics, where the Rosenbluth separation has been possible, is discussed.Comment: 17 pages, 5 figure

Photodisintegration of Three-Body Nuclei with Realistic 2N and 3N Forces

Total photonuclear absorption cross sections of $^3$H and $^3$He are studied using realistic NN and NNN forces. Final state interactions are fully included. Two NN potential models, the AV14 and the r-space Bonn-A potentials, are considered. For the NNN forces the Urbana-VIII and Tucson-Melbourne models are employed. We find the cross section to be sensitive to nuclear dynamics. Of particular interest in this work is the effect which NNN forces have on the cross section. The addition of NNN forces not only lowers the peak height but increases the cross section beyond 70 MeV by roughly 15%. Cross sections are computed using the Lorentz integral transform method.Comment: Results for Bonn potential with model Bonn rA instead of model rB. The Bonn rB results contained a small inexactness. After the correction it turned out that Bonn rA is more suited for our purpose because it leads to a binding energy of 8.15 MeV (about 0.25 MeV more than Bonn rB). In addition the results for the other realistic potentials models are improved at low energies (HH expansion was not completely convergent for the low-energy results). LaTeX, 8 pages, 4 ps figure

Method to solve integral equations of the first kind with an approximate input

Techniques are proposed for solving integral equations of the first kind with an input known not precisely. The requirement that the solution sought for includes a given number of maxima and minima is imposed. It is shown that when the deviation of the approximate input from the true one is sufficiently small and some additional conditions are fulfilled the method leads to an approximate solution that is necessarily close to the true solution. No regularization is required in the present approach. Requirements on features of the solution at integration limits are also imposed. The problem is treated with the help of an ansatz proposed for the derivative of the solution. The ansatz is the most general one compatible with the above mentioned requirements. The techniques are tested with exactly solvable examples. Inversions of the Lorentz, Stieltjes and Laplace integral transforms are performed, and very satisfactory results are obtained. The method is useful, in particular, for the calculation of quantum-mechanical reaction amplitudes and inclusive spectra of perturbation-induced reactions in the framework of the integral transform approach.Comment: 28 pages, 1 figure; the presentation is somewhat improved; to be published in Phys. Rev.

Incorporation of three-nucleon force in the effective interaction hyperspherical harmonic approach

It is shown how a bare three-nucleon force is incorporated into the formalism of the effective interaction approach for hyperspherical harmonics. As a practical example we calculate the ground state properties of 3H and 3He using the Argonne V18 nucleon-nucleon potential and the Urbana IX three-nucleon force. A very good convergence of binding energies and matter radii is obtained. We also find a very good agreement of our results compared to other high precision calculations.Comment: 17 pages, 3 figure

Improved (e,e') response functions at intermediate momentum transfers: the 3He case

A possibility of extending the applicability range of non-relativistic calculations of electronuclear response functions in the quasielasic peak region is studied. We show that adopting a particular model for determining the kinematical inputs of the non-relativistic calculations can extend this range considerably, almost eliminating the reference frame dependence of the results. We also show that there exists one reference frame, where essentially the same result can be obtained with no need of adopting the particular kinematical model. The calculation is carried out with the Argonne V18 potential and the Urbana IX three-nucleon interaction. A comparison of these improved calculations with experimental data shows a very good agreement for the quasielastic peak positions at $q=500,$ 600, 700 MeV/c and for the peak heights at the two lower $q$--values, while for the peak height at $q=700$ MeV/c one finds differences of about 20%.Comment: 10 pages, 4 figure

Total 4He Photoabsorption Cross Section Revisited: Correlated HH versus Effective Interaction HH

Two conceptually different hyperspherical harmonics expansions are used for the calculation of the total 4He photoabsorption cross section. Besides the well known method of CHH the recently introduced effective interaction approach for the hyperspherical formalism is applied. Semi-realistic NN potentials are employed and final state interaction is fully taken into account via the Lorentz integral transform method. The results show that the effective interaction leads to a very good convergence, while the correlation method exhibits a less rapid convergence in the giant dipole resonance region. The rather strong discrepancy with the experimental photodisintegration cross sections is confirmed by the present calculations.Comment: LaTeX, 7 pages, 3 ps figure