Role of the Final-State Interaction and Three-Body Force on the Longitudinal Response Function ofHe4

Abstract

We present an ab-initio calculation of the longitudinal electron scattering response function off 4 He with two-and three-nucleon forces and compare to experimental data. The full four-body continuum dynamics is considered via the Lorentz integral transform method. The importance of the final state interaction is shown at various energies and momentum transfers q. The three-nucleon force reduces the quasi-elastic peak by 10% for q between 300 and 500 MeV/c. Its effect increases significantly at lower q, up to about 40% at q=100 MeV/c. At very low q, however, data are missing.PACS numbers: 25.30.Fj, 27.10.+h, 31.15.xj Inelastic electron scattering off nuclei provides important informations on nuclear dynamics. Varying the momentum q, transferred by the electron to the nucleus, one can focus on different dynamical regimes. At lower q the collective behavior of nucleons is studied. As q increases one probes properties of the single nucleon in the nuclear medium and its correlations to other nucleons from longto short-range. Thus the inclusive longitudinal R L and transverse R T response functions are of particular importance. Different from R T , in a non-relativistic framework R L does not require the knowledge of implicit degrees of freedom (exchange currents), providing a clean leptonic probe of the nuclear Hamiltonian. In addition, the theoretical study of inclusive processes is important to help planning further investigations, for selected kinematics, via exclusive scattering experiments.In the '80 and '90's an intense experimental activity has been devoted to inclusive electron scattering, (e, e ′ ), in the so called quasi-elastic (q.e.) regime, corresponding to q-values of several hundred MeV/c and energy transfers ω around the q.e. peak (ω ≃ q 2 /2m). Here one can envisage that the electron has scattered elastically with a single nucleon of mass m. Various nuclear targets have been considered, from very light to heavy ones [1]. At these q one enters a very challenging regime, where nuclear and subnuclear degrees of freedom interwine. A very alive debate has taken place about the interpretation of those data. The two most discussed topics have been: (i) short-range correlations, i.e. the dynamical properties of nucleons at short distances; (ii) in medium modifications of the nucleon form factor. To date the debate is still open. More experiments are planned at Jefferson Laboratory (E05.110 at Hall A) which will contribute to those issues and a theoretical effort is needed to help interpreting old and new experimental results.The reason for concentrating on the q.e. regime has been the conviction that for such a kinematics the plane wave impulse approximation (PWIA) might be a reliable framework to describe the reaction. The neglect of the final state interaction (FSI) has the advantage to allow a simple interpretation of the cross section in terms of the dynamical properties of the nucleons in the ground state. Thus it is important to clarify the reliability of the PWIA (as well as of further refinements...

Search for three-nucleon force effects on the longitudinal response function ofHe4

“…In addition to what is shown in our recent Letter [9], here we investigate also other low-q values. Figure 2 shows that the increase of 3NF effects with decreasing q is confirmed.…”

“…Our results with the TM' force are obtained using the same model space as for the UIX potential and the accuracy of the convergence for the LIT is found to be at a percentage level, in analogy to that of the UIX as described in [9]. The cutoff of the TM' force has been adjusted on triton binding energy, when used in conjunction with the AV18 NN force.…”

Electromagnetic Reactions and Few-Nucleon Dynamics

“…Mass numbers A = 3 and A = 4 have been quite extensively studied in conjunction with the hyper-spherical harmonics expansion. For the 4 He case we have recently calculated the (longitudinal) response function S L (ω, q) to the charge density operator [33,34]. S L is well known for not being very sensitive to exchange currents at low q, so we focused on a sensitivity study of this observable to the 3NFs.…”

On the Structure of A=3 Nuclei

“…The results confirm the rapid decrease of forward-angle cross sections with increasing photon energy, whilst at backward angles, aided by the high precision of the measurement, which show the clear enhancement in the angular distribution and is a possible signature of three-body mechanis ms [17]. Also a schematic three-body forces in addition to a general t wo-body forces leads to a strongly improved description of the energies of light and mediu m mass nuclei [18], and there are effects of three-body force on the longitudinal response function of 4 He [19]. Further, wh ile trying to fit the nuclear matter binding energy and density simu ltaneously the results of the best two body interactions, all fall on the so called Coester band.…”

“…The composite nature of the nucleons, indicates that many-nucleon forces, and at the least the three-nucleon forces are necessary to explain many bound state properties. A lot of effort has been devoted to understand the correct nature of nuclear forces and currents and this has resulted in developments of accurate many-body techniques for evaluating them [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”