Frame dependence ofHe3transverse(e,e′

Abstract

The transverse electron scattering response function of 3 He was recently studied by us in the quasi-elastic peak region for momentum transfers q between 500 and 700 MeV/c. Those results, obtained using the Active Nucleon Breit frame (ANB), are here supplemented by calculations in the laboratory, Breit and ANB frames using the two-fragment model discussed in our earlier work on the frame dependence of the the longitudinal response function R L (q, ω). We find relatively frame independent results and good agreement with experiment especially for the lower momentum transfers. This agreement occurs when we neglect an ω-dependent piece of the one-body current relativistic correction. An inclusion of this term leads however to a rather pronounced frame dependence at q = 700 MeV/c. A discussion of this term is given here. This report also includes a correction to our previous ANB results for R T (q, ω).PACS numbers: 25.30.Fj, 21.30 showed that the ANB frame appeared to diminish the effects of using non-relativistic nuclear dynamics. In addition, a two-fragment model was introduced which was found to significantly reduce frame dependence. In that model one assumes a quasi-elastic knock-out of a nucleon such that the residual nucleus remains in its lowest energy state. The relative momentum of the two fragments is determined in a relativistically correct way and the energy that is used as input to the non-relativistic calculation is obtained from that momentum by the usual non-relativistic relation. Considering for example the lab system, the quasielastically knocked out nucleon has momentum q, thus a difference between non-relativistic and relativistic kinetic energies ofTaking for example q = 700 MeV/c one has ∆T 1b = 29 MeV. This relativistic effect is automatically taken into account in the two-fragment model. It is important to state that this model only fixes a kinematical input while the full three-nucleon dynamics is still treated completely via the LIT technique. Thus a comparison of calculations done in the ANB frame with those done in any other frame (including the ANB frame) but with the two-fragment model provides some indication of uncertainties due to non-covariance.In dealing with the transverse response function of 3 He near the quasi-elastic peak where the energy-momentum of the virtual photon is absorbed predominantly by the single ejected nucleon one can again adopt the two-fragment model. Compared to the longitudinal response function there is however a slight difference in applying the two-fragment model to the transverse response. For the former we did not include a two-body charge operator, while for the latter we do consider, as mentioned above, an MEC. It is not evident that such a two-body current should be taken into account in the two-fragment model, since it violates the assumption of a quasi-elastic knock-out. Instead one may assume the following scenario (lab-system): initially two nucleons have opposite and equal momenta p and −p while the 2 third nucleon is at rest. If the photo...

Relativistic effects in ab initio electron-nucleus scattering

“…This effect, is expected to be smaller in the ANB frame, where the ω-dependent correction in the current considered in Ref. [24] vanishes at the quasielastic peak.…”

“…This is consistent with the findings of Refs. [24,44] and their inclusion will be the subject of future work.…”

“…In Refs. [21][22][23][24][25], it was proposed that one should perform the nonrelativistic calculation in a specific reference frame, where relativistic effects are as small as possible. For example, in electron nucleon scattering one prefers the Breit system, where the initial nucleon is moving with −q/2.…”

“…Using the LIT method, the two-fragment model has been applied to the calculation of the 3 He longitudinal [21] and transverse response functions [24,25]. Meson exchange and ∆ isobar currents as well as relativistic corrections of order q 2 /m 2 for the one-body charge and current operators were included.…”

Some relativistic aspects of nuclear dynamics at the electrodisintegration of nuclei

“…In addition, one may note that the q = 700 MeV/c data are obtained [12] via averaging the data of various groups according to an authors' judgment. The ANB frame was employed also in the calculations of the transverse response [16,17].…”