First results for electromagnetic three-nucleon form factors from high-precision two-nucleon interactions

The electromagnetic form factors of the three-nucleon bound states were calculated in complete impulse approximation in the framework of the Covariant Spectator Theory for the new high-precision two-nucleon interaction models WJC-1 and WJC-2. The calculations use an approximation for the three-nucleon vertex functions with two nucleons off mass shell. The form factors with WJC-2 are close to the ones obtained with the older model W16 and to nonrelativistic potential calculations with lowest-order relativistic corrections, while the form factors with the most precise two-nucleon model WJC-1 exhibit larger differences. These results can be understood when the effect of the different types of pion-nucleon coupling used in the various models is examined.

Figure 1

The electromagnetic $3N$ current in CST for elastic electron scattering from the $3N$ bound state. A cross on a nucleon line indicates that the particle is on mass shell. Diagrams (A)–(F) define the complete impulse approximation (CIA), in which the photon couples to single nucleons, which can be off shell [(A) and (D)] or on shell before or after the photon-nucleon vertex [(B), (C), (E), and (F)]. The approximation denoted CIA-0 replaces the vertex function with two nucleons off mass shell in diagrams (B), (C), (E), and (F) by a vertex function with only one nucleon off mass shell. The interaction diagrams [(G)–(J)] describe processes in which the photon couples to two-body currents associated with the two-nucleon kernel.

Figure 2

Charge form factors of the $3N$ bound states, ${}^3\mathrm{H}$ (first row), ${}^3\mathrm{He}$ (second row), and the isoscalar (third row) and isovector (fourth row) combinations. In each case, the figure on the left shows the form factor in the traditional semilog plot, whereas the figure on the right shows the same form factor divided by a scaling function of Eq. (15) [2] on a linear scale. The solid line is the result for $\mathit{NN}$ model W16 in CIA; the dotted line is the approximation CIA-0 for the same model. The dashed line is model WJC-1, and the dash-dotted line is model WJC-2, both in CIA-0. For comparison, the solid line with theoretical error bars is the result of an IARC calculation by Marcucci [12] based on the AV18/UIX potential. All calculations employ the on-shell single-nucleon current, with the Galster parametrization of the nucleon form factors [11]. The solid circles represent the experimental data [13, 14, 15, 16, 17, 18, 19, 20, 21, 22].

Figure 3

Magnetic form factors of the $3N$ bound states, ${}^3\mathrm{H}$ (first row), ${}^3\mathrm{He}$ (second row), and the isoscalar (third row) and isovector (fourth row) combinations. In each case, the figure on the left shows the form factor in the traditional semilog plot, whereas the figure on the right shows the same form factor divided by a scaling function [2] on a linear scale. The meaning of the various curves is the same as in Fig. 2.