On the relativistic³D₁partial-wave contribution to the bound three-nucleon system

Abstract

Abstract. The bound state of three nucleons is investigated using the Faddeev equations within the Bethe-Salpeter approach. The relativistic and nonrelativistic nucleon-nucleon interaction is chosen in a multirank separable form. The extension for partial-states with L > 0 is done. Three partial-wave states -1 S 0 , 3 S 1 and 3 D 1 -are taken into account. The Gauss quadrature method is used to calculate the integrals and find the triton binding energy by iterations.

Relativistic rank-one separable kernel for helium-3 charge form factor

“…The equations describe these systems with pair potentials of any kind as bound and scattering states. The relativistic generalization of the Faddeev equations can be applied to a system of three relativistic particles [18,19,20,21,22]. In this case, the relativistic two-particle T matrix is taken as a solution of the Bethe-Salpeter equation (we call such a three-particle equation the Bethe-Salpeter-Faddeev equation, BSF).…”

“…To solve the BSF equation, it is necessary to know the potential of the nucleon-nucleon interaction in the explicit form. The separable kernels of NN interactions can be used [18,19,20,21,22] to simplify the calculations. In recent works, we have solved the BSF equation for rank-one separable kernels of NN interactions and took into account the two-nucleon states with the total angular momentum j = 0 − 1 [26].…”

On The Contribution of the P and D Partial-Wave States to the Binding Energy of the Triton in the Bethe-Salpeter-Faddeev Approach

“…In previous works [7,8] we considered the case of taking into account the D-wave not only in the two-particle t matrix, but also its amplitudes in the system of integral equations. In the present paper, the equation is generalized to the case of nonzero values of the angular momentum of a pair of nucleons (L > 0 : P -и D-states).…”

Sensitivity of elastic electron scattering off the 3He to the nucleon form factors

“…This equation describes these systems with a pair potential of any kind as bound and scattering states. In the case of a system of three relativistic particles, the relativistic generalization of the Faddeev equation can be applied [8][9][10][11]13]. In this case the relativistic two-particles T matrix is taken as a solution of the Bethe-Salpeter equation (we call such three-particle equation as Bethe-Salpeter-Faddeev equation, BSF) or the corresponding covariant spectator (or Gross) equation.…”

“…To solve the BSF equation, it is necessary to know the potential of the nucleonnucleon interaction in the explicit form. To simplify the calculations, the separable kernels of NN interactions can be used [9][10][11]13]. In recent works, we solved the BSF equation for the one-rank separable kernels of NN interactions and took into account the two-nucleon states with total angular momentum j = 0, 1 [12].…”