Low-energy expansions in nuclear physics

Construction of regular solutions of Schrödinger and Faddeev equations in the linear three-particle configuration limit

“…A construction of the scattering theory in this statement of the three-particle problem was given in [3]; the three-dimensional Faddeev equations were then actively used to calculate the characteristics of actual three-particle systems. The results of the first calculations performed in the framework of such equations were discussed in [19]. The three-dimensional Faddeev equations were recently derived in the two cases t = x and t = y in [20].…”

“…A comparative analysis of discrete spline analogues of such systems was given in [17]. In all such analogues of the Faddeev equations, it is easy to use the obtained asymptotic expansions (78)-(80) of the sought components Ψ ε iab and the proved constraints (82).…”

“…We now analyze the process of constructing the D σ -components Ψ εt m of series (48). We apply (47) and (49) and construct the image Ψ ε = P εt Ψ of series (17) with components (18) and thus prove that the D σ -components Ψ εt m are series in integer powers of y and in finite sums Ψ nεt m of the projections Y bβ | Ψ n aα of the components Ψ n aα of the general solution:…”

“…We replace the sought solution Ψ with series (17) to reduce Schrödinger equation (2) to the chain of recurrence relations in n…”

Structure of regular solutions of Faddeev equations near the pair impact point

“…The results of such studies were presented in [2]- [6] and in many other papers discussed in [7]. The most complete analysis of the structure of the wave function near the pair impact point was given in [8], where the sixdimensional Schrödinger equation was studied for a three-particle system with central pair interactions more general than the Coulomb interaction.…”