On the Asymptotic Behavior of Eigenfunctions of the Continuous Spectrum at Infinity in Configuration Space for the System of Three Three-Dimensional Like-Charged Quantum Particles

On asymptotic structure of three-body scattering states for the scattering problem of charged quantum particles

“…(Hereafter for simplicity we will omit the index 1 of the corresponding Jacobi coordinates, as the procedure itself of approximations correlation will be held as an example in the parabolic vicinity of the screen 1.) Therefore the first summand in the expression (8) describes well the potential V as long as the correction O x y 2…”

“…The diffraction approach in few-body quantum scattering problems with slowly (in the Coulomb way) decreasing repulsion pair potentials was previously discussed in literature [1]- [8] together with other approaches used in manybody scattering problems. Nevertheless the most interesting from the physical point of view case of quantum scattering of few Coulomb clusters (the system being in the Coulomb bound state) for a number of reasons remains not yet studied in detail despite the serious efforts made since the middle of the last century in the direction.…”

“…Note as well that the BBK-approximation is true only in the domain where both Jacobi coordinates corresponding to the chosen pairwise subsystem turn large. To be more exact, [9], [10], [3], [8] we introduce a domain…”

“…Note that the BBK presentation ceases to be true in the asymptotic (by r = x 2 j + y 2 j → ∞, j = 1, 2, 3)domains of the configuration space, where the Jacobi coordinate x j , j = 1, 2, 3 turns finite. The main result of the works [5], [8] is exactly in the construction of the BBK -approximation continuous extension into the asymptotic domains of the configuration space by the finite as well as small values of the Jacobi coordinate x j , j = 1, 2, 3. x j , j = 1, 2, 3. Note once again that these results were obtained in an assumption of the identity of the charge sign of all the particles included into the system, i.e.…”