Abstract:
It has been found that quantum mechanical three-body Schrödinger equation can be reduced to a
set of coupled differential equations when the projectile can be easily breakable into two
fragments when it is scattering on a heavy stable nucleus [1]. This coupled set of differential
equations is solved under appropriate boundary conditions, and this method, called CDCC, has
been found to be a very successful model in high energy quantum mechanical three body
calculations [2]. It can be shown, however, that the coupling potentials in the coupled
differential equations are actually long-range [3],[4] and asymptotic out going boundary
condition, which is used to obtain elastic and breakup S-matrix elements is not mathematically
justifiable. It has been found that the diagonal coupling potentials in this model takes the inverse
square form at sufficiently large radial distances [3]and non-diagonal part of coupling potentials
can be treated as sufficiently short-range to guarantee numeral calculations are feasible.
Therefore one has to justify that the long range part of diagonal potential has a very small effect
on elastic and breakup S-matrix elements to show that CDCC is mathematically sound
.Although the CDCC method has been successful in many cases, recent numerical
calculations[5],[6]indicate its unsatisfactory features as well. Therefore inclusion of the long
range part in the calculation is also essential. The main objective of this contribution is to show
that the effect of the long range part of the potentials on S-matrix elements is small.
