Separable Expansions of the TwoBody T Matrix for Local Potentials and Their Use in the Faddeev Equation
Abstract
An expansion of the offshell twobody T matrix is introduced in the form of a sum of terms separable in the initial and the finalmomentum variables. The convergence of this expansion is tested against exact solutions of several local potential problems. The substitution of the expansion into the Faddeev equations yields a set of coupled integral equations in one variable. As an example, the binding energy of three identical bosons is calculated using an Swave Yukawa potential for the twobody interaction. It is found that a stationary state exists for the potential strength G>=1.4, whereas a twobody bound state requires G>=1.8. An offshell effectiverange formula is introduced for problems in which the shape of the twobody potential is not well known. It is shown that the difference between the solutions of the Yukawa potential and the exponential potential with the same scattering length and effective range is comparable to the deviation of the offshell effectiverange formula from either solution.
 Publication:

Physical Review
 Pub Date:
 February 1967
 DOI:
 10.1103/PhysRev.154.1540
 Bibcode:
 1967PhRv..154.1540W