Geodesic
Interaction range perturbation theory for three-particle problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 2, pp. 275-287

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The limit of zero interaction range is correctly defined for a system of three spinless particles and three particles in a doublet state. The scattering amplitude is expanded with respect to the interaction range $r$, and the corrections of order $r\ln r$, $r$, and $r^2\ln^2r$ are found. An explicit model-independent asymptotic expression is obtained for the scattering amplitude in terms of the scattering length, and its accuracy is established. 
@article{TMF_1988_75_2_a11,
     author = {I. V. Simenog and D. V. Shapoval},
     title = {Interaction range perturbation theory for three-particle problem},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {275--287},
     publisher = {mathdoc},
     volume = {75},
     number = {2},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_75_2_a11/}
}
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I. V. Simenog; D. V. Shapoval. Interaction range perturbation theory for three-particle problem. Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 2, pp. 275-287. http://geodesic.mathdoc.fr/item/TMF_1988_75_2_a11/