Geodesic
Point interactions with internal structure as a limit of separable potentials
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 21, Tome 182 (1990), pp. 113-122

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The one-center point interactions with an additional “internal” canal are considered. The corresponding generalised Krein's resolvents in the functional sector are approximated by means of rank-one non-local interactions-in weak resolvent sense. The cut-off procedure in $p$-representation is formulated. 
@article{ZNSL_1990_182_a5,
     author = {K. A. Makarov and S. E. Cheremshantsev},
     title = {Point interactions with internal structure as a limit of separable potentials},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {113--122},
     publisher = {mathdoc},
     volume = {182},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1990_182_a5/}
}
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K. A. Makarov; S. E. Cheremshantsev. Point interactions with internal structure as a limit of separable potentials. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 21, Tome 182 (1990), pp. 113-122. http://geodesic.mathdoc.fr/item/ZNSL_1990_182_a5/