Geodesic
On resonant scattering by a~negative potential
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 16, Tome 138 (1984), pp. 184-193

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The dependence on a coupling constant $g>0$ of the total crosssection $\sigma(g)$ (of a fixed energy of a particle) for quantum scattering by a potential $gV(x)$ with a compact support is considered. It is found that for a central potential with a nontrivial negative part $\sigma(g)$ is unbounded for some sequence $g_l\to\infty$. Moreover the lower estimate $\sigma(g_l)\geqslant cg_l^{1/2}$, $c>0$, holds. On the contrary, for a positive repulsive potential (not necessarily central) the total cross-section is shown to be bounded uniformly in $g$. 
@article{ZNSL_1984_138_a12,
     author = {D. R. Yafaev},
     title = {On resonant scattering by a~negative potential},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {184--193},
     publisher = {mathdoc},
     volume = {138},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_138_a12/}
}
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D. R. Yafaev. On resonant scattering by a~negative potential. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 16, Tome 138 (1984), pp. 184-193. http://geodesic.mathdoc.fr/item/ZNSL_1984_138_a12/