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Near-threshold quantization and level densities for potential wells with weak inverse-square tails

URN to cite this document:
Moritz, Michael J. ; Eltschka, Christopher ; Friedrich, Harald
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Date of publication of this fulltext: 28 Apr 2010 11:42


For potential tails consisting of an inverse-square term and an additional attractive 1/r^m term, V(r)∼[ħ^2/(2M)][(γ/r^2)-(β^(m-2)/r^m)], we derive the near-threshold quantization rule n=n(E) which is related to the level density via ρ=dn/dE. For a weak inverse-square term, -1/4 < γ <3/4 (and m>2), the leading contributions to n(E) are n=^(E→0) A-B(-E)^sqrt[γ+1/4], so ρ has a singular ...


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