Scattering by a contact potential in three and lower dimensions
Scattering by a contact potential in three and lower dimensions
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DOI：
10.1088/0305-4470/34/9/308
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发表时间：
2001-03
期刊：
影响因子：
--
通讯作者：
Q. Lin
中科院分区：
文献类型：
--
作者：
Q. Lin
我们考虑了接触势Ω2δ(R)/2µrα对三维非相对论粒子的散射，定义为a→0极限为Ω2δ(r-a)/2µrα。令人惊讶的是，当α=1和Ω=-1时，它给出了一个不消失的横截面。当用球方势用球壳势作近似时，得到的结果基本相同，只是给出非零截面的参数Ω不同。研究了二维和一维的相似问题，得到了性质相同的结果。
We consider the scattering of nonrelativistic particles in three dimensions by a contact potential Ω2δ(r)/2µrα, which is defined as the a→0 limit of Ω2δ(r-a)/2µrα. It is surprising that it gives a nonvanishing cross section when α = 1 and Ω = -1. When the contact potential is approached by a spherical square well potential instead of the above spherical shell one, one obtains basically the same result except that the parameter Ω that gives a nonvanishing cross section is different. Similar problems in two and one dimensions are studied and results of the same nature are obtained.