Modified effective-range function
Modified effective-range function
复制标题
修改后的有效范围函数
DOI：
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发表时间：
1982
期刊：
影响因子：
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通讯作者：
L. P. Kok
中科院分区：
文献类型：
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作者：
H. Haeringen;L. P. Kok
本文导出了修正的有效射程函数K/supM//subl/（k/sup 2/）的一般公式。.这是与短程势有关的有效程函数K/sub l/（k/sup 2/）= k/sup 2 l/+1cotdelta/sub l/（k）的推广。这里，k/sup 2/是能量变量，并且delta/sub 1/（k）是相移。MERF K/sup M//sub 1/（k/sup 2/）可以与电势V（r）相关联，该电势V（r）允许分解成长程分量和短程分量。它是一个复k平面上的k/sup 2/的复实亚纯函数。这个（大）域由电势的短程部分决定。给出了K/sup M//sub l/（k/sup 2/）的一个简单公式，它对所有l = 0，1，. .如果势的长程部分在r = 0时是解析的，则可以使用它。对于l = 0，我们有简单表达式K/sup M//sub 0/（k/sup 2/）= Vertical Barf/sub 0/（k）Vertical Bar/sup-2/k（cotdelta/sup M//sub 0/（k）-i）+f ′/sub 0/（k，0）/f/sub 0/（k）。这里，f/sub 0/（k）和f/sub 0/（k，r）分别是与电位的长程部分相关联的Jost函数和Jost解，并且delta/sub M//sub>> 0/（k）是与总电位相关联的s波相移和长程电位的s波相移之间的差。f ′/sub 0/（k，0）中的素数表示关于r的微分。扩展到库仑势的情况下，违反了条件的解析在r = 0的简要讨论。«少
We derive a general formula for a modified effective-range function (MERF), K/sup M//sub l/(k/sup 2/), for all partial waves, l = 0, 1... . This is a generalization of the effective-range function associated with a short-range potential, K/sub l/(k/sup 2/) = k/sup 2l/+1cotdelta/sub l/(k). Here k/sup 2/ is the energy variable and delta/sub l/(k) the phase shift. The MERF K/sup M//sub l/(k/sup 2/) can be associated with a potential V(r) that allows a decomposition into a long-range and a short-range component. It is a complex real-meromorphic function of k/sup 2/ in the complex k plane in a domain containing the origin. This (large) domain is determined by the short-range part of the potential. We give a simple formula for K/sup M//sub l/ (k/sup 2/), valid for all l = 0, 1, ... . It can be used if the long-range part of the potential is analytic at r = 0. For l = 0 we have the simple expression K/sup M//sub 0/(k/sup 2/) = Vertical Barf/sub 0/(k)Vertical Bar/sup -2/k(cotdelta/sup M//sub 0/(k)-i) + f'/sub 0/(k,0)/f/sub 0/(k). Here f/sub 0/(k) and f/sub 0/(k,r) are the Jost function and Jost solution, respectively, associated with the long-range part of the potential, and delta/sup M//submore » 0/(k) is the difference between the s-wave phase shift associated with the total potential and that of the long-range potential. The prime in f'/sub 0/(k,0) denotes differentiation with respect to r. The extension to the case of the Coulomb potential which violates the condition of analyticity at r = 0 is briefly discussed.« less