Neutron refractive index: A Fermi-Huygens theory.
Neutron refractive index: A Fermi-Huygens theory.
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中子折射率：费米-惠更斯理论。
DOI：
10.1103/physrevb.32.6347
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发表时间：
1985
期刊：
影响因子：
--
通讯作者：
Gubernatis
中科院分区：
文献类型：
--
作者：
Warner;Gubernatis
通过对费米-惠更斯方法的推广，对中子折射率进行了多次散射计算。扩展包括通过积分半无限介质中的横向坐标，然后将游动的部分部分求和到无限量级，将问题投影到一维游动中。折射率的平方由n/sup 2/-1=-(4..pi..rob/k/sub0//sup2/)/(1+(4..pi..rob/sup2//nk/sub0/)..积分../sub0//sup无穷/da e 0asin(nk/sub0/a)h(A))给出，其中k/sub0/是入射波传播向量，b是核散射长度，Rho是原子核的数密度(比方说Ro等效数1/a/sub0//sup3/)，和h(A)=g(A)-1，其中g(A)是对分布函数。这些结果与用本构方程方法得到的结果相似，并提供了局域场效应的物理图像。当平均散射长度为零(总非相干)时，相关多重散射产生n/sup 2/-1近似(B/a/sub0/)/sup 4/(k/sub0/a/sub0/)/sup-2/ln((k/sub0/a/sub0/)/sup-1/)。因此，除非b很大(a共振)或k/sub0/..->；..0(超冷中子)，否则折射率非常接近于1。对数项的存在表明散射场的随机性明显降低了有效维度。
A multiple-scattering calculation of the neutron refractive index is performed by an extension of the Fermi-Huygens technique. The extension involves projecting the problem into a one-dimensional walk by integrating out the transverse coordinate in a semi-infinite medium and then partially summing parts of the walk to infinite order. The square of the refractive index is given by n/sup 2/-1 = -(4..pi..rhob/k/sub 0//sup 2/)/(1+ (4..pi..rhob/sup 2//nk/sub 0/) ..integral../sub 0//sup infinity/da e 0asin(nk/sub 0/a)h(a)), where k/sub 0/ is the incident wave propagation vector, b the nuclear scattering length, rho the number density of nuclei (rhoequivalent1/a/sub 0//sup 3/, say), and h(a) = g(a)-1, where g(a) is the pair distribution function. The results parallel those obtained by constitutive equation methods, and offer a physical picture of local-field effects. When the mean scattering length vanishes (total incoherence), correlated multiple scattering yields n/sup 2/-1approx.(b/a/sub 0/)/sup 4/(k/sub 0/a/sub 0/ )/sup -2/ ln((k/sub 0/a/sub 0/)/sup -1/). Thus, the refractive index is exceedingly close to unity unless b is large (a resonance) or k/sub 0/..-->..0 (ultracold neutrons). The presence of the logarithmic term indicates that randomness in the scattering field apparently reduces the effective dimension.