标题： Gersten-Nitzan 和 Ford-Webber 非辐射速率的超收敛表示 显示英文标题

标题： A superconvergent representation of the Gersten-Nitzan and Ford-Webber nonradiative rates

摘要： 对Gersten和Nitzan [J. Chem. Phys. 1981, 75, 1139]以及Ford和Weber [Phys. Rep. 1984, 113, 195]提出的准静态非辐射速率的一种替代表示形式，分别适用于偶极子的平行和垂直取向。给定偶极子到半径为a的球体表面的距离d，该表示形式包括四个基本解析函数和一个考虑剩余多极贡献的修正多极级数。这些解析函数可以根据短距离极限d ---> 0处的奇异性按降序排列，从d^{-3}到d^{-1}最后到ln (d/a)。替代表示形式表现出显著改进的收敛特性。在仅保留修正多极级数的剩余偶极子贡献的情况下，对于所有距离、任意粒子尺寸和发射波长以及广泛范围的介电常数，该表示形式与收敛速率至少有99.9%的一致性。表示形式的解析项揭示了复杂的距离依赖性，并可用于以前所未有的精度在熟悉的d^{-3}短距离行为和d^{-6}长距离行为之间进行插值。因此，这些表示形式对于在存在金属纳米颗粒或纳米天线的情况下，理解荧光团和半导体量子点的非辐射速率的距离行为，具有特别重要的定性和定量意义。作为副产品，还推导出了准静态非辐射速率的完整短距离渐近表达式。上述关于非辐射速率的结果可直接转化为所谓的图像增强因子Delta，这对于表面增强拉曼散射具有相关性。 显示英文摘要

摘要： An alternative representation of the quasistatic nonradiative rates of Gersten and Nitzan [J. Chem. Phys. 1981, 75, 1139] and Ford and Weber [Phys. Rep. 1984, 113, 195] is derived for the respective parallel and perpendicular dipole orientations. Given the distance d of a dipole from a sphere surface of radius a, the representations comprise four elementary analytic functions and a modified multipole series taking into account residual multipole contributions. The analytic functions could be arranged hierarchically according to decreasing singularity at the short distance limit d ---> 0, ranging from d^{-3} over d^{-1} to ln (d/a). The alternative representations exhibit drastically improved convergence properties. On keeping mere residual dipole contribution of the modified multipole series, the representations agree with the converged rates on at least 99.9% for all distances, arbitrary particle sizes and emission wavelengths, and for a broad range of dielectric constants. The analytic terms of the representations reveal a complex distance dependence and could be used to interpolate between the familiar d^{-3} short-distance and d^{-6} long-distance behaviors with an unprecedented accuracy. Therefore, the representations could be especially useful for the qualitative and quantitative understanding of the distance behavior of nonradiative rates of fluorophores and semiconductor quantum dots involving nanometal surface energy transfer in the presence of metallic nanoparticles or nanoantennas. As a byproduct, a complete short-distance asymptotic of the quasistatic nonradiative rates is derived. The above results for the nonradiative rates translate straightforwardly to the so-called image enhancement factors Delta, which are of relevance for the surface-enhanced Raman scattering.