MacDiarmid Institute for Advanced Materials and Nanotechnology, Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand.
J Acoust Soc Am. 2011 Jun;129(6):3465-9. doi: 10.1121/1.3575627.
A phase shift formulation of scattering by oblate and prolate spheroids is presented, in parallel with the partial-wave theory of scattering by spherical obstacles. The crucial step is application of a finite Legendre transform to the Helmholtz equation in spheroidal coordinates. In the long-wavelength limit the spheroidal analog of the spherical scattering length immediately gives the cross section. Analytical results are readily obtained for scattering of Schrödinger particle waves by impenetrable spheroids, and for scattering of sound waves by acoustically soft spheroidal objects. The method is restricted to scattering by spheroids whose symmetry axis is coincident with the direction of the incident plane wave.
提出了扁长和长球椭球体散射的相移公式，与球形障碍物散射的分波理论并行。关键步骤是在球坐标中对亥姆霍兹方程进行有限勒让德变换。在长波极限下，球型散射长度的椭球类比立即给出截面。对于不可穿透的椭球对薛定谔粒子波的散射，以及对声波对声学软椭球物体的散射，很容易得到解析结果。该方法仅限于对称轴与入射平面波方向重合的椭球体的散射。
