First Correction to the Geometric-Optics Scattering Cross Section from Cylinders and Spheres

Rubinow, S. I.; Wu, Tianfeng

doi:10.1063/1.1722537

Cited by 42 publications

(24 citation statements)

References 7 publications

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“…As an introduction to this physically based point of view, we briefly review how it has been applied previously to plane-wave scattering by a nonabsorbing spherical particle. For plane-wave incidence, forward scattering by a dielectric spherical particle is dominated by diffraction, the specular reflection forward glory, 29,30 and transmission through the particle. In this case, for a .…”

Section: Two Approximations To the Extinction Cross Section For Gaussmentioning

confidence: 99%

Failure of the optical theorem for Gaussian-beam scattering by a spherical particle

1995

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Section: Two Approximations To the Extinction Cross Section For Gaussmentioning

confidence: 99%

Failure of the optical theorem for Gaussian-beam scattering by a spherical particle

1995

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“…• ([pi(r, t), p;(0, 0)]) (19) and pi is the ion density operator. The ionic motion in the diffusive limit is governed by the relaxation equation…”

Section: B(k 0))mentioning

confidence: 99%

Mobility of negative ions in superfluid 3He-B

1979

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We calculate the mobility of negative ions in superfluid 3He-B. We first derive the general formula for the mobility, and show that to a good approximation the scattering of quasiparticles from an ion may be treated as elastic, both in the superfluid for temperatures not too far below the transition temperature and also in the normal state. The scattering cross section in the superfluid is then calculated in terms of normal state properties; as we show, it is vital to include the effects of superfluid correlations on intermediate states in the scattering process. We find that for quasiparticles near the gap edge, the quasiparticle-ion scattering amplitude has a resonant behavior, and that as a result of interference among many partial waves, the differential scattering cross section is strongly peaked in the forward direction and reduced at larger angles, in much the same way as in diffraction. The transport cross section for such a quasiparticle is strongly reduced compared to that for a normal state quasiparticle, and the mobility is consequently strongly enhanced. Detailed calculations of the mobility which contain essentially no free parameters, agree well with the experimental data.

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“…(96) is essential for describing the penumbra. We compare our result with the asymptotic form of the exact solution in the penumbra obtained in [5,6]. In the penumbra kl 0 ( kR and one can expand G r in powers of kl 0 .…”

Section: 4mentioning

confidence: 82%

“…(27), it is illustrative to consider the example of diffraction when the excluded volume V is a sphere of radius R. The exact expressions for the Green functions are known for this case and their asymptotic expansion for large kR ¼ ER=ð hvðEÞÞ has been obtained [1,5,6]. Besides making contact with previous work, the spherical case also exhibits some analytical properties of the Green function G c c that are essential in the construction of the solution for a more general obstacle.…”

Section: An Example: Diffraction By a Sphere In A Uniform Mediummentioning

confidence: 92%

Diffraction in the semiclassical approximation to Feynman's path integral representation of the Green function

Schaden

Spruch

2004

Annals of Physics

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We derive the semiclassical approximation to Feynman's path integral representation of the energy Green function of a massless particle in the shadow region of an ideal obstacle in a medium. The wavelength of the particle is assumed to be comparable to or smaller than any relevant length of the problem. Classical paths with extremal length partially creep along the obstacle and their fluctuations are subject to non-holonomic constraints. If the medium is a vacuum, the asymptotic contribution from a single classical path of overall length L to the energy Green function at energy E is that of a non-relativistic particle of mass E=c 2 moving in the two-dimensional space orthogonal to the classical path for a time s ¼ L=c. Dirichlet boundary conditions at the surface of the obstacle constrain the motion of the particle to the exterior half-space and result in an effective time-dependent but spatially constant force that is inversely proportional to the radius of curvature of the classical path. We relate the diffractive, classically forbidden motion in the ''creeping'' case to the classically allowed motion in the ''whispering gallery'' case by analytic continuation in the curvature of the classical path. The non-holonomic constraint implies that the surface of the obstacle becomes a zero-dimensional caustic of the particle's motion. We solve this problem for extremal rays with piecewise constant curvature and provide uniform asymptotic expressions that are approximately valid in the penumbra as well as in the deep shadow of a sphere.

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First Correction to the Geometric-Optics Scattering Cross Section from Cylinders and Spheres

Cited by 42 publications

References 7 publications

Failure of the optical theorem for Gaussian-beam scattering by a spherical particle

Failure of the optical theorem for Gaussian-beam scattering by a spherical particle

Mobility of negative ions in superfluid 3He-B

Diffraction in the semiclassical approximation to Feynman's path integral representation of the Green function

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