Born series for potential scattering

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Abstract

The Born series for the T matrix is considered with the class of potentials V(r)=V00dtA(t)×e-tr2. An explicit knowledge of A(t) is not necessary since the resulting scattering amplitude can be expressed in terms of V. The exact expressions for the first and second Born approximations are utilized to approximate the general nth-order term in the series. The series is explicitly summed to yield an expression for the scattering amplitude which reduces at high energy to the previous impact-parameter amplitude of Blankenbecler and Goldberger. The continuation of the series beyond its radius of convergence is discussed and exemplified with an exponential potential V=V0e-r. A few specific numerical examples are considered to illustrate the behavior of the resulting scattering cross section. Improvement of low-energy total cross sections is noted, particularly for repulsive or weakly attractive potentials.

Original languageEnglish (US)
Pages (from-to)620-627
Number of pages8
JournalPhysical Review A
Volume5
Issue number2
DOIs
StatePublished - Jan 1 1972

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scattering amplitude
scattering
Born approximation
scattering cross sections
radii
energy
cross sections
matrices

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

Cite this

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abstract = "The Born series for the T matrix is considered with the class of potentials V(r)=V00dtA(t)×e-tr2. An explicit knowledge of A(t) is not necessary since the resulting scattering amplitude can be expressed in terms of V. The exact expressions for the first and second Born approximations are utilized to approximate the general nth-order term in the series. The series is explicitly summed to yield an expression for the scattering amplitude which reduces at high energy to the previous impact-parameter amplitude of Blankenbecler and Goldberger. The continuation of the series beyond its radius of convergence is discussed and exemplified with an exponential potential V=V0e-r. A few specific numerical examples are considered to illustrate the behavior of the resulting scattering cross section. Improvement of low-energy total cross sections is noted, particularly for repulsive or weakly attractive potentials.",
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Born series for potential scattering. / Rabitz, Herschel Albert.

In: Physical Review A, Vol. 5, No. 2, 01.01.1972, p. 620-627.

Research output: Contribution to journalArticle

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AU - Rabitz, Herschel Albert

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AB - The Born series for the T matrix is considered with the class of potentials V(r)=V00dtA(t)×e-tr2. An explicit knowledge of A(t) is not necessary since the resulting scattering amplitude can be expressed in terms of V. The exact expressions for the first and second Born approximations are utilized to approximate the general nth-order term in the series. The series is explicitly summed to yield an expression for the scattering amplitude which reduces at high energy to the previous impact-parameter amplitude of Blankenbecler and Goldberger. The continuation of the series beyond its radius of convergence is discussed and exemplified with an exponential potential V=V0e-r. A few specific numerical examples are considered to illustrate the behavior of the resulting scattering cross section. Improvement of low-energy total cross sections is noted, particularly for repulsive or weakly attractive potentials.

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