1969
DOI: 10.1063/1.1671872
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Noniterative Solutions of Integral Equations for Scattering. II. Coupled Channels

Abstract: The recently developed method of homogeneous integral solutions for solving integral equations of scattering is extended to include coupled channels. The formalism is developed in matrix notation and applies without change both to purely local interactions and to combined nonlocal and local interactions. A numerical quadrature method for solving the integral equations is presented. This method does not require iteration or matrix inversions. Further, during the entire calculation of the wavefunction and T (or … Show more

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Cited by 124 publications
(10 citation statements)
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“…(5) terminates at r 0 r and Eqs. (5) are recognized as Volterra-type equations [15,16]. We replace the nonlocal exchange with an energy-dependent local potential, as suggested by Hara [17] within the free-electron gas model (HFEGE):…”
mentioning
confidence: 99%
“…(5) terminates at r 0 r and Eqs. (5) are recognized as Volterra-type equations [15,16]. We replace the nonlocal exchange with an energy-dependent local potential, as suggested by Hara [17] within the free-electron gas model (HFEGE):…”
mentioning
confidence: 99%
“…In this expression, U ll denotes the matrix elements of the local contributions to the interaction potential which include the static and correlation-polarization potentials. The integral form of these equations is solved with the Sams and Kouri method [43,44] extended by Rescigno and Orel to the multichannel case for a separable exchange potential [29,39]. The radial components of the wave function are expressed as a linear combination of homogeneous and inhomogeneous terms…”
Section: Scattered Wavementioning
confidence: 99%
“…For mathematical simplicity, we shall also assume that the interaction has “compact support” (i.e., it is zero outside the range of r max ): In general, however, our results will hold for interactions that are not too singular at r = 0 and that tend to zero faster than 1 / r 2 as r → ∞. Following Sams and Kouri and Kouri and Vijay, we rewrite eq 15 as But so we write eq 28 as We recognize that the factor [1 + + i ], although unknown, is simply a constant normalization so that where Equation 32 for u lk ( r ) has the tremendous virtue, compared to the Lippmann−Schwinger equation for ( r ), of being a Volterra integral equation, , and under iteration, it converges absolutely and uniformly for all appropriately measurable interactions because the kernel, G̃ l 0k ( r , r ‘) V ( r ‘), is triangular, implying that the Fredholm determinant is identically one …”
Section: Renormalization Of the Lippmann−schwinger Equationmentioning
confidence: 99%