Calculable methods for many-body scattering

Barrett, R.F.; Robson, B.A.; Tobocman, W.

doi:10.1103/revmodphys.55.155

Cited by 84 publications

(47 citation statements)

References 219 publications

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“…is the classical oscillator turning point corresponding to the oscillator length b, and ψ (−) l α (p α r n α ) (respectively ψ (+) l α (p α r n α )) are the familiar radial Coulomb modified incoming (respectively outgoing) wave functions, normalized to unit flux (see for instance [54]). …”

Section: Boundary Conditionsmentioning

confidence: 99%

A microscopic three-cluster model with nuclear polarization applied to the resonances of 7Be and the reaction 6Li(p, 3He)4He

et al. 2009

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A microscopic model for three-cluster configurations in light nuclei is presented. It uses an expansion in terms of Faddeev components for which the dynamic equations are derived. The model is designed to investigate binary channel processes in a compound system. Gaussian and oscillator bases are used to expand the wave function and to represent appropriate boundary conditions. We study the effect of cluster polarization on ground and resonance states of 7 Be, and on the astrophysical S-factor of the reaction 6 Li(p, 3 He) 4 He.

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Section: Boundary Conditionsmentioning

confidence: 99%

A microscopic three-cluster model with nuclear polarization applied to the resonances of 7Be and the reaction 6Li(p, 3He)4He

et al. 2009

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“…In the generator-coordinate method, because of the use of Slater determinants in the harmonic-oscillator model, the asymptotic behavior of the wave functions is not correctly treated. To solve this problem, the microscopic R-matrix method (MRM) extending the traditional R-matrix method [19,20] has been developed in Refs. [21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Scattering length and effective range for collisions between light ions within a microscopic model

Kamouni¹,

Baye²

2007

Nuclear Physics A

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“…One reason for this is the wish to adapt existing bound state program packages to the calculation of continuum states. Some of the methods using L 2 functions include the complex absorbing potential approach [1], stabilization approaches [2,3], and the many different types of R-matrix methods [4][5][6] including the box-variational method [7], which is used for quantum Monte Carlo scattering calculations [8].…”

mentioning

confidence: 99%

Elastic Scattering Using an Artificial Confining Potential

2008

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The discrete energies of a scattering Hamiltonian calculated under the influence of an artificial confining potential of almost arbitrary functional form can be used to determine its phase shifts. The method exploits the result that two short-range Hamiltonians having the same energy will have the same phase shifts upon removal of the confining potential. An initial verification is performed on a simple model problem. Then the stochastic variational method is used to determine the energies of the confined e À -He 2 S e system and thus determine the low energy phase shifts. The present Letter describes a novel strategy to calculate low energy elastic scattering. An artificial confining potential is added to the scattering Hamiltonian, and the discrete energies of this modified system are determined. We then show that two short-range potentials with the same energies in the confining potential have the same phase shifts when the confining potential is removed. This is similar to the box-variational method [7,9], where the energy inside an infinite-walled box is related to the phase shift. In its simplest form, the box-variational method requires the wave function, and thus the basis functions, to have a zero at the boundary (note that the logarithmic derivative at the boundary can, in principle, be set to any value). The ' ¼ 0 phase shifts for the nth positive energy state with energy E n are then given by the identity. In the present approach, almost any square integrable basis function can be used. Initially, we validate our strategy for scattering with a simple exponential potential. We then determine the low energy phase shifts for e À -He scattering to a higher degree of precision than any previous work [10][11][12] by using an explicitly correlated basis to generate the e À -He energies inside the confining potential.The problem is to solve the Schrödinger equation À r 2 2 þ VðrÞ ÉðrÞ ¼ EÉðrÞfor E > 0. The central potential VðrÞ will be assumed to be zero beyond some finite radius, say, R 0 . Now consider the related equationwhere W CP is a confining potential and E is defined relative to Vðr ! 1Þ. This potential has the property that W CP ! E as r ! 1. We choose W CP $ Oðr n Þ (n > 1) as r ! 1. The potential W CP ðrÞ should have an analytic form which has easy to evaluate matrix elements. Second, W CP ðrÞ should be negligible for r < R 0 . If these conditions are met, then it can be shown that the discrete energies E i of the solution of Eq. (2) can be used to determine the phase shifts of Eq.(1) at those energies. Consider a potential V 0 ðrÞ for which Eq. (2) has an eigenvalue E 0 . When r > R 0 , the solution of Eq. (2) will become an exponentially decreasing solution B 0 ðrÞ when E 0 < V 0 ðrÞ þ W CP ðrÞ. The amplitude B will depend on the specifics of V 0 ðrÞ, but the actual radial dependence of 0 ðrÞ does not depend on the form of V 0 ðrÞ. Now consider the behavior of the wave function for r < R 0 . One simply integrates the Schrödinger equation outward from the origin, and, since W CP ðrÞ is zero her...

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Calculable methods for many-body scattering

Cited by 84 publications

References 219 publications

A microscopic three-cluster model with nuclear polarization applied to the resonances of 7Be and the reaction 6Li(p, 3He)4He

A microscopic three-cluster model with nuclear polarization applied to the resonances of 7Be and the reaction 6Li(p, 3He)4He

Scattering length and effective range for collisions between light ions within a microscopic model

Elastic Scattering Using an Artificial Confining Potential

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