Lagrange-mesh R-matrix calculations

Malegat, L

doi:10.1088/0953-4075/27/21/001

Cited by 22 publications

(35 citation statements)

References 9 publications

(5 reference statements)

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“…, N and P N is a Legendre polynomial [24]. They are associated with a mesh of N pointsx i given by [19,12] …”

Section: Lagrange-mesh Methods Over the Internal Regionmentioning

confidence: 99%

“…(19) and (20) with the basis of N i functions ϕ j (r) defined over (0, a). A similar expansion is now used in the external region with an orthonormal basis of N e functions χ j (r) defined over (a, ∞).…”

Section: R-matrix Methods For Dirac Bound States 41 Expansion In the mentioning

confidence: 99%

“…The general case is considered in the next subsection. With expansions (19) and (20), a projection of Eq. (6) over ϕ i (r) leads to the system of equations in matrix form…”

Section: Internal and External Solutionsmentioning

confidence: 99%

“…In the Schrödinger case, a further simplification keeping a good convergence is obtained by combining the Lagrange-mesh method [17,18] with the R matrix [19,12]. The resulting method does not require any analytical or numerical calculation of matrix elements.…”

Section: Introductionmentioning

confidence: 99%

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CalculableR-matrix method for the Dirac equation

Baye

2015

Phys. Rev. A

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An efficient version of the calculable R-matrix method, a technique of determination of scattering and bound-state properties, is extended to the Dirac equation. The configuration space is divided into internal and external regions at the channel radius. In both regions, the introduction of a Bloch operator allows restoring the Hermiticity. The most general Bloch operator contains three free parameters. With a basis without constraint at the channel radius in the internal region, the phase shifts converge to the same value for any choice of these parameters. Nevertheless, some choices provide a faster convergence than others. The determination of the bound-state energies is performed with an extension of the method using a second set of basis functions in the external region. Neither the knowledge of asymptotic expressions nor a large channel radius are required. These R-matrix methods are particularly simple and very accurate when combined with the Lagrange-mesh method. No analytical or numerical evaluation of matrix elements is then necessary. Very accurate phase shifts are obtained with a Legendre mesh for various short-range potentials. A combination of Legendre and Laguerre meshes provides accurate energies for the bound states even for potentials with a Coulomb-like asymptotic behavior.

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“…, N and P N is a Legendre polynomial [24]. They are associated with a mesh of N pointsx i given by [19,12] …”

Section: Lagrange-mesh Methods Over the Internal Regionmentioning

confidence: 99%

Section: R-matrix Methods For Dirac Bound States 41 Expansion In the mentioning

confidence: 99%

“…The general case is considered in the next subsection. With expansions (19) and (20), a projection of Eq. (6) over ϕ i (r) leads to the system of equations in matrix form…”

Section: Internal and External Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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CalculableR-matrix method for the Dirac equation

Baye

2015

Phys. Rev. A

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“…The method can be used for quantum-mechanical bound-state [1][2][3][4]9] and scattering problems [11][12][13][14][15]. It is valid with non-local interactions [16,17].…”

Section: Introductionmentioning

confidence: 99%

Lagrange‐mesh method for quantum‐mechanical problems

Baye

2006

Physica Status Solidi (b)

109

139

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The Lagrange-mesh method is an approximate variational calculation with the simplicity of a mesh calculation because of the use of a consistent Gauss quadrature. The method can be used for quantum-mechanical bound-state and scattering problems with local and non-local interactions or with a semi-relativistic kinetic energy, and for solving the time-dependent Schrödinger equation. No analytical evaluation of matrix elements is needed. The accuracy is exponential in the number of mesh points and is not significantly reduced with respect to the corresponding variational calculations. Lagrange functions can be based on classical or non-classical orthogonal polynomials as well as on trigonometric and sinc functions, as described in examples. Some singularities can be handled with a regularization technique. Applications to three-body systems are discussed for various choices of coordinate systems. The helium atom and hydrogen molecular ion are presented as examples.

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Introduction to R-Matrix Theory: Potential Scattering

Burke

2010

R-Matrix Theory of Atomic Collisions

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Lagrange-mesh R-matrix calculations

Cited by 22 publications

References 9 publications

CalculableR-matrix method for the Dirac equation

CalculableR-matrix method for the Dirac equation

Lagrange‐mesh method for quantum‐mechanical problems

Introduction to R-Matrix Theory: Potential Scattering

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