Electron–molecule collision calculations using the R-matrix method

Tennyson, Jonathan

doi:10.1016/j.physrep.2010.02.001

Cited by 473 publications

(457 citation statements)

References 394 publications

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“…The method of the hyperspherical harmonics is very convenient for the description of the three-body structure of two-neutron halos that appear in Borromean nuclei 6 He, 11 Li, etc., at the very edge of the nuclear stability (see recent works [21,22], and references therein, for a more detailed discussion of the successes and challenges of this approach). The relative motion of three clusters is described in the space of 064308-6 hyperspherical coordinates (ρ, 5 ), and the nuclear wave function J π is decomposed on a basis of hyperspherical harmonics ϒ Kν ( 5 ) [20], J π = Kν ψ J π Kν (ρ)ϒ Kν ( 5 ).…”

Section: Discussionmentioning

confidence: 99%

“…Usually these transformations are rather awkward and tedious. Another approach to overcome the difficulty is to use a so-called invariant imbedding method, in which the propagated quantity is not a wave function matrix = {ψ in (r)}, but rather its logarithmic derivative −1 [6][7][8] or its inverse matrix R = −1 [9][10][11]. These methods have found broad application, especially for large coupled-channel calculations.…”

Section: Introductionmentioning

confidence: 99%

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Modified variable phase method for the solution of coupled radial Schrödinger equations

2011

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A modified variable phase method for the numerical solution of coupled radial Schrödinger equations, which maintains linear independence for different sets of solution vectors, is suggested. The modification involves rearrangement of coupled equations to avoid the usual numerical instabilities associated with components of the wave function in their classically forbidden regions. The modified method is applied to nuclear structure calculations of halo nuclei within the hyperspherical harmonics approach.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modified variable phase method for the solution of coupled radial Schrödinger equations

2011

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“…The R matrix is propagated to an asymptotic region where the radial wave functions describing the scattering electron can be matched to analytical expressions. For this purpose the inner region is propagated to the outer region potential until its solutions match with the asymptotic functions given by the Gailitis expansion [28]. Coupled single center equations describing the scattering in the outer region are integrated to identify the K-matrix elements.…”

Section: A Target Model Used For Low-energy Calculationsmentioning

confidence: 99%

Computation of electron-impact rotationally elastic total cross sections for methanol over an extensive range of impact energy (0.1 – 2000 eV)

Vinodkumar¹,

Limbachiya²,

Barot³

et al. 2013

Phys. Rev. A

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Theoretical rotationally elastic total cross sections for electron scattering from methanol over the incident energy range 0.1-2000 eV are presented. The computation of such cross sections for methanol is reported over such an extended energy range. We have employed two distinct formalisms to compute the cross sections across this energy range; between 0.1 eV and the ionization threshold of the target we have used the ab initio R-matrix method, while at higher energies the spherical complex optical potential method is invoked. The results from both formalisms match quite well at energies where they overlap and hence imply that they are consistent with each other. These total cross-section results are also in very good agreement with available experimental data and earlier theoretical data. The composite methodology employed here is well established and can be used to predict cross sections for other targets where data is scarce or not available.

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“…The Quantemol-N modules GAUSPROP and DENPROP [28] construct the transition density matrix from the target eigenvectors obtained from configuration integration (CI) calculation and generate the target properties. The multipole transition moments obtained are then used to solve the outer region coupled equations and the dipole polarizability α 0 .…”

Section: Theoretical Methodologymentioning

confidence: 99%

Theoretical total cross sections fore-SO2scattering over a wide energy range (0.1−2000 eV) revealing a 3.4-eV shape resonance

Vinodkumar¹,

Limbachiya²,

Barot³

et al. 2012

Phys. Rev. A

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We have used the ab initio R-matrix formalism at low impact energies (below the ionization threshold of the target) and the spherical complex optical potential methodology above the ionization threshold to generate total cross sections for e-SO 2 scattering over the energy range from 0.1 to 2000 eV. The eigenphase diagram and total cross section indicate a structure at 3.4 eV which is ascribed to a shape resonance, evidence for which appears in earlier experimental studies.

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Electron–molecule collision calculations using the R-matrix method

Cited by 473 publications

References 394 publications

Modified variable phase method for the solution of coupled radial Schrödinger equations

Modified variable phase method for the solution of coupled radial Schrödinger equations

Computation of electron-impact rotationally elastic total cross sections for methanol over an extensive range of impact energy (0.1 – 2000 eV)

Theoretical total cross sections fore-SO2scattering over a wide energy range (0.1−2000 eV) revealing a 3.4-eV shape resonance

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