Complex Kohn variational method: Application to low-energy electron-molecule collisions

Schneider, Barry I.; Rescigno, T. N.

doi:10.1103/physreva.37.3749

Cited by 109 publications

(63 citation statements)

References 27 publications

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“…The first electronic excitation energy of CH 3 OH is found to be 8.55 eV using the configuration interaction (CI) model, which agrees well with the calculated value of 8.53 eV reported by Vinodkumar et al [12], albeit higher compared to the theoretical value of 6.76 eV reported by Bouchiha et al [3] and the experimental value of 6.5 eV reported by Knoop et al [19]. The present dipole moment is 2.28 D, which is slightly higher compared to the theoretical value of 1.97 D [3] The most popular methodologies employed for low-energy electron collision calculations are the Kohn variational method [20,21], the Schwinger variational method [22][23][24], and the R-matrix method, of which the R matrix is the most widely used. The underlying idea behind the R-matrix method relies on the division of configuration space into two spatial regions, namely, the inner region and the outer region.…”

Section: A Target Model Used For Low-energy Calculationscontrasting

confidence: 45%

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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Section: A Target Model Used For Low-energy Calculationscontrasting

confidence: 45%

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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“…They are performed via an expansion of the wave functions of the scattering states in terms of a hyperspherical harmonic (HH) basis and using the complex form of the Kohn variational principle [45,46]. These new calculations reach a much higher degree of accuracy than those performed previously using the correlated hyperspherical harmonic (CHH) functions [10].…”

Section: B P-3 He Elastic Scatteringmentioning

confidence: 99%

Proton-He3elastic scattering at low energies

et al. 2006

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We present new accurate measurements of the differential cross section σ(θ) and the proton analyzing power Ay for proton-3 He elastic scattering at various energies. A supersonic gas jet target has been employed to obtain these low energy cross section measurements. The σ(θ) distributions have been measured at Ep = 0.99, 1.59, 2.24, 3.11, and 4.02 MeV. Full angular distributions of Ay have been measured at Ep = 1.60, 2.25, 3.13, and 4.05 MeV. This set of high-precision data is compared to four-body variational calculations employing realistic nucleon-nucleon (N N ) and threenucleon (3N ) interactions. For the unpolarized cross section the agreement between the theoretical calculation and data is good when a 3N potential is used. The comparison between the calculated and measured proton analyzing powers reveals discrepancies of approximately 50% at the maximum of each distribution. This is analogous to the existing "Ay Puzzle" known for the past 20 years in nucleon-deuteron elastic scattering.

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“…There exists a variety of methods for computing resonance parameters, though none have been sufficiently developed so as to provide a reliable algorithm that can be generally applied even to the low-lying resonances of small molecules. Scattering methods [5][6][7][8][9][10] treat the continuum with explicit use of scattering boundary conditions in order to compute observables like the crosssection. Stabilization methods 11,12 and associated analytic continuation methods, [13][14][15] use continuum eigenvalues from bound state calculations to extract resonance a) Electronic mail: mhg@cchem.berkeley.edu b) Electronic mail: cwmccurdy@ucdavis.edu parameters.…”

Section: Introductionmentioning

confidence: 99%

Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules

White

Head‐Gordon

McCurdy

2017

The Journal of Chemical Physics

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The computation of Siegert energies by analytic continuation of bound state energies has recently been applied to shape resonances in polyatomic molecules by several authors. We critically evaluate a recently proposed analytic continuation method based on low order (type III) Padé approximants as well as an analytic continuation method based on high order (type II) Padé approximants. We compare three classes of stabilizing potentials: Coulomb potentials, Gaussian potentials, and attenuated Coulomb potentials. These methods are applied to a model potential where the correct answer is known exactly and to the 2 Π g shape resonance of N − 2 which has been studied extensively by other methods. Both the choice of stabilizing potential and method of analytic continuation prove to be important to the accuracy of the results. We conclude that an attenuated Coulomb potential is the most effective of the three for bound state analytic continuation methods. With the proper potential, such methods show promise for algorithmic determination of the positions and widths of molecular shape resonances.

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Complex Kohn variational method: Application to low-energy electron-molecule collisions

Cited by 109 publications

References 27 publications

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

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

Proton-He3elastic scattering at low energies

Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules

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