### Abstract

The generalized Newton variational method is applied to the static-exchange approximation of the electron-hydrogen-atom scattering. Slater-type basis functions are employed to expand the amplitude density. Spurious singularities are encountered in both scattering processes. The width of the unphysical singularities is broader in the case of singlet scattering. Anomalous poles appear in narrow regions of the scale parameter and are in evident correlation with the zeros of the determinant of the free-particle Green's operator. As a by-product, simple least-squares extension of the generalized Newton variational method is developed in order to avoid spurious singularities and to recognize whether or not the convergence is of secondary nature.

Original language | English |
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Pages (from-to) | 7170-7178 |

Number of pages | 9 |

Journal | Physical Review A |

Volume | 44 |

Issue number | 11 |

DOIs | |

Publication status | Published - 1991 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A*,

*44*(11), 7170-7178. https://doi.org/10.1103/PhysRevA.44.7170

**Spurious singularities in the generalized Newton variational method.** / Apagyi, Barnabás; Lévay, P.; Ladányi, Károly.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 44, no. 11, pp. 7170-7178. https://doi.org/10.1103/PhysRevA.44.7170

}

TY - JOUR

T1 - Spurious singularities in the generalized Newton variational method

AU - Apagyi, Barnabás

AU - Lévay, P.

AU - Ladányi, Károly

PY - 1991

Y1 - 1991

N2 - The generalized Newton variational method is applied to the static-exchange approximation of the electron-hydrogen-atom scattering. Slater-type basis functions are employed to expand the amplitude density. Spurious singularities are encountered in both scattering processes. The width of the unphysical singularities is broader in the case of singlet scattering. Anomalous poles appear in narrow regions of the scale parameter and are in evident correlation with the zeros of the determinant of the free-particle Green's operator. As a by-product, simple least-squares extension of the generalized Newton variational method is developed in order to avoid spurious singularities and to recognize whether or not the convergence is of secondary nature.

AB - The generalized Newton variational method is applied to the static-exchange approximation of the electron-hydrogen-atom scattering. Slater-type basis functions are employed to expand the amplitude density. Spurious singularities are encountered in both scattering processes. The width of the unphysical singularities is broader in the case of singlet scattering. Anomalous poles appear in narrow regions of the scale parameter and are in evident correlation with the zeros of the determinant of the free-particle Green's operator. As a by-product, simple least-squares extension of the generalized Newton variational method is developed in order to avoid spurious singularities and to recognize whether or not the convergence is of secondary nature.

UR - http://www.scopus.com/inward/record.url?scp=35949010502&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35949010502&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.44.7170

DO - 10.1103/PhysRevA.44.7170

M3 - Article

VL - 44

SP - 7170

EP - 7178

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 11

ER -