### Abstract

We describe the coupling of electronic and nuclear motions in slow atomic collisions using a combination of the eikonal and time-dependent Hartree-Fock (TDHF) approximations. Starting with an eikonal representation of the total wave function, a wave function is constructed from classical trajectories in a way suitable for describing atomic collisions with velocities down to a fraction of an atomic unit. The TDHF formulation is developed in terms of its density operator. The differential equations coupling the density operator to the nuclear motions have been solved with a procedure developed to account for the coupling of fast (electronic) and slow (nuclear) degrees of freedom. This is based on a local-interaction picture and on a temporal linearization of the equations, allowing for the integration of the electronic density over large time intervals. Density-matrix equations are derived in a basis of traveling atomic orbitals, and numerical results are presented for H++H and He2++H. Good agreement is found with experimental results for H++H, comparing integral electron transfer cross sections from 2 to 2000 eV. In addition, an analysis of the time dependence of atomic orbital populations provides insight on electronic rearrangement during collisions and shows that even very small contributions from the driving forces of the nuclei on the electrons have a cumulative effect on the density operator that can substantially change final populations.

Original language | English (US) |
---|---|

Pages (from-to) | 322-336 |

Number of pages | 15 |

Journal | Physical Review A |

Volume | 50 |

Issue number | 1 |

DOIs | |

State | Published - 1994 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

**Time-dependent many-electron approach to slow ion-atom collisions : The coupling of electronic and nuclear motions.** / Micha, David A.; Runge, Keith A.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 50, no. 1, pp. 322-336. https://doi.org/10.1103/PhysRevA.50.322

}

TY - JOUR

T1 - Time-dependent many-electron approach to slow ion-atom collisions

T2 - The coupling of electronic and nuclear motions

AU - Micha, David A.

AU - Runge, Keith A

PY - 1994

Y1 - 1994

N2 - We describe the coupling of electronic and nuclear motions in slow atomic collisions using a combination of the eikonal and time-dependent Hartree-Fock (TDHF) approximations. Starting with an eikonal representation of the total wave function, a wave function is constructed from classical trajectories in a way suitable for describing atomic collisions with velocities down to a fraction of an atomic unit. The TDHF formulation is developed in terms of its density operator. The differential equations coupling the density operator to the nuclear motions have been solved with a procedure developed to account for the coupling of fast (electronic) and slow (nuclear) degrees of freedom. This is based on a local-interaction picture and on a temporal linearization of the equations, allowing for the integration of the electronic density over large time intervals. Density-matrix equations are derived in a basis of traveling atomic orbitals, and numerical results are presented for H++H and He2++H. Good agreement is found with experimental results for H++H, comparing integral electron transfer cross sections from 2 to 2000 eV. In addition, an analysis of the time dependence of atomic orbital populations provides insight on electronic rearrangement during collisions and shows that even very small contributions from the driving forces of the nuclei on the electrons have a cumulative effect on the density operator that can substantially change final populations.

AB - We describe the coupling of electronic and nuclear motions in slow atomic collisions using a combination of the eikonal and time-dependent Hartree-Fock (TDHF) approximations. Starting with an eikonal representation of the total wave function, a wave function is constructed from classical trajectories in a way suitable for describing atomic collisions with velocities down to a fraction of an atomic unit. The TDHF formulation is developed in terms of its density operator. The differential equations coupling the density operator to the nuclear motions have been solved with a procedure developed to account for the coupling of fast (electronic) and slow (nuclear) degrees of freedom. This is based on a local-interaction picture and on a temporal linearization of the equations, allowing for the integration of the electronic density over large time intervals. Density-matrix equations are derived in a basis of traveling atomic orbitals, and numerical results are presented for H++H and He2++H. Good agreement is found with experimental results for H++H, comparing integral electron transfer cross sections from 2 to 2000 eV. In addition, an analysis of the time dependence of atomic orbital populations provides insight on electronic rearrangement during collisions and shows that even very small contributions from the driving forces of the nuclei on the electrons have a cumulative effect on the density operator that can substantially change final populations.

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U2 - 10.1103/PhysRevA.50.322

DO - 10.1103/PhysRevA.50.322

M3 - Article

AN - SCOPUS:0000327653

VL - 50

SP - 322

EP - 336

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 1

ER -