# Semiclassical treatment of inelastic collisions between electrons and highly ionized atoms

## Abstract

The thesis is concerned with the calculation of excitation cross sections of ions by electron impact at intermediate energies in the limit of Z >> N/sub b/, where Z is the atomic number and N/sub b/ is the number of bound electrons. A semiclassical procedure is developed for calculating total cross sections using analytic bound states and averaged free electron wave functions derived in the second eikonal approximation. The analytic bound states are derived assuming a screened Coulomb potential and using orbital energies obtained from Hartree-Fock calculations. The functional form of the bound states reduces naturally to the hydrogen atom functions in the limit Z ..-->.. infinity. The free electron functions used are semiclassical solutions to the free electron Schroedinger equation with a screened Coulomb potential. An exact solution is obtained in the second eikonal approximation, including all classical path contributions. This solution is averaged to extract the focusing and acceleration effects resulting from the long range Coulomb potential of the ion. The results are presented in the form of Born-like cross section formulae and demonstrate the appropriate correction of the Born cross section which arises from the acceleration and focusing of the free electrons by the long range Coulombmore »

- Authors:

- Publication Date:

- Research Org.:
- California Univ., San Diego (USA)

- OSTI Identifier:
- 5411831

- Resource Type:
- Thesis/Dissertation

- Resource Relation:
- Other Information: Thesis (Ph. D.)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; ELECTRON-ION COLLISIONS; EXCITATION FUNCTIONS; INELASTIC SCATTERING; BOUND STATE; COULOMB FIELD; EIKONAL APPROXIMATION; HARTREE-FOCK METHOD; TOTAL CROSS SECTIONS; WAVE FUNCTIONS; COLLISIONS; CROSS SECTIONS; ELECTRIC FIELDS; ELECTRON COLLISIONS; FUNCTIONS; ION COLLISIONS; SCATTERING; 640304* - Atomic, Molecular & Chemical Physics- Collision Phenomena

### Citation Formats

```
Frasier, S M.
```*Semiclassical treatment of inelastic collisions between electrons and highly ionized atoms*. United States: N. p., 1984.
Web.

```
Frasier, S M.
```*Semiclassical treatment of inelastic collisions between electrons and highly ionized atoms*. United States.

```
Frasier, S M. Sun .
"Semiclassical treatment of inelastic collisions between electrons and highly ionized atoms". United States.
```

```
@article{osti_5411831,
```

title = {Semiclassical treatment of inelastic collisions between electrons and highly ionized atoms},

author = {Frasier, S M},

abstractNote = {The thesis is concerned with the calculation of excitation cross sections of ions by electron impact at intermediate energies in the limit of Z >> N/sub b/, where Z is the atomic number and N/sub b/ is the number of bound electrons. A semiclassical procedure is developed for calculating total cross sections using analytic bound states and averaged free electron wave functions derived in the second eikonal approximation. The analytic bound states are derived assuming a screened Coulomb potential and using orbital energies obtained from Hartree-Fock calculations. The functional form of the bound states reduces naturally to the hydrogen atom functions in the limit Z ..-->.. infinity. The free electron functions used are semiclassical solutions to the free electron Schroedinger equation with a screened Coulomb potential. An exact solution is obtained in the second eikonal approximation, including all classical path contributions. This solution is averaged to extract the focusing and acceleration effects resulting from the long range Coulomb potential of the ion. The results are presented in the form of Born-like cross section formulae and demonstrate the appropriate correction of the Born cross section which arises from the acceleration and focusing of the free electrons by the long range Coulomb potential. Comparison is made with the Coulomb-Born results; the results agree to within 10% in most cases.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1984},

month = {1}

}