Gábor VARGA
Investigation of He-Ni scattering by normalised distorted wave Born approximation (1984)
2. Interaction potential .............................................................................................................................3
2.1 Qualitative interpretation of neutral atom surface scattering ..................................................3
2.2 The semi-empirical relations of interaction potential ..............................................................7
2.3 The interaction potential .....................................................................................................11
3. Classical mechanics models ................................................................................................................14
3.1 General relations .................................................................................................................14
3.1.1 The n dimensional semi-infinity lattice ................................................................14
3.1.2 Determination of surface atom motion in semi-infinity lattice ...............................20
3.1.3 Solution function of 1D and 3D lattice ...............................................................22
3.1.4 Determination of surface atom motion on arbitrary lattice forces.........................24
3.1.5 Classical thermal motion of surface atoms ........................................................27
3.1.6 The role of repulsive and attractive forces ........................................................30
3.1.8 Classical model atom - surface scattering in 1D case ........................................36
3.2 Hard cubic model ...............................................................................................................41
3.3 Soft cubic model .................................................................................................................47
QUANTUM MECHANICAL MODELS
5. Discussion of scattering theory by Lippmann-Schwinger equations .....................................................62
5.1 Interaction representation ...................................................................................................62
5.2 S operator ..........................................................................................................................62
5.3 Transient probability ...........................................................................................................71
5.4 Lippmann-Schwinger equation ............................................................................................77
5.5 Potential scattering .............................................................................................................80
5.6 Distorted Born approximation ............................................................................................82
6.1 Hard wall model with Rayleigh condition ............................................................................85
6.1.1 Data set analysis ................................................................................................85
6.1.2 Hard wall model ................................................................................................89
6.1.4 Eikonal approximation .......................................................................................92
6.2 Normalised distorted wave Born approximation ..................................................................96
in the case of soft exponentially corrugated potential /NDWBA/
7. Interaction potential of He - metal surface as a function of coverage
.................................................105
7.1 Shape of the Ni surface .....................................................................................................106
8. Description of computer programs ....................................................................................................109
8.1 Classical and quantum mechanical programme ..................................................................109
8.2 Direct and inverse scattering problem in the case of NDWBA .........................................112
8.2.1 Determination of VG,0 Fourier coefficient ......................................................114
8.2.2 Determination of open channels ......................................................................116
8.2.3 Solution of inverse problem .............................................................................118
8.3 Graphical representation ...................................................................................................119
9. Analysis of numerical results .............................................................................................................120
9.1 Accuracy of results ...........................................................................................................120
9.2 Validity range of NDWBA ................................................................................................124
10. Summary ........................................................................................................................................126
11. References ......................................................................................................................................129
APPENDIX
1.2 Program list of hard wall model ..........................................................................................................2
2. Direct and inverse NDWBA programme:
2.1 block diagram .....................................................................................................................................4
2.2 programme list ...................................................................................................................................6
2.3 results ..............................................................................................................................................13
2.4 Results of hard wall model ................................................................................................................16