Atomic Shell ionization

8/10/2019 Atomic Shell ionization

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M. Guerra, F. Parente and J. P. Santos

Departamento de Fsica da Faculdade de Cincias eTecnologia da Universidade Nova de Lisboa, Monte daCaparica 2825-114 Caparica, Portugal

Centro de Fsica Atmica, Av. Prof. Gama Pinto 2, 1649-003Lisboa, Portugal

5 th SPARC Workshop and Collaboration MeetingSetember 23 28, Predeal, Romania


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Outline

Goals and Motivations

Historical Overview

The Binary Encounter Bethe Model

Results

Conclusions

Atomic L-Shell Ionization Cross Sections by Electron Impact

2


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Goals

Adapt the Binary Encounter Bethe (BEB) modelto the ionization of ions with several chargestates

Compute electron impact L-shell ionizationcross sections, using the BEB/RBEB model

Comparison with other experimental andtheoretical results


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4

Motivation

Semiconductor Fabrication

Plasma Modelling

Atmosferic Science

Astrophysics

Magnetic Fusion (Tokamaks)

Biomedical Applications Radiation therapy

Charged particles beams for cancer treatment


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Rutherford Scattering


5

2

22

0 14,

WT

Ra

dW

TWd

e- e-

e- e-

dW

WT

RaT

T

0 222

0 14

2

sin

1

2 42

0

mv

c

d

d

T Kinetic energy of the incident electronW Kinetic energy of the ejected electrona0 Bohrs radiusR Rydbergs constant

T-W Kinetic energy of the scattered electron


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Motts Scattering


6

2

0 22

22

0 1114WT

dWWTWTWWT

RaT

22

22

0 1114,

WTWTWWT

Ra

dWTWd


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Motts Scattering


7

T

Introducing the binding energyB and changing variables

BWE

22

22

0 1114,

WTWTEET

NRa

dW

TWd

valid only if W>>B


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Binary Encounter Theory The target electron is described as having a velocity distribution

The symmetry of the Motts expression is mantained in what

concerns the exchange of the scattered and ejected electron


8

3322

22

0 11

3

41114,

WTE

U

WTWTEEBUT

NRa

dW

TWd

T

Binary Encounter Theory

Modified Mott Expression

m

pU

2

2


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Binary Encounter Dipole Model BED

Combines the binary encounter theory with the dipoleinteraction of the Bethe theory for fast incident electrons


9

dw

wdf

wN

t

wtwNN

wtwt

NN

utB

S

dW

TWd

i

i

1

ln1

1

12

1

1

1

1

2

1

,

22

2204 BRNaS

BUu

BWw

BTt

dwdw

wdfNi

0


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10

1

ln11112

ln

1 2 t

t

tt

t

ut

StBEB

Differential oscillator strength for H has a simple shape

...1

2

w

b

dw

wdf

Binary Encounter Bethe Model BEB

Good agreement for total ionization cross sections up to 20 KeV


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Relativistic Version of BEB Model


11

cv

cv

cv

uu

bb

tt

2

2

2

2

2

2

'1

11

'1

11

'1

11

u

b

t

u

b

t

2

2

2

'

'

'

mcUu

mcBb

mcTt

2

1

2'1

'

2'1

'21

1

ln11

11'2ln

1ln

2

1

'2

4

2

2

2

2

2

2

2

222

42

0

t

t

b

t

t

t

t

t

tb

b

Nat t

t

t

but

RBEB


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K-shell ionization


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L-shell ionizationAtomic L-Shell Ionization Cross Sections by Electron Impact

13

Au

Pb Xe

Bi


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14

K-shell ionization

XePb

BiAu


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Conclusions Great versatility of the BEB/RBEB model in

obtaining electron impact cross sections for a

great variety of atoms Disagreements between the cross sections

calculated with BEB/RBEB, and experimentalcross sections are smaller than 10% for energies

lower than 1 MeV The lack of electron correlation might be the

cause of poor results for the K-shell of heavyelements


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Future Work

Calculate binding and kinetic energies of the Kand L-shell electrons taking into account

electron correlation

Modification of the BEB/RBEB expression tobetter account for ionization of ions with several

charge states Derive an analogous expression to theBEB/RBEB for positron impact ionization


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Aknowledgments


17

Fundao para a Cincia e TecnologiaPhD Grant SFRH/BD/38691/2007

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Documents

Atomic Shell ionization