Download Impact-ionization process of high-energy electrons on hydrogen

Yueying Qi， Lina Ning
Jiaxing University
Jianguo Wang
Institute of Applied Physics and Computational Mathematics
Yizhi Qu
University of the Chinese Academy of Sciences
R. K. Janev
Macedonian Academy of Sciences and Arts
content
Plasma conditions
possible atomic processes in plasmas
Fast-electron impact ionization process
Results and Discussion
Plasma conditions
Plasma parameters：
Coupling parameter：
  Z i e / Ri kT
Fermi degeneracy：
  kBT / EF
2
（Γ<<1， Weakly
Coupled parameter ）
Z
Debye potential V  r    exp  r / D 
r
（Γ>1，
Ion sphere model
strongly coupled parameter)
  1 Non-degeneracy
Classical plasma
  1 Degeneracy plasma
Quantum plasma
Possible atomic processes in plasmas
Y.Y.Qi，J.G.Wang, R.K.Janev; Phys. Rev. A, 78 (2008)062511
hv + H( nl ) Û H( n' l')
Photo-excitation
Y.Y.Qi, J.G.Wang, R.K.Janev; Phys Rev. A, 80 (2009)063404
+
hv
+
H
(
nl
)
Û
H
Photo-ionization
Y.Y.Qi，J.G.Wang, R.K.Janev, Eur. Phys. J. D 63, +e
(2011)327–337
Bremsstrahlung
Goingon
hv +H +e Û H +e
+
+
*
Y.Y.Qi，J.G.Wang, R.K.Janev, Phys. Plas. 16(2),(2009)023502
Electron-impact-excitation
e+H (nl ) Û e * + H (n ' l ')
Electron-impact-ionization
e+H (nl ) Û e+H + +e *
……
The present work
Fast-electron impact ionization process
 The potential between the nuclear and the atomic electron is
used
Ze
 r 
V ( r ; Z , D)  
exp   
r
 D
2
 And the interaction between the incident electron and the
target atom
 r r' 
Z
1
 r'
V (r , r '; Z , D)   exp    
exp  

r'
D 
 D r r'

Fast-electron impact ionization process
 If the incident electron is fast enough, the Bethe-
Inokuti theory is well served, where the expression
for the double differential cross section (DDCS) can
be expressed as two distinct factors: one dealing with
the incident electron only and the other dealing with
the target only, which is the generalized oscillator
strength density (GOSD) of atom and molecular, it is
related to the electronic structure of an individual
atom or molecular and can exhibit the interaction
between particle。
Fast-electron impact ionization process
 Similar to Bethe theory, GOSD is defined as
  
2
2
 l t l '
d GOSD
t
f
q     2
 2t  1 2l ' 1 


  M nl , l ' 
d
q    t ,l '
0 0 0
 Then DDCS is written as
ion
q 2   df
d  d    4 kb  
1

 
2
2
2
d   d

k



a

  q     
GOSD
 q      a
d
 The integration is used
ika r '
e
 r r '
e
4
iq  r
eikb r '  2
e
r r '
  q 2  


2
0

hartree  Degree 
Fast-electron impact ionization process
 The single differential cross section (SDCS) can be
calculated from DDCS
d ion  
d
 2 

0
ion

d

  
d
  a02


 sin  d 

hartree
d   d



The scaling transformations
ka   
Ka  Z , D 
Z
, kb    
Kb  Z , D 
Z
; q     kb     k a    
Q Z, D
Z
;  1  

Z
Results and Discussion
 The single differential cross sections from the 1s, 2s and 2p
are shown with incident electron energy 1KeV in the
screened cases with a number of Debye lengths
  1000,11.0,10.9,8.89,8.85,7.22,7.16, 4.55, 4.54,3.24,3.22a0
 The ionization of the electron-Hydrogen-like ions
collision is a multi-pole transition process, and the
final continuum electron is perhaps trapped in any
angular-momentum states, not only dipole transition
corresponding to the photo-ionization，multi-pole
shapes and the virtual-state resonances potentially
happen in the electron-impact ionization process for
the screened Coulomb interaction.
Results 1: SDCS from 2p
=1000a0
=11.0a0
=10.9a0
10
5
=8.89a0
=8.85a0
=7.22a0
10
4
FIG.1
10
3
10
2
10
1
10
0
=7.16a0
a=1KeV
Electron-impact
SDCS 2p orbital for
atomic hydrogen in
Debye plasmas
2
Single differential cross section(a0/Hartree)
.
10
-1
10
-2
-5
-4
-3
-2
-1
0
1
10
10
10
10
10
10
10
The ratio between the ejecting continuum electron energy and the ionization energy
Results 2: SDCS from 2p
10
7
10
6
10
5
10
4
10
3
10
2
10
1
10
0
=10.87a0
=10.88a0
FIG.2
=10.89a0
=10.90a0
2
Single differential cross section(a0/Hartree)
.
10
=10.91a0
=10.92a0
Electron-impact
SDCS 2p orbital
for atomic
hydrogen in
Debye plasmas
=10.93a0
a=1KeV
=10.94a0
-1
10
-5
-4
-3
-2
10
10
10
10
the ejecting continuum electron energy(a.u.)
-1
10
0
10
6
10
5
10
4
10
3
10
2
10
1
10
0
2
Single differential cross section(a0 /Hartree)
Results 3: SDCS from 2s
10
-1
10
-2
10
-3
10
Electron-impact
SDCS 2s orbital
for atomic
hydrogen in
Debye plasmas
a=1KeV
FIG.3
-5
10
-4
=4.54a0
=4.55a0
=7.16a0
=7.22a0
=8.85a0
=8.89a0
=10.9a0
=11.0a0
=1000a0
-3
-2
-1
10
10
10
emitting electron energy /I
10
0
10
1
GOSD
 GOSD is represented comprehensively by a three-
dimensional plot , called the Bethe surface, which
embodies all information concerning the inelastic
scattering of charged particles by an atom or molecular
in FBA, and is useful for analysis of quantities such as
the stopping power and the total inelastic-scattering.
 The Bethe surface is separated into three domains: the
above-threshold domain (red lines), the resonance
domain (green lines) and the large energy domain
(black lines).
Results 4: GOSD from 2p
Fig.4 Photographs of a plastic model of the Bethe surface from 2p orbital for atomic hydrogen in Debye plasmas
Fig.5 (Color online)Photographs of a plastic model of DDCS from 2p orbital in Debye plasmas
Matrix elements 1
Fig.6 Multi-pole transition matrix element from 2p for Hydrogen atom
Matrix elements 2
Fig.7Multi-pole transition matrix element from 2p for Hydrogen atom
Matrix elements 3
Fig.8 Multi-pole transition matrix element from 2p for Hydrogen
Matrix elements 4
Fig.9 Multi-pole transition matrix element from 2p for Hydrogen atom
CONCLUSION
In conclusion, we studied the plasma effects on the generalized
oscillator strength densities (Bethe surfaces), the double differential cross
sections, and the single cross sections from 2p state of hydrogen-like
ions in the Debye plasma environments in present work. The results
demonstrated that GOSD from 2p state happened to enormously vary
due to the plasma screening interactions, especially near the smaller
energy transfer (in the extremely low-energy) and the resonance domain
(the appearance of the quasi-bound state for l>0 or near-zero-energy
enhancement of the virtual state for l=0). The accessional minima, the
new broaden peak and remarkable augmentation always exist in GOSD
and DDCS; the multiple shape resonance and near-zero-energy
enhancement appear in SDCS, all which are dependent of the plasma
conditions. These effects should be considered in the simulation of
spectroscopy in the hot, dense plasmas.
Thanks for your attention!