Yueying Qi , Lina NingJiaxing University
Jianguo WangInstitute of Applied Physics and Computational Mathematics
Yizhi QuUniversity of the Chinese Academy of Sciences
R. K. JanevMacedonian Academy of Sciences and Arts
contentPlasma conditions possible atomic processes in plasmasFast-electron impact ionization processResults and Discussion
Plasma conditions
Coupling parameter:Fermi degeneracy:
Debye potential
Ion sphere model
Classical plasma
Quantum plasma
Plasma parameters:2
/i iZ e R kT
/B Fk T E
( Γ<<1, Weakly Coupled parameter )
( Γ>1,strongly coupled parameter)
1 Non-degeneracy
1 Degeneracy plasma
exp /Z
V r r Dr
Possible atomic processes in plasmas
hv H( nl ) H( n' l ')+ ÛPhoto-excitation++ ( ) +hv H nl H eÛPhoto-ionization
+ ( ) *+ ( ' ')e H nl e H n lÛElectron-impact-excitation
++ ( ) + + *e H nl e H eÛElectron-impact-ionization
*+ + +hv H e H e+ +ÛBremsstrahlung
… …
Y.Y.Qi , J.G.Wang, R.K.Janev; Phys. Rev. A, 78 (2008)062511
Y.Y.Qi, J.G.Wang, R.K.Janev; Phys Rev. A, 80 (2009)063404
Y.Y.Qi , J.G.Wang, R.K.Janev, Eur. Phys. J. D 63, (2011)327–337
Goingon
Y.Y.Qi , J.G.Wang, R.K.Janev, Phys. Plas. 16(2),(2009)023502
The present work
Fast-electron impact ionization processThe potential between the nuclear and the atomic
electron is used
And the interaction between the incident electron and the target atom
2
( ; , ) expZe r
V r Z Dr D
'' 1( , '; , ) exp exp
' '
r rZ rV r r Z D
r D r r D
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
Then DDCS is written as
The integration is used
Fast-electron impact ionization process
22
, '2, '
'2 1 2 ' 1
0 0 0GOSD t
nl lt l
l t ldf q t l M
d q
2 20
22 2
4 1GOSDion
b
a
df qd k qd ahartree Degreed d k dq
'' '
2 2
4
'a b
r riq rik r ik re
e e er r q
Fast-electron impact ionization processThe single differential cross section (SDCS) can
be calculated from DDCS
20
02 sin
ion iond dd ad hartreed d d
The scaling transformations
, , , 1, ; ;a ba b b a
K Z D K Z D Q Z Dk k q k kZ Z Z Z
Results and DiscussionThe 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
01000,11.0,10.9,8.89,8.85,7.22,7.16,4.55,4.54,3.24,3.22a
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
10-5 10-4 10-3 10-2 10-1 100 10110-2
10-1
100
101
102
103
104
105
a=1KeV
=1000a0 =11.0a
0 =10.9a
0
=8.89a0 =8.85a
0 =7.22a
0 =7.16a
0
The ratio between the ejecting continuum electron energy and the ionization energy
Sing
le d
iffer
entia
l cro
ss s
ectio
n(
a2 0/Har
tree
)
Electron-impact SDCS 2p orbital for atomic hydrogen in Debye plasmas
.
FIG.1
Results 2: SDCS from 2p
Electron-impact SDCS 2p orbital for atomic hydrogen in Debye plasmas
.
FIG.2
10-5 10-4 10-3 10-2 10-1 100
10-1
100
101
102
103
104
105
106
107
=10.87a0
=10.88a0
=10.89a0
=10.90a0
=10.91a0
=10.92a0
=10.93a0
=10.94a0
a=1KeV
the ejecting continuum electron energy(a.u.)
Sing
le d
iffer
entia
l cro
ss se
ctio
n(
a2 0/Har
tree
)
Results 3: SDCS from 2s
10-5 10-4 10-3 10-2 10-1 100 10110-3
10-2
10-1
100
101
102
103
104
105
106
=4.54a0 =4.55a
0 =7.16a
0
=7.22a0 =8.85a
0 =8.89a
0
=10.9a0 =11.0a
0 =1000a
0
a=1KeV
Sing
le d
iffer
entia
l cro
ss se
ctio
n(
a2 0 /Har
tree
)
emitting electron energy /I
FIG.3
Electron-impact SDCS 2s orbital for atomic hydrogen in Debye plasmas
GOSDGOSD 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
CONCLUSIONIn 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.
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