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.

Thanks for your attention!