Beryllium ion collisions and free-free transition in H plasma L. Liu - - PowerPoint PPT Presentation

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Beryllium ion collisions and free-free transition in H plasma

• L. Liu1, S. B. Zhang2, C.H.Liu3, Y. Wu1, J.G.Wang1 and R.K.Janve4

1 Institute of Applied Physics and Computational Mathematics, Beijing, China 2 Shaanxi Normal University, Xi’an, China 3 Southeast University, Nanjing, China 4 Macedonian Academy of Sciences and Arts, Skopje, Macedonia

The IAEA 1th RCM on Vapour Shielding, Vienna, 2019.03.13

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Part 1 Beryllium ion collisions

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Outline

• Motivation
• Theoretical method
• Results and discussions

H+-Be+→H(nl)+Be2+ →H++Be+(1s2nl), n>2 →H++Be2+(1s2)+e Be3+-Li→Be2++Li+

• Summary

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Heavy particle collisions

Astrophysics fusion energy

Environmental science

Agriculture

大气物理 臭氧层

Atmospheric physics High technology Natural resource Medicine

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Tokomak

Diverter/plasma edge Neutral Beam Injection Heating Diagnostics

Motivation

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Jupiter aurora

Jupiter aurora: EUV and X-ray

Oq+ + H2 → O(q-1)+(nl) + H2

+

O(q-1)+(nl) → O(q-1)+(n’l’) + hυ

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Outline

• Motivation
• Theoretical method
• Results and discussions

H+-Be+→H(nl)+Be2+ →H++Be+(1s2nl), n>2 →H++Be2+(1s2)+e Be3+-Li→Be2++Li+

• Summary

8

Theoretical method

 Fully quantum mechanical molecular

• rbital close-coupling (MOCC) method

 Two-center atomic orbital close-coupling (TC-AOCC) method

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MOCC method

• Molecular structure calculations

Multi-reference single- and double-excitation configration interaction (MRDCI) approach (Collaborated with Prof. R. Buenker)

• Scattering calculations

Close-coupling approach (Collaborated with Prof. P. C. Stancil)

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MOCC method

Approximations:

• Born-Oppenheim approximation (BO)
• Perturbed stationary-state approximation (PSS)

) | ( ) ( ) , ( R R F R

i i

   

  





System Hamilton: ) | ( 2 1 ) , (

2

R H R H

i ad R R i

      

) | ( ) , ( ) | ( ) | ( R R R R H

i i i ad

     

  



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Total wave function can be written as

) | ( ) ( ) , ( R R F R

i i

   

  





By the variation theory, the adiabatic close-coupling scattering equation is obtained: The coupled equations are transformed to a diabatic representation:

 

 

 



  

      

  

  

' ' ' , 2

) , ( 2 ) , ( ) , ( 2 R F V R F R E

d R d R R

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Using a partial wave decomposition method, the radial wavefunction and the S-matrix are obtained:

)} ( ) ( { 1 ) ( lim

' ' , ' , '

R k K R k j k R f

l l l lm R        

   

  l l l

iK I iK I S    The differential and integrate total cross sections are respectively:

2 , 2

)] (cos ) 1 2 ( [ 4 1 ) (   

l l l j i

P S l k d d



  



  

l j i l ij i tot

S l k k ) )( 1 2 ( ) (

2 , 2

  

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AOCC method

( ) H i t     

2

1 ( ) ( ) 2

r A A B B

H V r V r     

, ,

( )

A B A B

V r are the electron interactions with the target and Projectile. even-tempered basis

ˆ ( ) ( ) ( )

kr

l klm l k lm

r N r e Y r



 



  

, 1,2,...,

k k

k N    

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The atomic orbital states

( )

nlm r

 

can be obtained as

( ) ( )

nlm nk klm k

r c r     

The total wave function of the collision system

( , ) ( ) ( , ) ( ) ( , )

A B i i j j i j

r t a t r t b t r t     

 

  

The resulting first-order coupled equations for the amplitude ai(t) and bj(t) are

( ) i A SB HA KB     

†

( ) i B S A KA HB     

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The above equations can be solved under the initial conditions:

1

( ) , ( )

i i j

a b     

The cross sections for excitation and charge transfer are calculated as:

2 ,

2 | ( ) |

cx j j

b bdb  



 



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Outline

• Motivation
• Theoretical method
• Results and discussions

H+-Be+→H(nl)+Be2+ →H++Be+(1s2nl), n>2 →H++Be2+(1s2)+e Be3+-Li→Be2++Li+

• Summary

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H++ Be+(1s22l)→H(nl) + Be2+ /H+ + Be+(1s2nl),n>2

Adiabatic potential curves for (BeH)2+ system

The solid and dotted lines represent the and states, respectively.

2

2

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Radial and rotational coupling matrix elements for BeH2+

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Cross section results: Be+(1s22s) initial state

3 6 9 12 15 18 21 24 10

• 2

10

• 1

10 10

1

10

2

present AOCC

Energy (keV/u) Cross section (10

• 16cm

2)

Bransden present QMOCC

Total electron capture cross section for H+-Be+(2s) collisions.

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10 10

1

10

2

10

• 3

10

• 2

10

• 1

10 10

1

total n=1 n=2 n=3 n=4

Energy (keV/u) Cross section (10

• 16cm

2)

10 10

1

10

2

10

• 4

10

• 3

10

• 2

10

• 1

10 2s 2p 3s 3p 3d

Energy (keV/u) Cross section (10

• 16cm

2)

10 10

1

10

2

10

• 5

10

• 4

10

• 3

10

• 2

4s 4p 4d 4f

Energy (keV/u) Cross section (10

• 16cm

2)

n- and nl-partial electron capture cross section for H+-Be+(2s) collisions

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0.01 0.1 1 10 100 10

• 3

10

• 2

10

• 1

10 10

1

present AOCC 2p 3s 3p 3d

Energy (keV/u) Cross section (10-16cm2)

present QMOCC 2p 3s 3p 3d 1 10 100 10

• 2

10

• 1

4s 4p 4d 4f

Energy (keV/u) Cross section (10

• 16cm

2)

Cross sections for excitation to 2p, 3l and 4l states of Be+ in H+-Be+(1s22s) collisions.

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1 10 100 10

• 3

10

• 2

10

• 1

10 ionization

Energy (keV/u) Cross section (10

• 16cm

2)

AOCC ionization cross sections in H+-Be+(1s22s) collisions.

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Cross section results: Be+(1s22p) initial state

10

• 2

10

• 1

10 10

1

10

2

10

• 4

10

• 3

10

• 2

10

• 1

10 10

1

AOCC total n=1 n=2 n=3 n=4

Energy (keV/u) Cross section (10

• 16cm

2)

QMOCC total

Total and n-shell AOCC and 1s QMOCC electron capture cross sections in H+-Be+(1s22p) collisions.

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10 10

1

10

2

10

• 4

10

• 3

10

• 2

10

• 1

10 2s 2p 3s 3p 3d

Energy (keV/u) Cross section (10

• 16cm

2)

10 10

1

10

2

10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

4s 4p 4d 4f

Energy (keV/u) Cross section (10

• 16cm

2)

AOCC cross sections for electron capture to 4l states of H in H+-Be+(1s22p) collisions.

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10

• 2

10

• 1

10 10

1

10

2

10

• 3

10

• 2

10

• 1

10 10

1

AOCC 2s 3s 3p 3d QMOCC 2s 3s 3p 3d

Energy (keV/u) Cross section (10-16cm2)

10 10

1

10

2

10

• 2

10

• 1

10 4s 4p 4d 4f

Energy (keV/u) Cross section (10

• 16cm

2)

Cross sections for excitation to the 2s and 3l states of Be+ in H+-Be+(1s22p) collisions. AOCC cross sections for excitation to 4l states of Be+ in H+-Be+(1s22p) collisions.

26 1 10 100 10

• 3

10

• 2

10

• 1

10 ionization

Energy (keV/u) Cross section (10

• 16cm

2)

AOCC ionization cross section H+-Be+(1s22p) collisions.

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Molecular state Asymptotic atomic state Energy (eV)

• Expt. [13]

Theor. error 13Σ Be2+(1s2s)[3S]+Li+

• 29.913
• 29.676

0.237 21Σ Be2+(1s2s)[1S]+Li+

• 26.854
• 26.724

0.13 23Σ, 13Π Be2+(1s2p)[3P]+Li+

• 26.583
• 26.363

0.22 31Σ, 11Π Be2+(1s2p)[1P]+Li+

• 24.836
• 24.715

0.121 33Σ Be2+(1s3s)[3S]+Li+

• 9.495
• 9.363

0.132 41Σ Be2+(1s3s)[1S]+Li+

• 8.687
• 8.634

0.053 43Σ, 23Π Be2+(1s3p)[3P]+Li+

• 8.613
• 8.591

0.022 53Σ, 33Π, 13Δ Be2+(1s3d)[3D]+Li+

• 8.231
• 8.155

0.076 51Σ, 21Π, 11Δ Be2+(1s3d)[1D]+Li+

• 8.221
• 8.150

0.071 61Σ, 31Π Be2+(1s3p)[1P]+Li+

• 8.106
• 8.052

0.054 63Σ Be2+(1s4s)[3S]+Li+

• 2.786
• 2.579

0.207 71Σ Be2+(1s4s)[1S]+Li+

• 2.450
• 2.347

0.103 73Σ, 43Π Be2+(1s4p)[3P]+Li+

• 2.429
• 2.327

0.102 83Σ, 53Π, 23Δ Be2+(1s4d)[3D]+Li+

• 2.271
• 2.151

0.12 81Σ, 41Π, 21Δ Be2+(1s4d)[1D]+Li+

• 2.266
• 2.148

0.108 91Σ, 51Π, 31Δ Be2+(1s4f)[1F]+Li+

• 2.263
• 2.138

0.125 93Σ, 63Π, 33Δ Be2+(1s4f)[3F]+Li+

• 2.263
• 2.138

0.125 101Σ, 61Π Be2+(1s4p)[1P]+Li+

• 2.224
• 2.084

0.140 111Σ, 103Ʃ Be3+(1s)+Li(2s) 121Ʃ, 113Ʃ, 71,3П Be3+(1s)+Li(2p) 1.848 1.848

Table 1. Asymptotic separated-atom energies of BeLi3+ molecule.

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Adiabatic energies of BeLi3+ molecular ion. The solid, dashed, dotted and dash-dotted lines represent the Σ, Π, Δ and Φ states, respectively. (a) singlet states; (b) triplet states.

Be3+-Li

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Radial and rotational coupling matrix elements for the singlet and triplet states.

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Total electron capture cross section in Be3+-Li(2s) collisions.

31

Spin-resolved cross sections

10

• 1

10 10

1

10

2

10

3

10

4

10

5

10

• 2

10

• 1

10 10

1

10

2

(a) Energy(eV/u) Cross section(10

• 16cm

2)

4s(QMOCC) 4p 4d 4f

Singlet

4s(AOCC) 4p 4d 4f

10

• 1

10 10

1

10

2

10

3

10

4

10

5

10

• 3

10

• 2

10

• 1

10 10

1

10

2

Triplet Cross section (10-16cm2) Energy(eV/u) (b)

4s(QMOCC) 4p 4d 4f 4s(AOCC) 4p 4d 4f

Cross sections for electron capture to 4l singlet and triplet states of Be2+ ion.

32

10

• 1

10 10

1

10

2

10

3

10

4

10

5

10

• 3

10

• 2

10

• 1

10 10

1

(a) Cross section (10-16cm2) Energy (eV/u) Singlet

3s(Q M OCC) 3p 3d 3s(AOCC) 3p 3d 10

• 1

10 10

1

10

2

10

3

10

4

10

5

10

• 3

10

• 2

10

• 1

10 10

1

Triplet (b) Cross section(10-16cm2) Energy(eV/u)

3s(QM OCC) 3p 3d 3s(AOCC) 3p 3d

Cross sections for electron capture to 3l singlet and triplet states of Be2+ ion.

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10

• 1

10 10

1

10

2

10

3

10

4

10

5

10

• 1

10 10

1

10

2

Cross section (10-16cm2) n=4 Energy (eV/u)

singlet(QM OCC) triplet(QM OCC) singlet(AOCC) triplet(AOCC) 10

• 1

10 10

1

10

2

10

3

10

4

10

5

10

• 3

10

• 2

10

• 1

10 10

1

singlet(QM OCC) triplet(QM OCC)

Cross section (10-16cm2) n=3 Energy (eV/u)

sinlget(AOCC) triplet(AOCC)

Cross sections for electron capture to the n=4 and n=3 shells of singlet and triplet states of Be2+ ion.

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Outline

• Motivation
• Theoretical method
• Results and discussions

H+-Be+→H(nl)+Be2+ →H++Be+(1s2nl), n>2 →H++Be2+(1s2)+e Be3+-Li→Be2++Li+

• Summary

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• Using the MOCC and AOCC methods, the reliable CT

and EXC data can be obtained in a large energy range.

• Multi–electron system and very high charge ion problems

are still challenges.

Future works

• H+-Be(0,2,3)+, H+-Neq+(q=0-9), H+-Arq+(q=0-17)

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Part 2 Free-free transition in H plasma

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Saemann et al. Phys. Rev. Lett. 82, 4843 (1999)

K-shell emission spectra of solid Aluminum laser produced plasma

T=~300eV n=(5-10)×1023/cm3

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The Coulomb interaction screening is a general phenomenon in plasma; it is a collective effect of correlated many-particle Interactions; it strongly depends on the plasma environments; it strongly affects the electronic structure (spectral) properties of atoms/molecules and properties of their collision processes with respect to those for isolated systems.

plasma screening

2 1/3

Coupling parameter 3 / ( ) 4 Degeneracy parameter = /

B e e B e F

Ze k T n k T E     1 nearly ideal 1 nondegenerate 1 weakly nonideal 1 degenerate 1 strongly coupled               =

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.. / / 2 1

(Debye-H uckel potential) Hamiltonian 1 1 [ ] 2

n mn

r D r D r D n n m n n mn

Z Z e r r Z H e e r r

    

       

 

Debye plasma weakly coupled classical hot-dense plasma (Γ<<1,Θ>1)

e.g., laser induced plasmas, ICF plasma, stellar interiors …

pair-wise correlation approximation

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What we have done in Debye plasmas * Electronic structure * Emission spectra * Photoionization (non-relativistic & relativistic ) * Fast electron impact ionization * Low energy electron impact excitation * Low energy electron-impact ionization * Heavy particle collisions (excitation、charge transfer、 ionization) * free-free trantion

R.K. Janev, S.B. Zhang, and J.G. Wang, Matter and Radiation at Extremes 1, 237 (2016).

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Critical Debye length: 0.8403, 3.2267, 4.54104 a.u.

Energy levels (Ryd) of H in Debye plasma

s p d f g

42

Qi et al. Phys. Rev. A 78, 062511 (2008)

Lyman-α emission spectra of hydrogen

Redshift

43

Low energy electron impact excitation of hydrogen

S.B. Zhang, J.G. Wang and R.K. Janev, Phys. Rev. Lett. 104, 023203 (2010)

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Heavy particle collisions: excitation & charge transfer

2 2

( ) excitation (1 ) ( ) charge transfer He H nl He H s He nl H

   

        

Liu et al. Phys. Rev. A 77, 032709 (2008)

excitation charge transfer

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free-free absorption cross sections classical Kramers’ cross sections free-free Gaunt factor

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Non-relativistic free-free absorption Gaunt factors for the pure Coulomb potential and field-free cases

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free-free absorption Gaunt factors for different screening lengths

• Phys. Rev. A 99, 012705 (2019).

48

thermally averaged Gaunt factors

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Total thermally averaged Gaunt factors MNRAS (submitted)

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Summary

Free-free Gaunt factors, (total) thermally averaged one in H Debye plasma have been numerically studied in the non- relativistic level.

Future works

different plasmas, relativistic level, different objects

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Thanks for your attention!