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

Beryllium ion collisions and free-free transition in H plasma L. Liu 1 , S. B. Zhang 2 , C.H.Liu 3 , Y. Wu 1 , J.G.Wang 1 and R.K.Janve 4 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 1 th RCM on Vapour Shielding, Vienna, 2019.03.13 1

Part 1 Beryllium ion collisions 2

Outline • Motivation • Theoretical method • Results and discussions H + -Be + →H( nl )+Be 2+ →H + +Be + ( 1s 2 nl ), n>2 →H + +Be 2+ (1s 2 )+e Be 3+ -Li→Be 2+ +Li + • Summary 3

fusion energy Astrophysics Environmental science Medicine Heavy particle collisions Agriculture Natural resource Atmospheric 大气物理 High technology 臭氧层 physics 4

Diverter/plasma edge Motivation Neutral Beam Injection Heating Tokomak Diagnostics 5

Jupiter aurora Jupiter aurora: EUV and X-ray O q+ + H 2 → O (q-1)+ (n l ) + H 2 + O (q-1)+ (nl) → O (q-1)+ (n’ l ’) + hυ 6

Outline • Motivation • Theoretical method • Results and discussions H + -Be + →H( nl )+Be 2+ →H + +Be + ( 1s 2 nl ), n>2 →H + +Be 2+ (1s 2 )+e Be 3+ -Li→Be 2+ +Li + • Summary 7

Theoretical method  Fully quantum mechanical molecular orbital close-coupling (MOCC) method  Two-center atomic orbital close-coupling (TC-AOCC) method 8

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) 9

MOCC method Approximations:  Born-Oppenheim approximation (BO)  Perturbed stationary-state approximation (PSS)       ( R , ) F ( R ) ( | R )   i i  System Hamilton: 1       2 H ( R , ) H ( | R ) i R ad i  2 R        H ( | R ) ( | R ) ( R , ) ( | R )    ad i i i 10

Total wave function can be written as       ( R , ) F ( R ) ( | 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 d       d 2 E ( R , ) F ( R , ) 2 V F ( R , )     , ' '  R R R    ' 11

Using a partial wave decomposition method, the radial wavefunction and the S-matrix are obtained: 1     lm l lim f ( R ) { j ( k R ) K ( k R )}        , ' l , ' l ' k   R  '  l I iK  l S  l I iK The differential and integrate total cross sections are respectively:   d ( ) 1     l 2 [ ( 2 l 1 ) S P (cos )] i , j l  2 d 4 k l   2      l ( k ) ( 2 l 1 )( S ) tot ij 2 k i , j 12 l i

AOCC method  1         2 H V r ( ) V r ( ) ( H i ) 0 r A A B B  2 t V ( r ) are the electron interactions with the target and A B , A B , Projectile. even-tempered basis   ˆ      k r     l k ( ) r N ( ) r e Y ( ) r , k 1,2,..., N k klm l k lm 13

  nlm r ( ) The atomic orbital states can be obtained as       ( ) r c ( ) r nlm nk klm k The total wave function of the collision system           A B ( , ) r t a t ( ) ( , ) r t b t ( ) ( , ) r t i i j j i j The resulting first-order coupled equations for the amplitude a i (t) and b j (t) are      i A ( SB ) HA KB      † i B ( S A ) KA HB 14

The above equations can be solved under the initial conditions:      a ( ) , b ( ) 0 i 1 i j The cross sections for excitation and charge transfer are calculated as:       2 2 | b ( ) | bdb cx j , j 0 15

Outline • Motivation • Theoretical method • Results and discussions H + -Be + →H( nl )+Be 2+ →H + +Be + ( 1s 2 nl ), n>2 →H + +Be 2+ (1s 2 )+e Be 3+ -Li→Be 2+ +Li + • Summary 16

H + + Be + ( 1s 2 2l )→H( nl ) + Be 2+ /H + + Be + ( 1s 2 nl ),n>2 Adiabatic potential curves for (BeH) 2+ system The solid and dotted lines represent the and states, respectively. 2  2  17

Radial and rotational coupling matrix elements for BeH 2+ 18

Cross section results: Be + (1s 2 2s) initial state 24 21 2 ) 18 -16 cm 15 Cross section (10 12 9 present QMOCC present AOCC 6 Bransden 3 0 -2 -1 0 1 2 10 10 10 10 10 Energy (keV/u) Total electron capture cross section for H + -Be + (2s) collisions. 19

n- and nl -partial electron capture cross section for H + -Be + (2s) collisions 0 10 2s total 1 10 2p n=1 2 ) 2 ) 3s -16 cm -16 cm -1 n=2 10 3p n=3 3d Cross section (10 Cross section (10 0 n=4 10 -2 10 -1 10 -3 10 -2 10 -4 10 -3 10 0 1 2 10 10 10 0 1 2 10 10 10 Energy (keV/u) Energy (keV/u) -2 10 2 ) -16 cm Cross section (10 -3 10 4s -4 10 4p 4d 4f 20 -5 10 0 1 2 10 10 10 Energy (keV/u)

1 10 2 ) Cross section (10 -16 cm 2 ) -16 cm -1 10 0 10 Cross section (10 -1 10 4s present AOCC present QMOCC -2 4p 10 2p -2 2p 10 4d 3s 3s 4f 3p 3p 3d 3d -3 10 0.01 0.1 1 10 100 1 10 100 Energy (keV/u) Energy (keV/u) Cross sections for excitation to 2p, 3l and 4l states of Be + in H + -Be + (1s 2 2s) collisions. 21

0 10 2 ) -16 cm -1 Cross section (10 10 -2 10 ionization -3 10 1 10 100 Energy (keV/u) AOCC ionization cross sections in H + -Be + (1s 2 2s) collisions. 22

Cross section results: Be + (1s 2 2p) initial state 1 10 2 ) 0 10 -16 cm Cross section (10 -1 10 QMOCC total -2 10 AOCC total n=1 -3 10 n=2 n=3 n=4 -4 10 -2 -1 0 1 2 10 10 10 10 10 Energy (keV/u) Total and n-shell AOCC and 1s QMOCC electron capture cross sections 23 in H + -Be + (1s 2 2p) collisions.

-1 10 0 10 2 ) -16 cm 2 ) -2 10 -16 cm -1 10 Cross section (10 Cross section (10 -3 10 -2 10 2s 4s 2p 4p -4 10 3s -3 4d 10 3p 4f 3d -4 -5 10 10 0 1 2 0 1 2 10 10 10 10 10 10 Energy (keV/u) Energy (keV/u) AOCC cross sections for electron capture to 4 l states of H in H + -Be + (1s 2 2p) collisions. 24

1 0 10 10 4s Cross section (10 -16 cm 2 ) 4p 2 ) 0 10 -16 cm 4d 4f Cross section (10 -1 -1 10 10 QMOCC AOCC -2 2s 2s 10 3s 3s 3p 3p 3d 3d -3 -2 10 10 0 1 2 -2 -1 0 1 2 10 10 10 10 10 10 10 10 Energy (keV/u) Energy (keV/u) Cross sections for excitation to the 2 s and AOCC cross sections for excitation to 3 l states of Be + in H + -Be + ( 1s 2 2p ) collisions. 4l states of Be + in H + -Be + ( 1s 2 2p ) collisions. 25

0 10 2 ) -16 cm Cross section (10 -1 10 -2 10 ionization -3 10 1 10 100 Energy (keV/u) AOCC ionization cross section H + -Be + ( 1s 2 2p ) collisions. 26

Table 1. Asymptotic separated-atom energies of BeLi 3+ molecule. Energy (eV) Molecular state Asymptotic atomic state Expt. [13] Theor. error 1 3 Σ Be 2+ (1 s 2 s )[ 3 S]+Li + -29.913 -29.676 0.237 2 1 Σ Be 2+ (1 s 2 s )[ 1 S]+Li + -26.854 -26.724 0.13 2 3 Σ, 1 3 Π Be 2+ (1 s 2 p )[ 3 P]+Li + -26.583 -26.363 0.22 3 1 Σ, 1 1 Π Be 2+ (1 s 2 p )[ 1 P]+Li + -24.836 -24.715 0.121 3 3 Σ Be 2+ (1 s 3 s )[ 3 S]+Li + -9.495 -9.363 0.132 4 1 Σ Be 2+ (1 s 3 s )[ 1 S]+Li + -8.687 -8.634 0.053 4 3 Σ, 2 3 Π Be 2+ (1 s 3 p )[ 3 P]+Li + -8.613 -8.591 0.022 5 3 Σ, 3 3 Π, 1 3 Δ Be 2+ (1 s 3 d )[ 3 D]+Li + -8.231 -8.155 0.076 5 1 Σ, 2 1 Π, 1 1 Δ Be 2+ (1 s 3 d )[ 1 D]+Li + -8.221 -8.150 0.071 6 1 Σ, 3 1 Π Be 2+ (1 s 3 p )[ 1 P]+Li + -8.106 -8.052 0.054 6 3 Σ Be 2+ (1 s 4 s )[ 3 S]+Li + -2.786 -2.579 0.207 7 1 Σ Be 2+ (1 s 4 s )[ 1 S]+Li + -2.450 -2.347 0.103 7 3 Σ, 4 3 Π Be 2+ (1 s 4 p )[ 3 P]+Li + -2.429 -2.327 0.102 8 3 Σ, 5 3 Π, 2 3 Δ Be 2+ (1 s 4 d )[ 3 D]+Li + -2.271 -2.151 0.12 8 1 Σ, 4 1 Π, 2 1 Δ Be 2+ (1 s 4 d )[ 1 D]+Li + -2.266 -2.148 0.108 9 1 Σ, 5 1 Π, 3 1 Δ Be 2+ (1 s 4 f )[ 1 F]+Li + -2.263 -2.138 0.125 9 3 Σ, 6 3 Π, 3 3 Δ Be 2+ (1 s 4 f )[ 3 F]+Li + -2.263 -2.138 0.125 10 1 Σ, 6 1 Π Be 2+ (1 s 4 p )[ 1 P]+Li + -2.224 -2.084 0.140 11 1 Σ, 10 3 Ʃ Be 3+ (1 s )+Li(2s) 0 0 0 27 12 1 Ʃ, 11 3 Ʃ, 7 1,3 П Be 3+ (1s)+Li(2p) 1.848 1.848 0

Be 3+ -Li Adiabatic energies of BeLi 3+ 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. 28

Radial and rotational coupling matrix elements for the singlet and triplet states. 29

Total electron capture cross section in Be 3+ -Li(2s) collisions. 30