Basis Generator Method Calculations for Charge-Transfer Collisions Involving Few-Electron Systems. Tom Kirchner

Transcription

1 Basis Generator Method Calculations for Charge-Transfer Collisions Involving Few-Electron Systems Tom Kirchner

2 Few-electron dynamics Challenging because of nonseparability Interesting because of nonseparability Relevant for applications, but uncertainty estimates are difficult Today s presentation The basis generator method (BGM) for multielectron collision problems A few illustrations for (low-energy) charge-transfer collisions

3 Theoretical Considerations

4 Semiclassical approximation Justification: de Broglie wavelength of projectile λ K = h/p = h/(µv) a at E P 1 kev/amu (curved or) straightline projectile trajectory x x I _ e 1 1 _ r P z R(t) = (b,, vt) b _ r _R(t) P v_ 11 1 b: impact parameter v: projectile speed T 1 1 zi electrons described fully quantum mechanically

5 Semiclassical approximation Nonrelativistic theory: time-dependent Schrödinger equation (TDSE) ( = m e = e = 1) (Ĥe (t) i t ) ψ(t) =, ψ(t i ) = φ i Ĥ e (t) = ˆT e + ˆV e n (t)+ ˆV e e + Z pz t R(t) ˆTe : kinetic energies of electrons ˆV e n (t): time-dependent electron-nucleus Coulomb interaction ˆVe e : electron-electron Coulomb interaction

6 Discussion I Explicit solution feasible for N = 2 bare ion He (H 2 ) collisions Molecular close coupling Atomic close coupling Time-dependent lattice (TDL) methods Classical-trajectory Monte Carlo (CTMC)... N 3: (mostly) beyond present capabilities

7 Discussion II Approx. alternatives for N 2 target electrons model uncertainties Ansatz (independent electrons IEM): N Ĥ e (t) ĥ j (t), i t ψ j (r, t) = ĥ(t)ψ j(r, t) j=1 ĥ(t) = 1 2 Z T r Choice of v ee defines model Z p r R(t) + v ee(r, t) Time-dependent density functional theory (TDDFT) provides foundation

8 Choices: Discussion III v ee (r, t) = vee (r) no response v ee (r, t) = f(t)vee(r) global target response v ee (r, t) = v ee [ψ j ](r, t) microscopic response Standard methods can be used within IEM Basis Generator Method (BGM) : a close-coupling method based on atomic orbitals and dynamically adapted pseudo states Kirchner et al., PRA Lüdde et al. JPB 1996, Kroneisen et al. JPA 1999

9 Discussion IV Single-particle solutions many-electron info Option 1: IEM (multinomial) analysis e.g. single and double capture for N = 2: P 1 = 2p cap (1 p cap ) P 2 = pcap 2 Option 2: determinants (density matrices) Further options: correlation integrals, single-active electron model,... source of model uncertainties Lüdde and Dreizler JPB 1985 Baxter and Kirchner PRA 16

10 Illustrations

11 He 2+ - He: single and double capture single capture double capture MCHF IEM MCHF WB Fritsch Jana et al MCHF IEM MCHF WB Fritsch Ghosh et al. σtp [1 16 cm 2 ] σpp [1 16 cm 2 ] EP [kev/amu] EP [kev/amu] : two-electron : DFT-based Baxter and Kirchner, PRA 93, 1252 (16)

12 Ne 1+ - Ne: single capture snl [%] n = 4 n = 5 n = 6 Liu et al. BGM-net BGM-SEC no-resp. resp. s nl = σ nl / nl σ nl IEM level Liu et al., PRA 89, 1271 BGM: PRA 92, l E P = 4.54 kev/amu

13 Ne 1+ - Ne: x-ray spectra Counts n = 4 Ly-α n = 6 Ly-α Ly-β+ Ly-β expt. Liu et al. BGM-net BGM-SEC no-resp. resp. Ly-α Ly-α n = 5 Ly-β+ All n Ly-β Expt.: Ali et al., Astrophys. J. Lett. 716, L95 Liu et al., PRA 89, 1271 BGM: PRA 92, E P = 4.54 kev/amu X-ray energy [ev]

14 Molecules More difficult than atoms because of multi-center structure Electron dynamics can be described in similar way if small (e.g. H 2 O, CH 4 ) * Relevant for cometary x-ray emission * Kirchner et al, Adv. Quant. Chem. 65, 315 (13)

15 O 6+ - H 2 O, CH 4 : S,D,T capture O 6+ -H2O EP (kev/amu) BGM Expt. [15] CTMC [15] 1.17 SEC ± DEC ± TEC ± SEC ± DEC ± TEC ± O 6+ -CH4 EP (kev/amu) BGM Expt. [15] CTMC [15] 1.17 SEC ± DEC ± TEC ± SEC ± DEC ± TEC ± Expt & CTMC: Machacek et al., Astrophys. J. 89, 75 (15)

16 O 6+ - H 2 O, CH 4 : x-ray spectra (SC) Wavelength [nm] Wavelength [nm] s 2p 3d 2p 3p 2s 4s 2p 4d 2p 4p 2s.6 3s 2p 3d 2p 3p 2s 4s 2p 4d 2p 4p 2s.4.2 Ar 1.17 kev/amu.4.2 Ar 2.33 kev/amu Spectral counts H2O Spectral counts H2O.6.4 CH4.6.4 CH Photon energy [ev] Photon energy [ev] CTMC ( ): Machacek et al., Astrophys. J. 89, 75 (15) BGM no response ( ); BGM response ( )

17 Conclusions: multielectron systems Model uncertainties (IEM): Effective potential Multielectron analysis Subsequent processes (autoionization, radiative cascades,...) Uncertainty estimates currently based on: Comparisons of different model (variants) Comparisons with experimental data Need benchmark data for benchmark systems!

18 Ne 1+ - He,Ne,Ar: single n-capture (a) 8 Ne 1+ -He 6 4 expt.[2] Liu et al. BGM-net no-resp. resp. (b) 8 Ne 1+ -He 6 4 expt.[2] CTMC [2] BGM-SEC no-resp. resp. σ n rel [%] Ne 1+ -Ne σ n rel [%] Ne 1+ -Ne Ne 1+ -Ar Ne 1+ -Ar n n FIG. 3. (Color online) -state selective relative cross sections rel in the Ne 1+ -He, -Ne, and -Ar collision systems: (a) TC-BGM net rel E P = 4.54 kev/amu Liu et al., PRA 89, 1271 BGM: PRA 92, CTMC and Expt: Ali et al., Astrophys. J. Lett. 716, L95

19 Thanks to... York University M. Baxter A. Leung M. Horbatsch U Frankfurt H. J. Lüdde... and to you for your attention!