Photoionization of Ne 8+
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1 Photoionization of Ne 8+ M. S. Pindzola Department of Physics Auburn University, Auburn, Alabama This work was supported in part by grants from: US Department of Energy US National Science Foundation Computational work was carried out at: NERSC in Oakland, CA NCCS in Oak Ridge, TN
2 Collaborators S. A. Abdel-Naby, C. P. Ballance, and S. D. Loch Auburn University J. P. Colgan and C. J. Fontes Los Alamos National Laboratory F. J. Robicheaux Purdue University Article Single and Double Photoionization of Ne 8+, M. S. Pindzola, S. A. Abdel-Naby, F. Robicheaux, and J. Colgan Journal of Physics (London) B 47, (2014).
3 FLASH ACCELERATORS PHOTON SCIENCE PARTICLE PHYSICS Deutsches Elektronen-Synchrotron A Research Centre of the Helmholtz Association URL: Home / Facilities / FLASH FLASH FLASH FLASH INFOSCREEN FLASH ACCELERATOR PAGES FLASH, the Free-Electron LASer in Hamburg, started user operation in summer 2005 as the first free-electron laser for VUV and soft X-ray radiation. Currently it covers a wavelength range from 4.2 nm to about 45 nm in the first harmonic with GW peak power and pulse durations between 50 fs and 200 fs. It is operated in the "self-amplified spontaneous emission" (SASE) mode and offers five beamlines for users. Feedback Contact Imprint 2014 Deutsches Elektronen-Synchrotron DESY
4 TDCC Method for Atoms The time-dependent Schrodinger equation for a two-electron atomic ion is given by: where i Ψ( r 1, r 2, t) t H( r 1, r 2, t) = = H( r 1, r 2, t)ψ( r 1, r 2, t) 2 i=1 ( 1 2 2i Z ) + ri +E(t) cosωt 2 r i cosθ i i=1 1 r 1 r 2 Expanding in coupled spherical harmonics: Ψ( r 1, r 2, t) = Pl LS 1 l 2 l 1,l 2 r 1 r 2 m 1,m 2 C l 1l 2 L m 1 m 2 0Y l1 m 1 (θ 1, φ 1 )Y l2 m 2 (θ 2, φ 2 ) The time-dependent close-coupled equations are given by: LS Pl i 1 l 2 t = T l1 l 2 (r 1, r 2 )P LS l 1 l 2 + l 1,l 2 + L,l 1,l 2 V L l 1 l 2,l 1 l 2 (r 1, r 2 )P LS l 1 l 2 (r 1, r 2, t) W LL l 1 l 2,l 1 l 2 (r 1, r 2, t)p L S l 1 l 2 (r 1, r 2, t) where T l1 l 2 (r 1, r 2 ) is a sum over one-body kinetic and nuclear operators, Vl L 1 l 2,l (r 1, r 1 l 2 2 ) is a two body coupling operator, and Wl LL 1 l 2,l (r 1, r 1 l 2 2, t) is a sum over one-body radiation field operators.
5 TDCC Method for Atoms The time-dependent radial wavefunctions, P LS l 1 l 2, are represented on a two dimensional radial lattice: r 1 = 0.10, 0.20, 0.30,..., r 2 = 0.10, 0.20, 0.30,..., With 10 radial points for each core, the calculation uses 10,000 cores. The use of second derivatives in the Hamiltonian requires message passing between each core and its nearest neighbors. The number of coupled channels are given by: 1 S = ss, pp, dd, ff, gg, hh, ii 1 P = sp, ps, pd, dp, df, fd, fg, gf, gh, hg, hi, ih Time propagation is for oscillation periods. For t = the total number of time steps is close to 50,000.
6 5.0 Double to Single Photoionization of He TDCC (red), experiment (blue) Cross Section Ratio (%) Photon Energy (ev)
7 3 Double to Single Photoionization of Be TDCC (red), experiment (blue) 2.5 Cross Section Ratio (%) Photon Energy (ev)
8 RTDCC Method for Atoms The time-dependent Dirac equation for a two-electron atomic ion is given by: where H(t) = i Ψ( r 1, r 2, t) t = H(t) Ψ( r 1, r 2, t) H( r 1, r, t) c σ ( p 1 + A 1 (t)) c σ ( p 2 + A 2 (t)) G( r 1, r 2 ) c σ ( p 1 + A 1 (t)) H( r 1, r 2, t) 2c 2 G( r 1, r 2 ) c σ ( p 2 + A 2 (t)) c σ ( p 2 + A 2 (t)) G( r 1, r 2 ) H( r 1, r 2, t) 2c 2 c σ ( p 1 + A 1 (t)) G( r 1, r 2 ) c σ ( p 2 + A 2 (t)) c σ ( p 1 + A 1 (t)) H( r 1, r 2, t) 4c 2 p i = i i H( r 1, r 2, t) = 2 i=1 ( Z ) U i (t) + C( r 1, r 2 ) r i U i (t) = E(t)z i cosωt A i (t) = E(t) ω ẑi sin ( ω c y i ωt) + E(t) ω ẑi sin (ωt) C( r 1, r 2 ) = 1 r 1 r 2 G( r 1, r 2 ) = σ 1 σ 2 r 1 r 2 Expanding in coupled spin-orbit eigenfunctions: PPκ j J 1 κ 2 (r 1,r 2,t) 1,j 2 r 1 r 2 m 1,m 2 C j 1j 2 J m 1 m 2 MΦ +κ1,m 1 (θ 1, φ 1 )Φ +κ2,m 2 (θ 2, φ 2 ) i QPκ J 1 κ 2 (r 1,r 2,t) j Ψ( r 1, r 2, t) = 1,j 2 r 1 r 2 m 1,m 2 C j 1j 2 J m 1 m 2 M Φ κ 1,m 1 (θ 1, φ 1 )Φ +κ2,m 2 (θ 2, φ 2 ) i PQ J (r 1,r 2,t) j 1,j 2 r 1 r 2 m 1,m 2 C j 1j 2 J m 1 m 2 MΦ +κ1,m 1 (θ 1, φ 1 )Φ κ2,m 2 (θ 2, φ 2 ) QQ j J (r 1,r 2,t) 1,j 2 m 1,m 2 C j 1j 2 J m 1 m 2 M Φ κ 1,m 1 (θ 1, φ 1 )Φ κ2,m 2 (θ 2, φ 2 ) r 1 r 2
9 RTDCC Method for Atoms The time-dependent close-coupled equations are given by: i PPJM t = ( Z r 1 Z r 2 )PP JM c( r 1 κ 1 r 1 )QP JM c( κ 2 )PQ JM κ r 2 r 1 κ 2 2 < (κ 1, κ 2 )JM U 1 (t) + U 2 (t) (κ 1, κ 2 )J M > PP J M κ (r 1, r 1 κ 2 2, t) +ic +ic + + < (κ 1, κ 2 )JM σ A 1 (t) ( κ 1, κ 2 )J M > QP J M < (κ 1, κ 2 )JM σ A 2 (t) (κ 1, κ 2)J M > PQ J M < (κ 1, κ 2 )JM C( r 1, r 2 ) (κ 1, κ 2)J M > PP J M < (κ 1, κ 2 )JM G( r 1, r 2 ) ( κ 1, κ 2 )J M > QQ J M i QP JM t = ( Z r 1 Z r 2 2c 2 )QP JM +c( r 1 + κ 1 r 1 )PP JM +c( κ 2 )QQ JM κ r 2 r 1 κ 2 2 < ( κ 1, κ 2 )JM U 1 (t) + U 2 (t) ( κ 1, κ 2 )J M > QP J M κ (r 1, r 1 κ 2 2, t) ic ic + + < ( κ 1, κ 2 )JM σ A 1 (t) (κ 1, κ 2 )J M > PP J M < ( κ 1, κ 2 )JM σ A 2 (t) ( κ 1, κ 2 )J M > QQ J M < ( κ 1, κ 2 )JM C( r 1, r 2 ) ( κ 1, κ 2)J M > QP J M < ( κ 1, κ 2 )JM G( r 1, r 2 ) (κ 1, κ 2)J M > PQ J M
10 RTDCC Method for Atoms i PQJM t = ( Z r 1 Z r 2 2c 2 )PQ JM +c( r 1 κ 1 r 1 )QQ JM +c( + κ 2 )PPκ JM r 2 r 1 κ 2 2 < (κ 1, κ 2 )JM U 1 (t) + U 2 (t) (κ 1, κ 2 )J M > PQ J M κ (r 1, r 1 κ 2 2, t) ic ic + + < (κ 1, κ 2 )JM σ A 1 (t) ( κ 1, κ 2 )J M > QQ J M < (κ 1, κ 2 )JM σ A 2 (t) (κ 1, κ 2 )J M > PP J M < (κ 1, κ 2 )JM C( r 1, r 2 ) (κ 1, κ 2 )J M > PQ J M < (κ 1, κ 2 )JM G( r 1, r 2 ) ( κ 1, κ 2)J M > QP J M i QQJM t = ( Z r 1 Z r 2 4c 2 )QQ JM c( r 1 + κ 1 r 1 )PQ JM c( + κ 2 )QPκ JM r 2 r 1 κ 2 2 < ( κ 1, κ 2 )JM U 1 (t) + U 2 (t) ( κ 1, κ 2)J M > QQ J M κ (r 1, r 1 κ 2 2, t) +ic +ic + + < ( κ 1, κ 2 )JM σ A 1 (t) (κ 1, κ 2)J M > PQ J M < ( κ 1, κ 2 )JM σ A 2 (t) ( κ 1, κ 2 )J M > QP J M < ( κ 1, κ 2 )JM C( r 1, r 2 ) ( κ 1, κ 2 )J M > QQ J M < ( κ 1, κ 2 )JM G( r 1, r 2 ) (κ 1, κ 2 )J M > PP J M
11 RTDCC Method for Atoms The time-dependent radial wavefunctions, PPκ JM 1 κ 2, QPκ JM 1 κ 2, PQ JM, QQ JM are represented on a two dimensional radial lattice: r 1 = 0.01, 0.02, 0.03,..., 10.0 r 2 = 0.01, 0.02, 0.03,..., 10.0 With 10 radial points for each core, the calculation uses 10,000 cores. The use of first derivatives in the Hamiltonian requires message passing between each core and its nearest neighbors. The number of coupled channels are given by: (JM = 00) = ss, p p, pp, d d, dd, f f (JM = 10) = s p, ps, sp, ps, p d, d p, p d, dp, pd, dp, d f, f d, d f, fd (JM = 20) = s d, ds, sd, ds, pp, p p, pp, p f, f p, p f, fp Time propagation is for oscillation periods. For t = the total number of time steps is close to 50,000.
12 0.4 Double to Single Photoionization of Ne+8 TDCC (red), RDW (blue) Scaled Cross Section Ratio Photon Energy Ratio
13 20 Double Photoionization of Ne+8 TDCC (red), IERM (blue) Cross Section (barns) Photon Energy (ev)
14 Current Projects Two-Photon Triple Ionization of Li Double Photoionization of H 2 Double Photoionization of Li 2
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