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Diabatization: a simple way to get to high-lying excited states

Diabatization: a simple way to get to high-lying excited states. A.T. Le and C.D. Lin Dept. of Physics, KSU April 14, 2004. Outline. Introduction Diabatization procedure: what’s new? Doubly excited states of helium Antihydrogen formation in antiproton colliding with excited positronium.

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Diabatization: a simple way to get to high-lying excited states

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  1. Diabatization: a simple way to get to high-lying excited states A.T. Le and C.D. Lin Dept. of Physics, KSU April 14, 2004

  2. Outline • Introduction • Diabatization procedure: what’s new? • Doubly excited states of helium • Antihydrogen formation in antiproton colliding with excited positronium

  3. Introduction Difficulties with adiabatic basis: • Avoided crossings • Many channels need to be included • Difficult to do calculations with high excited states Diabatic basis has long been proposed. Our goal: • Simplified picture with less channelsinvolved • Practical calculations.

  4. Diabatization procedure Formal definition:  rotation of basis set How to actually define C-matrix? Smith’s definition: We require that Dare not sensitive to variation of R

  5. Diabatization procedure Eq. to define C: Selection criterion:  Diabatic basis depends on R and : bad (or good)? How to choose them??? We don’t know! We use R ~ 1 au and ~0.1;

  6. Notation:N(K,T)An 11(9,1)+ 10(8,1)+ 9(7,1)+

  7. N(N-2,0)+ curves for N=2-16

  8. Table 1: Comparison of HSCC with CI results Resonance positions for He(1P0) are given as –E (a.u.) N(K,T)An 1-channel HSCC CI 9(7,1)+9 4.039[-2] 4.027[-2] 9(6,0)-10 3.693[-2] 3.704[-2] 10(8,1)+10 3.284[-2] 3.273[-2] 11(9,1)+11 2.722[-2] 2.713[-2] 12(10,1)+12 2.292[-2] 2.286[-2] CI: Themilis et al, Euro. Phys. J. D 18, 227 (2002)

  9. Table 2: Comparison for 3(2,0)+n of He(1Se) Resonance positions are given as -E (a.u.). HSCC HSCC HSCC Complex n 1-channel 2-channel 15-channel rotation 3 0.3528 0.3536 0.3537 0.3535 4 0.2787 0.2806 0.2806 0.2810 5 0.2537 0.2560 0.2560 0.2560 6 0.2422 0.2438 0.2439 0.2438 7 0.2361 0.2371 0.2372 0.2371 8 0.2324 0.2330 0.2331 0.2331 9 0.2300 0.2304 0.2305 0.2305 10 0.2283 0.2287 0.2287 0.2287 11 0.2272 0.2274 0.2274 0.2274 12 0.2263 0.2265 0.2265 0.2265 Complex rotation: Burgers et al, JPB 28, 3161 (1995)

  10. Table 3:Comparison for 4(3,0)+n of He(1Se) Resonance positions are given as -E (a.u.). HSCC HSCC HSCC Complex n 1-channel 2-channel 14-channel rotation 4 0.2012 0.2017 0.2017 0.2010 5 0.1651 0.1664 0.1665 0.1657 6 0.1491 0.1514 0.1515 0.1508 7 0.1411 0.1428 0.1429 0.1426 8 0.1366 0.1377 0.1378 0.1377 9 0.1337 0.1345 0.1346 0.1246 10 0.1318 0.1323 0.1324 0.1325 11 0.1304 0.1308 0.1309 0.1310 12 0.1294 0.1298 0.1298 0.1299 13 0.1287 0.1289 0.1290 0.1293 Complex rotation: Burgers et al, JPB 28, 3161 (1995)

  11. Resonance positions for 3(2,0)+n of He(1Se) Coupling effect is not strong

  12. Resonance positions for 12(11,0)+n of He(1Se) For higher N, effect of coupling is much stronger loss of regularity

  13. ClassicalQuantum Regular Poisson distribution Chaotic Wigner distribution Wigner Poisson

  14. Antihydrogen formation • Progress in production of cold antihydrogen • Charge exchange: • Two-stage mechanism Other important mechanisms: Three-body recombination, spontaneous (laser stimulated) radiative recombination.

  15. Two-stage mechanism Hessels et al, PRA 57, 1668 (1998) Large # of cold p (105 at 4.2K) Large # of cold e+ (106 at 4.2K) Rydberg states: area ~ n4a02 ;

  16. Two-stage scheme • Lifetime Cs(37d) ~ few ms • Lifetime of Ps(n=25) ~1ms • can travel ~1m Production rate ~ 106/sec

  17. Energy correlation diagram At very low energy, only small number of the H states are populated.

  18. S-wave Hu et al, PRL (2002) 88, 063401 Faddeev Eq. approach HSCC: Ps(2,1) i/General agreement; positions of resonances; ii/But different behavior near threshold!

  19. Note: all the channel are adiabatic with many avoided crossing

  20. The channels are diabatic! H(4s) Ps(n=3) H(3s)

  21. Ps(5,1) Ps(4,1) H(n=7,1) H(n=5,1) Ps(6,1) H(n=8,1)

  22. Any regularities?

  23. Summary • Diabatization seems to work well; • Less channels, simpler for understanding; • “Quantum chaos” signature were found for 3D He; • Antihydrogen formation from high-excited Ps can be calculated; • Future directions: • Look for signature of “chaos” in the wave functions (Husimi distribution etc.) • For antihydrogen: • Any regularities??? • Higher partial waves

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