Diabatization: a simple way to get to highlying excited states

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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

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Outline

• Introduction
• Diabatization procedure whats new?
• Doubly excited states of helium
• Antihydrogen formation in antiproton colliding
  with excited positronium

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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 channels involved
• Practical calculations.

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Diabatization procedure
Formal definition
? rotation of basis set
How to actually define C-matrix? Smiths
definition We require that ?D are not
sensitive to variation of R
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Diabatization procedure
Eq. to define C
Selection criterion ? Diabatic basis depends
on ?R and ? bad (or good)? How to choose them???
We dont know! We use ?R 1 au and ?0.1
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NotationN(K,T)An
11(9,1)
10(8,1)
9(7,1)
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N(N-2,0) curves for N2-16
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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)
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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)
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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)

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Resonance positions for 3(2,0)n of He(1Se)
Coupling effect is not strong
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Resonance positions for 12(11,0)n of He(1Se)
For higher N, effect of coupling is much stronger
? loss of regularity
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Classical Quantum Regular
Poisson distribution Chaotic
Wigner distribution
Wigner
Poisson
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Antihydrogen formation

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

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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
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Two-stage scheme

• Lifetime Cs(37d) few ms
• Lifetime of Ps(n25) 1ms
• can travel 1m

Production rate 106/sec
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Energy correlation diagram
At very low energy, only small number of the H
states are populated.
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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!
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Note all the channel are adiabatic with many
avoided crossing
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The channels are diabatic!
H(4s)
Ps(n3)
H(3s)
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Ps(5,1)
Ps(4,1)
H(n7,1)
H(n5,1)
Ps(6,1)
H(n8,1)
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Any regularities?
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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