A.VoroninA.Voroninaa J.Carbonell J.Carbonellbb
a) P.N. Lebedev Physical Institute, a) P.N. Lebedev Physical Institute, MoscowMoscow
b) Institute des Sciences Nucleaires, b) Institute des Sciences Nucleaires, GrenobleGrenoble
HYDROGEN ANTIHYDROGEN
at sub-Kelvin Temperatures
HydrogenHydrogen-Antihydrogen-AntihydrogenWhy interesting?Why interesting?
11. . Intriguing physics ofIntriguing physics of atomatom--antiatom antiatom
What does What does CCPPT violation mean for HT violation mean for HH H ??
HH)HH (
HH)HH (
HH)HH (
CP
P
С
HydrogenHydrogen-Antihydrogen-AntihydrogenWhy interesting?Why interesting?
22. . Can we use H for fast deexcitation of Can we use H for fast deexcitation of H ? H ?
3. How long survive?3. How long survive?
4. Collisional shift and broadening of 4. Collisional shift and broadening of HH
HH
)(...)()p(pHH 0,LN, lnee
NS1S1SNS HHHH
HHHH--moleculemolecule andand
fundamental symmetriesfundamental symmetries
PnPnPsPsHHtotHH LSLSfin
LIIIin CC )1( )1(
PnPsPnPsHHHH LLLfin
LLLin PP )1( )1(
C-symmetry
P-symmetry
CP-symmetry
PnPsPnPstotHHHH LSSfin
ILILIin CPCP )1()( )1()(
CPT and HH-moleculeCPT and HH-molecule
CPT violation induces C-violation in HH hamiltonian:
SSSS HHHHHH СEE2121
C forbidden transitions: Cin=-1, Cfin=+1
hHHHHHH SSSSSS 2112121
hHHHHHH SSSPSP 111212 )(Cin=1 Cfin=-1
KinematicsKinematics
Quantum numbers of opened Quantum numbers of opened channelschannels
a.u. 10E )()( -5,,21 lnLNSS eeppHH
0 212n 22
1n 240L 0
PsPr
Ps
2
Pr
Ps
maxPr
total0
brNNNE
a.u. 10E )()( -5,,11 lnLNSS eeppHH
1n 34 PsmaxPr N
FORMALISMFORMALISM::2 component Wave-function2 component Wave-function
)exp())exp()(exp(
;
Pr
2
111
21
ripfSikRSikR
Ps
H
S
H
S
FF
F
21
PrPr
;)1(
;
ff is the quantum numbers set of opened Protonium channels
FORMALISM:FORMALISM:EquationsEquations
0)1(
)1(11
2
1
FF
FFTHH
V
EVRppHH
0)1(
1
1
2PrPsPs
FF
FFTTH
U
EURpp
Effective potentialEffective potential)1()1( 2 FFFFW UGVeff
operator nonlocal complex, -
0
)1(11
1
1
eff
eff
ppHH EVR
W
W
FFTHH
1
2)
1(
PrPsPs
FUTTHFG E
Rpp
ModelModel
),,(
),,()(,,
21
21211
Rrr
RrrRrrR
H
r1 r2
R H
Rr
1 2,n
1L 24,N21
,, Pr
,,
Pr,,2
l
PsmlnMLN
Ps rgRfrR
Pr
Ps
gfor system equations coupledget We
Variational calculation
Model:Model:Final equationFinal equation
0)()()1)(()1(1
0
RERURV
R nuclefflocpp WFFT
0)()(1
0
RERV
R locpp T
For R>1 a.u. :
All information about inelastic transitions is within complex operator Weff, which vanishes for R>1 a.u.
Unucl(R)-complex potential, describing nuclear absorption
-C6/R6
Quasibound states with inelastic width
1a.u.
Imaginary part of effective Imaginary part of effective interactioninteraction
0,0 0,25 0,5 0,75 1,0-0,6
-0,5
-0,4
-0,3
-0,2
-0,1
0,0
Im W (10 -2
a.u.)
Im W (R,R'=R)
R (a.u.)
Annihilation cross-sectionAnnihilation cross-section
-8.0 -7.5 -7.0 -6.5 -6.0 -5.5 -5.0
0
1
2
3
4
5
6
7
8
9
10
ann103 a.u.2
Quantum
Semiclassical
1/v
1/v2/3
Log10(E) a.u.
Hydrogen- Antihydrogen annihilation cross-section.
Scattering length: a=6.1-i2.7 a.u. , aat=5.2-i1.8 a.u.
Quantum featuresQuantum features
0.50 0.51 0.52 0.53 0.54
0
10
20
30
40
50
60
70
80
90
ann 103 a.u.2
Reduced mass (proton masses)
Quantum
Semiclassical
Annihilation cross-section for E=10-8 a.u. versus reduced mass
3 2/6
3 ECclass
EMaquant 2/Im4
max/min~ 10
Isotope effectIsotope effect
-8.0 -7.5 -7.0 -6.5 -6.0 -5.5 -5.0
0
10
20
30
40
ann 103 a.u.2
Log10(E) a.u.
HH
HD
a.u. 6.110.15a a.u. 7.21.6a 11 ii sHD
sHH
Oscillations with COscillations with C66
1.0 1.1 1.2 1.3 1.4 1.5 1.6
-25
-20
-15
-10
-5
-0
a.u.
C6free/C6
HH
Im a versus van der Waals constant C6
The effect of nuclear The effect of nuclear potentialpotential
0.0 0.5 1.0 1.5 2.0 2.5
V/Vnucl
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
-Im a, a.u. Im a versus strength of nuclear potential
Weakly-bound metastable states.
Long range 1/R6 interaction is responsible forreach spectrum of nearthreshold states.
EI, a.u. EII, a.u. <r>, a.u-8 10-6 -6.3 10-6+i1.8 10-5 Virtual state
-1.9 10-4 -4.3 10-4-i2.2 10-4 4.6-2.9 10-3 -5.2 10-3-i1.4 10-3 3.2-1.1 10-2 -2.8 10-2-i8.2 10-3 1.6
Energies and widths of nearthreshold HH states.Subscript I means states in pure 1/R6 potential(exponentially cut at short distance).Subscript II means states in full interaction, including thecontribution of inelastic processes.
Scattering length Scattering length oscillationsoscillations
0.50 0.51 0.52 0.53 0.54
-5
-3
-1
1
3
5
7
9
11
13
15
17
19Real part of scattering length
Versus reduced mass
a.u.
Reduced Mass (in proton masses)
Changing sign of real part of scattering length correspondsto appearance of new nearthreshold state.
Analytical expression for Analytical expression for scattering lengthscattering length
)82
2(cot 1
4/522
(3/4)2a
20
646
r
MCMC
Short range potential Weff + “long range”C6/R6
r0 is the range of Weff, about 1 rB, is phase shift produced by short-range complex interaction.
Weff
-C6/R6
r0
Im black sphere )4/exp(4/52
(3/4)2a 4
6 iMC
Im <<1-oscillations, Re is very important
Semitransparent
Im a/Im aat=1.5
Excitation transfer Excitation transfer reactionsreactions
2222
4
446
546
2~~
2~
Im~
2~2~
~
BBexch
BB
inel
BB
B
rMrna
rp
Mrn
p
a
rMrnMCa
rnC
CONCLUSIONSCONCLUSIONS 1. Nearthreshold weakly bound states is a 1. Nearthreshold weakly bound states is a
key to dynamics.key to dynamics. 2. Magnifying glass – enhancemant of 2. Magnifying glass – enhancemant of
short range (nuclear) effects inshort range (nuclear) effects in 3. Excitation transfer reactions can be a 3. Excitation transfer reactions can be a
tool for antihydrogen deexcitation.tool for antihydrogen deexcitation. 4. Fundamental symmetries of 4. Fundamental symmetries of
molecule-molecule-
can we check CPT with it?can we check CPT with it?
HH
HH
HH
Some Refferences:Some Refferences:1. M.Amoretti et al. Nature 419 (2002) 4561. M.Amoretti et al. Nature 419 (2002) 456
2 .G2 .G. Gabrielse et al. Phys. Rev. Lett. 89, 213401. Gabrielse et al. Phys. Rev. Lett. 89, 213401
(2002); Phys. Lett. B 507, 1 (2001)(2002); Phys. Lett. B 507, 1 (2001)
3. D.L. Morgan Jr. and V.W. Hughes: Phys. Rev. D2, 13893. D.L. Morgan Jr. and V.W. Hughes: Phys. Rev. D2, 1389
(1970); W. Kolos et al.: Phys. Rev. A11, 1792 (1975)(1970); W. Kolos et al.: Phys. Rev. A11, 1792 (1975)
4. G.V. Shlyapnikov et al.: Hyp. Int. 76, 31 (1993)4. G.V. Shlyapnikov et al.: Hyp. Int. 76, 31 (1993)
5. A.Yu. Voronin, J. Carbonell: Phys. Rev. A57, 43355. A.Yu. Voronin, J. Carbonell: Phys. Rev. A57, 4335
(1998); Nucl. Phys. A689(2001) 529c-532c(1998); Nucl. Phys. A689(2001) 529c-532c
6. J. Carbonell et al.: Few-Body Systems Suppl. 8, 428 (1995)6. J. Carbonell et al.: Few-Body Systems Suppl. 8, 428 (1995)
7 S. Johnsel, A.Saenz ,P. Froelich, B.Zygelman, A.Dalgarno , Phys.7 S. Johnsel, A.Saenz ,P. Froelich, B.Zygelman, A.Dalgarno , Phys.
Rev.A 64, 052712 (2001);Phys. Rev.A 63, 052722 (2001)Rev.A 64, 052712 (2001);Phys. Rev.A 63, 052722 (2001)
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