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

nSSSnS HHHH 11

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)

THANK YOU!THANK YOU!