1. Laser Irradiated Enhancement of Atomic Electron Capture Rate For New Physics Search
hep-ph Prog. Theor. Phys. 117
Takashi Shimomura
(Saitama Univ.)
In Collaboration with
Joe Sato and Takaaki Nomura
(Saitama Univ.)
February 1, 2007
KEKPH’07, KEK, Tsukuba

2. 1. Introduction
Electron capture processes have a potential Power to Search New Physics !
1. Majorana nature of neutrinos
2. Lepton Flavor Violations
M. Yoshimura, hep-ph/ , hep-ph/
Ikeda, Nakano, Sakuda, Tanaka and Yoshimura,
hep-ph/
3. Mono energetic neutrino beam
M. Rolinec and J. Sato, hep-ph/
J. Sato, Phys.Rev.Lett.95:131804,2005.
February 1, 2007
KEKPH’07, KEK, Tsukuba

3. Enhance the capture processes !
Electron capture processes are attractive !
But
The capture rate is generally low …
LFV and LNV are rare events…
To obtain a high statistics
Enhance the capture processes !
February 1, 2007
KEKPH’07, KEK, Tsukuba

4. another Enhance mechanism by a LASER
How to enhance the capture processes?
An interesting way is
LASER irradiation to an atom
M. Yoshimura, hep-ph/
Laser Power is
Laser Energy ～ several eV
Resonance
We found
another Enhance mechanism by a LASER
February 1, 2007
KEKPH’07, KEK, Tsukuba

5. Key point of our work Electron Capture Rate
Wave function of the electron
Amplitude of capture process with a free electron
Make the electron effectively heavier !
February 1, 2007
KEKPH’07, KEK, Tsukuba

6. Naïve explanation of our mechanism
Wave picture
Under the laser irradiation
Change of the de Broglie wave length
Change of the momentum
Change of the mass
Change of the energy
February 1, 2007
KEKPH’07, KEK, Tsukuba

7. 2. Non-Relativistic Equation with LASER filed
Dirac equation
Vector potential
Coulomb potential
The two identical lasers are irradiated from the both sides
Average photon number density
February 1, 2007
KEKPH’07, KEK, Tsukuba

8. Effective mass Diagonalized by U February 1, 2007
KEKPH’07, KEK, Tsukuba

9. The wave length of the laser is much larger than the size of the atom.
Neglect
assumptions
The wave length of the laser is much larger than the size of the atom.
the oscillation period of the laser is longer than the time interval which we consider.
Ignore the position dependence of U, meff
Ignore the time dependence of U, meff
February 1, 2007
KEKPH’07, KEK, Tsukuba

10. Non-Relativistic Limit
Take the direction of to z
Separate the time dependence
Virial theorem
February 1, 2007
KEKPH’07, KEK, Tsukuba

11. Solve the non-relativistic equation perturbatively
3. Wave Functions
Solve the non-relativistic equation perturbatively
In the following, we consider 1s state.
0th order
February 1, 2007
KEKPH’07, KEK, Tsukuba

12. Only l=even and m=0 states appear
1st order
2nd order
February 1, 2007
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13. Probability density is determined by the 0th order
February 1, 2007
KEKPH’07, KEK, Tsukuba

14. 4. Enhancement of Atomic Electron Capture Rate
Enhancement rate
Increase function of
February 1, 2007
KEKPH’07, KEK, Tsukuba

15. Intensity Dependence Enhancement rate Enhancement Rate
February 1, 2007
KEKPH’07, KEK, Tsukuba

16. Energy Dependence Enhancement rate Enhancement Rate February 1, 2007
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17. 5. Summary
We have investigated a mechanism to enhance atomic electron capture decay by a laser irradiation
The mass of electron becomes effectively heavier under the laser irradiation.
The non-relativistic equation with effective mass was derived.
The lower energy beam is better when the intensity is the same.
The order of magnitude enhancement can be theoretically achieved.
February 1, 2007
KEKPH’07, KEK, Tsukuba

18. February 1, 2007
KEKPH’07, KEK, Tsukuba

19. We considered the short time interval
We have to consider the time dependence of the laser for more realistic situations.
We replaced the vector potential by its time average
We have to calculate the time average of for longer time period.
February 1, 2007
KEKPH’07, KEK, Tsukuba

20. Static assumption is valid
In the following
Intensity,
Energy,
Static assumption is valid Å
Time average
February 1, 2007
KEKPH’07, KEK, Tsukuba

21. 4. Competitive Ionizations
Potential of the laser
Ammosov, et al. Zh. Eksp. Teor. Fiz, 1986
Tunnel Ionization
probability
Coulomb electric field
Laser electric field
tunneling
L’Huillier, et al. Phys.Rev.A, 1989
Multi-photon Absorption Ionization
Cross section
Vector potential
Large!
February 1, 2007
KEKPH’07, KEK, Tsukuba

22. Intensity Dependence
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23. February 1, 2007
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24. February 1, 2007
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25. February 1, 2007
KEKPH’07, KEK, Tsukuba

26. determined by the fundamental physics can enhance ?
Electron Capture Rate
determined by the fundamental physics
can enhance ?
a wave function of a bound electron at the center
amplitude of the capture process with the free electron
the Lorentz invariant phase space
February 1, 2007
KEKPH’07, KEK, Tsukuba

27. Table of Talk Introduction Non-Relativistic Equation with Laser Field
Probability Density
Competitive Ionizations
Enhancement of Atomic Electron Capture Rate
Summary and Future Work
February 1, 2007
KEKPH’07, KEK, Tsukuba