1. Joe Sato with Takaaki Nomura and Takashi Shimomura
Possibility of enhancing electron capture process by irradiating LASER beam
Joe Sato
with
Takaaki Nomura and Takashi Shimomura
Hep-ph/

2. １．Introduction
Electron capture process plays an important role in searching new physics!
Ex.
・Neutrino from capture process
Producing monochromatic neutrino beam
Joe Sato , Phys.Rev.Lett 95: (2005)
Hep-ph/
・Electron capture in atom → Positron emission
Lepton number violating process
M. Ikeda, I. Nakano, M. Sakuda and M. Yoshimura
Hep-ph/050662

3. Electron capture process is important!
In　those experiments
To get high precision,
high electron capture rate is needed
But, actual capture rate is generally low
We want to enhance capture rate!

4. How can we enhance electron capture rate?
Now, problem is
How can we enhance electron capture rate?
As a possibility to solve the question
Recently, enhancement of electron capture rate by LASER irradiation is theoretically suggested.
M. Ikeda, I. Nakano, M. Sakuda and M. Yoshimura　hep-ph/050662
Stimulated by this suggestion.
M. Yoshimura hep-ph/
We considered possibility to enhance electron capture rate by LASER irradiation.

5. We found new mechanism of enhancing electron capture rate.
As a result of consideration
We found new mechanism of enhancing electron capture rate.
In this talk, I show
・　Our mechanism/picture of enhancing
capture rate
・　Estimation of capture rate in our
mechanism

6. ２．The mechanism Rate of electron capture process ＝
Capture process amplitude
Atomic electron wave function at origin
Ｍ is determined by theory of capture process
We can’t change it
But…
We can change wave function by some action!

7. We remark wave function.２
｜value of wave function (hydrogen like) at origin｜ ３ ∝
（electron mass）
It is good, if effective mass becomes larger.
As a condition to make it possible
Atomic electron in LASER beam!
The picture
Electron in photon bath
Electron in LASER beam
Effective mass of electron would be larger!

8. Therefore, our mechanism is
Irradiating LASER beam to atom
Enhancement of effective electron mass in atom
Electron wave function at nuclei becomes large
Rate of electron capture by nuclei becomes large

9. ３．Effective mass and equation
Preparation：Electromagnetic field made by
LASER
We treat the electromagnetic field as outer field
：Coherent state
If one photon energy is about１eV
ＬＡＳＥＲ wave length～１μｍ

10. Note An atom in LASER We describe it by Dirac-eq
Coulomb potential
diagonalization
Including LASER field effect in mass
Note　we don’t assume
Note
Effective mass

11. ・Diagonalization matrix
We reduce Dirac-eq to “Shroedinger-eq” by using it

12. To simplify calculation
Reduced Dirac-eq is
To simplify calculation
・LASER wave length～１μｍ＞＞atomic size～１Å
We ignore dependence on space of M,U.
・We assume that LASER is irradiated in short period, so LASER can be thought as constant.
We ignore dependence on time of M,U
Calculating matrices

13. Taking nonrelativistic limit Dirac-eq Ｓｃｈｏｒｄｉｎｇｅｒ-eq
Taking direction of A to z
Reducing equation
Separating time dependence
We will solve it!

14. ４．Estimating capture rate
To estimate enhancement of capture rate
Estimation of wave function at origin is needed
But、the equation can’t be solved exactly
：Hydrogen like Hamiltonian（effective
mass M）
：perturbation
We estimate the wave function by perturbation theory

15. Calculating coefficients Ｆ、Ｇ、ｃ numerically
Ground state：
：0th order ground state of hydrogen like atom
（effective mass M）
：１次摂動
：2th order
（conservation of parity and magnetic quantum number） ～
S、ψ：depending on M、
F,G,ｃ:depending only on n
Calculating coefficients Ｆ、Ｇ、ｃ numerically
Confirming validity of perturbative calculation

16. Coefficients of l = 0 states

17. Coefficients of l = 2 states

18. Coefficients of l = 4 states

19. Confirming validity of perturbative calculation
Perturbative calculation is
valid
1st order＞2nd order

20. Estimation of the enhancement of capture rate
Wave function at origin
Only l = 0 states can contribute
Enhancement rate ＝
（　　　　　　　is ground state wave function without LASER）
We study it as function of intensity I and wave length λ

21. For this purpose…
We represent effective mass by I and λ
Long wave length and high intensity is better
Using this representation
We plot the enhancing rate as function of I and λ

22. Enhance rate as function of I
（photon energy =10^(-2) eV ）

23. Enhance rate as function of λ
(I＝10^10W/mm^2)

24. ５．Conclusion and problems
・Few times of enhancement of capture rate is possible. And when wavelength is about 0.01μｍ LASER intensity of 10^10 W/mm^2 is needed
・If intensity is same, longer wave length is better for enhancement
Problems
・We have to consider time dependence of LASER seriously in order to consider more realistic situation.
・We have to consider the possibility of ionization of atom