Possibility of enhancing electron capture process by irradiating
Possibility of enhancing electron capture process by irradiating LASER beam Joe Sato with Takaaki Nomura and Takashi Shimomura Hep-ph/0605031
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: 131804(2005) Hep-ph/0503144 ・Electron capture in atom → Positron emission Lepton number violating process M. Ikeda, I. Nakano, M. Sakuda and M. Yoshimura Hep-ph/050662
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!
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. Stimulated by this suggestion. M. Ikeda, I. Nakano, M. Sakuda and M. Yoshimura hep-ph/050662 M. Yoshimura hep-ph/0507248 We considered possibility to enhance electron capture rate by LASER irradiation.
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
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!
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 Electron in LASER beam bath Effective mass of electron would be larger!
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
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 about１ e. V ＬＡＳＥＲ wave length～１μｍ
An atom in LASER We describe it by Dirac-eq Coulomb potential Including LASER field effect in mass diagonalization Note we Note don’t assume Effective mass
・Diagonalization matrix We reduce Dirac-eq to “Shroedinger-eq” by using it
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
Taking nonrelativistic limit Dirac-eq Ｓｃｈｏｒｄｉｎｇｅｒ-eq ¨ Taking direction of A to z Reducing equation Separating time dependence We will solve it!
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
Ground state： ： 0 th order ground state of hydrogen like atom （effective mass M） ：１次摂動 ： 2 th 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
Coefficients of l = 0 states
Coefficients of l = 2 states
Coefficients of l = 4 states
Confirming validity of perturbative calculation 1 st order＞ 2 nd order Perturbative calculation is valid
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
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
Enhance rate as function of I （photon energy =10^(-2) e. V ）
Enhance rate as function of λ (I＝ 10^10 W/mm^2)
５．Conclusion and problems conclusion ・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
- Slides: 24
