Analysis of cascade dynamics and x-ray yields for K - p and K - d atoms by Monte-Carlo method

1. IUT Analysis of cascade dynamics and x-ray yields for K-p and K-d atoms by Monte-Carlo method S. Z. Kalantari Department of Physics Isfahan University of Technology Isfahan, IRAN International Workshop on Hadronic Atoms and Kaonic Nuclei Trento,Italy ECT* 13 October 2009

2. IUT IUT • Introduction • Cascade processes of Exotic atoms • Experiments on kaonic hydrogen atoms • Kinetics of cascade processes of Kaonic atoms • Simulation results of K-p and K-d atoms

3. Introduction • Exotic atoms • When a heavy negative particle (µ-, π-, K-,…) enters • a hydrogen isotope target an exotic hydrogen atom is formed. • Muonic atoms • Hadronic atoms are Kaonic atom reduced mass and charge of the nuclues, Resp. The values of the nl states of Kaonic hydrogen have a peak around the following values. (J.S. Cohen, Phys. Rev., 27(1983)167.

4. Cascade processes Cascade processes of muonic atoms

5. Cascade processes of Kaonic atoms

6. Kaonic Hydrogen X-ray yields from cascade of kaonic atoms are important to test strong interaction and the theory of QCD in low energies. The K-series transitions are main experimental interest since they are more affected by the strong interaction. The 1s shift and width are related to the real and imaginary parts of the scattering length by the Deser-Trueman formula

7. experimental results for K-p atoms KEK experiment results (1998) The pure electromagnetic value of the kaonic hydrogen Kαx-ray is 6480±1 eV. Hence: The long standing kanic hydrogen puzzle is resolved ===================================== DEAR collaboration results (2005) It is a more precise experiment

8. Cascade processes of Kaonic atoms I) Chemical Dissociation It is important at large n (n≥(mKp)1/2) II) Radiative Transition (Kx)n (Kx)n´ + at low excited State is dominated Average over l-value of initial state and summed over the final state. Bethe H.A. and Salpeter E.E.1975,Quantum Mechanics of one and two electron atoms

9. Cascade processes of Kaonic atoms III) External Auger effect Is the excitation energy of K-x atom Is the Ionization energy of hydrogen molecule Leon M. and Bethe H., Phys. Rev.,127(1962)636

10. Cascade processes of Kaonic atoms We have used the extended method of Leon and Bethe for Stark mixing rates which was done by Trada. It gives the more completed rates of stark mixing. (K-x)nl + x’ (K-x)nl´+ x’ IV) Stark Mixing M. Leon and H.A. Bethe, Phys. Rev. 127(1962)636. (m=0) E.Borie and M. Leon, Phys. Rev. A 21(1980)1460. (∆l=±1) T.P. Trada and R.s. Hayano, Phys Rev. C 55(1997)73. (all possible transitions)

11. (K-x)n +x´ (K-x)n+ x´ (K-x)n +x´ (K-x)n-1 + x´ Cascade processes of Kaonic atoms V) Deceleration (elastic scattering) L.I. Menshikov and L.I. Ponomarev, Z. Phys. D 2(1986)1 VI) Coulomb deexcitation It produces accelerated kaonic atoms L. Bracci and G. Fiorentini, Nuovo Cimento A,43(1977)9.

12. Cascade processes of Kaonic atoms VII) Nuclear absorption Table of the absorption X-Sec for K-p atoms in n=4 with respect to kinetic energy (a02). The cross-sections have been calculated by Jensen by Close-Coupling method for n=2-5 and we have used the results as an Input for our Code T.S. Jensen and V.E. Markushin, Eur. Phys. J. D 19(2002)165.

13. Cascade processes of Kaonic atoms VIII) Nuclear Reaction From the Deser formula Are taken from experimental results or theoretical calculations, otherwise they are treated as a free parameter IX) Weak decay Where is the mean life time of Kaon

14. Kineticsof cascade processes of Kaonicatoms Monte-Carlo method *Total transition rate from excited state n is: *Transition probability from n n´ (n´ <n)due to ith mechanism in a kinetic energy E is : *Cumulative distribution function:

15. Kineticsof cascade processes of Kaonicatoms Monte-Carlo method I) Calculate the cumulative distribution function at specific energy PDF(n,j,E). II) Generate a random number R in the Interval (0,1) . III) If PDF(n,j,E)< R <PDF(n,j+1, E) then j th mechanism transition is accepted. Then by the same proceed we can determine n’ If the collisional process is every one of the scattering, Stark mixing or Coulomb deexcitation, We should determine the kinetic energy of kaonic atom after collision. Otherwise, It is continued from step (III) for the new n state. We should also determine the time of transition.

16. Monte-Carlo Simulation Flow Chart Target density, Φ Initial kinematic energy of atom,Ek Initial principal quantum number,ni Initial number of Kaonik atoms,NM Initial Stage Start for I th Kaonic atom Ei=Ek,Ni=ni NT(Kα)=0, NT(Kβ)=0, NT(Kγ)=0 Call radiation,Stark,Auger,… subroutines to calculate the rates of transitions Determining of the probabilities at energy E, and Generate a random number ,R Calculation Stage if PDFj<R<PDFj+1 then j th process is occurred then determine Call subroutine to calculate If radiation transition is occurred NT(k)=NT(k)+1 Ei=Ef , Ni=nfNOIf nf=1 or absorption take place YES NO m=m+1, if m <NM YES stop

17. X-ray yields from muonic atoms by Monte-Carlo method

18. Comparison our results with the other results

19. Simulation results for K-p and K-d atoms Density of the target can affect the X-ray yields.

20. Simulation results for K-p and K-d atoms Density dependency of the Stark mixing percent in K-p and K-d atoms .

21. Simulation results for K-p and K-d atoms Percent of nuclear reaction in K-p and K-d atoms .

22. Simulation results for K-p and K-d atoms Contributions of kaon absorption in different states and decay of kaon in K-p atoms as a function of dencity. At the DEAR density (0.031 LHD) the contribution of the kaon absorption at 1s state is approximately 13%, at ns states with n>1 is 65% and at np states with n>1 is 22%.

23. Simulation results for K-p and K-d atoms Normalized moderation time of kaon with various initial kinetic energy as a function of hydrogen density.

24. Simulation results for K-p and K-d atoms Stopping probability of kaon beam with various initial kinetic energy as a function of hydrogen target density.

25. Simulation results for K-p and K-d atoms Variation of the KαX-ray yields per incoming kaon with respect to Γ2p. The two existing data points have also been shown. Γ2p =0.105±0.002 meV Is suggested for the 2p strong interaction width in K-p atom.

26. Simulation results for K-p and K-d atoms Density dependence of the X-ray yields per incoming kaon in Hydrogen target. The two existing experimental data points have also been shown. We have predicted the optimum range of the hydrogen density 0.03-0.06 LHD to reach high x-ray yields in experiment.

27. Simulation results for K-p and K-d atoms Density dependence of the Kα X-ray yields per incoming kaon in deuterium targets. For different considered Γ2p.

28. Simulation results for K-p and K-d atoms Density dependence of the Ktot X-ray yields per incoming kaon in deuterium targets. For different considered Γ2p. We have predicted the optimum range of the deuterium density 0.03-0.06 LHD to reach high x-ray yields in experiment. It may be interested for SIDDHARTA experiment.

29. Simulation results for K-p and K-d atoms Kinetic energy distribution of K-p atoms in 2p state.

30. Doppler broadening effect on the measured with of x-ray yields Kinetic energy distribution of K-p atoms in 2p state at the instat Of 2p 1s radiative transition.

31. Simulation results of K-p atoms • Doppler broadening effect on the measured with of x-ray yields Where And Γm1s is considered from DEAR experiment

32. IUT

33. Simulation results for K-p and K-d atoms Comparison of the X-ray yields per stopped kaon in two cases, with considering constant kinetic energy and without considering constant kinetic energy of K-p atoms.