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μd Diffusion in Protium

This study aims to simulate the diffusion of μd (muonic deuterium) and determine the effect that deuterium concentration has on the observed decay rate, providing insights into the measurement's criticality and the importance of accurately knowing cd (deuterium concentration).

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μd Diffusion in Protium

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  1. μd Diffusion in Protium Brendan Kiburg UIUC Gatchina Meeting June 14-18, 2004 2nd Workshop on MUON Project

  2. The μd’s are weakly influenced by the protium potential and diffuse quickly at our energies. • At experimental density, v ~ 10 cm/μs . • μd + p  μd +p has RT minimum at ~1.7 eV. • This effect first seen for electrons scattering off of argon, krypton and xenon Problem and Goals Goal: Simulate μd diffusion to determine the effect deuterium concentration has on the observed decay rate. This will tell us how well we need to know cd and how critical the measurement is. Kiburg, Gatchina Russia

  3. µd is Born : Tc, Td Tc > Td ? Get Scatter, Ts YES NO Td > Ts ? Fill differential histos to Ts YES CM kinematics NO Generate Scatter Angles Update Particle Position And Momentum Td >Ts ? YES END NO Update Decay Spectra E, Position, Time, etc… Kiburg, Gatchina Russia

  4. BK PK, mucat Various Cross Sections Generated from Simulation Used to pick the next scatter '2->2 ' Deceleration mud+H->mud+H File 'mud_p.fcn' 'CP ' 5 Ec:T=300 1992 1981.287e6 938.272e6 1981.287e6 938.272e6 0.0 0.04 100. 1.000E-03 4.763E+01 3.772E-01 1.312E-01 3.284E-01 5.514E-02 6.659E-02 3.000E-03 7.485E+01 4.567E-01 6.134E-02 1.248E-01 8.244E-03 8.249E-03 1.000E-02 1.252E+02 4.851E-01 5.600E-02 4.406E-02 2.450E-03 9.282E-04 5.000E-02 2.154E+02 4.795E-01 1.450E-01 6.085E-02 7.545E-03 1.298E-03 0.1 243.45 0.4611 0.215 0.1141 0.0208 0.0043 0.3 226.46 0.3933 0.4205 0.3058 0.1034 0.0238 0.5 178.80 0.3073 0.5621 0.5393 0.2582 0.0648 1 102.17 0.0512 0.4266 1.1482 1.083 0.3302 1.2 90.82 0.0011 0.0718 1.2009 1.5083 0.4929 1.5 92.76 0.0671 -0.5941 0.8864 1.902 0.6874 2 133.3 0.3508 -1.1986 -0.007 1.7613 0.7574 3 320.9 0.6652 -1.0529 -0.8686 1.0186 0.6218 4 600.8 0.7661 -0.7231 -1.131 0.6161 0.5546 5 945. 0.8092 -0.4558 -1.2486 0.3715 0.5352 6 1347. 0.8329 -0.2468 -1.3273 0.2008 0.5477 7 1781. 0.8483 -0.0749 -1.3921 0.0621 0.5787 8 2248. 0.8583 0.071 -1.4468 -0.0605 0.6197 9 2777. 0.8653 0.1955 -1.4981 -0.1728 0.6702 10 3335. 0.8708 0.3034 -1.5506 -0.279 0.7303 12 4608. 0.8782 0.4787 -1.6579 -0.4784 0.8722 14 6095. 0.8857 0.6131 -1.7922 -0.6699 1.0585 Kiburg, Gatchina Russia

  5. µd is Born : Tc, Td Tc > Td ? Get Scatter, Ts YES NO Td > Ts ? Fill differential histos to Ts YES CM kinematics NO Generate Scatter Angles Update Particle Position And Momentum Td >Ts ? YES END NO Update Decay Spectra E, Position, Time, etc… Kiburg, Gatchina Russia

  6. The parameters of every µd were recorded every 10 ns for all living µd Kiburg, Gatchina Russia

  7. µd is Born : Tc, Td Tc > Td ? Get Scatter, Ts YES NO Td > Ts ? Fill differential histos to Ts YES CM kinematics NO Generate Scatter Angles Update Particle Position And Momentum Td >Ts ? YES END NO Update Decay Spectra E, Position, Time, etc… Kiburg, Gatchina Russia

  8. Angular Distributions 3 eV (CM Frame) 10 eV (CM Frame) Forward Scattering Small delta E Backward Scattering Large delta E Kiburg, Gatchina Russia

  9. Ang Dist 2 Kiburg, Gatchina Russia

  10. µd is Born : Tc, Td Tc > Td ? Get Scatter, Ts YES NO Td > Ts ? Fill differential histos to Ts YES CM kinematics NO Generate Scatter Angles Update Particle Position And Momentum Td >Ts ? YES END NO Update Decay Spectra E, Position, Time, etc… Kiburg, Gatchina Russia

  11. The distance from the origin and Td Kiburg, Gatchina Russia

  12. Energy at the decay time in the lab frame RT minimum ~1.7 eV in CM Kiburg, Gatchina Russia

  13. Radial Distribution at Td Kiburg, Gatchina Russia

  14. R BK: Time slices representing the decay radial distributions  PK: Mucat result  Kiburg, Gatchina Russia

  15. The mud population, normalized for every time slice Kiburg, Gatchina Russia

  16. Kiburg, Gatchina Russia

  17. The radial distribution is shown, without regard for Td Kiburg, Gatchina Russia

  18. Decay times of all muD within given cylindrical rings Kiburg, Gatchina Russia

  19. There are still many things to consider before strong conclusions can be made • Input information will be changed to actual distributions • Real detector geometry will be implemented • MC will be modified to produce data events for the analysis software • Zero extrapolations will be made Kiburg, Gatchina Russia

  20. Eloss as a function of incident energy Kiburg, Gatchina Russia

  21. Muonic deuterons wander through protium (Ramsauer-Townsend Effect). • Consider lowest order partial-wave expansion at low E • l=0 sin2l ; for l =180 then =0 E must remain low so only l = 0 matters ½ wavelength in the box, outside the same Kiburg, Gatchina Russia

  22. µd with cylindrical requirement Kiburg, Gatchina Russia

  23. Most µd have a significant number of scatters Number of Particles Scatters Per Particle Kiburg, Gatchina Russia

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