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Ab initio calculation of effective Sherman function in MeV Mott scattering

Kurt Aulenbacher Institut für Kernphysik der Universität-Mainz PESP-2008 3. October 2008. Ab initio calculation of effective Sherman function in MeV Mott scattering. OUTLINE: 1 .) MeV Mottpolarimeter at MAMI: Hardware and performance 2.) Reproducibility

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Ab initio calculation of effective Sherman function in MeV Mott scattering

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  1. Kurt Aulenbacher Institut für Kernphysik der Universität-Mainz PESP-2008 3. October 2008 Ab initio calculation of effective Sherman function in MeV Mott scattering OUTLINE: 1.) MeV Mottpolarimeter at MAMI: Hardware and performance 2.) Reproducibility 3.) Determination of effective Sherman function 4.) Discussion: accuracy limits. ….work in progress…. done by Valeri Tioukine and K.A.

  2. Kurt Aulenbacher Institut für Kernphysik der Universität-Mainz PESP-2008 3. October 2008 Why MeV Mott polarimetry? 1.) Statistical FOM=S2eff*Isc/I0 is minor issue at MAMI beam intensities 2.) Measurement at all relevant beam currents without changing beam conditions at source/injection 3.) Good reproducibility (Monitor feature) 4.) Negligible depolarization in (recirculating) Linacs, independend of acc. conditionsrelevant for experiments! What about 5.)Check absolute accuracy of HE polarimeters? Purpose of this talk: Demonstrate 1-4, investigate 5

  3. Set-up (schematic) Wien filter (In plane spin rotation) RTM-1 (14 MeV) DE=1.5MeV*cos(f) Electron-gun 100keV E=2MeV f Mott-Polarimeter Measures Asymmetry Aexp=P*S Klystron Beam energy range: 1-3.5 MeV Influence of atomic and nuclear form factors on analyzing power S should be small!

  4. Analyzing power In elastic scattering S can be calculated exactly for any radial potential. In our energy range deviations induced by form factors (charge distributions) are ~1%

  5. Mott Set-up Plastikszintillator Kollimator, 4mm-dia Upper spectrometer (exploded view) Incoming beam Vacuum window/slit Collimator Plastic szintillator PM to beam dump Goldtarget(s) Lower spectrometer The purpose of spectrometers is background reduction, energy resolution is moderate (>100)

  6. Doublefocussing Magnet Target-camera Detektor/PM Shielding (removed) Moving direction of Goldtargets in Vacuum +viewscreen/empty target 10cm Hardware: V. Tioukine

  7. Measurement speed Typically operate at large Wien angles ~90 deg! Asymmetry ~ sin(qWien) Average rate and Seff depend on target thickness

  8. Thickest ‚Sheet‘ target has best statistical efficency S2eff*k*d Thin ‚Foil‘ targets have lower heat production and comparable (radiative) cooling suitable for high intensities (0.1 mm tested >100 mA)

  9. Reproducibility Asymmetry is insensitive (<1% level) to beam movements, target movements (knitter!) and accelerator adjustment by inexperienced operators But: ~0.7% drift observed within 8 hours: Reason probably q.e. correlated polarization variation (see Y. Mamaev et al. Proc. Spin 2000 p.920)  Simultaneous ‚Vector‘-polarimeter in preparation

  10. Seff determination Extrapolation procedure must by physically motivated! Important: Length scale of depolarizing effect!

  11. D Asymmetry dilution S74 ~0 Elastical ‚Doublescattering‘ (Wegener 1956) S164>>S90 Gay (1991): Multiple coulomb scattering convoluted with plural large angle scattering + energy resolution D Worst case: Dilution ~ qrms~(d/lfree)1/2 Dilution by particles from smaller ‚large ‘angle‘ ~qrms

  12. ‚Tentative‘ determination of Seff Error contribution from extrapolation: DP/P < 0.028  much too large! Thinner targets could make apparatus less robust and/or cause additional morphology problems (holes).

  13. Cross-check: 2 MeV Idea: Get rid of extrapolation and calculate Seff(d) from first principles: M. Khakoo et al. Phys. Rev. A 64, 052713 (2001)): Monte Carlo Simulation

  14. (M. Khakoo et al. Phys. Rev. A 64, 052713 (2001)) After a scattering process occurs (lfree), the corresponding angles Q;F (+Energy loss) are attributed due to cross sections ( prob. densities). The cross sections for elastic scattering are described by: But: The direction of Spinvector P is changed after the scattering. Monte Carlo Spin Tracking • (Many) Particles are tracked under this conditions until they leave the target. • Seff(d,DQ,DE) is determined from the azimuthal asymmetry of the distribution

  15. Spin-Tracking: Output . 1 MeV, 155-170 degree, 1 mm-Target statistics: 66740 1 MeV, 155-170 degree, 100nm-Target 109 input particles (1011 scattering processes ) Computational cost: 100 hours (PC ~5 GFLOP)

  16. Test with 100keV data Experimental data (Old MAMI-Mott E/DE=12) are only reproduced with realistic cross section: Forward direction is important Inelastic contribution may change slope of MC-curve

  17. Spin-Tracking: MeV-Range 2 MeV (100hours computing time) 1 MeV (100 hours computing time) • good stat. accuracy requires small PC farm (100Gflop  possible) • High accuracy cross section calculation needed (in progress) • missing: exact treatment of inelastic scattering/bremstrahlung • Better confidence in Target morphology and rel. thickness variations • expected if compared to 100keV (or lower) Mott.

  18. Conclusion • MAMI MeV Mott is easy to handle, still compact and offers ‚good‘ reproducibility • Highest current range (10nA-100mA) of all Polarimeters at MAMI • Ab initio calculation of effective Sherman function could eliminate several problems of ‚foil thickness extrapolation‘. • The theoretical error in S0 may be small but due to the fact that Z/a~1 an (experimental?) treatment of radiative corrections could be necessary to estimate it.

  19. Wahrscheinlichkeitsdichten ‚invertierbar‘ numerisches Absuchen Bestimmung von d für geg. ZZ1 Auflösung transz. Gleichung nach Newton Die physikalischen Größen s, ds/dW und S bestimmen die Wahrscheinlichkeitsdichten der Variabeln d,q,f. Wahrscheinlichkeitsdichte für d: Wahrscheinlichkeitsdichte für q: Wahrscheinlichkeitsdichte für f:

  20. Polneu= Spin-Tracking lfrei=7-12nm  typischerweise finden in einer 100nm dicken Folie im Mittel etwa 10 Streuungen statt, bevor das Teilchen die Folie wieder verlässt (meistens kleine Winkel) • Tracking: • Nach jeder Streuung bildet die Impulsrichtung des Teilchens die neue • Polarachse (q=0). • 2.Anwendung von Rotationsmatrizen, um auf das • Laborsystem zurückzurechnen, um Position des Teilchens im Labsystem • zu kennen • 3.) Die inhom. Verteilung in f wird durch die Richtung der bei der Streuung • vorliegenden transversalen Polarisation definiert. • 4. Nach jeder Streuung um Winkel q,f wird die Polarisation transformiert • q,f definiert die Lage der Streunormalen n. R,L sind weitere Funktionen von f,g

  21. Spin-Tracking: Output Wenn Teilchen die Folie verlässt (vorwärts od. Rückwärts) wird auf File geschrieben: Azimuthwinkel, Polarwinkel, maximale Tiefe im Target, gesamte Laufstrecke u.E.m. ´Teilchenrate C-Programm ‚ranundwink‘: 109Teilchen in 1mm Folie: (1011-Streuungen) in ca. 100Stunden (Dell-PC) entspricht bei 1MeV output 66740 Teilchen in 155-170 Grad

  22. Spin-Tracking: Stimmts? Die experimentellen Daten werden nur reproduziert, wenn die bestmögliche Wirkungsquerschnittsberechnung als Input verwendet wird!

  23. Spin-Tracking: MeV-Bereich Zur systematischen Analyse wird noch benötigt: 100Gflop Rechner ( ZDV) Berechnung Wq bei MeV Energien mit realistischem Goldpotential

  24. Zusammenfassung • Mottpolarimeter gut reproduzierbares, einfach bedienbares Monitorinstrument • Absolutunsicherheit z.Zt. DP/P=+-4% • Unsicherheit durch unbekannten Verlauf von S(Targetdicke) kann durch direkte Computersimulation wahrscheinlich minimiert werden.DP/P<2% möglich. • Verbleiben Strahlungskorrekturen Gegenmassnahmen: (S(Z), neue theoretische Rechnung (a/Z=0.6), Gegenchecks bei 100keV)  DP/P<1% (????)

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