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Ab Initio Calculation of Effective Sherman Function in MeV Mott Scattering

This presentation discusses the ab initio calculations of the effective Sherman function in MeV Mott scattering, focusing on hardware and performance aspects of the MeV Mott polarimeter at MAMI. It reviews the reproducibility of measurements, explores the determination of the effective Sherman function, and discusses accuracy limits. Key points include the statistical figure of merit, measurement at various beam currents without changing conditions, and the negligible depolarization in recirculating linacs. Work is ongoing to validate the methodology and enhance the understanding of uncertainties.

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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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