Ab initio calculation ….

1

Ab initio calculation of effective Sherman function in MeV Mott scattering

Kurt AulenbacherInstitut für Kernphysik der Universität-Mainz

PESP-20083. October 2008

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.

Ab initio calculation ….

2

Why MeV Mott polarimetry?

Kurt AulenbacherInstitut für Kernphysik der Universität-Mainz

PESP-20083. October 2008

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. conditionsrelevant for experiments!

What about 5.)Check absolute accuracy of HE polarimeters?

Purpose of this talk: Demonstrate 1-4, investigate 5

Ab initio calculation ….

3

Set-up (schematic)

Electron-gun 100keV

Wien filter (In plane spin rotation)

Mott-PolarimeterMeasures Asymmetry Aexp=P*S

RTM-1 (14 MeV)

E=1.5MeV*cos()E=2MeV

Beam energy range: 1-3.5 MeV Influence of atomic and nuclear form factors on analyzing power S should be small!

Klystron

Ab initio calculation ….

4

Analyzing powerIn elastic scattering S can be calculated exactly for any radial potential.

In our energy range deviations induced by form factors (charge distributions) are ~1%

Ab initio calculation ….

5

Goldtarget(s)

to beam dump

PlastikszintillatorKollimator, 4mm-diaMott Set-up Upper spectrometer (exploded view)

Lower spectrometer

Plastic szintillator

PM

Incoming beamVacuum window/slit

The purpose of spectrometers is background reduction, energy resolution is moderate (>100)

Collimator

Ab initio calculation ….

6

Shielding(removed)

Doublefocussing Magnet

Detektor/PM

Moving direction of Goldtargets in Vacuum+viewscreen/empty target

Target-camera

Hardware: V. Tioukine

10cm

Ab initio calculation ….

7

Measurement speed

Asymmetry ~ sin(Wien)

)1(

exp

effPStRNNNNNA

2

2

exp

exp2/122

2

exp

exp

)(21))(1(

)(21

effeff

effmess PSRA

APS

PSRAA

t

Average rate and Seff depend on target thickness

Typically operate at large Wien angles ~90 deg!

Ab initio calculation ….

8

Thickest ‚Sheet‘ target has best statistical efficency S2

eff*k*d

Thin ‚Foil‘ targets have lower heat production and comparable (radiative) cooling suitable for high intensities

(0.1 m tested >100 A)

Ab initio calculation ….

9

ReproducibilityAsymmetry 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

Ab initio calculation ….

10

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

Ab initio calculation ….

11

Asymmetry dilution

S164>>S90

S74 ~0Elastical ‚Doublescattering‘ (Wegener 1956)

01

0

deff kd

SS

D

Gay (1991): Multiple coulomb scattering convoluted with plural large angle scattering + energy resolution

010 )exp( AkdAAS deff

nm

dkSS

Free

Freeeff

12

/0

D

Dilution by particles from smaller ‚large ‘angle‘ ~rms

Worst case: Dilution ~ rms~(d/free)1/2

Ab initio calculation ….

12

‚Tentative‘ determination of Seff

Error contribution from extrapolation: P/P < 0.028 much too large!Thinner targets could make apparatus less robust and/or cause additional morphology problems (holes).

Ab initio calculation ….

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

Ab initio calculation ….

14

Monte Carlo Spin Tracking(M. Khakoo et al. Phys. Rev. A 64, 052713 (2001))• After a scattering process occurs (free), the corresponding angles

(+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.

LRSdd

tot ,,;; 0

)(1

)))(sin()cos(()(*))cos()sin(()('PnS

PnLRPnnLRnPnSP

• (Many) Particles are tracked under this conditions until they leave the target.

• Seff(d,,E) is determined from the azimuthal asymmetry of the distribution

Ab initio calculation ….

15

Spin-Tracking: Output.

109 input particles (1011 scattering processes )Computational cost: 100 hours (PC ~5 GFLOP)

1 MeV, 155-170 degree, 1 m-Targetstatistics: 66740

1 MeV, 155-170 degree, 100nm-Target

Ab initio calculation ….

16

Test with 100keV data

Experimental data (Old MAMI-Mott E/E=12)are only reproduced with realistic cross section: Forward direction is importantInelastic contribution may change slope of MC-curve

Ab initio calculation ….

17

Spin-Tracking: MeV-Range

• 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 variationsexpected if compared to 100keV (or lower) Mott.

1 MeV (100 hours computing time) 2 MeV (100hours computing time)

Ab initio calculation ….

18

Conclusion

• MAMI MeV Mott is easy to handle, still compact and offers ‚good‘ reproducibility

• Highest current range (10nA-100A) 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/~1 an (experimental?) treatment of radiative corrections could be necessary to estimate it.

Ab initio calculation ….

19

Wahrscheinlichkeitsdichten

Die physikalischen Größen , d/dund S bestimmen die Wahrscheinlichkeitsdichten der Variabeln d,.

22

.

22

**),,(

),,(),,((),(

gfgffgiZES

dZEgZEfdddZE

hungDiracGleicLsg

Wahrscheinlichkeitsdichte für d:Wahrscheinlichkeitsdichte für :Wahrscheinlichkeitsdichte für : ))sin()(1(

21)'(

)'(1)'(

)'exp()'(

PS

dd

dnnd

p

p

p

)1ln(*)1ln(1)(

)exp(1')'exp()(1)(00

ZZZZn

ZZd

dndddnndPZZ

Frei

dPichtelichkeitsdWahrschein

d

Bestimmung von d für geg. ZZ1

‚invertierbar‘

numerisches Absuchen

Auflösung transz. Gleichung nach Newton

0 100 2000

0.5

1

Winkel [Grad]

P(Th

eta)

1

7.324 103

PM

179.90 M

10

Ab initio calculation ….

20

Spin-Trackingfrei=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: 1. Nach jeder Streuung bildet die Impulsrichtung des Teilchens die neue Polarachse (=0). 2.Anwendung von Rotationsmatrizen, um auf das Laborsystem zurückzurechnen, um Position des Teilchens im Labsystem zu kennen3.) Die inhom. Verteilung in wird durch die Richtung der bei der Streuungvorliegenden transversalen Polarisation definiert. 4. Nach jeder Streuung um Winkel wird die Polarisation transformiert definiert die Lage der Streunormalen n. R,L sind weitere Funktionen von f,g

Sherman n Pol( ) n R sin ( ) L cos ( )( ) n n Pol( )[ ] R cos ( ) L sin ( )( ) n Pol( )

1 Sherman n Pol( )Polneu=

Ab initio calculation ….

21

Spin-Tracking: OutputWenn 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 1m Folie: (1011-Streuungen) in ca. 100Stunden (Dell-PC)entspricht bei 1MeV output 66740 Teilchen in 155-170 Grad

Ab initio calculation ….

22

Spin-Tracking: Stimmts?

Die experimentellen Daten werden nur reproduziert, wenn die bestmögliche Wirkungsquerschnittsberechnung als Input verwendet wird!

Ab initio calculation ….

23

Spin-Tracking: MeV-Bereich

Zur systematischen Analyse wird noch benötigt:100Gflop Rechner ( ZDV) Berechnung Wq bei MeV Energien mit realistischem Goldpotential

Ab initio calculation ….

24

Zusammenfassung• Mottpolarimeter gut reproduzierbares, einfach

bedienbares Monitorinstrument• Absolutunsicherheit z.Zt. P/P=+-4%• Unsicherheit durch unbekannten Verlauf von

S(Targetdicke) kann durch direkte Computersimulation wahrscheinlich minimiert werden.P/P<2% möglich.

• Verbleiben Strahlungskorrekturen Gegenmassnahmen: (S(Z), neue theoretische Rechnung (/Z=0.6), Gegenchecks bei 100keV)

P/P<1% (????)