POLARIMETER FOR PHOTON LINEAR POLARIZATION MEASUREMENT AT INTERMEDIATE ENERGIES Objective 05

1. POLARIMETER FOR PHOTON LINEAR POLARIZATION MEASUREMENT AT INTERMEDIATE ENERGIESObjective 05 National Scientific Center «Kharkov Institute of Physics and Technology» Kharkov, Ukraine

2. The work was supported by: • the European Community – Research Infrastructure Action under the FP6 "Structuring the European Research Area" Programme (through the Integrated Infrastructure Initiative "Hadron Physics")- Eurotag – European Tagged Photon Facilities (spokesperson K.Livingstone, Glasgow) • STCU project 3239 (spokesperson V.Ganenko, Kharkov)

3. Some general remarks • At present one of the main problems in photon (linear) polarization experiments is accurate determination of the photon beam polarization with accuracy ~1-2%. There are various approaches for CB polarization determination: calculations, measurements. • Discussion at the workshop has shown that at present the CB polarization is calculated with accuracy ~5%. Procedure includes: -CB spectrum description (with various experimental factors including); -the CB polarization calculation with these experimental parameters. • There is principle limitation of such approach: Born approximation - the rectilinear beam particle’s trajectories in the crystal. But in real case there exist particles, trajectories of which are far from the straight line. And there number depends on orientation. • Including real particles dynamic in crystal is needed.

4. More preferable is a direct measurement of the polarization by photon polarimeter. • The main requirement to a “good” polarimeter is high efficiency and accuracy of the polarization measurement. So, the process to be used for polarization measurement: -must have large cross section. -must have the analyzing power (sensitivity of the process characteristics to photon polarization) of the process high enough in the energy range where measurements are performed; -the analyzing power must be known with high accuracy (calculated or measured); -must weakly depend on energy in this range; -be easy measurable. The following QED processes satisfy some of these requirements: -pair photoproduction in the field of nuclei, ZZee; -triplet photoproduction (ee pair photoproduction in the field of atomic electrons), eeee.

5. Some features of the pair and triplet processes Pair photoproductionZZee • Proposition to use the process for polarization measurement was put forward at 1950-th (C.N. YangPhys.Rev. 77 (1950) 722; J.H Berlin, L. Madansky Phys.Rev. 78 (1950) 623). As was shown (L.C. Maximon, H. Olsen, Phys. Rev. 126, 310 (1962)), the plane of emitted ee pairs correlated with a direction of the photon polarization, and preferably lays in the plane of photon polarization. • The main experimental problem is the small angle between the pair components, which decreases with photon energy increases. • At first the azimuthal distribution of one pair particle was measured. The problem of small angles was resolved by using magnetic spectrometer to separate electrons and positrons. At that the analyzing power decreased.

6. Perspective scheme was proposed by B. Wojtsekhowski (B. Wojtsekhowski et al. Polarimeter for High energy Photons, Jlab technical note 98-039,1998; C.de Jager at al. A pair plarimeter for linearly polarized high energy photons. Eur Phys JA (2004) 19, s01, 275-278). It was based on measurement the azimuthal distribution of the vector, connectingthe positron and electron crossing points of the detectorplane.

7. It is most easily measurable parameter which provides the sufficiently large analyzing power (~0.14), which can be increased by selection of nearly symmetric pairs up to ~0.2. The differential on azimuthal angle cross section of the reactions can be presented as The kinematics of the pair photoproduction =pair(Z,) is cross section for the pair and =tr(,q) for triplet photoproduction process with unpolarized photons, P is the degree of photon polarization,  is the asymmetry of the process when P=1 (or analyzing power),  is the azimuthal angle counted from the photon polarization direction, sign (+) for pair and () for triplet production.

8. Triplet photoproduction eeee. • To use the triplet photoproduction for linear photon polarization measurement was proposed by Kharkov theorists Boldyshev and Peresunko (V.F. Boldyshev, Y.P. Peresunko, Sov. J. Nucl. Phys. 14, 576 (1972); 19, 75 (1974)). It was shown, that azimuthal distribution of the recoil electrons correlated with direction of the linear photon polarization. One can use these two processes simultaneously. The kinematics of the pair photoproduction

9. At the triplet photoproduction : • recoil electrons are emitted under large angles (up to 800) and have energy enough for registration up to ~10 MeV. There kinematical characteristics are very convenient for registration; • there angular and energy distributions weakly depend on photon energy; • the analyzing power is sufficiently large (~0.14) and weakly depend on photon energy up to hundreds GeV. • There are two main disadvantages of the triplet process: - the real triplet yield is sufficiently less than yield of the pair photoproduction; - background of the δ-electrons which decreases the analyzing power.

10. There were some attempts to built photon polarimeter on the base of triplet photoproduction process. It is the polarimeter of Japan group (Y. Iwata et al. NIM, A336 (1993) 146-159) and the GWU group (R. Pivel, G. Feldman et al., ‘Triplet Production Polarimeter at SAL.’ Workshop on “Polarized Photon Polarimetry” June 2-3, 1998, The George Washington University, Washington, DC). Their principle schemes are similar. The idea laid in the foundation was to measure the azimuthal asymmetry of the recoil electrons averaged on rather wide ranges of polar and azimuthal angles. The main advantage of the “classic” scheme is simplicity and cheapness. The analyzing power of the triplet process (for 100% polarization) measured by Japan group for energy  = 360 MeV was: = 0.060.018 (for selection pairs with the opening angles less 3.50); = 0.0880.026 (for angles less 0.70). For GWU polarimeter the measured analyzing power was ~0.03 These experimental values of are considerably less than theoretical prediction for analyzing power ~0.14.

11. Polarimeter of the Japan group • Construction. The scheme of the polarimeter is shown in Fig. 1. Linearly polarized photons come to polyethylene target of 1.2 mm thick. Before the target a veto counter was placed. The azimuthal angular distribution of recoil electrons were measured by eight telescopes placed under polar angler of 300 to the photon beam. Each telescope had a polar angular with of 11.40 and azimuthal angular width of 230 and consisted of E counter (10101 mm3) to select the minimum ionizing particles and E counter (16 mm 50 mm) for measurement total energy of the particles. The particle energies were limited to be less ~5 MeV. • The e+e pairs are detected by the pair telescope and hodoscope. The pair telescope counters (3 and 6 mm thick) select a pair of minimum ionizing particles by setting the threshold at twice the pulse height of the minimum ionization. Opening angle of the pair is obtained from hit pattern on the hodoscope.

12. Method of investigation • We studied processes from the point of view to use them for photon polarization measurement. • The investigations were carried out by simulation method with using the developed code for modeling processes which take place at the polarized photons interaction with matter of the polarimeter target. • The code is based on the GEANT-3 package which was supplemented by some subroutines, because: • photon polarization was not included in the GEANT-3 package; • the GEANT-3 has no code for the triplet photoproduction process calculation. • So, the GEANT-3 code for ee pair photoproduction has been modified to take into account effects of the photon linear polarization and the code of the process of triplet photoproduction has been added.

13. Polarized photon beam moves along Z axis and falls on the target. The points of interaction along Z axis are determined in a random way. If interaction has happened type of theprocess and kinematic characteristics of the particles is determined. Then a way of every particle is tracked up to exit the target. • The particles flying off in forward direction are fixed on the “detector” plane, placed at distance 1.5 cm from the target. Type and kinematical parameters of the particles are determined. • Such a way it was accumulated data base of all processes and particles produced in the target by polarized photon for various photon energies and the target thickness. The scheme of simulation.

14. General relations of the QED processes The yield of the QED processes on 104 photons as a function of the photon energy. Thickness of plastic target is 1mm. The recoil electrons with momentum q>q0=0.1MeV/c were taken into account

15. Recoil electron yield strongly depends on its momentum. But recoils with low energies are mainly emitted under large angles, so for plastic target ~0.5 mm thick the recoil electrons, burn with q<0.5 MeV/c, are practically remain in the target. • In simulation the threshold recoil momentum for triplet events generation was q0=0.5 MeV/c. In this case the triplet yield is ~20 times less than the pair’s yield.

16. Table 1. The QED processes detected on the “detector” plane. q>q0=0.5 MeV/c.

17. Particles distributions for the e+epair and triplet production Electron distributions from pair production on the “detector” plane. Left: the polar angle distributions for various photon energies. Right: two-dimensional (polar angle – energy) distribution for E=1000MeV. Target is plastic (C6H6) of 0.5 mm thick.

18. The distributions of the distances between the electron and positron crossings the detectorplane (AB vectors) have maximums which depends on photon energy. Width on half of the height (FWHM) is varied from ~7cm for E~50MeV to ~2-3  mm for E~3 GeV. Such properties allow one to measure azimuthal dependence of these segments by the microstrip detectors with distances between strips ~100mkm for photon energies up to 2-3GeV. Distribution of the distances between the electron and positron crossings the detector plane on distance 100cm from the target

19. Recoil electrons distributions The energy distributions of the recoil electrons for E=1000MeV in the polarimeter target (1) and on the detector plane (2). Target is plastic 0.5 mm thick, q0=0.5MeV/c. • Typical energy and angular distributions of the recoil electrons are shown for two cases: • (1) at the production point (corresponds to theoretical distributions); • (2) on the “detector” plane where the multiple scattering influence reveals itself. • The recoils yield sharply increases with their energy decreasing, so the overwhelming part of them are at the energies ~<4-5MeV.

20. The angular distributions of the recoil electrons for E=1000MeV in the polarimeter target (1) and on the detector plane (2). Target is plastic 0.5 mm thick, q0=0.5MeV/c. • The yield increases at large angles of the recoil electron emission. Due to kinematical relation between energy and emission angle, the simulation threshold q0~0.5MeV/c leads to cutting the recoils with the polar outlet angle r~>650. • Because the electrons emitted under large angles have low energy (~<2MeV at >400), they are strongly scattered in the target material (up to ~150-200), thus upper side of the angular distribution is smeared and long tail of low energy scattered electrons appears, the maximum of the angular distribution is shifted to angle ~30-400

21. Two dimensional distribution demonstrate kinematically allowed physical region for the recoil electrons which is typical for all photon energies qmin(r)qqmax(r). There are two branches (the only upper branch is clearly seen). Two dimensional (angle-energy) recoil electron distributions in the polarimeter target (gray points) and on the detector plane (black points). Target is 0.5 mm plastic, q>q0=0.5 MeV/c. E=1000MeV. The recoil electrons are emitted preferably near borders. The multiple scattering smears the sharp boundary and makes distribution wider, and large “electron tail” of the low energy electrons appears at angles more than 600.

22. From statistical point of view it is profitable to decrease threshold of the recoil electrons registration, but there are many multiple scattered low energy electrons that must be rejected the electron detection should be limited by the angles r<450 and limit the recoil electron energy Er~1 MeV. • The recoil electron distributions practically does not depend on the photon energy in the range under study, E~50-3000 MeV

23. Two dimensional the δ-electrons distributions demonstrate that they are very similar to the recoil electron distributions. There is concentration of the δ-electrons near the upper branch of the kinematically allowed region for the recoil electrons. They are disseminated in the bulk of the recoil electrons and it is difficult to separate them. But there are some differences between these particle fractions distributions that may allow if not discriminate the δ-electrons in whole but decrease their contribution and influence on analyzing power of the triplet polarimeter. Two dimensional (angle-energy) δ-electrons distributions on the detector plane.

24. The recoil and δ-electrons distributions are strongly peaked but at energies Er~<1 MeV number of the δ-electrons essentially exceed number of the recoil electrons. • Situation becomes opposite at higher energies. The part of the δ-electrons quickly reduces up to ~25% at Er~2 MeV, but there is few the particles at this energy range, Er>2 MeV. The energy distributions of the recoil (1) and (2) δ- electronson the detector plane. E=1000MeV Target is plastic 0.5 mm thick, q0=0.5MeV/c.

25. The angular distributions of the recoil (1) and (2) δ- electronson the detector plane. E=1000MeV . Target is plastic 0.5 mm thick, q0=0.5MeV/c. • There is difference in their angular dependences. The recoil electron distributions for all photon energies have maximum at angles ~300-400 where the yield of the recoil electrons exceed the δ-electrons yield. The δ-electron’s distributions smoothly increase with angle increasing and have maximum at angles, ~500-600 where the yield of the δ-electrons exceeds the recoils yield.

26. The calculation shows, that energy and angular dependences of the ratio R=Nrec/(Nrec+Ndel) practically does not depend on photon energy. Contribution of the δ-ray is considerable at low electron energies (<1-1.5MeV) and at the angles>500 where it part reaches. • The angular interval ~100-400 for recoil electron registration is preferable from the point of view of the δ-ray background contribution. In this angular range contribution of the δ-electrons does not exceed ~25% for photon energies under study. • It contribution could be decreased (up to 10-15%) with increasing the electron energy threshold, up to ~1-2 MeV. At that considerably decreases the number of recoil electrons. The energy and angular distributions of the ratio recoil electrons yield to total electron yield. Target is plastic 0.5 mm thick, q0=0.5MeV/c.

27. Analyzing power of the pair and triplet photoproduction processes The analyzing power was obtained by fitting the corresponding azimuthal distributions for the above characteristics of both processes: the vectors AB for pairs and recoil electrons for triplets by the formula dN/d~A0[1+Pcos(2)] A0 and  are fitting parameters. • Theoretical estimations give the value of analyzing power for these processes ~0.14 if there are no any selection the reaction events. But there are some effects which reduce this value: • multiple scattering particles in the polarimeter target; • δ-electron background (for triplets) The azimuthal dependence of the vector AB. Target is plastic 0.5 mm thick.

28. Influence of the multiple scattering.One can compare asymmetry in the place of particles birth and on the detector plane. In the place of birth the asymmetry is ~0.14 that agrees with theoretical prediction. Due to multiple electron scattering analyzing power reduces up to ~0.09 for both processes for target 0.5 mm plastic. - electron contribution decreases asymmetry recoil electrons up to ~0.06. Asymmetry practically does not depend on photon energy in the range under study. Asymmetry of the recoil electrons as a function of photon energy in the target (squares), on the detector plane (circles), on the detector plane when the - electrons are taken into account (triangles). Target 0.5mm C6H6. Curve is theoretical calculation. Asymmetry of the pair photoproduction in the target (black squares) and on the detector plane (red circles) as a function of photon energy. Target C6H6, 0.5mm.

29. Asymmetry of the process as a function of the target thickness is smoothly increase with thickness decreasing. -without events selection the asymmetry can be increased up to ~<0.11; -selection of the symmetrical pairs can increase asymmetry up to ~0.2…0.24. -simulation agrees with the Woitsekhovski calculation on the base of H. Olsen, L.C. Maximon, Phys. Rev. 114, 887,1959 formulas. Asymmetry of the pair photoproduction on the detector plane as function of the target thickness. Points: simulation results for E=1 GeV. C6H6- green triangles (0.1, 0.3 and 0.5 mm) Al – black triangles (0.1 and 0.3 mm) Si - red circles (0.1 and 0.3 mm) Cross – symmetrical pairs, C6H6 0.5 mm. Curve is the result for 2GeV and symmetrical pairsfrom Wojtsekhowski et al. NIM A515(2003) 605

30. Asymmetry of the for triplets process as a function of the target thickness is smoothly increase with thickness decreasing. -one can see influence of the δ-electron background. It restricts ~<0.09 if there is no any events selection - GWU and Japan groups results agree with the thickness dependence. • Asymmetry of the recoil electrons on the detector plane as function of the target thickness. Points: simulation for E=1 GeV with (empty) and without (full) the δ-electron. • C6H6- circles (0.1, 0.3 and 0.5 mm) • Al –triangles (0.1 and 0.3 mm) • Si –squares (0.1 and 0.3 mm)

31. Selection of the symmetrical pairs. The analyzing power of the process can be essentially increased if one will select events with nearly equal energies of electron and positron of created pair. The theoretical estimations show that asymmetry can be increased from ~0.14 up to ~0.25 (or 1.8 times as large). For real targets increasing some less, up to ~0.15 (for 0.5mm C6H6) and up to ~0.2 (0.1mm C6H6). Asymmetry of the pair photoproduction in the target (red circles) and on the detector plane (empty circles) as a function of positron energy. E=1GeV, target 0.5 mm C6H6. Curve is the result for 2GeV and symmetrical pairsfrom Wojtsekhowski et al. NIM A515(2003) 605

32. Asymmetry of the pair photoproduction in the target (red circles) and on the detector plane (empty circles)as a function of photon energy for E+=E-. Target 0.5 mm C6H6. • Curve is the result for 2GeV and symmetrical pairsfrom Wojtsekhowski et al. NIM A515(2003) 605

33. Comparison with the experimental asymmetry A=Pof the pair photoproduction as a function of photon energy fromS.deJager et al. Eur Phys JA (2004) 19,s01 275-278.The expected photon polarization P=0.93 at E=2.4GeV. The experimental asymmetry A=P as a function of the photon energy for all pairs. The curve show the dependence of the photon beam polarization. Target is the carbon 0.1 mm thick. Red circles are the simulation results. The results for the pairs selection with the condition 0.8<E+/E<1.2.

34. Triplet photoproduction. Selection of the symmetrical pairs gives for recoil electron’s asymmetry increasing up to ~0.12 for real case. The asymmetry of the recoil electrons on the detector plane as a function of positron energy. E=1GeV. Full points (without) and empty (with) δ-electrons. Target C6H6 0.3mm (circles) and 0.5mm (triangles).

35. Another way to increase the analyzing power is the recoil electrons selection near the boundary of the physical range. At the physical region border =1, but it quickly reduces, so that averaged on all angles  and momenta value of the (q0) decreases up to ~0.14. • There was taken the range limited by the angular range 200-400 and two lines: • (i)- by curves 2 (theoretical border + 1 MeV) and 3 (theoretical border 0.7); • (ii)- by curve 2 (theoretical border + 1 MeV) and 4 (theoretical border 0.5). Selection of the recoil electrons range near bounder of the physical range.

36. Squares- asymmetry on the detector plane without δ-electron taking into account; circles- with δ-electron taking into account; triangles- with δ-electron background taking into account and selection electrons in the range (i). • Such selection increase the analyzing power from ~0.06 to ~0.09 for all pairs under selection the recoil electrons in the range (i). Asymmetry averaged over targets C6H6 (thickness 0.1, 0.3, 0.5 mm), Al (0.1 і 0.3 mm), Si (0.1 і 0.3 mm). Photon energy is 1000 МеV.

37. Summarize results for triplets C6H6 – 0.5mm Eγ=1000MeV 150<θ<400 C6H6 – 0.3mm Eγ=1000MeV 150<θ<400 One can expect to obtain for triplet process analyzing power ~0.15 if will use selection the symmetrical pairs and along the trace simulataneousely.

38. 1000 МэВ All pairs 1000 MeV Pairs 0.8<E+/E<1.2 All triplets with delta electrons 1000 MeV Triplets

39. Summary • Analyzing power of both processes does not depend on photon energy in interval under study, 30-2000 MeV. • ee-pairs production process. For plastic target 0.1 mm thick the value of analyzing power can be obtained: -0.11 if not to apply any selection; -0.2 if the selection of events of ee-pairs with energies of electrons and positrons in interval 0.8<E+/E<1.2 to use. • Triplet production at using plastic C6H6 target 0.3 mm thick: - 0.07 if not any selections are applied; - 0.09 if the selection in physical range to produce - 0.12 at the ee-pairs selection with energies of electrons and positrons in interval 0.35<E+/E<0.65; - 0.16 if two simultaneous selections (2 and 3) are performed .

40. At the photon beam intensity 106/s during for 2 hours it is possible to measure polarization of the beam (at P=100%) with accuracy ~1%, using process of the ee-pairs production and with accuracy ~5%, using process of the triplet photoproduction. • Two processes should be used simultaneously.

41. The draft design of the photon polarimeter prototype of was developed, in which two processes were simultaneously used for polarization measurement – the e+e-pairs and triplet production. The expected accuracy of the polarization measurement during an hour in the real MAX-lab conditions is ~1% for the e+e-pair and ~5% for the triplet processes. • .