A review of currently available high-energy photon polarimeters, which use the effect of asymmetry of recoil electron yield during triplet photoproduction, is presented. The influence of both multiple scattering of electrons and d-electron production in the target medium on the decrease of the experimentally observed asymmetry is considered. The graphs of effective asymmetry and the figure of merit versus target thickness are given

Boldyshev, V.F.

Peresunko, Yu.P.

Vinokurov, E.A.

Наукова електронна бібліотека періодичних видань НАН України (Vernadsky National Library of Ukraine)

E X P E R I M E N T A L  M E T H O D S  A N D  C O M P U T A T I O N SA POSSIBILITY TO MEASURE THE LINEAR POLARIZATION OF PHOTONS BY USING TRIPLET PHOTOPRODUCTIONV.F. Boldyshev, Yu.P. Peresunko , E.A. VinokurovNational Science Center “Kharkov Institute of Physics and Technology”, Kharkov, UkraineA review of currently available high-energy photon polarimeters, which use the effect of asymmetry of recoil electron yield during triplet photoproduction, is presented. The influence of both multiple scattering of electrons and δ-electron production in the target medium on the decrease of the experimentally observed asymmetry is considered. The graphs of effective asymmetry and the figure of merit versus target thickness are given.PACS: 29.27.Hj  29.90. +r.1. GENERAL CHARACTERISTICS OF THE METHODThe possibility of measuring the linear photon-beam polarization by measuring the asymmetry of recoil elec-tron yield in the process of triplet photoproduction γ+e– → e– + e– + e+ has first been indicated by the KIPT group [1–4]. The cross section for the recoil electron yield has the form:)2cos1(2cos2 1)(1)()(1ϕσϕσσϕσpi Λ+=+= PPdd tlt , (1)where  )(tσ  is  the  total  cross  section  for  unpolarized photons, σ(l) is a part of cross section due to the photon polarization, P is the degree of linear photon-beam po-larization, )()( / tl σσ=Λ  is the asymmetry of the yield of recoil electrons for P=1, ϕ1 is the azimuthal angle.The detailed analysis of this process and the devel-opment  of  a  new method,  which,  in  principle,  allows measuring the linear photon-beam polarization in a wide range of photon energies from 25 MeV to several TeV, been  performed  in  [5].  Possibilities  of  constructing tracking devices and high-speed counters for these mea-surements have been discussed.About 90% of recoil electrons detectable at the ex-periment momentum mcqq 10 ≈≥ have a polar angle Θ1≥20°, that makes it possible to determine reliably their az-imuthal angle  ϕ1. The values σ(t) and  σ(l) increase, and the  asymmetry  Λ slightly  decrease  and  tend  to  the asymptotical value with an increase in the photon ener-gy ω. It is possible to choose such a region of kinemat-ics’ variables, where σ(t) and σ(l) are of the order of sev-eral mbn and the asymmetry is not less than Λ~0.11. 2. THE USE OF THE TRACKING DEVICESThe tracking devices have a slow rate of  statistics acquisition. To measure the photon-beam linear polar-ization by these devices, one should use all the range of allowed values for recoil electron moment with q > q0..The  helium-filled  streamer  chamber  SK–600  has been used in the course of a trial experiment [6] to mea-sure the degree of linear polarization of a beam of co-herent bremsstrahlung (CB) with an electron energy of 600 MeV in  the  LUE–2000 with  a  photon  energy  of 60 MeV at  the coherent  peak.  The method developed was used in this experiment for the first time. The photon polarization determined by means of the asymmetry method gives P=0.68±0.94.For the determination of photon polarization by the least-squares method (LSM) and by the maximum like-lihood method (MLM), two sets of events were used. The first one contained events with all θ1 and the second contained events with  θ1< 60•. With these sets the fol-lowing P values were obtained: P=0.53±0.45      and          P=0.59±0.83   (LSM),P=0.66±0.54       and         P=0.66±1.18  (MLM).All  five  values  for  the degree of  polarization,  ob-tained by the method of asymmetry of recoil electrons of triplets, agree with  P=0.65±0.15 determined on the basis of the coherent bremsstrahlung theory.These results mean that the method under considera-tion can be used for measuring the photon-beam polar-ization. At the same time, it  is  clear that tracking de-vices cannot be effective monitors of the polarization of photon beams. For this purpose short-response time de-tectors should be used.3. THE USE OF HIGH–SPEED COUNTERSThe  polarimeters  based  on  the  method considered have been developed in Japan [7-8], Germany [9], and USA [10]. The scintillation counters with short response times were used for registration of both the recoil elec-trons and the e+e–-pairs [7-8], [10]. Plastic plates of dif-ferent thickness were used as targets. By the method un-der discussion the Tokyo group [11] measured the ener-gy spectra of observed asymmetry (PΛ product) in the range of photon energies from 240 to 620 MeV with the use  of  a  polarimeter,  which  was  installed  in  the  CB beam. This experiment has corroborated the validity of the method. The  mentioned  experiments  show  that  in  the  real case the observable asymmetry value of the yield of re-coil electrons is less than the values predicted in [1-5]. Actually, the important effects which reduce the observ-able asymmetry of recoil electron yield in the polarime-ter considered are the multiple scattering of slow elec-trons and the  δ-ray production by fast particles of the e+e– pair  produced  in  the  medium  of  target,  air,  and counters.The multiple scattering of  charged particles  in the matter is described by the Moliere theory [12]. Accord-ing to this theory, for a rather thick layer of medium the PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2001, № 1.Series: Nuclear Physics Investigations (37), p. 63-65.63Gauss approximation to the angular distribution of parti-cle deviation from the initial direction is valid202 /2/1)20()(ΘΘ−−Θpi=Θ eF , (2)where  02015XxEMeVβ=Θ ,  E is the particle energy in MeV,  β  is  the  particle  velocity  ,  X0 is  the  radiation length, x is the  particle path length in the matter.After averaging the initial distribution (1) taking into ac-count (2) we get).12cos1()())1(2cos)()()((1220 ϕΘ−Λ+σ=ϕ−ϕσ+σϕϕ=ϕσpi ∫ePtlPtFddd(3)The macroscopic cross section for the yield of recoil electrons produced by the  photon at  the  point  x after these  electrons  traversed  the  target  layer  of  thickness (L-x), is given by).2cos1)(()2cos1(),(1)()(1)()(11ϕσρϕσρbePxLAZNePdxAZNLxbxLtALxxLbtAtr−−−−−Λ+−=Λ+=Σ ∫(4)Here  022115XEMeVb = β ,  L is the target thickness in cm, AZN A /ρ  is the number of electrons in 1 cm3 (ρ - density,  NA –  Avogadro  number,  AZ ,  –  averaged atomic number and atomic weight of medium, respec-tively). Considering that points of triplet production are uniformly distributed inside the target with the probabil-ity density )()(1)(1 xLxLxF −ΘΘ= , and averaging over the target thickness L, we shall obtain the following ex-pression   for the macroscopic cross section:.12cos)1(2)(212)(),()(1)(ϕ−+−Λ+σρ=Σ=Σ ∫LbLbeLbPLtAZANdxLxtrxFLtr(5)As regards the production of δ-rays, they are mainly due to the Moliere and Bhabha scattering of  fast parti-cles from the e+e–-pair by the electrons of the target. The total cross section for this process is given to an accura-cy of 1/γ [13,14] as220)( 12 βpiσ cuteetr= , (6)where  r0  is  the classical  radius of  electron,  m is  the electron  mass,  ;1/ −= mEt cutcut , 22 1 −−= γβ  mE /1=γ ,  1E  is the initial particle energy , Ecut  is the minimal detectable energy of  δ-electrons. The number of e+e– pairs which are produced at the point x of the tar-get  with  an  average  charge  Z ,  is )()( )( ZAxNx pairApair σρ=Σ . Each particle of the pair can produce the following number of δ–electrons in the remaining  layer  (L-x)  of  the  target:: )()()( eeA AZNxLx σρδ −=Σ .  Taking into account that photons are producing e+e–-pairs inside the target uni-formly with the probability density F1(x), and averaging over x, we shall get  the expression for the quantity of δ-electrons produced by each photon in the target of thick-ness L:.32)()()()()()(12LZpairAANeeAZANxpairxxdxFσρσρ=ΣδΣ=δΣ ∫(7)In the experiments considered, the events of triplet photoproduction and the events  of  e+e–-pair  photopro-duction followed by  δ-electron knocking-out cannot be distinguished. Therefore the effective macroscopic cross section will be equal to the sum of macroscopic cross sections of these two processes:( )ϕδ 2cos1)( efftefftreff PΛ+Σ=Σ+Σ=Σ , (8)where ( )LDLAZN tAteff +=Σ 12)()( σρ (9)and the effective azimuthal asymmetry equalsLDLbeLbLbeff +−+Λ=Λ−11)(22 (10)Here the parameter D is:     )()()( )(32tpairAee ZANDσσρσ= . (11)The parameters  b and  D  entering into expressions (8)–(11) are strongly dependent on the minimal observ-able momentum of electron,  q0. For the following esti-mations it  is reasonable to set  E and  Ecut entering, re-spectively,  into  (2)  and  (6),  equal  to 220 mqEE cut +== .  In  our  numerical  calculations we shall use the approximation from [14] for  σ(pair)(Z) and the asymptotic expression from [4, 5] for  σ(t).  We assume  that  the  target  is  a  plastic  plate  (polystyrene, C8H8,  ρ=1.032 g  cm-3,  X0=42.4 cm,  13/7/ ≈AZ )  of different thickness.Fig. 1 shows the effective asymmetry Λeff (Eq. (10)) as a  function of  target  thickness.  Curves  1to 3 corre-spond to different minimal observable moments of the electron, q0.. The dashed curves 1a to 3a correspond to the  case,  where  the  effect  of  δ-electron  production (D=0) with the same q0 values as for curves 1 to 3 was neglected.  The  difference  between  solid  and  dashed curves shows the importance of taking into account the δ-electron production effect. It can be seen that the se-lection of the events with a greater  q0 value is appears more effective for measuring the photon-beam polariza-tion by the method under consideration.650,0 0,1 0,2 0,3 0,4 0,50,000,020,040,060,080,100,120,140,163a2a1a 321Effective asymmetryTarget thickness, cmFig. 1.  Effective  asymmetry  as  a  function  of  polystyrene target  thickness.   Curve  1 corresponds to q0=1 MeV/c,  2   – q0=2 MeV/c,  3   –  q0=5 MeV/c. The dashed curves (1a to 3a) correspond to the D=0 case  with the same q0 values as for curves 1 to 3An important characteristic of the experiment is the figure of merit, effeffF ΣΛ=2 . It is well known that rela-tive error of the measurements is minimal if the figure of merit is maximal. Fig. 2 shows the figure of merit as a function of tar-get thickness for different q0  values. The units used are the number of recoil electrons and δ-electrons emerging from the target per initial photon. It is evident that for the most of experiments [7,8,11], where the scintillation counters of recoil  electrons were tuned to register the events with  q>1 MeV/c, it would be more effective to use the target with a thickness of about 1 mm.0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,40,00,00,00,00,00,00,10,10,10,1321Figure of Merit, event/photon*108Target thickness, cmFig. 2.  Figure  of  merit, 2)( efftreff ΛΣ ,  as  function  of  polystyrene target thickness.  The curve  1 corresponds to q0=1 MeV/c, 2–q0=2 MeV/c, 3–q0=5 MeV/cIn conclusion, we would like to note that up till now no sequential analysis of the whole set of effects which are  accompanying  the  measurements  of  photon-beam linear  polarization  by  the  method  considered  has  not been performed. This task demands for numerous calcu-lations to be done with the help of the GEANT code. So, the present work should be regarded as information on only preliminary results of the study.ACKNOWLEDGMENTThe  authors  would  like  to  thank  W.J. Briscoe, G. Feldman, and G.V. O’Rielly for helpful discussion of the test experiment results before publication. One of us, Yu.P., thanks for hospitality during his visit in George Washington University.REFERENCES1. V.F. Boldyshev,  Yu.P. Peresun’ko.  Electron-positron pair photoproduction on electrons and anal-ysis of photon beam polarization //  Yad. Fiz. 1971, v. 14, 1027-1032 (Sov. J. Nucl. Phys. 1972, v. 14, p. 576).2. V.F. Boldyshev,  Yu.P. Peresun’ko.  On  determina-tion of photon polarization from asymmetry of the recoil  electrons  in  triplets  //  Yad.  Fiz. 19,  1974, v. 144-147 (Sov. J. Nucl. Phys. 1974, v. 19, p. 75).3. E.V. Vinokurov, E.A. Kuraev. Triplet formation by polarized photons // Zh. Eksp. Teor. Fiz. 1972, v. 63, p. 1142-1150 (Sov. Phys. JETP. 1973, v. 36, p. 602).4. E.V. Vinokurov,  N.P. Merenkov.  On production of triplets by high-energy polarized photons // Yad. Fiz. 1975,  v. 21,  p. 781-784 (Sov. J.  Nucl.  Phys.  1975, v. 21, 403).5. V.F. Boldyshev,  E.A. Vinokurov,  N.P. Me-renkov, Yu.P. Peresun’ko. Measurement of photon-beam linear polarization using asymmetry of the re-coil electrons from the photoproduction of e+e- pairs on electrons // Phys. Part. Nucl. 1994, v. 25, p. 292-331;  Fiz.  Elem.  Chastits  At.  Yadra,  1994,  v. 25, p. 696-778.6. V.F. Boldyshev, E.A. Vinokurov, V.I. Voloschuk et al. Measurement of linear polarization of photon by using the asymmetry of the recoil electrons in photo-production of triplets //  Yad.Fiz. 1992. v. 58, p. 43-49.7. I. Endo  et  al.  Detection  of  recoil  electrons  in  the triplet  photoproduction  by  linearly  polarized  high-energy photons.  Annual  Report  1986,  Institute  for Nuclear Study University of Tokyo, p. 79-81. 8. I. Endo et al. Detection of Recoil Electrons in Triplet Photoproduction // NIM, 1989, v. A 280, p. 144-146.9. F.  Schafer  et  al.  Analyzer  for  Linearly  Polarized Photon Using Triplet Production. Gordon Research Conf. on Photonuclear Reactions, Aug. 5-10, 1990, Tilton, New-Hampshire, 1990.10.R. Pivel, G. Feldman et al.  ‘Triplet Production Po-larimeter at SAL.’ Workshop on “Polarized Photon Polarimetry” June 2-3, 1998, The George Washing-ton University, Washington, DC.11.G. Ivata  et  al.  New  Polarimeter  for  High  Energy Gamma-Rays // NIM, 1993, v. A336, 146-149.12.Moliere Z. Theorie der Streung schneller geledener Teilchen  I:  Einzelstreuung  am  abgerschmitten Coulomb-Field  //  Z. Naturforsch. 1947,  Bd.  2a, s. 133; Bethe H.A. Moliere’s theory of multiple scat-tering // Phys. Rev. 1953, v. 89, p. 1256-1266.13.V.B.  Berestetskii.  E.M.  Lifshicts,  L.P.  Pitaevskii, Relativistic  Quantum  Theory,  part  1,  M.,  1966, 480 p.14.GEANT User’s Guide. CERN, W5013, 1994.ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2000, №2.Серия: Ядерно-физические исследования (36), с. 3-6.64

A possibility to measure the linear polarization of photons by using triplet photoproduction

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A possibility to measure the linear polarization of photons by using triplet photoproduction

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