- Email: [email protected]
Polarization of recoil protons from the reaction γp → π0p in the proton energy range 450–800 MeV
Nuclear Physics B166 (1980) 525-533 © North-Holland Publishing Company
POLARIZATION OF RECOIL PROTONS FROM THE REACTION yp_~ ~.Op IN THE PHOTON ENERGY RANGE 450-800 MeV A.S. BRATASHEVSKIJ, V.G. GORBENKO, A.I. DEREBCHINSKIJ, A.Ya. D E R K A C H , Yu.V. ZHEBROVSKIJ, A.A. ZYBALOV, I.M. K A R N A U K H O V , L.Ya. KOLESNIKOV, O.G. KONOVALOV, A.A. LUKHANIN, A.S. OMELAENKO, A.L. RUBASHKIN, P.V. SOROKIN, E.A. SPOROV, A.E. TENISHEV and S.G. T O N A P E T Y A N The Kharkov Physical-Technical Institute, Acad. Sci. of Ukr. SSR, Kharkov, USSR
Received 7 August 1979 (Revised 6 December 1979) Measurements of secondary-proton polarization from the reaction No-->~r°p have been performed in the photon energy range 500-800 MeV at c.m. pion emission angles 100°, 120°, 140°. The experiment was carried out using an optical spark chamber telescope at the output of the magnetic spectrometer. The obtained experimental data are included in a Walker-type analysis in order to verify the parameters of the resonances Pu(1470), D13(1570) and Su(1535). Proton polarization in the reaction No-~ ~Op was measured for a photon energy of 450 MeV at a c.m. pion emission angle of 105° using photons linearly polarized at 45° to the reaction plane. A liquid hydrogen target in the field of a superconducting magnet was used for the separation of the Px' and Pz' components of the secondary-proton polarization vector. Data are obtained for three components (Px', Py, Pz') of the proton polarization. The obtained results are compared with predictions of different multipole analyses of photoproduction.
1. Introduction Experimental studies of single-pion photoproduction from nucleons play an important role in the understanding of electromagnetic characteristics of baryon resonances. The knowledge of the proton coupling and of the types of transition responsible for the resonance excitation allows one to make a comparison with quark model predictions, thereby promoting their further improvement, on the one hand, and stimulating theoretical and experimental studies of electromagnetic hadron interactions, on the other. The solution of this task would require systematic data on the 525
526
A.$. Bratashevskif et al. / Polarization of recoil protons
set of nine independent experimental observables; i.e., data determined by the complete experiment requirements [1]. The current theoretical studies of pion photoproduction from nucleons [2-5] cannot provide unambiguous solutions for radiative widths of certain resonances as they involve the data of only four experimental observables (viz., the differential cross sections, the polarization vector component perpendicular to the reaction plane Py, T and Z asymmetries) which have a non-systematic character. Therefore, parallel to extending the knowledge on the above-mentioned observables, it is also necessary to obtain information on the other quantities, this is necessitated by the requirement to establish at least two polarization parameters of the particles participating in the reaction under study. Here we describe the technique for proton polarization measurements in the reaction yp ~ ~r°p using photons linearly polarized at an angle ~ = 450 to the reaction plane. Data have been obtained for three components P~,, Py,, P~, of the secondary-proton polarization vector at Ey = 450 MeV at a c.m. pion emission angle of 105 ° and for the component Py of the proton polarization in the photon energy range from 500 to 800 MeV at pion emission angles of 100 °, 120o and 140 ° in the c.m.s.
2. Experimental equipment The experiment was performed in the photon beam of the Kharkov 2 GeV electron linear accelerator. The experimental arrangement is shown schematically in fig. 1. The photons passed through a liquid hydrogen target and then were monitored with a Wilson quantometer. The polarization of secondary protons was measured by a spark-chamber telescope [7] located at the exit of one of the magnetic spectrometers. The angular acceptance of the spectrometer was set by an input collimator (Col) to +0.33 °. The telescope comprised a spark chamber with 42 graphite electrodes having the dimensions 350 x 350 x 7 mm 3 (SC-42). The amount of carbon material in SC-42 (46 g/cm 2) corresponded to the maximum range of a proton with energy 250 MeV. For polarization measurements of protons with energies above 250 MeV, graphite blocks (12C) of an appropriate thickness could be placed in front of the SC-42 chamber. In this case, to determine the direction of the incident particles and particles scattered in the blocks, spark chambers (SC-5), each containing five aluminium electrodes of thickness 0.04 ram, were used. In the absence of the blocks the chambers SC-5 were used to determine the directions of the tracks of protons before they enter the chamber analyzer (SC-42). The protons were identified by the momentum assigned by the magnetic spectrometer and by their range before they stopped in SC-42. The spark chambers were triggered by time-coincidence scintillation counters C1, C2, C3. The momentum of the incident proton was determined by the coordinate of the traversal of the spectrometer focal
A.S. Bratashevski] et al. / Polarization of recoil protons
527
METER
~"
T~ET
-5
Fig. 1. General layout of the experiment. Col: spectrometer input collimators; C1, C2, C3, C4, C5, C6: scintillation counters; Cu: copper moderator; SC: spark chambers; C12: graphite blocks. line with an accuracy better than 0.25%. On recording the proton spectra in a wide momentum range (Ap/p = 7%) it was possible to choose separate spectrum sections in order to obtain the polarization values with the required energy resolution (AE~/). The maximum errors in measurements of azimuthal and polar scattering angles were estimated to be 0.065 and 0.014. rad, respectively. In our experiment the telescope of scintillation counters C4, C5, C6 and the second spectrometer helped to control the stability of the photon-beam parameters by the proton yield from the hydrogen target.
3. Py polarization of recoil protons from the reaction 7P -~ O p in the photon energy range 500-800 MeV In the course of the experiments we obtained 620 000 proton tracks of which 43 500 scattering events satisfying the selection criteria were used for calculations of the polarization. The proton polarization (Py) was calculated by the method of maximum likelihood. The experimental results are listed in table 1 and are shown in fig. 2. The polarization values were obtained with energy resolution AEv = ±10 MeV. We made an attempt to estimate the effect, which might be introduced by the new results, on an analysis similar to that found in ref. [2] (MW). For this purpose, we used the MW-data on the Born term and on the contributions to the photoproduction amplitude from the non-resonance "background", whereas the four parameters
528
A.S. Bratashevskif et al. / Polarization of recoil protons
Table 1 Energy dependences of the proton polarization for pion emission angles 100 °, 120 °, 140 ° in the c.m.s. Ev (MeV)
100 °
120 °
480 500 510 520 540 560 580 600 620 640 660 680 700 720 740 760 780 790 800
-0.158 2 0.107 -0.201 2 0.094
-0.203 2 0.150 -0.257 2 0.105
-0.318 2 0.090 0.388 + 0.094 -0.384 + 0.102 -0.431 + 0.095 -0.597 + 0.093 -0.657 + 0.095 -0.742 2 0.094 -0.778 + 0.095 -0.797 + 0.093 -0.722 + 0.090 -0.724 + 0.068 -0.721 2 0.080 -0.541 20.074 -0.504 + 0.071
-0.439 2 0.094 -0.394 2 0.084 -0.395 + 0.090 -0.637 2 0.090 -0.605 + 0.088 -0.682 2 0.077 -0.757 2 0.092 -0.755 + 0.093 0.575 + 0.092 -0.727 + 0.080 -0.761 + 0.097 -0.741 + 0.072 -0.591 +0.086 -0.529 ± 0.096 -0.564 + 0.137 a
140 °
-0.300+0.178 a -0.401 + 0.127 -0.381 + 0.096 -0.355 + 0.083 -0.451 + 0.082 -0.511 + 0.092 -0.645 + 0.096 -0.586 2 0.096 -0.714 2 0.094 0.813 2 0.079 -0.797 2 0.069 -0.809 + 0.071 -0.551 + 0.142
-0.438±0.103
a The polarization values were obtained with the energy resolution AE~, = 25 MeV. The errors quoted in the table are statistical.
A + ( W o ) of the r e s o n a n c e s Pl1(1470), D13(1510) a n d Sl1(1535), d o m i n a n t in the c o n s i d e r e d e n e r g y region, were o b t a i n e d f r o m t h e p r e s e n t data by the X 2 minimization method. T h e o b t a i n e d results are q u o t e d in the s e c o n d line of table 2. T h e first line p r e s e n t s the M W - p a r a m e t e r s w h i c h were used as initial ones in t h e X 2 m i n i m i z a tion. It is s e e n f r o m t h e table t h a t the values A 1 - a n d B2 of the r e s o n a n c e s P l 1 ( 1 4 7 0 ) a n d D13(1510) are very close to the c o r r e s p o n d i n g p a r a m e t e r s of the M W - a n a l y s i s , w h e r e a s t h e p a r a m e t e r s A 2 a n d A o ÷ of the r e s o n a n c e s D13(1510) a n d $11(1535) differ c o n s i d e r a b l y f r o m t h o s e of the MW-analysis. Fig. 2 c o m p a r e s the e x p e r i m e n t a l e n e r g y d e p e n d e n c e of the p o l a r i z a t i o n with the results of the M W - a n a l y s i s a n d of the p h e n o m e n o l o g i c a l analysis b a s e d o n the dispersion relations [4] (the solid a n d d a s h e d curves). A fair a g r e e m e n t is o b t a i n e d for the M W - a n a l y s i s (the ratios t , 2 / ( t h e n u m b e r of points) are 1.17 a n d 2.14 for analyses [2] a n d [4], respectively). It is also seen t h a t the a g r e e m e n t b e t w e e n t h e o r e t i c a l a n d e x p e r i m e n t a l d e p e n d e n c e s b e c o m e s m u c h worse as the angle increases (the M W - a n a l y s i s yields X 2 / ( t h e n u m b e r of points) as 0.4, 1.4, 1.8 for angles of 100 °, 120 °, 140 °, respectively).
529
A.$. Bratashevskij et al. / Polarization of recoil protons r'0t O, '
'
~
' ]
-Q5
0
Fig. 2. Energy dependences of the proton polarization from the reaction yp~ O p . O, ~, I): the data taken from ref. [15]; C): our present results. The solid curve shows the results of the MW-analysis [2]; the dashed curve, the results of the work [4]; the dash-dotted curve represents fit 1.
Table 2 The values of A+(W °) resonance parameters (the MW-representation) Pl1(1470)
D13(1510)
Type of fit
A 1-
A2
MW fit I
-0.60+0.20 -0.68±0.08
-0.05+0.05 -0.33±0.10
$11(1535)
g2
B2
Ao ÷
Degrees of freedom
-1.51+0.10 -1.52-4-0.05
-0.60+0.12 -0.28±0.07
3.20 1.13
A dash-dotted curve shows the energy d e p e n d e n c e obtained from fit 1, which provides a somewhat better a g r e e m e n t with the experimental data, particularly for 140 °. H o w e v e r , one should bear in mind that the results of such a " l i m i t e d " analysis may be affected in a certain way by the selection of the non-resonance background, as well as by contributions from other resonances.
A.S. Bratashevskij et al. / Polarization of recoil protons
530
4. Measurements of proton polarization vector components Px', Pr', Pz' using linearly polarized photons In these experiments we made measurements with linearly polarized photons for the following three orientations of a diamond monocrystal [6]. (i) The crystal orientation corresponded to the absence of the coherent part of the photon spectrum, the photon polarization being zero. The quantities measured were the yield C o and the polarization of protons for the noncoherent part of the photon spectrum (pO). (ii) The photon-polarization vector for the investigated energy region is directed at an angle ~b ---45°. The measured quantities were the proton yield C +45 and the proton polarization p+45. (iii) The photon-polarization vector is directed at an angle d~ = - 4 5 °. The quantities measured were C -45 and p-45. The components of the proton polarization vector were determined by the asymmetry in scattering of the protons by carbon nuclei and were calculated by the method of maximum likelihood. In our case the likelihood function included the scattering events satisfying the following criteria: (a) The energy losses in the scattering (AE) are no more than 10 MeV. This is explained by the lack of information on the analysing power of carbon for 2xE > 10 MeV. (b) The polar scattering angles 0/> 5°. This criterion is necessary to separate the contribution from the multiple Coulomb scattering. (c) The tracks of protons before scattering are no more than +60 mm away from the telescope geometrical axis. The consideration of this criterion allows one to exclude the artificial asymmetry brought about by the scattering geometry. The proton polarization vector component lying in the reaction plane is defined a s ~p±45 e x p at which one obtains the maximum value of the likelihood function N
±45 L(Pexp ) = l] I1 + (l~°P ° + #±45p±45)A(EiOg) sin Cg[, g=l
(1)
where N is the number of the events with proton scattering by the polarization analyzer, satisfying the selection criteria; A(Eg, Og) is the analysing power of carbon [8] in scattering of a proton with an energy Eg at a polar angle 0i; Cg is the azimuthal scattering angle (the angle between the reaction plane and the scattering plane)./x ° and/z ±4s are the relative proton yields from non-coherent and coherent parts of the photon spectra, respectively; they are given by [.£0= C 0 / C ± 4 5
/,,£±45 = ( C ± 4 5 _
C0)/C±45.
(2)
After taking logarithms and making a series expansion of expression (1) we obtain :t:45 the maximum value of L(Pexp ) as p±45
(p±45
= ,-~xp - Iz°e°)/tz
±45
(3)
A.S. Bratashevskif et al. / Polarization of recoil protons
531
The presence of the spectrometer's magnetic field, perpendicular to the reaction plane, results in the rotation of the components Px, and P~, by an angle a E9]: a = E / m ( l g - 1)B,
(4)
where E and m are the total energy and mass of the proton, respectively; B is the rotation angle of the particle in the spectrometer magnetic field (30°); g = 2.793 for the proton. The polarization of recoil nucleons is described in the x', y', z' coordinate system, where the axes OX', OY' and OZ' are directed, respectively, along the vectors (k × q) × q, (k × q) and q (k and q being the c.m. momenta of the photon and pion, correspondingly). Hence, the polarization in the reaction plane Px'z, is related to Px' and Pz' by Px'~' = Px' cos a +Pz' sin a .
(5)
The values of the components p±4S are defined in the following way: 1 + 4 5 +(1 -Pv)Px'z' P + 4 5 = ~[(1+ Pv)Px,z, - 4 5 ]' p
Since
45
(6)
1 +45 -45 = ~l(1-Pv)Px,z, +(I+P~)Px,~, [.
p+45=_p-45, then (7)
Px,z,= p+451pv = -P-45]Pv,
where Pv is the degree of the photon beam polarization. The sign difference between p+45and p-45 was used for controlling and suppressing any artificial asymmetry in proton scattering "up-down" in the polarization analyzer. To separate the components Px, and Pz' we used an additional subrotation of the proton spin by an angle/3 in the 2.8 T magnetic field, perpendicular to the reaction plane, which was created around the hydrogen target by a superconducting magnet [10]. Two series of measurements were performed: (1) the field around the target is directed along the magnetic spectrometer field; (2) the target field is opposite to the spectrometer field. Here, the component Px,z, for the series (1) and (2) is given by the relations x'z' p(l~
~
Px, cOs(a+/3)+P~,sin(a+/3)
p(2~ x'z'
~
P~,cos(c~ - - /3)+P~,sin(a-/3)
(8) •
The solution of this set of equations allows one to separate the components P~, and P~, of the proton polarization vector. In this work the data on the polarization vector components lying in the reaction plane were obtained simultaneously with information on the component perpendicular to this plane. In this case the likelihood function was obtained by substituting cos ~ for sin ~ in eq. (1).
A.S. Bratashevskij et al. / Polarization of recoil protons
532 Table 3 E v (MeV)
0,,
P~,
Pr'
450
105 °
-0.363±0.152
P='
0.108±0.090
0.132±0.117
In the course of measurements we obtained 216 000 proton tracks stopped in the spark-chamber telescope, of which 8500 scattering events, satisfying the selection criteria, were used for calculations of the components of the proton polarization vector. As a result, we obtained information on the Px', P,.', Pz' components of y 0.2
o
~
L
...... ~..- ...... ~__ ~..
0.2[
f - . _~,
|.',,,
\\
-~
~
/-/
-0 • 6 \ \ \~ N . . . . . .
_../;_...; ........
-
...........................
..-"
o2/ -"
~2__
-
J //
i
/
/ql
1
•
/11
/1
I
~._/'//
"
~
i
i
]
"
i
Pz' O. 4
j'~"
~ "" ~
//
0.2
I ',.,'~ ~ - 0 . 2 ~|
//"
"',,~
~ . ~ " - -..
.....-;.z
/ i / ....... ......./ /
"~-...-=..-_.-.~........ .',---. . . . .
-0.4 1
@s(deg ) 0
30
60
90
120
150
180
Fig. 3. Px', lay, Pz' components of the proton-polarization vector in yp-> ~.Op at E-/= 450 MeV: O: results of the present work; O: ref. [12]; ID: ref. [13]; ~ : ref. [14]. Dashed, dash-dotted and dotted lines are energy-independent analysis solutions [11], the solid line is the result of the analysis [2], the dash-double dotted line comes from the analysis [3].
A.$. Bratashevskii et al. / Polarization of recoil protons
533
the recoil-proton polarization in the reaction yp ~ 7r°p at a photon energy of 450 MeV and a pion emission angle of 1050 in the centre of mass. The energy resolution was AEv = +20 MeV. The obtained results are listed in table 3. Fig. 3 shows our present results compared with the results of an energyindependent multipole analysis [11] and phenomenological analyses [2, 3] with the isobar model as a basis. The angular dependence of Py, shows our previous results [12] from the double polarization experiments and the data of other laboratories [13, 14]. Satisfactory agreement can be seen for the results [13] obtained under experimental kinematic conditions similar to ours. The comparison of our present data with the theoretical calculations [2, 3, 11] shows a better agreement with the phenomenological analyses [2, 3] even though in this case one cannot find a satisfactory agreement for all the three quantities (ex', Py', Pz'). This prompts the necessity to obtain systematic highly accurate experimental information on the components of the proton polarization vector for wider ranges of energies and angles.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
I.S. Barker, A. Donnachie and J.K. Storrow, Nucl. Phys. B95 (1975) 347. W.J. Metcalf and R.L. Walker, Nucl. Phys. B76 (1974) 253. P. Feller et al., Nucl. Phys. B l l 0 (1976) 397. I. Aznauryan et al., Yerevan preprint YPI-264(57)-77. I.M. Barbour, R.L. Crawford and N.H. Parsons, Nucl. Phys. B141 (1978) 253. V.G. Gorbenko et al., Yad. Fiz. 24 (1976) 961. A.I. Derebchinskij et al., ZhETF (USSR) 66 (1974) 68. V.Z. Peterson, preprint, URCL-10622 (1963). D.E. Lundquist et al., Phys. Rev. 168 (1968) 1527. A.Ya. Derkach et al., Cryogenics 18 (1978) 539. V.B. Ganenko et.al., Yad. Fiz. 24 (1976) 545. V.G. Gorbenko et al., Yad. Fiz. 27 (1978) 1204. J.O. Maloy et al., Phys. Rev. 139 (1965) B733. S. Hayakawa et al., J. Phys. Soc. Japan 25 (1968) 307. D. Menze, W. Pfeil and R. Wilcke, Bonn Univ. preprint 7-1 (1977).
POLARIZATION OF RECOIL PROTONS FROM THE REACTION yp_~ ~.Op IN THE PHOTON ENERGY RANGE 450-800 MeV A.S. BRATASHEVSKIJ, V.G. GORBENKO, A.I. DEREBCHINSKIJ, A.Ya. D E R K A C H , Yu.V. ZHEBROVSKIJ, A.A. ZYBALOV, I.M. K A R N A U K H O V , L.Ya. KOLESNIKOV, O.G. KONOVALOV, A.A. LUKHANIN, A.S. OMELAENKO, A.L. RUBASHKIN, P.V. SOROKIN, E.A. SPOROV, A.E. TENISHEV and S.G. T O N A P E T Y A N The Kharkov Physical-Technical Institute, Acad. Sci. of Ukr. SSR, Kharkov, USSR
Received 7 August 1979 (Revised 6 December 1979) Measurements of secondary-proton polarization from the reaction No-->~r°p have been performed in the photon energy range 500-800 MeV at c.m. pion emission angles 100°, 120°, 140°. The experiment was carried out using an optical spark chamber telescope at the output of the magnetic spectrometer. The obtained experimental data are included in a Walker-type analysis in order to verify the parameters of the resonances Pu(1470), D13(1570) and Su(1535). Proton polarization in the reaction No-~ ~Op was measured for a photon energy of 450 MeV at a c.m. pion emission angle of 105° using photons linearly polarized at 45° to the reaction plane. A liquid hydrogen target in the field of a superconducting magnet was used for the separation of the Px' and Pz' components of the secondary-proton polarization vector. Data are obtained for three components (Px', Py, Pz') of the proton polarization. The obtained results are compared with predictions of different multipole analyses of photoproduction.
1. Introduction Experimental studies of single-pion photoproduction from nucleons play an important role in the understanding of electromagnetic characteristics of baryon resonances. The knowledge of the proton coupling and of the types of transition responsible for the resonance excitation allows one to make a comparison with quark model predictions, thereby promoting their further improvement, on the one hand, and stimulating theoretical and experimental studies of electromagnetic hadron interactions, on the other. The solution of this task would require systematic data on the 525
526
A.$. Bratashevskif et al. / Polarization of recoil protons
set of nine independent experimental observables; i.e., data determined by the complete experiment requirements [1]. The current theoretical studies of pion photoproduction from nucleons [2-5] cannot provide unambiguous solutions for radiative widths of certain resonances as they involve the data of only four experimental observables (viz., the differential cross sections, the polarization vector component perpendicular to the reaction plane Py, T and Z asymmetries) which have a non-systematic character. Therefore, parallel to extending the knowledge on the above-mentioned observables, it is also necessary to obtain information on the other quantities, this is necessitated by the requirement to establish at least two polarization parameters of the particles participating in the reaction under study. Here we describe the technique for proton polarization measurements in the reaction yp ~ ~r°p using photons linearly polarized at an angle ~ = 450 to the reaction plane. Data have been obtained for three components P~,, Py,, P~, of the secondary-proton polarization vector at Ey = 450 MeV at a c.m. pion emission angle of 105 ° and for the component Py of the proton polarization in the photon energy range from 500 to 800 MeV at pion emission angles of 100 °, 120o and 140 ° in the c.m.s.
2. Experimental equipment The experiment was performed in the photon beam of the Kharkov 2 GeV electron linear accelerator. The experimental arrangement is shown schematically in fig. 1. The photons passed through a liquid hydrogen target and then were monitored with a Wilson quantometer. The polarization of secondary protons was measured by a spark-chamber telescope [7] located at the exit of one of the magnetic spectrometers. The angular acceptance of the spectrometer was set by an input collimator (Col) to +0.33 °. The telescope comprised a spark chamber with 42 graphite electrodes having the dimensions 350 x 350 x 7 mm 3 (SC-42). The amount of carbon material in SC-42 (46 g/cm 2) corresponded to the maximum range of a proton with energy 250 MeV. For polarization measurements of protons with energies above 250 MeV, graphite blocks (12C) of an appropriate thickness could be placed in front of the SC-42 chamber. In this case, to determine the direction of the incident particles and particles scattered in the blocks, spark chambers (SC-5), each containing five aluminium electrodes of thickness 0.04 ram, were used. In the absence of the blocks the chambers SC-5 were used to determine the directions of the tracks of protons before they enter the chamber analyzer (SC-42). The protons were identified by the momentum assigned by the magnetic spectrometer and by their range before they stopped in SC-42. The spark chambers were triggered by time-coincidence scintillation counters C1, C2, C3. The momentum of the incident proton was determined by the coordinate of the traversal of the spectrometer focal
A.S. Bratashevski] et al. / Polarization of recoil protons
527
METER
~"
T~ET
-5
Fig. 1. General layout of the experiment. Col: spectrometer input collimators; C1, C2, C3, C4, C5, C6: scintillation counters; Cu: copper moderator; SC: spark chambers; C12: graphite blocks. line with an accuracy better than 0.25%. On recording the proton spectra in a wide momentum range (Ap/p = 7%) it was possible to choose separate spectrum sections in order to obtain the polarization values with the required energy resolution (AE~/). The maximum errors in measurements of azimuthal and polar scattering angles were estimated to be 0.065 and 0.014. rad, respectively. In our experiment the telescope of scintillation counters C4, C5, C6 and the second spectrometer helped to control the stability of the photon-beam parameters by the proton yield from the hydrogen target.
3. Py polarization of recoil protons from the reaction 7P -~ O p in the photon energy range 500-800 MeV In the course of the experiments we obtained 620 000 proton tracks of which 43 500 scattering events satisfying the selection criteria were used for calculations of the polarization. The proton polarization (Py) was calculated by the method of maximum likelihood. The experimental results are listed in table 1 and are shown in fig. 2. The polarization values were obtained with energy resolution AEv = ±10 MeV. We made an attempt to estimate the effect, which might be introduced by the new results, on an analysis similar to that found in ref. [2] (MW). For this purpose, we used the MW-data on the Born term and on the contributions to the photoproduction amplitude from the non-resonance "background", whereas the four parameters
528
A.S. Bratashevskif et al. / Polarization of recoil protons
Table 1 Energy dependences of the proton polarization for pion emission angles 100 °, 120 °, 140 ° in the c.m.s. Ev (MeV)
100 °
120 °
480 500 510 520 540 560 580 600 620 640 660 680 700 720 740 760 780 790 800
-0.158 2 0.107 -0.201 2 0.094
-0.203 2 0.150 -0.257 2 0.105
-0.318 2 0.090 0.388 + 0.094 -0.384 + 0.102 -0.431 + 0.095 -0.597 + 0.093 -0.657 + 0.095 -0.742 2 0.094 -0.778 + 0.095 -0.797 + 0.093 -0.722 + 0.090 -0.724 + 0.068 -0.721 2 0.080 -0.541 20.074 -0.504 + 0.071
-0.439 2 0.094 -0.394 2 0.084 -0.395 + 0.090 -0.637 2 0.090 -0.605 + 0.088 -0.682 2 0.077 -0.757 2 0.092 -0.755 + 0.093 0.575 + 0.092 -0.727 + 0.080 -0.761 + 0.097 -0.741 + 0.072 -0.591 +0.086 -0.529 ± 0.096 -0.564 + 0.137 a
140 °
-0.300+0.178 a -0.401 + 0.127 -0.381 + 0.096 -0.355 + 0.083 -0.451 + 0.082 -0.511 + 0.092 -0.645 + 0.096 -0.586 2 0.096 -0.714 2 0.094 0.813 2 0.079 -0.797 2 0.069 -0.809 + 0.071 -0.551 + 0.142
-0.438±0.103
a The polarization values were obtained with the energy resolution AE~, = 25 MeV. The errors quoted in the table are statistical.
A + ( W o ) of the r e s o n a n c e s Pl1(1470), D13(1510) a n d Sl1(1535), d o m i n a n t in the c o n s i d e r e d e n e r g y region, were o b t a i n e d f r o m t h e p r e s e n t data by the X 2 minimization method. T h e o b t a i n e d results are q u o t e d in the s e c o n d line of table 2. T h e first line p r e s e n t s the M W - p a r a m e t e r s w h i c h were used as initial ones in t h e X 2 m i n i m i z a tion. It is s e e n f r o m t h e table t h a t the values A 1 - a n d B2 of the r e s o n a n c e s P l 1 ( 1 4 7 0 ) a n d D13(1510) are very close to the c o r r e s p o n d i n g p a r a m e t e r s of the M W - a n a l y s i s , w h e r e a s t h e p a r a m e t e r s A 2 a n d A o ÷ of the r e s o n a n c e s D13(1510) a n d $11(1535) differ c o n s i d e r a b l y f r o m t h o s e of the MW-analysis. Fig. 2 c o m p a r e s the e x p e r i m e n t a l e n e r g y d e p e n d e n c e of the p o l a r i z a t i o n with the results of the M W - a n a l y s i s a n d of the p h e n o m e n o l o g i c a l analysis b a s e d o n the dispersion relations [4] (the solid a n d d a s h e d curves). A fair a g r e e m e n t is o b t a i n e d for the M W - a n a l y s i s (the ratios t , 2 / ( t h e n u m b e r of points) are 1.17 a n d 2.14 for analyses [2] a n d [4], respectively). It is also seen t h a t the a g r e e m e n t b e t w e e n t h e o r e t i c a l a n d e x p e r i m e n t a l d e p e n d e n c e s b e c o m e s m u c h worse as the angle increases (the M W - a n a l y s i s yields X 2 / ( t h e n u m b e r of points) as 0.4, 1.4, 1.8 for angles of 100 °, 120 °, 140 °, respectively).
529
A.$. Bratashevskij et al. / Polarization of recoil protons r'0t O, '
'
~
' ]
-Q5
0
Fig. 2. Energy dependences of the proton polarization from the reaction yp~ O p . O, ~, I): the data taken from ref. [15]; C): our present results. The solid curve shows the results of the MW-analysis [2]; the dashed curve, the results of the work [4]; the dash-dotted curve represents fit 1.
Table 2 The values of A+(W °) resonance parameters (the MW-representation) Pl1(1470)
D13(1510)
Type of fit
A 1-
A2
MW fit I
-0.60+0.20 -0.68±0.08
-0.05+0.05 -0.33±0.10
$11(1535)
g2
B2
Ao ÷
Degrees of freedom
-1.51+0.10 -1.52-4-0.05
-0.60+0.12 -0.28±0.07
3.20 1.13
A dash-dotted curve shows the energy d e p e n d e n c e obtained from fit 1, which provides a somewhat better a g r e e m e n t with the experimental data, particularly for 140 °. H o w e v e r , one should bear in mind that the results of such a " l i m i t e d " analysis may be affected in a certain way by the selection of the non-resonance background, as well as by contributions from other resonances.
A.S. Bratashevskij et al. / Polarization of recoil protons
530
4. Measurements of proton polarization vector components Px', Pr', Pz' using linearly polarized photons In these experiments we made measurements with linearly polarized photons for the following three orientations of a diamond monocrystal [6]. (i) The crystal orientation corresponded to the absence of the coherent part of the photon spectrum, the photon polarization being zero. The quantities measured were the yield C o and the polarization of protons for the noncoherent part of the photon spectrum (pO). (ii) The photon-polarization vector for the investigated energy region is directed at an angle ~b ---45°. The measured quantities were the proton yield C +45 and the proton polarization p+45. (iii) The photon-polarization vector is directed at an angle d~ = - 4 5 °. The quantities measured were C -45 and p-45. The components of the proton polarization vector were determined by the asymmetry in scattering of the protons by carbon nuclei and were calculated by the method of maximum likelihood. In our case the likelihood function included the scattering events satisfying the following criteria: (a) The energy losses in the scattering (AE) are no more than 10 MeV. This is explained by the lack of information on the analysing power of carbon for 2xE > 10 MeV. (b) The polar scattering angles 0/> 5°. This criterion is necessary to separate the contribution from the multiple Coulomb scattering. (c) The tracks of protons before scattering are no more than +60 mm away from the telescope geometrical axis. The consideration of this criterion allows one to exclude the artificial asymmetry brought about by the scattering geometry. The proton polarization vector component lying in the reaction plane is defined a s ~p±45 e x p at which one obtains the maximum value of the likelihood function N
±45 L(Pexp ) = l] I1 + (l~°P ° + #±45p±45)A(EiOg) sin Cg[, g=l
(1)
where N is the number of the events with proton scattering by the polarization analyzer, satisfying the selection criteria; A(Eg, Og) is the analysing power of carbon [8] in scattering of a proton with an energy Eg at a polar angle 0i; Cg is the azimuthal scattering angle (the angle between the reaction plane and the scattering plane)./x ° and/z ±4s are the relative proton yields from non-coherent and coherent parts of the photon spectra, respectively; they are given by [.£0= C 0 / C ± 4 5
/,,£±45 = ( C ± 4 5 _
C0)/C±45.
(2)
After taking logarithms and making a series expansion of expression (1) we obtain :t:45 the maximum value of L(Pexp ) as p±45
(p±45
= ,-~xp - Iz°e°)/tz
±45
(3)
A.S. Bratashevskif et al. / Polarization of recoil protons
531
The presence of the spectrometer's magnetic field, perpendicular to the reaction plane, results in the rotation of the components Px, and P~, by an angle a E9]: a = E / m ( l g - 1)B,
(4)
where E and m are the total energy and mass of the proton, respectively; B is the rotation angle of the particle in the spectrometer magnetic field (30°); g = 2.793 for the proton. The polarization of recoil nucleons is described in the x', y', z' coordinate system, where the axes OX', OY' and OZ' are directed, respectively, along the vectors (k × q) × q, (k × q) and q (k and q being the c.m. momenta of the photon and pion, correspondingly). Hence, the polarization in the reaction plane Px'z, is related to Px' and Pz' by Px'~' = Px' cos a +Pz' sin a .
(5)
The values of the components p±4S are defined in the following way: 1 + 4 5 +(1 -Pv)Px'z' P + 4 5 = ~[(1+ Pv)Px,z, - 4 5 ]' p
Since
45
(6)
1 +45 -45 = ~l(1-Pv)Px,z, +(I+P~)Px,~, [.
p+45=_p-45, then (7)
Px,z,= p+451pv = -P-45]Pv,
where Pv is the degree of the photon beam polarization. The sign difference between p+45and p-45 was used for controlling and suppressing any artificial asymmetry in proton scattering "up-down" in the polarization analyzer. To separate the components Px, and Pz' we used an additional subrotation of the proton spin by an angle/3 in the 2.8 T magnetic field, perpendicular to the reaction plane, which was created around the hydrogen target by a superconducting magnet [10]. Two series of measurements were performed: (1) the field around the target is directed along the magnetic spectrometer field; (2) the target field is opposite to the spectrometer field. Here, the component Px,z, for the series (1) and (2) is given by the relations x'z' p(l~
~
Px, cOs(a+/3)+P~,sin(a+/3)
p(2~ x'z'
~
P~,cos(c~ - - /3)+P~,sin(a-/3)
(8) •
The solution of this set of equations allows one to separate the components P~, and P~, of the proton polarization vector. In this work the data on the polarization vector components lying in the reaction plane were obtained simultaneously with information on the component perpendicular to this plane. In this case the likelihood function was obtained by substituting cos ~ for sin ~ in eq. (1).
A.S. Bratashevskij et al. / Polarization of recoil protons
532 Table 3 E v (MeV)
0,,
P~,
Pr'
450
105 °
-0.363±0.152
P='
0.108±0.090
0.132±0.117
In the course of measurements we obtained 216 000 proton tracks stopped in the spark-chamber telescope, of which 8500 scattering events, satisfying the selection criteria, were used for calculations of the components of the proton polarization vector. As a result, we obtained information on the Px', P,.', Pz' components of y 0.2
o
~
L
...... ~..- ...... ~__ ~..
0.2[
f - . _~,
|.',,,
\\
-~
~
/-/
-0 • 6 \ \ \~ N . . . . . .
_../;_...; ........
-
...........................
..-"
o2/ -"
~2__
-
J //
i
/
/ql
1
•
/11
/1
I
~._/'//
"
~
i
i
]
"
i
Pz' O. 4
j'~"
~ "" ~
//
0.2
I ',.,'~ ~ - 0 . 2 ~|
//"
"',,~
~ . ~ " - -..
.....-;.z
/ i / ....... ......./ /
"~-...-=..-_.-.~........ .',---. . . . .
-0.4 1
@s(deg ) 0
30
60
90
120
150
180
Fig. 3. Px', lay, Pz' components of the proton-polarization vector in yp-> ~.Op at E-/= 450 MeV: O: results of the present work; O: ref. [12]; ID: ref. [13]; ~ : ref. [14]. Dashed, dash-dotted and dotted lines are energy-independent analysis solutions [11], the solid line is the result of the analysis [2], the dash-double dotted line comes from the analysis [3].
A.$. Bratashevskii et al. / Polarization of recoil protons
533
the recoil-proton polarization in the reaction yp ~ 7r°p at a photon energy of 450 MeV and a pion emission angle of 1050 in the centre of mass. The energy resolution was AEv = +20 MeV. The obtained results are listed in table 3. Fig. 3 shows our present results compared with the results of an energyindependent multipole analysis [11] and phenomenological analyses [2, 3] with the isobar model as a basis. The angular dependence of Py, shows our previous results [12] from the double polarization experiments and the data of other laboratories [13, 14]. Satisfactory agreement can be seen for the results [13] obtained under experimental kinematic conditions similar to ours. The comparison of our present data with the theoretical calculations [2, 3, 11] shows a better agreement with the phenomenological analyses [2, 3] even though in this case one cannot find a satisfactory agreement for all the three quantities (ex', Py', Pz'). This prompts the necessity to obtain systematic highly accurate experimental information on the components of the proton polarization vector for wider ranges of energies and angles.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
I.S. Barker, A. Donnachie and J.K. Storrow, Nucl. Phys. B95 (1975) 347. W.J. Metcalf and R.L. Walker, Nucl. Phys. B76 (1974) 253. P. Feller et al., Nucl. Phys. B l l 0 (1976) 397. I. Aznauryan et al., Yerevan preprint YPI-264(57)-77. I.M. Barbour, R.L. Crawford and N.H. Parsons, Nucl. Phys. B141 (1978) 253. V.G. Gorbenko et al., Yad. Fiz. 24 (1976) 961. A.I. Derebchinskij et al., ZhETF (USSR) 66 (1974) 68. V.Z. Peterson, preprint, URCL-10622 (1963). D.E. Lundquist et al., Phys. Rev. 168 (1968) 1527. A.Ya. Derkach et al., Cryogenics 18 (1978) 539. V.B. Ganenko et.al., Yad. Fiz. 24 (1976) 545. V.G. Gorbenko et al., Yad. Fiz. 27 (1978) 1204. J.O. Maloy et al., Phys. Rev. 139 (1965) B733. S. Hayakawa et al., J. Phys. Soc. Japan 25 (1968) 307. D. Menze, W. Pfeil and R. Wilcke, Bonn Univ. preprint 7-1 (1977).