- Email: [email protected]
Comments on “Measurement of the polarization of a pulsed electron beam with a Møller polarimeter in the coincidence mode”
Nuclear Instruments and Methods in Physics Research A 370 ( 1996) 644-645
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH
Sectlon A
EL.!X’VIER
Comments on “Measurement of the polarization of a pulsed electron beam with a Moller polarimeter in the coincidence mode” A. Feltham* Institut
f iir Physik, Universitiit Basel, Klingelbergstr. Received
I August 1995
A recent article [I] has described results from a Moller polarimeter which was employed to measure the polarization of the electron beam at the Bates Linear Accelerator Center. In this article the authors claim to have measured the electron beam polarization to good statistical precision with small systematic uncertainties. I would like to draw attention to a particular aspect of their analysis which raises doubts as to the accuracy of the final results presented. The issue in question is the choice of effective analyzing powers employed in the analysis. It seems that the authors have used the nominal QED value of A,(&, = 90”) = - G as the effective analyzing power of their polarimeter. I assume this value was chosen after considering the small angular acceptance of their collimator. It is true that for such a small acceptance, the influence on the effective analyzing powers due to finite geometry and physical effects such as multiple scattering and radiative losses are negligible. One non-negligible effect, however, which the authors state specifically was neglected in their analysis, is the influence of the atomic motion of the bound target electrons on the analyzing powers [2] of their polarimeter. The role of the atomic motion effect (AME) in Molter polarimetry is well documented [2,3]. Two aspects of the design of this polarimeter [I ] combine to make it highly sensitive to the AME. The first is the small acceptance of the system. It is easy to show that the potential deviation of the scattered electron trajectories due to the AME is comparable to the angular opening of the collimators used in their experiment. The Moller laboratory scattering angle, 13,,which assumes a free target electron, is modified by the fact that the target has motion [3]: 8 = 13,Vm where p is the momentum of the bound electron, z^ the incident beam direction, and m, the electron mass, which determines the scale of the effect. Thus a momentum of Ip .z^(= 40 keV/c is sufficient to bring an electron event,
* Tel. +41 61267 [email protected].
3728,
fax
+41
61267
3784,
82, 4X6 Basel, Switzerland
e-mail
016%9002/96/$015.00 0 1996 Elsevier Science B.V. All rights reserved SSDI 0168-9002(95)01288-5
destined for the centre of the collimator (at &, = 1.96”). outside the acceptance of the collimator (52.5 mm at 1.75 m from the target)‘. Since only the inner shell electrons have a significant probability of such a large momentum, the preferential loss of these events results in effect, which increases the measured an “anti-dilution” asymmetry. This is because these electrons carry none of the spin polarization of the atom and therefore Moller scattering off of them has no asymmetry. The second way in which the sensitivity of this polarimeter to the AME is enhanced is due to the fact that the polarimeter is operated in coincidence mode. The same polarimeter operating in “single-arm” mode would be much less sensitive to the AME since it would have the possibility of compensating for the loss of zero asymmetry events through the in-scattering of similar events normally outside the collimator acceptance. This compensation appears to have been overlooked in the Levchuck paper [2], which erroneously predicted large effects for the single-arm mode of this same Bates polarimeter [4]. Here the coincidence requirement’, however, precludes the possibility of compensation since the AME shifts the scattered electrons in the opposite direction with respect to the collimator, i.e. if one Moller electron, nominally outside the angular acceptance, is shifted into the acceptance by the AME, its scattering partner is shifted farther away. Both electrons must be detected in order to establish a Moller event when operating in coincidence mode. To obtain a quantitative understanding of the effects mentioned above, I have modified an existing Monte Carlo code’ using information provided in the paper [ 1.41. My
’ The circular opening of the collimator enhances this sensitivity further. * A coincidence system need not be sensitive to the AME [5] and there exist configurations where the single-arm method is highly sensitive to the AME [-il. ’ It is an adaptation of a code developed by Swartz [3]. which is being used in the design of the CEBAF Hall C coincidence Moller polarimeter.
A. Feltham
I Nucl. Instr. and Meth. in Phw. Res. A 370 (19961 642-63.~
analysis primarily studied the influence, at the collimator4’5, of the AME on the effective analyzing powers. First of all, when ignoring the atomic motion, an analyzing power consistent with the nominal value of A /L = - t was found. When the possibility of atomic motion was included in the analysis, however, an effective analyzing power of A,, = 0.821?0.003 (errors statistical only) was obtained. This represents a 5.6% increase in the effective analyzing powers of the coincidence polarimeter, an effect larger than the combined systematic and statistical errors quoted in the paper [ 11. The size of this modification, relative to the 2.8% systematic error quoted in the paper [ 11, indicates that it is unacceptable to neglect the influence of the AME in the determination of the effective analyzing powers of this polarimeter. Based on my incomplete analysis, the measured value of the beam polarization should be reduced by almost 6%. A more complete analysis, however, should include details of the elements appearing downstream of the collimator. Depending on detector size an increased effect is possible due to the quadrupole magnet which enhances f&, when separating the scattered electrons from a A thin, opaque collimator was considered. ’ Insufficient information was provided for a detailed study of the downstream elements.
645
the primary beam. In addition, due to the considerable size of the AME in this application, one should also study the sensitivity of the analyzing powers to the knowledge of the atomic momentum distributions used in the analysis. As was suggested by Levchuck [2]. it is possible to build a Moller polarimeter which is insensitive to the AME if the & acceptance is sufficiently large. In fact this approach has already been successfully employed in a large acceptance coincidence polarimeter [5] at SLAC. For this polarimeter, which reached a 2% overall uncertainty despite poor duty cycle of SLAC (2 X IO -a 1, the correction due to the AME amounted to less than 0.5%.
References
[II K.B. Beard et al., Nucl. Instr. and Meth. A 361 ( 1995) 46. t-7.1LG. Levchuk. Nucl. Instr. and Meth. A 345 (1994) 496. [31 M. Swartz et al., SLAC-PUB-6467. ( 1994) submitted to Nucl. Instr. and Meth. 141 J. Anington et al., Nucl. Instr. and Meth. A 31 I ( 1992) 39. [51 A. Feltham and P. Steiner, Proc. Conf. on Perspectives in Nuclear Physics at Intermediate Energies, Trieste, Italy, May. 1995.
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH
Sectlon A
EL.!X’VIER
Comments on “Measurement of the polarization of a pulsed electron beam with a Moller polarimeter in the coincidence mode” A. Feltham* Institut
f iir Physik, Universitiit Basel, Klingelbergstr. Received
I August 1995
A recent article [I] has described results from a Moller polarimeter which was employed to measure the polarization of the electron beam at the Bates Linear Accelerator Center. In this article the authors claim to have measured the electron beam polarization to good statistical precision with small systematic uncertainties. I would like to draw attention to a particular aspect of their analysis which raises doubts as to the accuracy of the final results presented. The issue in question is the choice of effective analyzing powers employed in the analysis. It seems that the authors have used the nominal QED value of A,(&, = 90”) = - G as the effective analyzing power of their polarimeter. I assume this value was chosen after considering the small angular acceptance of their collimator. It is true that for such a small acceptance, the influence on the effective analyzing powers due to finite geometry and physical effects such as multiple scattering and radiative losses are negligible. One non-negligible effect, however, which the authors state specifically was neglected in their analysis, is the influence of the atomic motion of the bound target electrons on the analyzing powers [2] of their polarimeter. The role of the atomic motion effect (AME) in Molter polarimetry is well documented [2,3]. Two aspects of the design of this polarimeter [I ] combine to make it highly sensitive to the AME. The first is the small acceptance of the system. It is easy to show that the potential deviation of the scattered electron trajectories due to the AME is comparable to the angular opening of the collimators used in their experiment. The Moller laboratory scattering angle, 13,,which assumes a free target electron, is modified by the fact that the target has motion [3]: 8 = 13,Vm where p is the momentum of the bound electron, z^ the incident beam direction, and m, the electron mass, which determines the scale of the effect. Thus a momentum of Ip .z^(= 40 keV/c is sufficient to bring an electron event,
* Tel. +41 61267 [email protected].
3728,
fax
+41
61267
3784,
82, 4X6 Basel, Switzerland
016%9002/96/$015.00 0 1996 Elsevier Science B.V. All rights reserved SSDI 0168-9002(95)01288-5
destined for the centre of the collimator (at &, = 1.96”). outside the acceptance of the collimator (52.5 mm at 1.75 m from the target)‘. Since only the inner shell electrons have a significant probability of such a large momentum, the preferential loss of these events results in effect, which increases the measured an “anti-dilution” asymmetry. This is because these electrons carry none of the spin polarization of the atom and therefore Moller scattering off of them has no asymmetry. The second way in which the sensitivity of this polarimeter to the AME is enhanced is due to the fact that the polarimeter is operated in coincidence mode. The same polarimeter operating in “single-arm” mode would be much less sensitive to the AME since it would have the possibility of compensating for the loss of zero asymmetry events through the in-scattering of similar events normally outside the collimator acceptance. This compensation appears to have been overlooked in the Levchuck paper [2], which erroneously predicted large effects for the single-arm mode of this same Bates polarimeter [4]. Here the coincidence requirement’, however, precludes the possibility of compensation since the AME shifts the scattered electrons in the opposite direction with respect to the collimator, i.e. if one Moller electron, nominally outside the angular acceptance, is shifted into the acceptance by the AME, its scattering partner is shifted farther away. Both electrons must be detected in order to establish a Moller event when operating in coincidence mode. To obtain a quantitative understanding of the effects mentioned above, I have modified an existing Monte Carlo code’ using information provided in the paper [ 1.41. My
’ The circular opening of the collimator enhances this sensitivity further. * A coincidence system need not be sensitive to the AME [5] and there exist configurations where the single-arm method is highly sensitive to the AME [-il. ’ It is an adaptation of a code developed by Swartz [3]. which is being used in the design of the CEBAF Hall C coincidence Moller polarimeter.
A. Feltham
I Nucl. Instr. and Meth. in Phw. Res. A 370 (19961 642-63.~
analysis primarily studied the influence, at the collimator4’5, of the AME on the effective analyzing powers. First of all, when ignoring the atomic motion, an analyzing power consistent with the nominal value of A /L = - t was found. When the possibility of atomic motion was included in the analysis, however, an effective analyzing power of A,, = 0.821?0.003 (errors statistical only) was obtained. This represents a 5.6% increase in the effective analyzing powers of the coincidence polarimeter, an effect larger than the combined systematic and statistical errors quoted in the paper [ 11. The size of this modification, relative to the 2.8% systematic error quoted in the paper [ 11, indicates that it is unacceptable to neglect the influence of the AME in the determination of the effective analyzing powers of this polarimeter. Based on my incomplete analysis, the measured value of the beam polarization should be reduced by almost 6%. A more complete analysis, however, should include details of the elements appearing downstream of the collimator. Depending on detector size an increased effect is possible due to the quadrupole magnet which enhances f&, when separating the scattered electrons from a A thin, opaque collimator was considered. ’ Insufficient information was provided for a detailed study of the downstream elements.
645
the primary beam. In addition, due to the considerable size of the AME in this application, one should also study the sensitivity of the analyzing powers to the knowledge of the atomic momentum distributions used in the analysis. As was suggested by Levchuck [2]. it is possible to build a Moller polarimeter which is insensitive to the AME if the & acceptance is sufficiently large. In fact this approach has already been successfully employed in a large acceptance coincidence polarimeter [5] at SLAC. For this polarimeter, which reached a 2% overall uncertainty despite poor duty cycle of SLAC (2 X IO -a 1, the correction due to the AME amounted to less than 0.5%.
References
[II K.B. Beard et al., Nucl. Instr. and Meth. A 361 ( 1995) 46. t-7.1LG. Levchuk. Nucl. Instr. and Meth. A 345 (1994) 496. [31 M. Swartz et al., SLAC-PUB-6467. ( 1994) submitted to Nucl. Instr. and Meth. 141 J. Anington et al., Nucl. Instr. and Meth. A 31 I ( 1992) 39. [51 A. Feltham and P. Steiner, Proc. Conf. on Perspectives in Nuclear Physics at Intermediate Energies, Trieste, Italy, May. 1995.