The Sign of the Measured Asymmetry in NPOL and the Sense of Rotation of the Polarization Vector through CHARYBDIS. T.Reichelt March 2001 Abstract : With "proton polarity" in CHARYBDIS neutrons leaving the target towards NPOL have their polarization vector spinning counterclockwise when transversing the magnetic field. This sense of rotation is independent of the electron helicity. 1.The sign of the measured asymmetry in NPOL for Charybdis off. The reference frame,to which the components of the neutron's polarization vector refer, is defined here as in [1], namely : z-axis in q-direction - q being the virtual photon's three-vector, y-axis given by pin x pout where pin is the beam momentum and pout the momentum of the scattered electron, x-axis such that one has a right handed system. This means for the set-up in Hall C,that y is pointing to the floor and x to the right,when looking from the target to the front detectors of the polarimeter NPOL.In the following "right" and "left" will always have this meaning. The same reference frame is used in [2], where the sideways and longitudinal components of the polarization vector are calculated as functions of the neutron's electric ( Gen ) and magnetic ( Gmn ) formfactors. Here Px is proportional to Gen/Gmn,positive and independent of the beam polarization. (Note that the sign of Px is wrong in fig.5 !). Pz is positive and - as long as Gen**2<< Gmn**2 - only dependent of the kinematics, not of the formfactors. a is the beam polarization : a > 0 means mostly helicity=+1 electrons and a < 0 means mostly helicity = -1 electrons. a*Px is the sideways component of the polarization vector and a*Pz is the longitinal component. For positive helicity events a*Px is pointing to the right and a*Pz pointing towards NPOL. For negative helicity events the directions are reversed. Note, that helicity means here the true helicity of the beam electrons, not the labeling ! With the usual definition of the analyzing power Ay [1] and the fact that for small angles in n,p scattering - as used in the polarimeter NPOL - Ay is positive [3], the following statement results : For positive helicity events the upper rear counters in NPOL have a higher count rate than the lower rear counters. For negative helicity events the order is reversed. The events registered during the data taking are labeled h+ and h-.T his labeling does not reflect their true (physical) helicity status ! The relationship between the labeling and the true helicity depends on the status of the lambda/2 plate and can be deduced by Moller scattering. For the runs in November and December 2000 it has been found that [4] : lambda/2 plate in: h+ labeled events belong to a>0, they are positive helicity events lambda/2 plate out: h+ labeled events belong to a<0, they are negative helicity events For h- labeled events the sign of a and consequently their helicity status are reversed. In the case where Charybdis is off,the final result is then : For h+ labeled events with lambda/2 plate being "in" and h- labeled events with lambda/2 plate being "out",the upper rear counters have the higher count rate. Reversing the sense of one of the two components lambda/2 plate "in" or "out" h label "+" or "-" and leaving the other unchanged reverses the sign of the measured asymmetry. This can be expressed in the following formula : [1] l * h = sign Here l = +1 for lambda/2 plate "in" and -1 for "out" h = +1 for h+ events and -1 for h- events If sign = 1,the upper rear counters have the higher count rate. If sign = -1,the lower rear counters have the higher count rate. 2. The sense of rotation of the polarization vector in Charybdis. When the neutrons transverse the field of Charybdis,their polarization vector is rotated, mixing the sideways and longitudinal components. The sens of rotation depends on the orientation of the field. The polarity of the power supply can be "proton polarity" or "electron polarity". In the first case the corresponding EPICS variable shows a + sign and in the second case a - minus sign. Note that the signs of the shunt readings are opposite to this ! It has been established by measurement that for "proton polarity" the field in Charybdis is pointing upwards [5]. In this case protons emerging from the target are deflected to the right and their polarization vector is spinning clockwise when looking from above. Consequently the neutron polarization vector is spinning counterclockwise.With the preceding results the sign of the asymmtry in NPOL can be calculated. 3. The sign of the measured asymmetry in NPOL for Charybdis "on". In the following it is assumed, that the precession angles are always larger than arctan(Px/Pz), which means that the polarization vector can flip over. At this particular angle (about 11 degrees in the Galster parametrisation, nearly independent of Q**2 ) the sideways component is zero. Under this assumption the results of 1. and 2. can be summarized in : For Charybdis being in "proton polarity" the upper rear counters have the lower count rate for positive helicity events. Since reversing the sense of the Charybdis field - "proton" or "electron" polarity - will change the sign of the measured asymmetry in NPOL,the formula [1] can be expanded to : [2] c * l * h = sign Here c = +1 for "proton polarity" and c = -1 for "electron polarity" If sign = +1, the upper rear counters have the lower count rate. If sign = -1, the upper rear counters have the higher count rate. The results in 1. and 3. have been deduced for the runs taken in November 2000. They remain valid also for other run periods,provided the corresponding Moller measurements give a positive polarization when the lambda/2 plate is "in". References [1] G.G. Ohlsen, P.W. Keaton : Techniques for measurement of spin1/2 and spin 1 polarization tensors in NIM 109 (1973) 41 G.G. Ohlsen : Polarization transfer and spin correlation experiments in nuclear physics in Rep. Prog. Phys. 35 (1972) 717 [2] R.G.Arnold, C.E.Carlson,F.Gross : Polarization transfer in elastic electron scattering from nucleons and deuterium in PR 23 (1981) 363 [3] R.Madey, A.Semenov : Improvement in the Polarimeter Efficiency by Adding a Third Layer of Detectors to Each of the Rear Arrays, Report of the Gen-Collaboration [4] T.Reichelt : The determination of the electron helicity in the Hall C beamline via Moller scattering, Report of the Gen-Collaboration [5] Two independent measurements were made with the same result, see HCLOG # 34 650 of March 17th and # 34 771 of March 21st