This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Bacher, A.D.

Li, P.

Lisantti, J.

Olmer, C.

Opper, A.K.

Sawafta, R.

Schwandt, P.

Sowinski, J.

Stephenson, E.J.

Wells, S.P.

Wissink, S.W.

English

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ELASTIC SCATTERING 
PRECISE DETERMINATIONS O F  PROTON ANALYZING POWERS 
FOR 180-200 MeV ELASTIC SCATTERING ON 12C AND 4He 
S.W. Wissink, A.D. Ba.cher, P. Li, J. Lisantti, C. Olmer, A.K. Opper, R. Sawafta, 
P. Schwandt, J .  Sowinski, E.J. Stephenson, and S.P. Wells 
Indiana Univer~ity Cyclotron Facility, Bloomington, Indiana 4 7405 
Measurements of reaction analyzing powers (and recently other spin observables as 
well) frequently achieve statistical accuracies significantly smaller than their corresponding 
systematic uncertainties. These latter effects aze due largely to lack of precise knowledge 
of the incident beam polarization, either in absolute terms or even in a, relative sense, 
i.e., from one measurement to the next. Though recent progress in the development of 
in-beam high-energy polarimetry' has greatly iniproved one's a.bility to monitor these 
relative fluctuations, such devices must be calibrated against a well-determined analyzing 
power standard, few of which exist in the intermediate energy regime. Double-scattering 
experiments provide such information in principle, though in practice the method is subject 
to many sources of uncertainty, both statistical and ~ys t e rna t i c .~ -~  
We have employed another technique, previously unused at intermediate energies, 
which relies on the quadratic relationship that exists among three of the polarization 
observables in f + 0 t $ + 0 spin configuration reactions, namely 
(In this case, it is also true that P = Ay, DNNl = 1, DLLl = DSS1 and DSLr = -DtSl). 
By choosing kinematic regimes (bombarding energies and scattering angles) where Ay is 
known to approach f 1, one can then determine Ay very accurately through much less 
precise measurements of DLL1 and DsLl, which become very small. This can be seen more 
clearly by rewriting the above relation as 
As an example, if DLLl and DsLr are both measured to be 0.05 f 0.02, then in this case 
lAyl = 0.9975 f 0.0014. 
In addition to this reduction in the statistical error, because one is using a nullmethod, 
i.e., searching for small asymmetries rather thaa large ones, sensitivities to many potential 
sources of systematic error are also minimized as lAyl a,pproaches 1. Accurate knowledge 
of the magnitude of the beam polarization is not needed to determine a zero-crossing; 
uncertainties in the effective analyzing power of the focal plane polarimeter become less 
important for the same reasons. Possible error due to spin-dependent dead-time correc- 
tions also disappear, as counting rates beco~ne comparable for all in-plane spin orienta- 
tions. It is also important to realize that a spin-flip at the polarized ion source results in 
an exact spin-reversal of the in-plane polarization components even at  the  ~pectrometer 
focal plane, i.e., after a nuclear scattering. The focal plane polarimeter thus functions as 
a true double-arm polarimeter, so standard analysis techniques can be employed to elim- 
inate sensitivity to all instrumental asymmetries to at least first-order. Previous detailed 
calibration measurements5 for the normal (vertical) polarization, however, have shown no 
evidence for such asymmetries for this device. 
To make these measurements most useful for beam polarization and cross-calibration 
checks, we have chosen targets that axe easy to obtain and handle, and reactions with 
large cross sections in angle ranges where Ay is known to be close to f 1. Proton elastic 
scattering near Tp = 200 MeV on 4He and 12C satisfies all these requirements. Moreover, 
the use of lighter nuclei results in relatively slowly varying angular distributions tha.t do 
not impose severe restrictions on the angular resolution of the detector system, and allows 
for easy separation of the elastic peak of interest from those due to contaminent nuclei in 
the target material. The resolutiorl constraints are therefore minimal and no background 
subtraction is required, thus removing any possible ambiguities in the extraction of peak 
yields. 
Precise measurements of DLLl and DSLr for proton elastic scattering have now been 
completed at incident proton energies of ZOO, 190, and 180 MeV for 12C and at 180 MeV 
for 4He. At each energy, complete sets of measurements were made at three angles (in 1" 
steps) that spanned the region where A, was a maximum. These data were the first mea- 
surements of in-plane polarization transfer observables taken with the K600 spectrometer 
system, and extensive calibration procedures for this experiment (E290) were integrated 
directly into the in-plane measurements ,' thus ensuring, for example, that the effective 
analyzing power assumed for the focal plane polarimeter was determined using the same 
beam energy, spectrometer angle calibration, and analysis software as were used for the 
actual measurements. Preliminary results for the 12C data are presented in Figure 1. 
The most interesting results were obtained for p + 12C scattering at -190 MeV, where 
optical model calculations7 suggested that Ay should be very close to 1. After completing 
our first round of off-line event replay at this energy, our best determination of Ay at 8,, 
= 19.0" ( B l a b  = 17.3") at Tp = 188.9 MeV yields a value of Ay = 0.99963+:::::?ji. This 
error includes both statistical uncertainties and our best estimates of systematic contribu- 
tions that arise due to lack of precise knowledge of the beam polarization magnitude and 
orientation and the effective analyzing power of the K600 focal plane polarimeter. 
Determinations of A, at other energies and angles have correspondingly larger un- 
certainties as the analyzing power decreases from unity. In addition, the DLtr and DsLl 
values shown for 200 and 180 MeV are the on-line results for only two of the three angles 
measured, and represent only about 30-40% of the total data collected. It is significant 
nonetheless that the energy dependence is rather smooth, as suggested by the solid lines 
in Figure 1. Continuity arguments would therefore require that at an energy somewhaA 
below 189 MeV the locus of DLLt and DSL1 values will cross the origin; at that energy 
there will necessarily be an angle (near 0,, = 19.0") at which Ay is identically equal to 1. 
Our goal for this work is to map out a region in scattering angle and bombarding 
energy over which Ay is known absolutely to within several tenths of a percent. This 
information can then be used to cross-calibrate other devices, e.g., one could compare the 
leftlright asymmetry seen in an in-beam polarimeter to the spin-uplspin-down asymmetry 
measured simultaneously in the K600 spectrometer when operating within this energy and 
angle grid. The 4He results in particular should prove useful for normalization of earlier 
p-p analyzing power data8 in which both helium and hydrogen gases were used during 
data acquisition. 
Figure 1. Preliminary results of DLL1 and DSLt measurements for p + l2 C elastic scattering 
at 200, 190, and 180 MeV. The solid lines are meant only to guide the eye to suggest the 
energy dependence of the curves. The dashed circles indicate contours of Ay = 0.96, 0.98, 
0.99, 0.995, and 0.999 as one moves towards the origin. 
1. A.K. Opper et al., IUCF Scientific and Technical Report (1988) p. 89. 
2. M. W. McNaughton, Proceedings of the 5th International Symposium on Polarization 
Phenomena in Nuclear Physics. (Sa.nte Fe, 1980), AIP Conf. Proc. Vol. 69, p. 818. 
3. M. Clajus et al., Nucl. Instr. Meth. A281, 17 (1989). 
4. P.D. Eversheim et al., Phys. Lett. B 234, 253 (1990). 
5. E.J. Stephenson et aL, IUCF Scientific and Technical Report (1988) p. 94. 
6. S.W. Wissink et al., Experimental Facilities Development - K600 Spectrometer FPP, 
IUCF Scientific and Technical Report, May 198-April 1990. 
7. P. Schwandt , private communication. 
8. J. Sowinski et al., IUCF Scientific and Technical Report (1986) p. 11. 


Precise Determinations of Proton Analyzing Powers for 180-200 MeV Elastic Scattering on 12-C and 4-He

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Precise Determinations of Proton Analyzing Powers for 180-200 MeV Elastic Scattering on 12-C and 4-He

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