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

Bacher, A.D.

Betker, A.C.

Black, T.C.

Choi, S.

Franklin, W.A.

Jiang, K.

Schmitt, W.M.

Sowinski, J.S.

Stephenson, E.J.

Wissink, S.W.

Yu, C.

English

IUScholarWorks

NUCLEON-NUCLEON AND FEW-BODY STUDIES 
A COMPLETE SET OF IN-PLANE SPIN-TRANSFER COEFFICIENTS 
FOR SMALL ANGLE pp ELASTIC SCATTERING AT 200 MeV 
W.A. Franklin, S.W. Wissink, A.D. Bacher, A.C. Betker, T.C. Black, 
S. Choi, K.Jiang, W.M. Schmitt, J.S. Sowinski, E.J. Stephenson, and C. Yu 
Indiana University Cyclotron Facility, Bloomington, Indiana 4 7408 
Current potential models1 of the nucleon-nucleon (NN) interaction can describe much 
of the low- and intermediate-energy NN scattering database with a X 2  per datum fairly 
close to 1. In spite of these successes, however, there remains significant controversy over 
the value of one of the most fundamental parameters in such models, the pion-nucleon 
coupling constant g:. Difficulties encountered initially in reproducing both the pp scat- 
tering data and the ground-state properties of the deuteron2 led to speculation as to 
whether this coupling could be strongly charge-dependent.3 Though later analyses of the 
NN (both pp and np) (Ref. 1) and ?rN (Ref. 4) data showed no clear signature for charge- 
dependence, the large value for gZk extracted in a recent study of the np cross section at 
back angles5 has only served to muddy the waters further. An additional complication, 
and one whose severity is difficult to gauge, arises from the fact that those who model 
the interaction have generally employed different criteria for data selection, different con- 
ventions for renormalizing data sets, and have emphasized different energy ranges in their 
analysis. Thus, discrepancies at the few percent level for remain, even when only pp 
scattering is ~onsidered.~ 7' 
On the experimental side, while it is clear that some of the existing data must be in 
error ( e.g., when two measurements of nominally the same quantity differ by 4 or 5 standard 
deviations), it is also true that some of the most critical kinematic regimes remain relatively 
unexplored. Detailed analysis and simulations have shown7v8 that precise knowledge of a 
specific set of spin observables, over the kinematic region where single pion exchange should 
dominate the hadronic interaction (q 0.3-0.8 fm-' ) , can provide significant constraints 
on the value of g:. To identify these observables, we note that in a momentum-space 
representation, the first-order potential for the exchange of a pseudo-scalar particle takes 
the form:' 
where MN is the (average) nucleon mass and ak is the Pauli spin matrix for the kth 
nucleon. By measuring an appropriate combination of spin-transfer observables, one can 
isolate that component of the NN interaction which exhibits a spin-longitudinal structure 
identical to that found in Eq. (1). Explicitly, this component - the "6" amplitude in the 
KMT form~lation, '~ for example - can be expressed in the following model-independent 
manner: 
In conjunction with the DNN1 data measured recently at IUCF," the measurements de- 
scribed here constitute a robust set of high precision data that will allow us to map out 
the momentum-transfer dependence of the S amplitude in a regime where it is expected to 
be changing rapidly, due largely to single pion exchange. 
Data for experiment E383 were acquired in three runs during 1995-96. Measurements 
of the lab-frame observables DLLl, DLs/, DSLl, and Dss/ were completed at 5 angles 
( B l a b  x so, 7.5", lo0 ,  12", and 15"), at an average beam energy of 197.9 MeV. The ba- 
sic measurement involved the scattering of protons, whose polarization vector had been 
precessed to lie in the (horizontal) reaction plane, from a thin CH2 foil target. The higher- 
energy, forward-going protons were momentum analyzed with the K600 spectrometer and 
focal plane detectors, and their sideways polarization components determined using elas- 
tic scattering from natural carbon in the focal plane polarimeter (FPP). The low-energy 
recoil protons were detected with a thin (500 pm) stopping silicon microstrip detector 
located inside the scattering chamber. No coincidence requirement between the protons 
was imposed in hardware, so that a 'singles' analysis of the focal plane data, after suitable 
background subtraction, was possible. This detection scheme, developed during the DNN/ 
measurement," is a very effective way to eliminate background. 
Because the K600 is a horizontal-bending device, the in-plane polarization components 
of the scattered protons precess in the spectrometer's magnetic field. Taking this into 
account, the measured FPP asymmetry (i. e., the yield asymmetry between protons that 
scatter downward or upward in the FPP analyzer) can be expressed in the following form: 
E ~ p p  = AFPP (pL sin a D L p  + p~ sin a. DSLI + p ~ ,  cos a DLSI + ps  cos a Dssl) , (3) 
where pr, and ps  are, respectively, the longitudinal and sideways components of the beam 
polarization, and a is the angle of spin-precession experienced by the scattered protons 
within the spectrometer. In order to isolate the individual spin-t ransfer coefficients, it 
is clear from Eq. (3) that one must be able to vary both the direction of the incident 
beam polarization and also the degree of spin precession for the outgoing protons. The 
former was effected through use of the two high-energy beamline solenoids, while the latter 
entailed making measurements under essentially identical conditions, but with the K600 in 
either its (usual) medium-dispersion configuration or in its newly developed low-dispersion 
mode of operation.12 By pushing the ratio of field strengths in the two main K600 dipoles 
to the extremes of their acceptance limits for each configuration, changes in a of close to 
90" were achieved. The considerable effort required to switch from one configuration to 
the other, which involves moving the entire FPP apparatus, dictates that the needed data 
be taken over several different running periods. 
The experiment was designed to minimize sensitivity to most systematic errors, so the 
statistical uncertainty in each data point (typically f 0.01) should be the dominant source 
of error. For these particular measurements, we are also aided by the fact that parity 
conservation forbids any induced in-plane polarization in the nuclear scattering, so that 
a spin 'flip' at the ion source results in an exact reversal of the in-plane polarization at 
the K600 focal plane. This allows us to use a cross-ratio technique to calculate the FPP 
asymmetries, thereby cancelling most geometric or spin-dependent false asymmetries to all 
orders.13 We also benefit from the recent precise determination of AFPP, the effective ana- 
lyzing power of the FPP, over the energy range of interest,14 although we have carried out 
additional checks of this calibration, including several tests the FPP in its low dispersion 
location. 
The presence of carbon in our primary target provides several other features useful 
for control or monitoring of systematic error. Perhaps most importantly, the location of 
the p + 'H peak relative to the discrete p + 12C states in the K600 focal plane allows us 
to determine the absolute scattering angle to within a few hundredths of a degree. Due 
to the strong angular dependence exhibited by some of these observables, this level of 
accuracy is crucial. Of all the l2 C states, the elastic peak is of particular interest, in that 
the spin observables for this state must adhere to certain constraints,13 which serves to 
further check the consistency of our analysis. Finally, we note that one complication for 
in-plane spin-transfer studies is that the precession of the scattered-proton polarization in 
the magnetic fields of the K600 must be accurately determined. Details on measurements 
we have carried out for this purpose are provided in another article in this report.15 
In Fig. 1 we present our preliminary (on-line) results for all of the pp observables 
studied here. The error bars represent statistical uncertainties only. Based on our expe- 
rience with analysis of previous pp measurements, we expect that the data points could 
move up or down by as much as 2-3 standard deviations in the final analysis, so it would 
be premature to make detailed comments on the implications of these data for particular 
models or phase-shift solutions at this time. On the other hand, we believe that the size of 
our final error bars (statistical plus systematic contributions) should not differ significantly 
from those shown here. If so, these data should provide a means of discriminating among 
different predictions, for example, for the observable DLL1 , which is expected7 t heoreti- 
cally to be most sensitive to the value of g$ Towards this end, analysis of the present 
forward-angle data (E383) is continuing, and measurements that will extend the data sets 
to larger angles (E397) have been scheduled for the summer of 1996. 
1. V.G.J. Stoks et al., Phys. Rev. C 49, 2950 (1994). 
2. R. Machleidt and F. Sammarruca, Phys. Rev. Lett. 66, 564 (1991); R. Machleidt and 
G.Q. Li, ?rN Newsletter 9, 37 (1993). 
3. A.W. Thomas and K. Holinde, Phys. Rev. Lett. 63, 2025 (1989). 
4. R.A. Arndt et al., Phys. Rev. Lett. 65, 157 (1990). 
5 .  T.E.O. Ericson et al., Phys. Rev. Lett. 75, 1046 (1995). 
6. V. Stoks and J.J. de Swart, Phys. Rev. C 47, 761 (1993). 
7. D.V. Bugg and R. Machleidt, Phys. Rev. C 52, 1203 (1995) 
8. D.V. Bugg, private communication. 
9. R. Machleidt, in Advances in Nuclear Theory, Vol. 19, eds. J.W. Negele and E. Vogt 
(1989) p. 189. 
10. A.K. Kerman, H. MacManus, and R.M. Thaler, Ann. Phys. 8, 551 (1959). 
11. S.M. Bowyer et al., IUCF Sci. and Tech. Rep., May 1993 - April 1994, p. 3; S.M. 
Bowyer, Ph.D. thesis, Indiana University (unpublished), 1994. 
E383 Preliminary Data 
\ :h - 
\ ..' * 
---- Nijm I 
------- Arndt SP94 
............ Arndt C200 \ .' 
Figure I .  Preliminary results from analysis of experiment E383, and predictions from 
current potential models and partial-wave analyses. The long-dashed line represents the 
Nijmegen I potential, while the short-dashed and dotted lines correspond to Arndt's multi- 
energy (0-1.6 GeV) and local energy (175-225 MeV) phase shift solutions. 
12. W.A. Franklin et al., IUCF Sci. and Tech. Rep., May 1994 - April 1995, p. 185. 
13. S.W. Wissink et al., Phys. Rev. C 45, R504 (1992). 
14. S.M. Bowyer et al., in Proc. 1l th Int. Syrnp. on High Energy Spin Physics, eds. K.J. 
Heller and S.L. Smith (AIP, NY, 1995)) p. 152. 
15. W.A. Franklin et al., "Precise Determination of Proton Spin-Precession Angles in the 
K600 Spectrometer and Beamline," contribution to this report. 


A Complete Set of In-plane Spin-transfer Coefficients for Small Angle pp Elastic Scattering at 200 MeV

https://scholarworks.iu.edu/dspace/bitstream/2022/329/1/iucf1995-96_03-06.pdf

A Complete Set of In-plane Spin-transfer Coefficients for Small Angle pp Elastic Scattering at 200 MeV

Abstract

Similar works

Full text

Available Versions

IUScholarWorks