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The 3He spin analysing power of 27 MeV protons
Nuclear Physics A242 (1975) 309--316; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
T H E 3He S P I N A N A L Y S I N G P O W E R O F 27 MeV P R O T O N S * R. H. WARE, W. R. SMYTHE and P. D. INGALLS ,t Nuclear Physics Laboratory, Department of Physics and Astrophysics, University of Colorado, Boulder, Colorado 80302, USA Received 27 December 1974 Abstract: The aHe spin analysing power of hydrogen (protons) has been measured at a c.m. energy of 20 MeV at 14 c.m. angles from 40 ° to 160°. The measurement of aHe target polarization was calibrated by measuring the aHe spin analysing power of 4He at an energy and angle where it was --1.00. The proton-aHe differential elastic scattering cross section is also reported at a c.m. energy of 20.0 MeV for 36 c.m. angles from 20° to 170°. E I"
NUCLEAR REACTIONS 3He(p, p), E = 27 MeV; measured Pa(O), tr(0). Polarized
/
target.
1. introduction The elastic scattering of protons by 3He nuclei has received considerable attention in recent years. A general review of studies of the four-nucleon system has recently been published by Fiarman and Meyerhof t), which includes a summary of studies o f the p-aHe system. A phase-shift analysis o f p-3He scattering in the 4-11 MeV range was published by Baker, McSherry and Findley 2) in 1969, which placed further constraints on the phase-shift parameters published earlier by Morrow and Haebedi 3). This analysis included measurements of cross section, proton polarization, aHe polarization and a spin correlation parameter. In 1971, Baker et al. 4) reported a phase-shift analysis of cross-section, proton and 3He polarization, and spin correlation data near 19.4 MeV which was consistent with the analysis at lower energies. A subsequent unpublished phase-shift analysis by Morales-Pena 5) employing some additional cross-section and proton polarization data at higher energies extended p-aHe phase-shift values to 35 MeV. This paper reports measurements of the 3He spin analysing power of protons, denoted by P3, for 14 angles at a proton energy of 26.8 MeV, and measurements o f the differential elastic scattering cross section at 26.7 MeV. These data should help to further refine the phase-shift parameters in this energy region. Also reported are seven measurements of the 3He spin analysing power of alpha particles near an alpha energy of 15.5 MeV and a laboratory scattering angle of 47 °. t Work supported in part by the US Atomic Energy Commission. ,t Present address: California Institute of Technology, Pasadena, California, 91109 USA. 309
310
R.H. WARE et al.
These data were used to calibrate the 3He target polarization 6) and may also be useful to further refine the phase-shift parameters calculated by Hardy et al. ~) for 4He-aHe scattering. All uncertainties reported which are not otherwise labeled are standard errors (67 ~ confidence limits).
2. The experimental method The experimental arrangement consisted of a sealed 3He gas target located in a nonmagnetic scattering chamber with a plexiglass top which allowed the infrared, circularly polarized optical pumping light to irradiate the target. A vertical, 3 Gauss magnetic field was provided by a 1 m diameter Helmholtz coil pair. The direction of the 3He polarization could be changed from down to up by rotating a quarter wave plate by 90 ° which changed the pumping light from right hand to left hand circular polarization. Scattered particles were detected by two identical solid state E - A E detector telescopes located symmetrically on opposite sides of the beam in the horizontal plane. The polarized 3He target consisted of a 10 cm diameter pyrex glass bulb, which was cleaned with a 4He r.f. discharge, evacuated, refilled with aHe to a pressure of 4 Torr, and then sealed by fusing its pyrex filling tube. The beam entrance and exit windows consisted of 4 pm thick Havar foils t sealed to the ends of the 8 mm pyrex tube from which the target sphere was blown. The observed scattered particles excited either through the thin glass walls (0.2 ram) or through windows each consisting of Havar foil sealed with a low vapor pressure epoxy ,t to cover a rectangular hole cut in the glass sphere with a micro-sand-blaster. It was important to target lifetime to locate the sealing epoxy so that it had a minimum area exposed to the aHe and so that it was shielded as much as possible from bombardment by charged particles. Typically a target would withstand 0.1 C of 27 MeV protons or 0.005 C of 16 MeV alphas before its polarization began to decrease due to impurity release. Normally one or two data points were determined before a new target had to be employed. Additional target construction details are available elsewhere s). Target polarizations of 5 to 16 ~o were achieved and measured by optical pumping methods described by Colgrove et al. 9). The measurement uses an equation for the absorption of light by the 3He metastable atoms, which was reported by Baker et al. 2). The value of their parameter p was set equal to 0.02 and the polarization calibration experiment described below was used to determine the value o f their parameter f, for which a value of 0.80_+0.07 was obtained. The use of other initial choices o f p ranging from 0 to 0.056 with the corresponding value o f f chosen to agree with the calibration experiment resulted in a total variation in the polarization values of less than 4.5 ~ . t Hamilton Watch Co., Precision Metals Division, Lancaster, Pennsylvania 17604, USA. *t "Torr Seal", Varian Associates, Palo Alto, California.
3He(p, p)
311
Beams of protons and alpha particles from the University of Colorado cyclotron were energy analysed by a bending magnet whose magnetic field was measured by nuclear magnetic resonance, and which had been calibrated by time-of-flight techniques. Beam energies quoted refer to the energy at the centre of the target and are uncertain by 0.3 70 or less. Proton beam currents of up to 250 nA were used, but it was found to be necessary to limit the alpha particle beam current to a maximum of 100 nA. Higher alpha beam currents produced up to a 50 70 decrease in the target polarization. At 100 nA no such decrease was observed. The beam current was run through the target during the 15 min optical pump equilibrating time which preceded each run. Similar effects were not observed with the proton beam but presumably would occur at higher currents. Each detector telescope consisted of a pair of slits mounted in front of one or two solid state particle detectors. The contribution of multiple scattering in the target windows to the total angular resolution was significant and is included with the results. Scattered protons and recoil 3He from the polarized 3He target were detected by requiring a coincidence between a AE (100 pm) and an E (4500 pro) silicon detector. For the calibration experiment the scattered alphas and the recoil 3He nuclei were detected in each telescope by a single E (100 pm) silicon detector, and were identified by their energy. Signals from both telescopes were recorded simultaneously by routing the E or E+ AE signals to different 256-channel blocks of a Nuclear Data 50/50 pulse height analyser according to whether the event was in the left or the right telescope. The reduction of data for a measurement of the 3He spin analysing power for the case where the scattered protons were observed will be described. The other cases are similar. A set of data consists of one run with the target polarization up and one with it down. At least two independent sets of data were taken at each angle as a consistency check. The peak areas were determined and corrected for background by using a least squares Gaussian fitting computer program. The background correction to the peak area was always less than 5 %. If the net number of counts per microcoulomb in the left (right) telescope is denoted by L (R) and a superscript + ( - ) is added to indicate that the polarization is up (down), then the 3He spin analysing power P3 is given by:
1FL++R--L--R+ ] P3 -- P L Y + R -
+L- ~-~
'
where P is the polarization of the target and the Basel sign convention 1o) has been followed.
3. Target polarization calibration Previously, nuclear physicists using polarized 3He targets have depended on an optical absorption method of polarization measurement 9). The method involves the knowledge of certain transition probabilities, of the degree of circular polarization
312
R . H . W A R E et al.
of the light and of the spectral line shape o f the pumping light.The resulting uncertainty of the target polarization was typically 12 to 15 ~ o f the value. In recent work Plattner and Baeher 6) have pointed out the existence of certain points where the analysing power must pass through _ 1. F r o m phase-shift behaviour they indicate that for 3He-4He scattering such a point exists near 86 ° c.m. scattering angle and 15.3 MeV alpha laboratory energy. This point was used to cheek the calibration TABLE 1 Target polarization calibration data Lab energy (MeV)
Lab angle (deg)
c.m. angle (deg)
c.m. A0 (deg)
aHe spin analysing power (~o)
Target polar. (~o)
15.20 15.31 15.58 15.75 15.75 15.75 15.75
47.0 47.0 47.0 50.0 47.0 45.5 44.0
86.0 86.0 86.0 80.0 86.0 89.8 92.2
4.4 4.3 4.2 4.4 4.1 3.8 3.6
--79.54-3.3 --85.04-3.0 --78.04-8.6 --76.64-2.9 -- 85.5 4- 3.0 --100.04-4.4
7.6 4-0.1 11.7 4-0.1 5.0 4-0.1 12.8 4-0.02 12.60 4-0.05 12.8 4-0.1 12.8 4-0.2
--95.64-8.3
Measured values of the spin analysing power P observed when alpha particles are scattered from the polarized 3He target are listed. The observed particles are recoil 3He nuclei. The values of target polarization as determined by optical absorption measurement have been corrected to adjust the spin analysing power at 45.5° from --1.02 to --1.00, thus calibrating the target polarization. A 5 ~o systematic probable error is estimated for this calibration.
T
i Ea =15.75 MeV tY
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O
-O.9
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z ,¢[ z
-or
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-0.6
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35
40
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t
50
55
SHe-RECOIL LAB ANGLE (DEGREES)
152
t
15.4
15.6
15.8
ALPHA LAB ENERGY (MeV)
Fig. I. The search for the polarization calibration point. Measured values o f spin analysing power o f SHe-4He elastic scattering are shown. A four-point angular distribution at 15.75 MeV is shown on the left and an excitation function at a SHe recoil angle o f 470 is shown on the right. Plattner and Bacher 6) predicted that the analysing power passed through --1 near the point marked by arrows. The curves are drawn through points taken from the contour map produced by Hardy e t al. 7) from phase-shift data, The angular distribution point at 45.5 ° wasused as the calibration point.
3He(p, p)
313
o f the polarized target. The results of two four-point searches, one each in energy and angle, about the predicted point are listed in table 1 and plotted in fig. 1. The topography of the region has been generally described by H a r d y et al. 7) in a contour plot calculated f r o m phase shifts. The present results confirm the energy independence o f spin analysing power in this region and suggests that the m a x i m u m occurs at a slightly larger c.m. angle than was predicted. Unfortunately, data could not be taken on the small laboratory angle side of the maximum, due to the temporary unavailability o f very thin particle detectors to do the particle identification which became necessary as the SHe and 4He peaks began to overlap. Future experimenters should have no trouble remedying this defect and achieving better definition of the m a x i m u m in analysing power. In spite of this shortcoming, it is felt that confidence in the polarization calibration is increased to the point where the polarization uncertainty is reduced to 5 ~ of the value, after adjusting the parameters to normalize the polarization to - 1 . 0 0 at the 45.5 ° point. This renormalization involved increasing the optically measured target polarization value by only 2 ~ , so the agreement of the two methods is excellent. 4. Proton-SHe elastic scattering To facilitate future phase-shift analyses, the proton-3He differential elastic scattering cross section also was measured at a proton laboratory energy of 26.70-t-0.05 MeV at c.m. angles between 20 ° and 170 °. The magnetically analysed proton b e a m TABLE2 Centre-of-mass differential elastic scattering cross section for 26.70 MeV protons incident on aHe c.m. angle (deg) 20.1 23.4 26.7 30.0 33.3 36,6 39.8 46.3 52.6 58.9 65.1 71.2 77.1 82.9 88.6 94.1 99.5 104.7
d~ ~ (mb/sr) 114 120 116 110 105 97.2 91.0 73.9 59.8 48.4 37.2 27.7 21.2 15.8 11.8 8.56 6.18 4.45
c.m. angle (deg) 109.8 112.3 114.7 117.1 119.5 124.1 128.5 132.8 137.0 141.1 145.0 148.8 152.5 156.2 159.7 163.2 166.6 170.0
The probable error in cross section is 3 ~. and the angular resolution is 2.6 ° c.m.
d~ ~_Q (mb/sr) 3.21 2.89 2.54 2.37 2.32 2.57 3.20 4.28 5.91 7.79 10.0 12.6 15.2 17.9 20.6 23.2 25.6 26.8
TABLE 3 Values of the aHe spin analysing power of hydrogen, P a , measured with 26.8 MeV protons incident on a polarized aHe target Lab angle (deg)
c.m. angle (deg)
c.m. A0 (deg)
aHe spin analysing power (~o)
Observed particle
Exit window
Target polar. (~o)
30 40 50 60 70 80.4 90.2 100.5 109.5 114.4 120 130 140 150 38 a)
39.81 52.64 65.11 77.12 88.60 99.93 110.01 119.94 128.11 132.34 137.03 145.01 152.54 159.72 50.04
1.2 2.4 2.5 2.7 2.7 2.7 2.8 2.9 2.9 2.9 3.3 3.3 0.95 0.91 1.3
--5.84-1.8 --7.64-1.2 --13.1~:1.6 --15.94-3.1 --19.24-1.4 --18.54-2.8 --12.54-2.2 20.84-3.4 34.44-2.8 31.94-2.5 25.24-4.5 21.54-2.6 10.94-1.6 7.7d:1.5 --6.84-1.1
p p p p p 3He aHe aHe 3He 3I-Ie p p p p p
Havar glass glass glass glass Havar Havar Havar Havar Havar glass glass Havar Havar Havar
10.54-0.1 16.54-0.9 16.44-0.1 16.54-0.5 14.14-0.2 9.24-0.6 10.24-0.1 10.54-0.1 9.94-0.2 10.24-0.1 10.34-0.7 12.04-0.2 13.24-0.3 13.24-0.6 14.34-0.3
The sign of Pa is in accordance with the Basel convention lo). The c.m. angular resolution ./tO includes the effect of multiple scattering in the exit window. The particle detected and the window through which it passed are listed in the fifth and sixth columns. The error associated with P3 does not include the 5 ~o target polarization calibration uncertainty. =) Value measured at 19.4 MeV. I000
I
u
~
1
E
[
1
l
°e°°oe o
I00 b..
E
•
~
b "u
•
• oo°
• 10
I
•
f
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I
[
[
I
n
20
40
60
80
I00
\.. I
120
I
140
I
160
180
CENTRE OF MASS ANGLE (DEGREES)
Fig. 2. Centre of mass proton-aHe elastic scattering cross section, at 20.0 MeV c.m. energy. The data were obtained by observing the scattering of 26.70 MeV protons from a sealed target containing aHe gas. The data point size is larger than the probable error for all points.
SHe(p, p)
.6
315
~; PRESENT EXP. 26,8MeV
.5
BAKER, et ol. 19.4 MeV
•
MeV
.4 Q2 M.I
.3
o o_
.2
z O3
\
.I 0
z
-.I
25.0 MeV
z 0O3 -f-
-.2 -.3 -.4 -.5
-.6 0
i
i
i
i
20
40
60
80
i
I00
i
120
i
140
i
160
180
c.m• SCATTERING ANGLE (DEGREES)
Fig. 3. The aHe spin analysing power of protons• The values measured with 26.8 MeV protons are s h o w n with the values which Baker et aL 4) obtained at 19.4 MeV for comparison. Only statistical errors are shown. Not included is an additional systematic contribution of 12 ~o (19.4 MeV) and 5 ~ (26.8 MeV) from uncertainty in the target polarization. Experimentally there is no difference Jn the analysing power at the two energies• The two smooth curves are predictions by Morales-Pena 5) for 25 and 27.5 MeV protons calculated from his phase-shift analysis of scattering data.
from the cyclotron was focussed on a sealed 3He gas target of a type previously • lescribed 11). Scattered protons defined by a slit system were detected and identified by an E - A E pair of solid state detectors. The cross-section values have been assigned a probable error of 3 ~o, which is derived by combining the following contributions in quadrature: geometry measurement (1.5 ~o), counting statistics and background .correction (1 ~o), beam current integration (1 ~), beam alignment (1 ~o), target gas density (0.7 ~o), detector et~ciency correction 12) of 1.3 ~ (0.5 ~), 3He gas purity •correction of 0.5 ~o (0.5 ~o), geometric corrections for finite beam and aperture :size 13) 0.12 ~ and the beam heating effect 14) was estimated to be less than 1 ,(1 ~). The results are given in table 2 and shown in fig. 2. 5. The SHe spin analysing power of protons: results and discussion The measured values of the 3He spin analysing power of protons (P3) at a c.m. .energy of 20.0 MeV are listed in table 3. These data were obtained with 26.8 MeV protons incident on a polarized 3He target. As a check against possible systematic errors P3 was also measured at 0 .... = 50° at a proton lab energy of 19.4 MeV, where P3 had previously been measured by Baker et aL 4). Although this is not a severe test because the measured analysing power is so small ( - 0 . 0 6 8 _ 0.011), it is in good .agreement with the previous measurement ( - 0.079-t- 0.010).
316
R . H . W A R E et aL
The experimental values of the 3He spin analysing power obtained at 26.8 MeV are identical, with experimental error, to those obtained at 19.4 MeV by Baker et al. This apparent energy independence may be accidental. Morales-Pena 5) has carried out a phase-shift analysis of existing data on the p-3He system from 18 MeV to 57 MeV. Although he had no 3He spin analysing power data above 19.4 MeV, he has predicted the 3He spin analysing power at proton lab energies of 25.0 MeV and 27.5 MeV. His predictions, together with the present 26.8 MeV results, are shown in fig. 3. It can be seen that his work predicts a strong variation with energy between 25 and 27.5 MeV. The experimental points at 26.8 MeV fall between his two predictions at back angles where the analysing power is large, and show a larger analysing power than either of his predictions at forward angles where the analysing power is small. While the present measurements cannot be said to violently disagree with his predictions, if they are taken together with the 19.4 MeV data there is a strong suggestion that the energy dependence may not be as pronounced as he suggests. Only additional measurements can resolve this question. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14)
S. Fiarman and W. E. Meyerhof, Nucl. Phys. A206 (1973) 1 S. D. Baker, D. H. McSherry and D. O. Findley, Phys. Rev. 178 (1969) 1616 L. W. Morrow and W. Haeberli, Nucl. Phys. A126 (1969) 225 S. D. Baker, T. A. Cahill, P. CatiUon, J. Durand and D. Garreta, Nucl. Phys. AI60 (1971) 428 J. R. Morales-Pena, Ph.D. thesis, Univ. of California (Davis) 1970 G. R. Plattner and A. D. Bacher, Phys. Lett. 36B (1971) 211 D. M. Hardy, R. J. Spiger, S. D. Baker, Y. S. Chen and T. A. Tombrello, Phys. Lett. 31B (1970) 355 R. H. Ware, Ph.D. thesis, Univ. o f Colorado, 1974 F. D, Colegrove, L. D. Schearer and G. K. Walters, Phys. Rev. 132 0963) 2561 Basel convention, Helv. Phys. Acta, Suppl. 6 0961) 436 T. R. King and R. Smythe, Null. Phys. A183 0972) 657 T. R. King, J. J. Kraushaar, R. A. Ristinen, R. Smythe and D. M. Stupin, Nucl. Instr. 88 (1970) 17 E. A. Silverstein, Nucl. Instr. 4 (1959) 53 P. W. Allison and R. Smythe, Nucl. Phys. A121 (1968) 97
T H E 3He S P I N A N A L Y S I N G P O W E R O F 27 MeV P R O T O N S * R. H. WARE, W. R. SMYTHE and P. D. INGALLS ,t Nuclear Physics Laboratory, Department of Physics and Astrophysics, University of Colorado, Boulder, Colorado 80302, USA Received 27 December 1974 Abstract: The aHe spin analysing power of hydrogen (protons) has been measured at a c.m. energy of 20 MeV at 14 c.m. angles from 40 ° to 160°. The measurement of aHe target polarization was calibrated by measuring the aHe spin analysing power of 4He at an energy and angle where it was --1.00. The proton-aHe differential elastic scattering cross section is also reported at a c.m. energy of 20.0 MeV for 36 c.m. angles from 20° to 170°. E I"
NUCLEAR REACTIONS 3He(p, p), E = 27 MeV; measured Pa(O), tr(0). Polarized
/
target.
1. introduction The elastic scattering of protons by 3He nuclei has received considerable attention in recent years. A general review of studies of the four-nucleon system has recently been published by Fiarman and Meyerhof t), which includes a summary of studies o f the p-aHe system. A phase-shift analysis o f p-3He scattering in the 4-11 MeV range was published by Baker, McSherry and Findley 2) in 1969, which placed further constraints on the phase-shift parameters published earlier by Morrow and Haebedi 3). This analysis included measurements of cross section, proton polarization, aHe polarization and a spin correlation parameter. In 1971, Baker et al. 4) reported a phase-shift analysis of cross-section, proton and 3He polarization, and spin correlation data near 19.4 MeV which was consistent with the analysis at lower energies. A subsequent unpublished phase-shift analysis by Morales-Pena 5) employing some additional cross-section and proton polarization data at higher energies extended p-aHe phase-shift values to 35 MeV. This paper reports measurements of the 3He spin analysing power of protons, denoted by P3, for 14 angles at a proton energy of 26.8 MeV, and measurements o f the differential elastic scattering cross section at 26.7 MeV. These data should help to further refine the phase-shift parameters in this energy region. Also reported are seven measurements of the 3He spin analysing power of alpha particles near an alpha energy of 15.5 MeV and a laboratory scattering angle of 47 °. t Work supported in part by the US Atomic Energy Commission. ,t Present address: California Institute of Technology, Pasadena, California, 91109 USA. 309
310
R.H. WARE et al.
These data were used to calibrate the 3He target polarization 6) and may also be useful to further refine the phase-shift parameters calculated by Hardy et al. ~) for 4He-aHe scattering. All uncertainties reported which are not otherwise labeled are standard errors (67 ~ confidence limits).
2. The experimental method The experimental arrangement consisted of a sealed 3He gas target located in a nonmagnetic scattering chamber with a plexiglass top which allowed the infrared, circularly polarized optical pumping light to irradiate the target. A vertical, 3 Gauss magnetic field was provided by a 1 m diameter Helmholtz coil pair. The direction of the 3He polarization could be changed from down to up by rotating a quarter wave plate by 90 ° which changed the pumping light from right hand to left hand circular polarization. Scattered particles were detected by two identical solid state E - A E detector telescopes located symmetrically on opposite sides of the beam in the horizontal plane. The polarized 3He target consisted of a 10 cm diameter pyrex glass bulb, which was cleaned with a 4He r.f. discharge, evacuated, refilled with aHe to a pressure of 4 Torr, and then sealed by fusing its pyrex filling tube. The beam entrance and exit windows consisted of 4 pm thick Havar foils t sealed to the ends of the 8 mm pyrex tube from which the target sphere was blown. The observed scattered particles excited either through the thin glass walls (0.2 ram) or through windows each consisting of Havar foil sealed with a low vapor pressure epoxy ,t to cover a rectangular hole cut in the glass sphere with a micro-sand-blaster. It was important to target lifetime to locate the sealing epoxy so that it had a minimum area exposed to the aHe and so that it was shielded as much as possible from bombardment by charged particles. Typically a target would withstand 0.1 C of 27 MeV protons or 0.005 C of 16 MeV alphas before its polarization began to decrease due to impurity release. Normally one or two data points were determined before a new target had to be employed. Additional target construction details are available elsewhere s). Target polarizations of 5 to 16 ~o were achieved and measured by optical pumping methods described by Colgrove et al. 9). The measurement uses an equation for the absorption of light by the 3He metastable atoms, which was reported by Baker et al. 2). The value of their parameter p was set equal to 0.02 and the polarization calibration experiment described below was used to determine the value o f their parameter f, for which a value of 0.80_+0.07 was obtained. The use of other initial choices o f p ranging from 0 to 0.056 with the corresponding value o f f chosen to agree with the calibration experiment resulted in a total variation in the polarization values of less than 4.5 ~ . t Hamilton Watch Co., Precision Metals Division, Lancaster, Pennsylvania 17604, USA. *t "Torr Seal", Varian Associates, Palo Alto, California.
3He(p, p)
311
Beams of protons and alpha particles from the University of Colorado cyclotron were energy analysed by a bending magnet whose magnetic field was measured by nuclear magnetic resonance, and which had been calibrated by time-of-flight techniques. Beam energies quoted refer to the energy at the centre of the target and are uncertain by 0.3 70 or less. Proton beam currents of up to 250 nA were used, but it was found to be necessary to limit the alpha particle beam current to a maximum of 100 nA. Higher alpha beam currents produced up to a 50 70 decrease in the target polarization. At 100 nA no such decrease was observed. The beam current was run through the target during the 15 min optical pump equilibrating time which preceded each run. Similar effects were not observed with the proton beam but presumably would occur at higher currents. Each detector telescope consisted of a pair of slits mounted in front of one or two solid state particle detectors. The contribution of multiple scattering in the target windows to the total angular resolution was significant and is included with the results. Scattered protons and recoil 3He from the polarized 3He target were detected by requiring a coincidence between a AE (100 pm) and an E (4500 pro) silicon detector. For the calibration experiment the scattered alphas and the recoil 3He nuclei were detected in each telescope by a single E (100 pm) silicon detector, and were identified by their energy. Signals from both telescopes were recorded simultaneously by routing the E or E+ AE signals to different 256-channel blocks of a Nuclear Data 50/50 pulse height analyser according to whether the event was in the left or the right telescope. The reduction of data for a measurement of the 3He spin analysing power for the case where the scattered protons were observed will be described. The other cases are similar. A set of data consists of one run with the target polarization up and one with it down. At least two independent sets of data were taken at each angle as a consistency check. The peak areas were determined and corrected for background by using a least squares Gaussian fitting computer program. The background correction to the peak area was always less than 5 %. If the net number of counts per microcoulomb in the left (right) telescope is denoted by L (R) and a superscript + ( - ) is added to indicate that the polarization is up (down), then the 3He spin analysing power P3 is given by:
1FL++R--L--R+ ] P3 -- P L Y + R -
+L- ~-~
'
where P is the polarization of the target and the Basel sign convention 1o) has been followed.
3. Target polarization calibration Previously, nuclear physicists using polarized 3He targets have depended on an optical absorption method of polarization measurement 9). The method involves the knowledge of certain transition probabilities, of the degree of circular polarization
312
R . H . W A R E et al.
of the light and of the spectral line shape o f the pumping light.The resulting uncertainty of the target polarization was typically 12 to 15 ~ o f the value. In recent work Plattner and Baeher 6) have pointed out the existence of certain points where the analysing power must pass through _ 1. F r o m phase-shift behaviour they indicate that for 3He-4He scattering such a point exists near 86 ° c.m. scattering angle and 15.3 MeV alpha laboratory energy. This point was used to cheek the calibration TABLE 1 Target polarization calibration data Lab energy (MeV)
Lab angle (deg)
c.m. angle (deg)
c.m. A0 (deg)
aHe spin analysing power (~o)
Target polar. (~o)
15.20 15.31 15.58 15.75 15.75 15.75 15.75
47.0 47.0 47.0 50.0 47.0 45.5 44.0
86.0 86.0 86.0 80.0 86.0 89.8 92.2
4.4 4.3 4.2 4.4 4.1 3.8 3.6
--79.54-3.3 --85.04-3.0 --78.04-8.6 --76.64-2.9 -- 85.5 4- 3.0 --100.04-4.4
7.6 4-0.1 11.7 4-0.1 5.0 4-0.1 12.8 4-0.02 12.60 4-0.05 12.8 4-0.1 12.8 4-0.2
--95.64-8.3
Measured values of the spin analysing power P observed when alpha particles are scattered from the polarized 3He target are listed. The observed particles are recoil 3He nuclei. The values of target polarization as determined by optical absorption measurement have been corrected to adjust the spin analysing power at 45.5° from --1.02 to --1.00, thus calibrating the target polarization. A 5 ~o systematic probable error is estimated for this calibration.
T
i Ea =15.75 MeV tY
W
- 1.0
O
-O.9
@.r = 4 7 "
N
<~ -0.s
!
,,
z ,¢[ z
-or
IX. 0
-0.6
-0.5
35
40
45
t
50
55
SHe-RECOIL LAB ANGLE (DEGREES)
152
t
15.4
15.6
15.8
ALPHA LAB ENERGY (MeV)
Fig. I. The search for the polarization calibration point. Measured values o f spin analysing power o f SHe-4He elastic scattering are shown. A four-point angular distribution at 15.75 MeV is shown on the left and an excitation function at a SHe recoil angle o f 470 is shown on the right. Plattner and Bacher 6) predicted that the analysing power passed through --1 near the point marked by arrows. The curves are drawn through points taken from the contour map produced by Hardy e t al. 7) from phase-shift data, The angular distribution point at 45.5 ° wasused as the calibration point.
3He(p, p)
313
o f the polarized target. The results of two four-point searches, one each in energy and angle, about the predicted point are listed in table 1 and plotted in fig. 1. The topography of the region has been generally described by H a r d y et al. 7) in a contour plot calculated f r o m phase shifts. The present results confirm the energy independence o f spin analysing power in this region and suggests that the m a x i m u m occurs at a slightly larger c.m. angle than was predicted. Unfortunately, data could not be taken on the small laboratory angle side of the maximum, due to the temporary unavailability o f very thin particle detectors to do the particle identification which became necessary as the SHe and 4He peaks began to overlap. Future experimenters should have no trouble remedying this defect and achieving better definition of the m a x i m u m in analysing power. In spite of this shortcoming, it is felt that confidence in the polarization calibration is increased to the point where the polarization uncertainty is reduced to 5 ~ of the value, after adjusting the parameters to normalize the polarization to - 1 . 0 0 at the 45.5 ° point. This renormalization involved increasing the optically measured target polarization value by only 2 ~ , so the agreement of the two methods is excellent. 4. Proton-SHe elastic scattering To facilitate future phase-shift analyses, the proton-3He differential elastic scattering cross section also was measured at a proton laboratory energy of 26.70-t-0.05 MeV at c.m. angles between 20 ° and 170 °. The magnetically analysed proton b e a m TABLE2 Centre-of-mass differential elastic scattering cross section for 26.70 MeV protons incident on aHe c.m. angle (deg) 20.1 23.4 26.7 30.0 33.3 36,6 39.8 46.3 52.6 58.9 65.1 71.2 77.1 82.9 88.6 94.1 99.5 104.7
d~ ~ (mb/sr) 114 120 116 110 105 97.2 91.0 73.9 59.8 48.4 37.2 27.7 21.2 15.8 11.8 8.56 6.18 4.45
c.m. angle (deg) 109.8 112.3 114.7 117.1 119.5 124.1 128.5 132.8 137.0 141.1 145.0 148.8 152.5 156.2 159.7 163.2 166.6 170.0
The probable error in cross section is 3 ~. and the angular resolution is 2.6 ° c.m.
d~ ~_Q (mb/sr) 3.21 2.89 2.54 2.37 2.32 2.57 3.20 4.28 5.91 7.79 10.0 12.6 15.2 17.9 20.6 23.2 25.6 26.8
TABLE 3 Values of the aHe spin analysing power of hydrogen, P a , measured with 26.8 MeV protons incident on a polarized aHe target Lab angle (deg)
c.m. angle (deg)
c.m. A0 (deg)
aHe spin analysing power (~o)
Observed particle
Exit window
Target polar. (~o)
30 40 50 60 70 80.4 90.2 100.5 109.5 114.4 120 130 140 150 38 a)
39.81 52.64 65.11 77.12 88.60 99.93 110.01 119.94 128.11 132.34 137.03 145.01 152.54 159.72 50.04
1.2 2.4 2.5 2.7 2.7 2.7 2.8 2.9 2.9 2.9 3.3 3.3 0.95 0.91 1.3
--5.84-1.8 --7.64-1.2 --13.1~:1.6 --15.94-3.1 --19.24-1.4 --18.54-2.8 --12.54-2.2 20.84-3.4 34.44-2.8 31.94-2.5 25.24-4.5 21.54-2.6 10.94-1.6 7.7d:1.5 --6.84-1.1
p p p p p 3He aHe aHe 3He 3I-Ie p p p p p
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10.54-0.1 16.54-0.9 16.44-0.1 16.54-0.5 14.14-0.2 9.24-0.6 10.24-0.1 10.54-0.1 9.94-0.2 10.24-0.1 10.34-0.7 12.04-0.2 13.24-0.3 13.24-0.6 14.34-0.3
The sign of Pa is in accordance with the Basel convention lo). The c.m. angular resolution ./tO includes the effect of multiple scattering in the exit window. The particle detected and the window through which it passed are listed in the fifth and sixth columns. The error associated with P3 does not include the 5 ~o target polarization calibration uncertainty. =) Value measured at 19.4 MeV. I000
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140
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180
CENTRE OF MASS ANGLE (DEGREES)
Fig. 2. Centre of mass proton-aHe elastic scattering cross section, at 20.0 MeV c.m. energy. The data were obtained by observing the scattering of 26.70 MeV protons from a sealed target containing aHe gas. The data point size is larger than the probable error for all points.
SHe(p, p)
.6
315
~; PRESENT EXP. 26,8MeV
.5
BAKER, et ol. 19.4 MeV
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c.m• SCATTERING ANGLE (DEGREES)
Fig. 3. The aHe spin analysing power of protons• The values measured with 26.8 MeV protons are s h o w n with the values which Baker et aL 4) obtained at 19.4 MeV for comparison. Only statistical errors are shown. Not included is an additional systematic contribution of 12 ~o (19.4 MeV) and 5 ~ (26.8 MeV) from uncertainty in the target polarization. Experimentally there is no difference Jn the analysing power at the two energies• The two smooth curves are predictions by Morales-Pena 5) for 25 and 27.5 MeV protons calculated from his phase-shift analysis of scattering data.
from the cyclotron was focussed on a sealed 3He gas target of a type previously • lescribed 11). Scattered protons defined by a slit system were detected and identified by an E - A E pair of solid state detectors. The cross-section values have been assigned a probable error of 3 ~o, which is derived by combining the following contributions in quadrature: geometry measurement (1.5 ~o), counting statistics and background .correction (1 ~o), beam current integration (1 ~), beam alignment (1 ~o), target gas density (0.7 ~o), detector et~ciency correction 12) of 1.3 ~ (0.5 ~), 3He gas purity •correction of 0.5 ~o (0.5 ~o), geometric corrections for finite beam and aperture :size 13) 0.12 ~ and the beam heating effect 14) was estimated to be less than 1 ,(1 ~). The results are given in table 2 and shown in fig. 2. 5. The SHe spin analysing power of protons: results and discussion The measured values of the 3He spin analysing power of protons (P3) at a c.m. .energy of 20.0 MeV are listed in table 3. These data were obtained with 26.8 MeV protons incident on a polarized 3He target. As a check against possible systematic errors P3 was also measured at 0 .... = 50° at a proton lab energy of 19.4 MeV, where P3 had previously been measured by Baker et aL 4). Although this is not a severe test because the measured analysing power is so small ( - 0 . 0 6 8 _ 0.011), it is in good .agreement with the previous measurement ( - 0.079-t- 0.010).
316
R . H . W A R E et aL
The experimental values of the 3He spin analysing power obtained at 26.8 MeV are identical, with experimental error, to those obtained at 19.4 MeV by Baker et al. This apparent energy independence may be accidental. Morales-Pena 5) has carried out a phase-shift analysis of existing data on the p-3He system from 18 MeV to 57 MeV. Although he had no 3He spin analysing power data above 19.4 MeV, he has predicted the 3He spin analysing power at proton lab energies of 25.0 MeV and 27.5 MeV. His predictions, together with the present 26.8 MeV results, are shown in fig. 3. It can be seen that his work predicts a strong variation with energy between 25 and 27.5 MeV. The experimental points at 26.8 MeV fall between his two predictions at back angles where the analysing power is large, and show a larger analysing power than either of his predictions at forward angles where the analysing power is small. While the present measurements cannot be said to violently disagree with his predictions, if they are taken together with the 19.4 MeV data there is a strong suggestion that the energy dependence may not be as pronounced as he suggests. Only additional measurements can resolve this question. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14)
S. Fiarman and W. E. Meyerhof, Nucl. Phys. A206 (1973) 1 S. D. Baker, D. H. McSherry and D. O. Findley, Phys. Rev. 178 (1969) 1616 L. W. Morrow and W. Haeberli, Nucl. Phys. A126 (1969) 225 S. D. Baker, T. A. Cahill, P. CatiUon, J. Durand and D. Garreta, Nucl. Phys. AI60 (1971) 428 J. R. Morales-Pena, Ph.D. thesis, Univ. of California (Davis) 1970 G. R. Plattner and A. D. Bacher, Phys. Lett. 36B (1971) 211 D. M. Hardy, R. J. Spiger, S. D. Baker, Y. S. Chen and T. A. Tombrello, Phys. Lett. 31B (1970) 355 R. H. Ware, Ph.D. thesis, Univ. o f Colorado, 1974 F. D, Colegrove, L. D. Schearer and G. K. Walters, Phys. Rev. 132 0963) 2561 Basel convention, Helv. Phys. Acta, Suppl. 6 0961) 436 T. R. King and R. Smythe, Null. Phys. A183 0972) 657 T. R. King, J. J. Kraushaar, R. A. Ristinen, R. Smythe and D. M. Stupin, Nucl. Instr. 88 (1970) 17 E. A. Silverstein, Nucl. Instr. 4 (1959) 53 P. W. Allison and R. Smythe, Nucl. Phys. A121 (1968) 97