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Tensor polarization of deuterons from the 9Be(p, d)8Be reaction for Ep = 1.6–3.8 MeV
2.B
] I
Nuclear Physics All9 (1968) 97--112; (~) North-Holland Publishing Co., Amsterdam N o t to be reproduced by p h o t o p r i n t or microfilm without written permission f r o m the publisher
TENSOR POLARIZATION OF DEUTERONS F R O M T H E 9Be(p, d)SBe R E A C T I O N F O R Ep = 1.6-3.8 MeV A. J. FROELICH and S. E. DARDEN Department of Physics, University of Notre Dame, Notre Dame, Indiana t Received 24 June 1968 Abstract: The tensor polarization of the deuterons from the aBe(p, d)SBe reaction was measured for proton energies in the range 1.6-3.8 MeV and for lab emission angles between 10° and 90°. The tensor polarization was measured by observing the deviation from isotrcpy of the proton angular distribution of the SHe(d, p)4He reaction, when the deuterons from the 9Be(p, d)SBe reaction were incident on a 3He gas cell with energies below 600 keV. The largest magnitude of polarization observed occurred at/~p = 2.0 MeV, 0tab = 10°, where t~0 was found to be 0.53 :k0.08. For proton bombarding energies below 2.6 MeV, a pronounced energy dependence of the polarization is present, while in the energy range 2.7-3.8 MeV less variation was observed. Neither a DWBA calculation using spin-orbit potentials nor a plane-wave calculation including deuteron D-state effects has been successful in reproducing the magnitude and angular variation of the tensor polarization data, although the differential cross-section data above Ep = 2.5 MeV strongly suggest that the (p, d) "pick-up" reaction is the predominant reaction mechanism at these bombarding energies. E
NUCLEAR REACTION 9Be(p, d)SBe, Ep = 1.6-3.8 MeV, AEp = 300 keV; measured tensor polarizations t~q(Olab~ 90°).
[
I
1. Introduction A l t h o u g h it has been realized for some time that spin-dependent forces are of imp o r t a n c e in direct reactions 1), the n a t u r e a n d extent of these forces have n o t yet been completely established. Analyses of elastic-scattering m e a s u r e m e n t s using polarized beams have given some i n f o r m a t i o n o n the vector spin-orbit potential for nucleons a n d deuterons interacting with nuclei 2, a), b u t little knowledge has been gained a b o u t tensor spin-orbit potentials for deuterons 3, 4) except that phase-shift analyses of deuteron elastic scattering and polarization data indicate some such potential is required [refs. s, 6)]. While distorted-wave B o r n a p p r o x i m a t i o n ( D W B A ) calculations which include vector spin-orbit terms i n the optical potentials 7) have been f o u n d to be useful in establishing the j - d e p e n d e n c e of Pd(0) for (d, p) reactions i n d u c e d by vectorpolarized deuterons a), they have n o t been very successful in reproducing n u c l e o n polarizations observed in stripping reactions. The extent of d e u t e r o n tensor-polarization effects in stripping a n d pick-up reactions has n o t yet been established. Such effects c a n influence m e a s u r e d asymmetries in the t Work supported in part by the U.S. Office of Naval Research under Contract No. Nonr.-1623 (05). 97
98
A.J. FROELICH AND S. E. DARDEN
nucleons emitted from stripping reactions induced b y polarized deuterons 1). For example, Gofman et al. 9) measured the asymmetry in protons emitted from the zZC(d, p)l 3C and 14N(d, p)l 5N stripping reactions initiated by deuterons which had been elastically scattered from carbon at an incident deuteron energy of 13.6 MeV. From the similar angular dependence of the asymmetry obtained for the two cases, these authors concluded that either the spin-orbit interaction can be neglected in the stripping reaction, or that tensor polarization effects in (d, p) reactions are small. If it is assumed that both conclusions are valid, the asymmetry of protons emitted in a (d, p) stripping reaction induced by a deuteron beam having polarization Pa is given by e = 3PpPa, where Pp is the proton polarization produced by unpolarized deuterons [refs. lo, 11)]. Previous investigators 13-15) had made this assumption in attempting to measure the vector polarization of deuterons from the 9Be(p, d)SBe reaction. At a proton bombarding energy of 3 MeV and deuteron emission angle of 30 °, Lambert et al. 13) obtained a value Pd = 0.11 _+0.05, while Verbinski and Bokhari 15) reported Pa = 0.17___0.05. Since the former authors used the 2H(d, p)3H reaction as an analyser, and the latter employed the 12C(d, p)l 3C reaction, the similarity of their results is consistent with the results of Gofman et al. 9). However, recent measurements by Petitjean et al. 16) and by Ad'yasevich et al. 17), using beams from polarized-ion sources, demonstrate that the 2H(d, p)3H reaction is highly sensitive to deuteron tensor polarization as well as vector polarization. In addition, substantial tensor polarization of the deuterons from the 9Be(p, d)SBe reaction has been measured by the authors is) for proton energies of 2.5 and 3.7 MeV and by Ivanovich et al. 19) t for proton energies from 4.9 to 9.8 MeV. For all of these measurements, the 3He(d, p)4He reaction 2o) was used as an analyser. A preliminary DWBA calculation presented with the earlier 9Be(p, d)SBe tensor polarization data is) failed to give quantitative agreement but appeared to predict the correct signs of the tensor parameters t* t2~. Moreover, the tensor polarization reported by Ivanovich et al. 19) exhibits a significant energy dependence over the entire energy range investigated. Johnson 21) proposed that the D-state component of the deuteron wave function might affect the tensor polarization. A perturbation calculation using plane waves showed that tensor polarization of the order of 0.05 could be obtained for deuterons from (p, d) reactions simply by including the effect of the D-state. Although this result establishes the necessity of including the D-state in any accurate calculations, the plane-wave calculation failed to reproduce the angular distributions of the t2~ and does not yield the sort of energy dependence observed by Ivanovich et al. Since the angular distribution data for the 9Be(p, d)SBe reaction have been well reproduced at angles less than 60 ° by direct reaction calculations 22-25), one might expect a sufficiently sophisticated calculation to reproduce the polarization data as well. The lack of agreement of measured and calculated tensor polarizations prompted us to ? T h e s i g n o f t21 as r e p o r t e d i n ref. as) s h o u l d be r e v e r s e d . t t W e h a v e a d o p t e d t h e n o t a t i o n t2~ = (T~e).
aBe(p, d)SBe REACTION
99
extend the previous measurements of this laboratory. In addition to measurements at energies where the direct-reaction mechanism appears to predominate, data were also taken in the vicinity of the previously reported 22) broad resonances in the 9Be(p, d)SBe cross section at proton energies of 1.65 and 2.3 MeV corresponding to excitation energies of 8.07 and 8.66 MeV in the compound nucleus 10B. it was hoped that these latter measurements might provide information on spin and parity assignments for these states. Proton bombarding energies were in the range Ep(lab) = 1.6-3.8 MeV. Measurements of the tensor polarization of deuterons emitted at lab angles between 10 ° and 50 ° were carried out in 10 ° intervals for eight proton energies, with some additional measurements at angles of 60 °, 65 ° and 90 ° for selected energies.
2. Experimental method The essential details of the experimental method and equipment employed for these measurements have been described previously 18, 19), therefore only the briefest description will be presented with comments appropriate to this particular experiment. The method consisted of bombarding thin beryllium foils with a proton beam from the Notre Dame electrostatic accelerator and observing the anisotropy in the yield of the 3He(d, p)4He reaction when the deuterons from the 9Be(p, d)SBe reaction were incident on a 3He target cell. Four thin CsI(TI) crystals were used to detect the protons emitted from the analysing reaction at four different angular positions, and the t2q were determined from the relative normalized counting rates of the detectors. Since the tensor polarization analysing power of the 3He(d, p74He reaction is relatively well known 2 o7 for deuteron energies below 600 keV, the deuterons were degraded in energy by absorber foils before entering the gas cell. The upper limit of 600 keV for the use of 3He(d, p)4He as a reliable analysing reaction is our best estimate based on a consideration of the available data for this reaction and for the mirror 3H(d, n)4He reaction 26). l~or low incident deuteron energies, the angular distribution of the protons from the 3He(d, p)4He reaction is given by the following formula
[ref. 277]: ~(0, 4, E~7 = ~o(E.){1-:(E.)[~/~(3 cos20- l)t2o --x/3 sin 0 cos 0 cos t~t2t +½n/3 sin20 cos 2~bt22]},
(1)
where the t2q describe the tensor polarization of the incident deuteron beam, tro the cross section for an unpolarized deuteron beam, 0 the c.m. reaction angle and q~ the azimuthal angle of the protons referred to the coordinate system in which the t2~ are specified. This coordinate system as used here is the same as in ref. 187, i.e. the z-axis is parallel to the deuteron beam direction, and the y-axis is defined by k v x ka, where kp and kd are the momenta of the incident and outgoing beams in the (p, d) reaction. The parameter p ( E 7 is a measure of the relative strength of the two possible s-wave channels in the 3He(d, p)aHe reaction, the polarization-sensitive J~ = ½+ channel
100
X.J.
F R O E L I C H A N D S. E. D A R D E N
and the polarization-insensitive J~ = ½+ channel; it is given in ref. 6) based on the measurements of Brown et al. 2 0).
3. Apparatus Some modifications of the apparatus used in the previous measurements were made [ref. is)]. The single-absorber foil mount was replaced by a set of four frames placed along the deuteron beam path, and these could be positioned by rods extending through the top of the reaction chamber. Four foil positions are available on each frame, therefore a suitable combination of absorber foils could be inserted for each measurement without opening the reaction chamber. The chamber exit foil was removed, and the 3He cell was vacuum-sealed directly to the chamber by means of an O-ring in order to permit measurements on deuterons having an energy as low as 1350 keV, the energy loss in the SHe cell entrance foil being 750 keV for deuterons of that energy. A set of collimating slits was introduced between the beryllium target position and the absorber foils; this resulted in an angular acceptance of 7 ° for the 3He cell. For the data reported here, the SHe cell was filled to a pressure of 4.7 atm or less. At 4.7 atm, deuterons entering the cell with an energy of 500 keV are stopped within its volume. In order to minimize the deterioration of the beryllium targets which results from beam bombardment, two different types of target holders were tried. The first is a rotating frame device 2s) which is constructed such that the axis of rotation of the target is parallel to the reaction plane. Proper vertical adjustment of the target holder causes the beam to describe a circular path on the target as it rotates, thus effectively spreading the beam over more of the target area. Unfortunately, the poor heat transfer from the rotating frame to the rest of the structure made operation with this device marginal when the beam current exceeded 5#A. The alternate target holder, used for the majority of the measurements, is a water-cooled hollow brass cylinder soldered to a plate capable of holding four individual target frames. Efficient heat removal is obtained by cementing target foils to the frames, which are screwed to the plate to make good thermal contact. The photomultiplier spectra of the protons from the 3He(d, p)aHe reaction were improved over those obtained in the earlier measurements 1s) by reducing the voltage on the photomultiplier tubes. As in the previous experiment, the spectra from the four detectors were accumulated in four quadrants of a 256-channel memory; however, instead of a 256-channel analyser, a 256-channel section of a Nuclear Data-160 analyser was used. This allowed several spectra to be stored in memory before readout was required.
4. Experimental procedure For each individual measurement, the procedure followed was (i) to determine the target foil orientation which would result in a proton energy loss of approximately
eBe(p, d)SBe REACTION
101
300 keV, (ii) to determine the combination of absorber foils for which the deuterons at the angle of observation enter the 3He cell with a m a x i m u m energy of about 600 keV, (iii) to verify steps (i) and (ii) by measuring the yield from the analysing reaction as a function of proton bombarding energy, (iv) to accumulate a sufficient number of counts for a calculation of the tzq to an average statistical accuracy of __+0.05, (v) to obtain a normalization of the counting rates in the various detectors by initiating the analysing reaction with unpolarized deuterons and (vi) to measure any background present in the counter spectra. These steps were not necessarily carried out in chronological order; item (v) was usually performed at the outset of each measurement since it provided a rapid and convenient check on the electronics. Also, background runs were taken at regular intervals during the course of a measurement in order to minimize errors introduced by amplifier drift and target deterioration. The beryllium targets employed in this investigation were thin self-supporting foils t of thickness 1.6 mg/cm z and 2.7 mg/cm z. These foils are 270 and 450 keV thick, respectively, to a 1500 keV proton beam. In order to maintain a degree of uniformity in the data accumulation, it was decided to fix the proton energy loss in the beryllium target at 300 keV regardless of the bombarding energy chosen for each measurement. This was achieved by orienting the Be foil at the proper angle to the incident beam direction. In most cases, placing the plane of the target a t an angle to the incident beam direction decreased the energy spread of the outgoing deuterons from the 9Be(p, d)SBe reaction below what it would be for a normally incident beam. This energy spread is caused mainly by the difference in energy loss for protons and deuterons in beryllium and was usually less than 100 keV. In order to ensure that the energy of the deuterons entering the 3He cell did not exceed 600 keV, a series of foils was usually employed to reduce the energy of the emitted deuterons. Once the maximum energy of deuterons emerging from the target foil was established, the absorber foil or combination of foils which would reduce that energy to 1350 keV was inserted between the 3He cell and the Be target. To confirm that the deuterons entered the 3He cell with an energy of approximately 600 keV, the yield in all four detectors of protons from the 3He target was measured as a function of the energy of the protons incident on the beryllium target. This yield curve was then compared with that calculated taking into account the energy loss in the beryllium foil, the slowing-down foils and the 3He cell entrance foil. I f the comparison between measured and calculated yield curves showed that the desired bombarding energy was compatible with the choice of absorber foils used for the yield-curve measurement, data could be taken at the nominal bombarding energy. In most cases, the proper bombarding energy for the foils used in the yield measurement was within 100 keV of the desired energy and was used instead of the nominal energy for the data runs. Use of the measured yield curve to determine the proper bombarding energy is estimated to be accurate to about ___50 keV in the choice of bombarding energy. This t The foils were obtained from the Brush Beryllium Co., Cleveland, Ohio.
102
A . J . F R O E L I C H A N D S. E. D A R D E N
method of determining the proper bombarding energy was checked for one measurement by replacing the 3He cell with an energy-calibrated solid state detector. The operating conditions for the measurement, i.e. bombarding energy, target foil thickness and angle and absorber foils used, were reproduced as accurately as possible, and a foil cut from the same sheet as the 3He cell entrance foil was placed in front of the detector to simulate the 3He cell entrance foil. Although greatly obscured by the 9Be(p, p)9Be elastic-scattering peak, the ground-state deuteron group in the resulting spectrum could be seen to have a m a x i m u m energy of about 630 keV. Once a satisfactory yield curve had been obtained for a given energy and angle, tensor polarizations were measured in a series of runs. The beam current passing through the beryllium target was collected on the beam stop and fed to a current integrator; the duration of each run was chosen to yield at least 100 counts per detector in the peak regions of the detector spectra. Interspersed between these measurements were background runs of comparable duration made with a 25.4/~m tantalum foil intercepting the deuterons incident on the 3I[e cell. A minimum of approximately 1000 proton counts per detector was accumulated for each measurement. To eliminate effects arising from differences in detector solid angles and efficiencies, deuterons elastically scattered from a 9.7 mg/cm z thick gold foil target were used for normalization measurements. For most of these measurements, the reaction chamber was set at a lab observation angle of 50 ° with a foil angle of 25 °, and no absorber foils were used. Yield curves measured under these conditions indicated a deuteron bombarding energy of 2.1 MeV. The deuterons scattered from Au can safely be assumed to be unpolarized, since at this low energy and forward emission angle, Rutherford scattering certainly predominates. This assumption was confirmed by the fact that the relative counting rates for a deuteron-gold scattering angle of 50 ° did not differ from those obtained when the deuteron beam from the accelerator was put directly into the 3He cell. Normalization runs were usually made at the outset of each series of measurements. The high counting rate of about 250 counts per min per detector also made it convenient to use the scattered beam in checking the amplifiers and routing circuitry. It was desired in this investigation to accumulate a set of measurements covering the bombarding energy range of our accelerator. It was also intended that the angular range of the measurements be as great as possible. The rapid energy variation of the 9Be(p, d)SBe cross section below 1.5 MeV made measurements with 300 keV thick targets seem pointless and established at these energies a lower energy limit to the measurements; using significantly thinner targets would have required inordinately long data-accumulation times. The average proton beam current used in this investigation varied from about 3/~A to 7#A. The lower figure was obtained when the accelerator source output was poor; the upper limit was dictated by the inability of the target to dissipate the heat produced by the passage of larger beam currents through it. The counting rate of each proton detector varied from a m a x i m u m of 6 counts/min at a bombarding energy of
9Be(p, d)aBe REACTION
103
3.8 MeV and an observation angle of 10 ° to a minimum of 40 counts/h at 2.8 MeV and 70 ° , respectively. The extremely low counting rates at large observation angles made it impractical to extend the measurements beyond 50 ° for more than a few energies. The average data-taking time at one energy and angle was 10 h.
5. Results of the measurements
The counting rates for the four detectors were converted to the t2~ by use of eq. (1). Normalized measured counting rates in the four detectors were equated to expressions obtained by integrating eq. (1) over the solid angles subtended by the detectors, and the resulting four equations were solved for the t2q. The coefficient p which was used was determined by averaging the measured value 6, z o) of p over the deuteron energies occurring in the 3He cell weighted by the 3He(d, p)4He cross section. The result is
I p(E) o'(E)dE (p) = '
(dE/dx)E
: ~(E)dE
0.89+0.02,
(2)
(dE/dx)~ where the integrals have been approximated by sums. The t2q obtained by this procedure are referred to the outgoing deuteron direction in the lab system as described in sect. 2; the corresponding center-of-mass values are obtained by transforming the measured t2q to a coordinate system in which the z-axis is along the direction of the outgoing deuteron beam in the c.m. system, and the y-axis is unchanged. Geometrical effects involved in the data reduction arise from the uncertainties in the point of origin of the deuteron beam, in the mean position at which the analysing reaction occurs and in the angles at which the protons from the 3He(d, p)4He reaction are observed. Since the incident beam was collimated to a size less than one-tenth that of the entrance aperture of the 3He cell, corrections for the spatial extension of the source of the deuterons can be safely neglected. Calculations were performed to estimate the effect of the displacement of the point at which the 3He(d, p)4He reaction occurs from the geometrical center of the gas cell. This displacement was calculated for the experimental arrangement used for these measurements from the 9Be(p, d) 8Be and Au(d~ d)Au differential cross sections. The displacement is in the direction of smaller scattering or reaction angle and affects chiefly the measured value of The calculated effect was significantly less than the statistical uncertainties, and no correction was made for it. The background counting rates were determined for each measurement by accumulating data for a fraction of the running time with a 25 # m tantalum foil inserted between the beryllium target and the 3He cell. This insured that no deuterons entered the 3He cell, and only background spectra were obtained under these conditions. Typical backgrounds encountered amounted to about 5 ~ of the counting rate for
tzl.
104
A.
J 4
~
J. FROELICH
i
t2o
!
!
~
I
'
i
i
[
_~_ r
i
-}-@
i
t~,
'@'
2
[
2.o
I
I
2.5 .3.o Ep (MeV)
,++ +,
|
3.6
1.5
Fig. 1. The measured tza as functions o f proton bombarding energy for a lab observation angle o f 20 ° . I
i
1
I
I
0.2 Ep = 2.7 MeV
{{{
-0.2
-0.4
0.2
-0.6
t2,
t2, I
-0.2
-O'iI
~
{
{
.... PWaA,D-stote] --
---~---+~
-L__I
DWBA
J
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20
i
P
I
I
40
I
I
'
I
~
r
60 8e.m. (degrees)
'
I
I
{{
-0°
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I
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I
i
I/
,
-0'2[ I
i
T
-0..' r
3.5
t2o -0.2
-0.4
2.5 5.0 Ep (MeV)
Ep = 3.7 MeV
{
t2o
t2z
2.0
Fig. 2. The measured t2~ as functions o f proton bombarding energy for a lab observation angle o f 50 °.
t
0.4 0.2
I ; I
+4-+_+ 4-
-0.2
J
0"e.rn.= 56.7*
+
o.2
--{-++_{_4__-{ ---{-
h.5
i
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-o2
-
i
I
-4-! -{-i
i
0.2
0.Z
t~,
S. E. DARDEN
i
8c ~-- 2 5 0 °
0.2
AND
80
I00
Fig. 3. Angular distributions o f the tensor polarization for/~v = 2.7 MeV. The curves are discussed in the text.
i
{{{
I
~ I
2O
40
60
80
Ocm.(degrees) Fig. 4. Angular distributions o f the tensor polarization for/~p = 3.7 MeV.
aBe(p, d)aBe REACTION
105
detector 3 and about half that amount for the other detectors. The background counts appeared to arise from neutrons produced in the 9Be(p, n)gB reaction. The polarization parameters t2q obtained from the counter ratios and corrected for the efficiency of the analysing reaction are presented in figs. 1 and 2 as functions of the average proton bombarding energy for mean c.m. observation angles of 23 ° and 56 °, respectively. Similar data were obtained for angles of 11 °, 34 ° and 45 °. Angular distributions of the t2q measured at average proton bombarding energies of 2.7 and 3.7 MeV are shown in figs. 3 and 4, respectively. The energy dependence of the polari-
0.2
tzo
--+-
+----~
[
,
-0.2
0L,a= 30°
-0.4 0.2
t21
----+ ~---+- ~
-0.2 o present work -OA
Ivonovich et ol Dorden and Froelich
0.2
t2z -0.2 L 2
F
! 4
I
I I 6 E'p ( M e V )
I
I
IO
Fig. 5. Summary of 30° measurements; points labelled Ivanovich et al. are from ref. la), while those labelled Darden and Froehlich are from ref. is).
zations measured at 11 ° is similar to that shown for 23 °, while the 46 ° data resemble the 30 ° data shown in fig. 5. All of the data obtained are given in table 1 with the c.m. angles corresponding to the lab observation angles at each energy. Because of the small Q-value of the reaction, the difference between lab and c.m. angles changes by less than 1° over the proton energy range of the measurements. The t2~ display some variation with bombarding energy, particularly below Ep = 2.7 MeV. Most pronounced is the energy dependence of t z o , which ranges from +0.53_+0.08 atEp = 2.00 MeV to -0.204-0.10 at Ep = 3.16 MeV for 0.... = 11.5°. The values of tzt appear to be generally positive in the energy region below Ep = 2.2 MeV and generally negative from Ep = 2.2 MeV up to the highest energy measured. Essentially zero values of t22 were found below Ep = 2.0 MeV, and generally nega-
106
A. J. FROELICH AND S. E. DARDEN
TABLE 1
Measured tensor polar~ations t~(Oe.m, ) 0 lab (deg.)
0
~p
c.m.
(deg.)
lab (MeV)
10.0
11.4 11.5 11.5 11.5 11.5 11.5 11.5 11.5 11.5 11.6
1.60 2.00 2.27 2.50 2.61 2.78 2.97 3.16 3.55 3.70
0.281 ±0.077 0.531 ±0.078 0.396 ±0.043 0.2644-0.069 --0.155 ±0.082 --0.201 ±0.083 --0.1244-0.075 --0.1994-0.098 --0.148±0.090 0.013±0.057
0.0274-0.030 0.072±0.031 0.020 ±0.016 --0.016±0.025 --0.1984-0.032 --0.128 ±0.031 --0.133±0.028 --0.128±0.032 --0.0944-0.034 --0.103±0.024
0.000±0.044 0.049±0.048 0.044 ±0.026 0.026±0.040 0.0184-0.043 --0.087 ±0.048 --0.0384-0.044 0.013 ±0.046 --0.022±0.049 --0.018±0.034
20.0
22.8 22.9 22.9 22.9 23.0 23.0 23.0 23.0 23.0 23.0
1.78 2.00 2.25 2.45 2.65 2.80 2.95 3.16 3.43 3.66
0.180!0.025 0.217 t0.073 0.322 ±0.068 0.121 ±0.066 --0.026 ±0.067 --0.133±0.088 --0.126±0.086 --0.176±0.040 --0.130±0.083 --0.160±0.089
0.038 ±0.029 O.126 ±0.030 --0.016 ±0.025 --0.109 ±0.028 --0.233 &0.032 --0.206±0.037 --0.222±0.035 --0.207 ~0.018 --0.162±0.033 --0.100±0.031
--0.031 ±0.046 0.083 ±0.047 0.035 ±0.040 --0.020 ±0.040 --0.075 ±0.046 --0.086i0.052 0.034±0.049 --0.005±0.024 --0.090±0.053 0.007 ±0.046
30.0
34.1 34.2 34.3 34.3 34.3 34.4 34.4 34.4 34.4 34.4 34.5
1.66 2.00 2.25 2.52 2.66 2.65 ~) 2.91 3.03 3.26 3.50 3.68
0.220±0.046 0.242 ±0.040 0.138i0.038 0.049 ±0.080 --0.074 ±0.097 0.064±0.055 --0.001 +0.087 --0.090±0.086 --0.233±0.094 --0.166±0.098 --0.087±0.081
0.085±0.018 0.061 ±0.015 --0.007±0.016 --0.161 ±0.036 --0.260 ±0.042 --0.211 ±0.027 --0.244 ±0.041 --0.127±0.035 --0.132±0.035 --0.130±0.038 --0.054&0.030
0.022±0.028 0.106 ±0.025 --0.104±0.025 --0.041 ±0.048 --0.161 ±0.064 --0.090 ±0.036 --0.168 ±0.060 --0.072±0.050 --0.1654-0.056 --0.179 ±0.061 --0.095±0.048
40.0
45.3 45.4 45.5 45.6 45.6 45.7 45.7 45.8
1.72 2.05 2.25 2.70 2.90 3.12 3.58 3.82
0.082 ±0.071 0.266 ±0.066 0.112 ±0.070 0.117±0.053 --0.220 ±0.096 --0.218 ±0.067 --0.085 ±0.086 --0.336±0.101
O.128 I0.031 0.067 ±0.026 0.004±0.027 --0.156±0.023 --0.215 ±0.039 --0.111 ±0.025 --0.198 ±0.038 --0.200±0.038
--0.013 ± 0 . ~ 4 0.107 ±0.043 --0.048 ±0.043 --0.100±0.034 --0.103 ±0.054 --0.095 ±0.037 --0.135 t 0 . 0 5 5 --0.147±0.055
t2o
tz~
107
9Be(p, d)aBe REACTION TABLE 1 (continued)
0
0
~p
lab (deg.)
c.m. (deg.)
lab (MeV)
50.0
56.1 56.4 56.4 56.5 56.6 56.7 56.7 56.8 56.8
1.35 1.73 1.86 2.27 2.50 2.70 2.95 3.30 3.63
--0.1994-0.090 0.002 ±0.072 0.015 4 - 0 . 0 7 5 0.008 4-0.077 0.1044-0.072 0.165 4-0.079 --0.081 4-0.082 --0.1174-0.087 --0.4844-0.120
--0.0544-0.033 0.090 4-0.027 0.1344-0.033 --0.029 3:0.033 --0.121 4-0.032 --0.107 4-0.032 --0.113 4-0.035 --0.1344-0.036 --0.1744-0.040
--0.0904-0.052 --0.045 4-0.048 --0.0265:0.046 --0.2044-0.059 --0.1884-0.053 --0.083 4-0.050 --0.203 4-0.058 --0.0524-0.052 --0.0924-0.060
60.0
67.1 67.5 67.7
1.68 2.70 3.63
0.193 4-0.087 0.147-t-0.046 --0.087 4-0.097
0.186 4-0.040 --0.0024-0.018 --0.220 4-0.040
0.002 -t-0.053 --0.1394-4-0.032 --0.054 4-0.053
65.0
72.9 73.0
2.93 3.67
--0.129 4-0.107 0.110 4-0.087
--0.032 -t-0.040 --0.184 -t-0.038
0.055 4-0.062 -- 0.097 4-0.054
70.0
78.2
2.70
0.3364-0.078
--0.039 4-0.030
--0.083 4-0.049
90.0
98.7
2.68
0.0844-0.073
t2o
t21
0.023 4-0.030
t2e
--0.1074-0.052
The tensor moments are referred to the coordinate system with the z-axis in the direction of the outgoing deuteron in the c.m. system. a) AE~ = 800 keV; AEo = 300 keV otherwise.
tive values were m e a s u r e d at the other energies except near 2.00 MeV, where positive values were o b t a i n e d at all angles investigated. The extreme value of t2~ observed was - 0 . 2 7 - t - 0 . 0 5 at E o = 2.95 MeV a n d 0 .... = 23.0 °, while for t2z the largest value m e a s u r e d was - 0 . 2 0 + 0 . 0 5 at Ep = 2.27 MeV a n d 0 . . . . = 56.5 °. F o r purposes of comparison, the results of Ivanovich et al. between 4.9 a n d 9.8 M e V p r o t o n energies are shown in fig. 5 with the data obtained at this l a b o r a t o r y for a lab angle of 30 °. The variation with b o m b a r d i n g energy is evident for all three tensor parameters.
6. Analysis and discussion The p r o t o n b o m b a r d i n g energies used in this investigation correspond to the region o f excitation of 10B f r o m 7.9 to 10.2 MeV. Since the 8Be(g.s.)+ d system has isospin T = 0, it is expected that levels in 1°B having p r e d o m i n a n t l y T = 0 character will play the m o s t significant role in the reaction. The level scheme of ~°B* near a n excitation energy of 8 MeV is complicated a n d has n o t been clearly established; however,
108
A . J . FROELICH AND S. E. DARDEI~
T = 0 levels in i°B have been tentatively assigned 29, 30) for excitation energies of 7.87, 8.07 and 8.66 MeV corresponding to proton bombarding energies of 1.45, 1.65 and 2.30 MeV, respectively. Weber, Davis and Marion 22) measured excitation curves for the 9Be(p, d)SBe reaction at six observation angles for proton energies between 0.8 and 3.0 MeV. Buccino and Smith 31) reported a time-of-flight study of the 9Be(d, n)l°B reaction and suggested the possibility of two levels near 8.1 MeV in 10B." One notable feature of their spectra is that the neutron group corresponding to the 8.1 MeV level(s) has an experimental width ( F W H M ) near 200 keV, whereas the width reported by Hornyak et al. 32) for the 8.07 MeV level is 800__+200 keV. Since the energy resolution of the present investigation was 300 keV, information on only the broadest of levels could be obtained; thus, spectroscopic information on the 8.07 MeV level could be extracted from the tensor polarization data only if the level width is substantially greater than 300 keV. The 8.66 MeV level of 10B appears as a resonance at Ep = 2.3 MeV in both the 9Be(p, d)SBe and 9Be(p, ~)6Li reactions; these were observed both by Weber et aL 22) and Morita et al. 23), who extended the (p, d) angular distribution measurements of Weber et al. to Ep = 3.30 MeV. If, for low bombarding energies, the 9Be(p, d)SBe reaction proceeds predominantly via one- or two-compound-nucleus resonances at any given energy, the angular distributions of the intensity and the polarization of the emitted deuterons should be expressible as sums of relatively few associated Legendre functions, as given, for example, by the general formula of Welton 33). Once a set of spin-parity assignments is chosen, this formula is parameterized only by the products R~R v of the R-matrix amplitudes, and a fit to the data may be attempted when the appropriate angular momentum coupling coefficients are calculated. If incoming and outgoing partial waves for the 9Be(p, d)SBe reaction are limited g* to I = 0, 1 and 2, the number of possible combinations R~Rv reduces to about 50; omission of a possible 0 - level because of its required d-wave formation and isotropic decay leads to possible spin and parity assignments of 1-, 2 - , 1 +, 2 + or 3 + to the Ep = 1.65 and 2.3 MeV 9Be(p, d)SBe resonances corresponding to the 8.07 and 8.66 MeV levels of ~°B*. Unless the two levels are formed in different incident channel spin states, the lack of odd-order terms in the angular-distribution data indicate that the levels involved have the same parity. Also, the angular-distribution data at the 1.65 MeV resonance have the form da/df2 = (14+ 18P2(cos 0))mb/sr,
(3)
which cannot be obtained for any single J~-value among those discussed above. It follows that two or more combinations R*R~ are required in order to reproduce the angular-distribution data alone. An attempt was made to find spin and parity assignments for the 8.07 and 8.66 MeV levels of l°B* which satisfied both the 9Be(p, d)SBe angular-distribution data and
9Be(p, d)aBe REACTION
109
the tensor polarization measurements. For each possible R~Rv corresponding to a unique set of spins, incident and outgoing orbital angular momenta and channel spins, the coefficients involved in the general formulae for a(0) and atzq were calculated. A subroutine to calculate the latter quantities according to Welton's formula was incorporated into a general search program a4) which varied the products R*Rv until a relative minimum was found in the function defined by
+ £ ((at2q)e(O)--(tTt2a)m(O)]2, O,q \
A(at2q)m(O)
(4)
]
where c and m refer to computed and measurec[ quantities and the A are the experimental uncertainties; the sum is performed over the angles of observation at a given bombarding energy. At least three of the possible R~Rv were used in each calculation. Choices made for possible levels contributing to the Ep = 1.65 MeV resonance were 2+-3 +, 1+-2 +, 1+-3 + and 1 - - 2 - ; attempts were made to reproduce the data at proton energies of 1.6, 1.8 and 2.0 MeV. Although several choices of initial values of the parameters were tried, relatively p o o r values of Z2 were obtained in every case. N o combination of parameters resulted in a value of Z2 per degree of freedom within an order of magnitude of unity. Of the 50 possible products R*R~which could enter the cross section and polarization formulae with the restriction l, l' _-< 2, only four combinations of these products satisfied the requirements that the angular distribution near a proton energy ot 1.6 MeV have approximately the form of eq. (3), and that the calculated t20 be positive at forward angles. As an example, a parameter set corresponding to two levels with spin and parity assignments 3 + and 2 - but formed via separate channel spins was not used, since it results in a negative t2o. No calculations were performed assuming more than two levels to be contributing at a given energy, since the number of parameters required would be excessive. The apparent m a x i m u m of t 2 o at forward angles of observation occurs at an energy between the resonances at Ep = 1.65 and 2.3 MeV in the 9Be(p, d)aBe total cross section, thus suggesting that any analysis in terms of states in 10B will have to include interference terms arising from overlapping resonances. The failure of the calculations to reproduce the angular dependence of the lower-energy data suggests that either several levels are contributing to the reaction, or that a direct reaction mechanism contributes significantly to the cross section below Ep = 2 MeV. In spite of some changes in sign, the measured polarization appears to vary relatively slowly with energy above 2.6 MeV, which would be expected if a direct reaction mechanism predominates at these energies. If, on the other hand, the observed effects in this energy region were to be attributed entirely to a small number of states in 10B. ' these would require widths on the order of 500 keV or more in order to produce the
110
A . J . F R O E L I C H A N D S. E. D A R D E N
observed energy dependence of the data. As pointed out above, the cross section data for bombarding energies above 2.5 MeV are strongly indicative of a direct reaction process. The results shown in figs. 1-5 are not inconsistent with this assumption, as they vary rather gradually with bombarding energy. After initial measurements 18) of the t2q from the 9Be(p, d)aBe reaction were carried out in this laboratory, a preliminary direct reaction calculation of the t2q using the DWBA with a spin-orbit potential added to the central optical-model potentials was performed by Satchler. Since aBe is not available as a target nucleus, 9Be(d, d)gBe data were used to fix the parameters for the deuteron optical potential. For the calculation reported here, the target nucleus was assumed to be described by a p~ neutron moving about a aBe core. The optical potentials used were of the Woods-Saxon type with some surface absorption. The various strength and range parameters were chosen from fits to 9 B e + p scattering at 9 MeV and 9 B e + d scattering at 10 MeV. These calculations yielded values of t2q, which were typically smaller than the measured values by an order of magnitude, as can be seen from the solid curves in fig. 3. Possible weaknesses in the DWBA calculation are, in addition to the absence of D-state effects, the lack of tensor spin-orbit potentials in the deuteron-nucleus optical potential and the spherical symmetry of the deuteron-nucleus potential well. Removal of the latter shortcoming would require a more sophisticated calculation than has been attempted to date. More recently, Johnson 21) investigated the effect of including the D-state of the deuteron on the calculated tensor polarization using a perturbation approach with the plane-wave theory. The results of these calculations for a proton energy of 2.5 MeV are given by the dashed curves in fig. 3. In Johnson's calculations, the tensor parameters are expressed as functions of the ratio of D-state to S-state momentum probability amplitudes as follows: 16n y~ (K) A (K) + 8 - ~A z (K) t2a = - T I+A2(K) '
(5)
where K = ½k~-k~,
A(K) = u2(K)/uo(K), where u o and u 2 are the radial parts of the S- and D-components of the deuteron wave function in momentum space. The data fail to follow even qualitatively the form given in eq. (5), since both Y~ (K) and A (K) are slowly varying functions of proton bombarding energy for any given angle of observation. In particular, the changes in sign of t21 with proton energy at a lab observation angle of 30 ° as shown in fig. 5 are inconsistent with this formula. However, it was pointed out by Johnson that the plane-wave polarization calculations probably underestimate the D-state effects somewhat. The presence of non-negligible tensor polarizations, at angles and energies where the vector polarization measurements described in sect. 1 were made, calls into ques-
9Be(p, d)SBe REACTION
111
tion the validity of the assumptions used in these experiments to obtain the vector polarization from the data. The simple relationship
da/d~2 =
(da/df2)o(1 + 3PpPd)
must be replaced by the general expression 3 5) which includes second-rank polarization effects. Inclusion of the second-rank effects requires knowledge of the tensor polarization produced in the 9Be(p, d)SBe reaction as well as the tensor analysing powers of the 12C(d, p)l 3C and 2H(d, p)3H reactions. Assuming the tensor polarization effects in the above reactions to be comparable in magnitude to those found for the 9Be(p, d)SBe reaction, the contribution of those effects to the measured asymmetries would be of the same order as were observed 12-15).
7. Summary The tensor polarization of deuterons emitted from the 9Be(p, d)SBe reaction has been measured at several angles of observation for proton bombarding energies ranging from 1.6 to 3.8 MeV. Substantial values of the t2q were found. The failure to reproduce even qualitatively the polarization and cross-section data for energies near the cross-section maxima at 1.65 and 2.3 MeV proton energy in terms of simple excitation of one or two levels in 1oB suggests that either several levels are involved, or that appreciable direct reaction is occurring at these energies. The energy and angular dependence of the data above E v = 2.6 MeV appear to be generally consistent with the assumption of a predominantly direct reaction mechanism. However, comparison of the data with the limited direct-reaction calculations available leads to the conclusion that such simplifications as lack of spin-dependent distortion and neglect of the D-state of the deuteron cannot be used in a DWBA calculation, if polarization effects are to be reproduced by the theory. A more complete calculation, which removes both of these restrictions and takes into account tensor terms in the deuteron-nucleus potential as well as the distortion of the initial and final nuclei, may be required to reproduce the data. It might be of interest to investigate other deuteron-producing direct reactions, such as (SHe, d) reactions, to see if significant tensor polarization effects are present. The authors are grateful to Messrs. K. Corrigan, J. Hevezi, J. T. Klopcic and T. G. Sauer for their assistance in taking the data.
References 1) L. J. B. Goldfaxb, Proc. Int. Symp. on polarization phenomena of nucleons (Birkh[iuser Verlag, Basel, 1966) p. 203 2) L. Rosen, ibid., p. 253 3) P. Schwandt and W. Haeberli, Nucl. Phys. A l l 0 (1968) 585 4) J. Raynal, Phys. Lett. 7 (1963) 281 5) L. C. Mclntyre and W. Haeberli, Nucl. Phys. Agl (1967) 382
112
A.J. FROELICH AND S. E. D A R D E N
6) H. Meiner, E. Baumgartner, S. E. Darden, P. Huber and G. R. Plattner, Helv. Phys. Acta 40 (1967) 483 7) G. R. Satchler, Nucl. Phys. 55 (1964) 1 8) T. J. Yule and W. Haeberli, Phys. Rev. Lett. 19 (1967) 756 9) Yu. V. Gofman, N. I. Zaika, A. V. Mokhnach, O. F. Nemets, P. L. Shmarin and A. M. Yasnogorodskii, J. Nucl. Phys. (USSR) 5 (1967) 718; Soy. J. Nucl. Phys. 5 (1967) 510 10) G. L. Vysotskii and A. G. Sitenko, ZhETF (USSR) 36 (1959) 1143; JETP (Soy. Phys.) 9 (1959) 812 11) L. J. B. Goldfarb and R. C. Johnson, Nucl. Phys. 18 (1960) 353 12) R. Barloutaud, H. Faraggi, L. Rosen and S. M. Shafroth, J. de Phys. 21 (1960) 369 13) J. M. Lambert, L. Madansky and G. E. Owen, Phys. Rev. 124 (1961) 1959 14) M. S. Bokhari and V. V. Verbinski, Bull. Am. Phys. Soc. 9 (1964) 627 15) V. V. Verbinski and M. S. Bokhari, Phys. Rev. 143 (1966) 688 16) C.L. Petitjean, P. Huber, H. Paetz gen. Schieck and H. R. Striebel, Helv. Phys. Acta, 40 (1967) 401 17) B. P. Ad'yasevich, Yu. P. Polunin and D. E. Fomenka, J. Nucl. Phys. (USSR) 5 (1967) 713; Sov. J. Nucl. Phys. 5 (1967) 507 18) S. E. Darden and A. J. Froelich, Phys. Rev. 140 (1965) B69 19) M. Ivanovich, H. Cords and G. U. Din, Nucl. Phys. A97 (1967) 177 20) L. Brown, H. A. Christ and H. Rudin, Nucl. Phys. 79 (1966) 459 21) R. C. Johnson, Nucl. Phys. A90 (1967) 289 22) G. Weber, L. W. Davis and J. B. Marion, Phys. Rev. 104 (1956) 1307 23) S. Morita, T. Tohei, T. Nakagawa, T. Hasegawa, H. Ueno and Hsu Chu-chtmg, Nucl. Phys. 66 (1965) 17 24) T. Yanabu, S. Yamashita, S. Kakigi, D. Nguyen, K. Takimoto, Y. Yamada and K. Ogino, J. Phys. Soc. Japan 19 (1964) 1818 25) F. H. Read and J. M. Calvert, Proc. Phys. Soc. 77 (1961) 65 26) W. Tr~ichslin, H. Biirgisser, P. Huber, G. Michel and H. R. Striebel, Helv. Phys. Acta 38 (1965) 523 27) L. C. Mclntyre, Ph.D. thesis, University of Wisconsin (1965) available from University Microfilms, Ann. Arbor, Michigan, USA 28) W. A. Schier, Ph.D. thesis, University of Notre Dame (1964) 29) J. D. Purvis, F. Ajzenberg-Selove and L. M. Polsky, Phys. Rev. 162 (1967) 1005 30) T. Lauritsen and F. Ajzenberg-Selove, Nucl. Phys. 69 (1966) 1 31) S. G. Buccino and A.B. Smith, Phys. Lett. 19 (1965) 234 32) W. F. Hornyak, C. A. Ludemann and M. L. Roush, Nucl. Phys. 50 (1964) 424 33) T.A. Welton, in Fast neutron physics, Part II, ed. by J. B. Marion and L. J. Fowler (Interscience, New York, 1963) p. 1349 34) W. D. Davidon, ANL-5990 Rev. (1959) 35) G. R. Satchler, Nucl. Phys. 3 (1958) 67
] I
Nuclear Physics All9 (1968) 97--112; (~) North-Holland Publishing Co., Amsterdam N o t to be reproduced by p h o t o p r i n t or microfilm without written permission f r o m the publisher
TENSOR POLARIZATION OF DEUTERONS F R O M T H E 9Be(p, d)SBe R E A C T I O N F O R Ep = 1.6-3.8 MeV A. J. FROELICH and S. E. DARDEN Department of Physics, University of Notre Dame, Notre Dame, Indiana t Received 24 June 1968 Abstract: The tensor polarization of the deuterons from the aBe(p, d)SBe reaction was measured for proton energies in the range 1.6-3.8 MeV and for lab emission angles between 10° and 90°. The tensor polarization was measured by observing the deviation from isotrcpy of the proton angular distribution of the SHe(d, p)4He reaction, when the deuterons from the 9Be(p, d)SBe reaction were incident on a 3He gas cell with energies below 600 keV. The largest magnitude of polarization observed occurred at/~p = 2.0 MeV, 0tab = 10°, where t~0 was found to be 0.53 :k0.08. For proton bombarding energies below 2.6 MeV, a pronounced energy dependence of the polarization is present, while in the energy range 2.7-3.8 MeV less variation was observed. Neither a DWBA calculation using spin-orbit potentials nor a plane-wave calculation including deuteron D-state effects has been successful in reproducing the magnitude and angular variation of the tensor polarization data, although the differential cross-section data above Ep = 2.5 MeV strongly suggest that the (p, d) "pick-up" reaction is the predominant reaction mechanism at these bombarding energies. E
NUCLEAR REACTION 9Be(p, d)SBe, Ep = 1.6-3.8 MeV, AEp = 300 keV; measured tensor polarizations t~q(Olab~ 90°).
[
I
1. Introduction A l t h o u g h it has been realized for some time that spin-dependent forces are of imp o r t a n c e in direct reactions 1), the n a t u r e a n d extent of these forces have n o t yet been completely established. Analyses of elastic-scattering m e a s u r e m e n t s using polarized beams have given some i n f o r m a t i o n o n the vector spin-orbit potential for nucleons a n d deuterons interacting with nuclei 2, a), b u t little knowledge has been gained a b o u t tensor spin-orbit potentials for deuterons 3, 4) except that phase-shift analyses of deuteron elastic scattering and polarization data indicate some such potential is required [refs. s, 6)]. While distorted-wave B o r n a p p r o x i m a t i o n ( D W B A ) calculations which include vector spin-orbit terms i n the optical potentials 7) have been f o u n d to be useful in establishing the j - d e p e n d e n c e of Pd(0) for (d, p) reactions i n d u c e d by vectorpolarized deuterons a), they have n o t been very successful in reproducing n u c l e o n polarizations observed in stripping reactions. The extent of d e u t e r o n tensor-polarization effects in stripping a n d pick-up reactions has n o t yet been established. Such effects c a n influence m e a s u r e d asymmetries in the t Work supported in part by the U.S. Office of Naval Research under Contract No. Nonr.-1623 (05). 97
98
A.J. FROELICH AND S. E. DARDEN
nucleons emitted from stripping reactions induced b y polarized deuterons 1). For example, Gofman et al. 9) measured the asymmetry in protons emitted from the zZC(d, p)l 3C and 14N(d, p)l 5N stripping reactions initiated by deuterons which had been elastically scattered from carbon at an incident deuteron energy of 13.6 MeV. From the similar angular dependence of the asymmetry obtained for the two cases, these authors concluded that either the spin-orbit interaction can be neglected in the stripping reaction, or that tensor polarization effects in (d, p) reactions are small. If it is assumed that both conclusions are valid, the asymmetry of protons emitted in a (d, p) stripping reaction induced by a deuteron beam having polarization Pa is given by e = 3PpPa, where Pp is the proton polarization produced by unpolarized deuterons [refs. lo, 11)]. Previous investigators 13-15) had made this assumption in attempting to measure the vector polarization of deuterons from the 9Be(p, d)SBe reaction. At a proton bombarding energy of 3 MeV and deuteron emission angle of 30 °, Lambert et al. 13) obtained a value Pd = 0.11 _+0.05, while Verbinski and Bokhari 15) reported Pa = 0.17___0.05. Since the former authors used the 2H(d, p)3H reaction as an analyser, and the latter employed the 12C(d, p)l 3C reaction, the similarity of their results is consistent with the results of Gofman et al. 9). However, recent measurements by Petitjean et al. 16) and by Ad'yasevich et al. 17), using beams from polarized-ion sources, demonstrate that the 2H(d, p)3H reaction is highly sensitive to deuteron tensor polarization as well as vector polarization. In addition, substantial tensor polarization of the deuterons from the 9Be(p, d)SBe reaction has been measured by the authors is) for proton energies of 2.5 and 3.7 MeV and by Ivanovich et al. 19) t for proton energies from 4.9 to 9.8 MeV. For all of these measurements, the 3He(d, p)4He reaction 2o) was used as an analyser. A preliminary DWBA calculation presented with the earlier 9Be(p, d)SBe tensor polarization data is) failed to give quantitative agreement but appeared to predict the correct signs of the tensor parameters t* t2~. Moreover, the tensor polarization reported by Ivanovich et al. 19) exhibits a significant energy dependence over the entire energy range investigated. Johnson 21) proposed that the D-state component of the deuteron wave function might affect the tensor polarization. A perturbation calculation using plane waves showed that tensor polarization of the order of 0.05 could be obtained for deuterons from (p, d) reactions simply by including the effect of the D-state. Although this result establishes the necessity of including the D-state in any accurate calculations, the plane-wave calculation failed to reproduce the angular distributions of the t2~ and does not yield the sort of energy dependence observed by Ivanovich et al. Since the angular distribution data for the 9Be(p, d)SBe reaction have been well reproduced at angles less than 60 ° by direct reaction calculations 22-25), one might expect a sufficiently sophisticated calculation to reproduce the polarization data as well. The lack of agreement of measured and calculated tensor polarizations prompted us to ? T h e s i g n o f t21 as r e p o r t e d i n ref. as) s h o u l d be r e v e r s e d . t t W e h a v e a d o p t e d t h e n o t a t i o n t2~ = (T~e).
aBe(p, d)SBe REACTION
99
extend the previous measurements of this laboratory. In addition to measurements at energies where the direct-reaction mechanism appears to predominate, data were also taken in the vicinity of the previously reported 22) broad resonances in the 9Be(p, d)SBe cross section at proton energies of 1.65 and 2.3 MeV corresponding to excitation energies of 8.07 and 8.66 MeV in the compound nucleus 10B. it was hoped that these latter measurements might provide information on spin and parity assignments for these states. Proton bombarding energies were in the range Ep(lab) = 1.6-3.8 MeV. Measurements of the tensor polarization of deuterons emitted at lab angles between 10 ° and 50 ° were carried out in 10 ° intervals for eight proton energies, with some additional measurements at angles of 60 °, 65 ° and 90 ° for selected energies.
2. Experimental method The essential details of the experimental method and equipment employed for these measurements have been described previously 18, 19), therefore only the briefest description will be presented with comments appropriate to this particular experiment. The method consisted of bombarding thin beryllium foils with a proton beam from the Notre Dame electrostatic accelerator and observing the anisotropy in the yield of the 3He(d, p)4He reaction when the deuterons from the 9Be(p, d)SBe reaction were incident on a 3He target cell. Four thin CsI(TI) crystals were used to detect the protons emitted from the analysing reaction at four different angular positions, and the t2q were determined from the relative normalized counting rates of the detectors. Since the tensor polarization analysing power of the 3He(d, p74He reaction is relatively well known 2 o7 for deuteron energies below 600 keV, the deuterons were degraded in energy by absorber foils before entering the gas cell. The upper limit of 600 keV for the use of 3He(d, p)4He as a reliable analysing reaction is our best estimate based on a consideration of the available data for this reaction and for the mirror 3H(d, n)4He reaction 26). l~or low incident deuteron energies, the angular distribution of the protons from the 3He(d, p)4He reaction is given by the following formula
[ref. 277]: ~(0, 4, E~7 = ~o(E.){1-:(E.)[~/~(3 cos20- l)t2o --x/3 sin 0 cos 0 cos t~t2t +½n/3 sin20 cos 2~bt22]},
(1)
where the t2q describe the tensor polarization of the incident deuteron beam, tro the cross section for an unpolarized deuteron beam, 0 the c.m. reaction angle and q~ the azimuthal angle of the protons referred to the coordinate system in which the t2~ are specified. This coordinate system as used here is the same as in ref. 187, i.e. the z-axis is parallel to the deuteron beam direction, and the y-axis is defined by k v x ka, where kp and kd are the momenta of the incident and outgoing beams in the (p, d) reaction. The parameter p ( E 7 is a measure of the relative strength of the two possible s-wave channels in the 3He(d, p)aHe reaction, the polarization-sensitive J~ = ½+ channel
100
X.J.
F R O E L I C H A N D S. E. D A R D E N
and the polarization-insensitive J~ = ½+ channel; it is given in ref. 6) based on the measurements of Brown et al. 2 0).
3. Apparatus Some modifications of the apparatus used in the previous measurements were made [ref. is)]. The single-absorber foil mount was replaced by a set of four frames placed along the deuteron beam path, and these could be positioned by rods extending through the top of the reaction chamber. Four foil positions are available on each frame, therefore a suitable combination of absorber foils could be inserted for each measurement without opening the reaction chamber. The chamber exit foil was removed, and the 3He cell was vacuum-sealed directly to the chamber by means of an O-ring in order to permit measurements on deuterons having an energy as low as 1350 keV, the energy loss in the SHe cell entrance foil being 750 keV for deuterons of that energy. A set of collimating slits was introduced between the beryllium target position and the absorber foils; this resulted in an angular acceptance of 7 ° for the 3He cell. For the data reported here, the SHe cell was filled to a pressure of 4.7 atm or less. At 4.7 atm, deuterons entering the cell with an energy of 500 keV are stopped within its volume. In order to minimize the deterioration of the beryllium targets which results from beam bombardment, two different types of target holders were tried. The first is a rotating frame device 2s) which is constructed such that the axis of rotation of the target is parallel to the reaction plane. Proper vertical adjustment of the target holder causes the beam to describe a circular path on the target as it rotates, thus effectively spreading the beam over more of the target area. Unfortunately, the poor heat transfer from the rotating frame to the rest of the structure made operation with this device marginal when the beam current exceeded 5#A. The alternate target holder, used for the majority of the measurements, is a water-cooled hollow brass cylinder soldered to a plate capable of holding four individual target frames. Efficient heat removal is obtained by cementing target foils to the frames, which are screwed to the plate to make good thermal contact. The photomultiplier spectra of the protons from the 3He(d, p)aHe reaction were improved over those obtained in the earlier measurements 1s) by reducing the voltage on the photomultiplier tubes. As in the previous experiment, the spectra from the four detectors were accumulated in four quadrants of a 256-channel memory; however, instead of a 256-channel analyser, a 256-channel section of a Nuclear Data-160 analyser was used. This allowed several spectra to be stored in memory before readout was required.
4. Experimental procedure For each individual measurement, the procedure followed was (i) to determine the target foil orientation which would result in a proton energy loss of approximately
eBe(p, d)SBe REACTION
101
300 keV, (ii) to determine the combination of absorber foils for which the deuterons at the angle of observation enter the 3He cell with a m a x i m u m energy of about 600 keV, (iii) to verify steps (i) and (ii) by measuring the yield from the analysing reaction as a function of proton bombarding energy, (iv) to accumulate a sufficient number of counts for a calculation of the tzq to an average statistical accuracy of __+0.05, (v) to obtain a normalization of the counting rates in the various detectors by initiating the analysing reaction with unpolarized deuterons and (vi) to measure any background present in the counter spectra. These steps were not necessarily carried out in chronological order; item (v) was usually performed at the outset of each measurement since it provided a rapid and convenient check on the electronics. Also, background runs were taken at regular intervals during the course of a measurement in order to minimize errors introduced by amplifier drift and target deterioration. The beryllium targets employed in this investigation were thin self-supporting foils t of thickness 1.6 mg/cm z and 2.7 mg/cm z. These foils are 270 and 450 keV thick, respectively, to a 1500 keV proton beam. In order to maintain a degree of uniformity in the data accumulation, it was decided to fix the proton energy loss in the beryllium target at 300 keV regardless of the bombarding energy chosen for each measurement. This was achieved by orienting the Be foil at the proper angle to the incident beam direction. In most cases, placing the plane of the target a t an angle to the incident beam direction decreased the energy spread of the outgoing deuterons from the 9Be(p, d)SBe reaction below what it would be for a normally incident beam. This energy spread is caused mainly by the difference in energy loss for protons and deuterons in beryllium and was usually less than 100 keV. In order to ensure that the energy of the deuterons entering the 3He cell did not exceed 600 keV, a series of foils was usually employed to reduce the energy of the emitted deuterons. Once the maximum energy of deuterons emerging from the target foil was established, the absorber foil or combination of foils which would reduce that energy to 1350 keV was inserted between the 3He cell and the Be target. To confirm that the deuterons entered the 3He cell with an energy of approximately 600 keV, the yield in all four detectors of protons from the 3He target was measured as a function of the energy of the protons incident on the beryllium target. This yield curve was then compared with that calculated taking into account the energy loss in the beryllium foil, the slowing-down foils and the 3He cell entrance foil. I f the comparison between measured and calculated yield curves showed that the desired bombarding energy was compatible with the choice of absorber foils used for the yield-curve measurement, data could be taken at the nominal bombarding energy. In most cases, the proper bombarding energy for the foils used in the yield measurement was within 100 keV of the desired energy and was used instead of the nominal energy for the data runs. Use of the measured yield curve to determine the proper bombarding energy is estimated to be accurate to about ___50 keV in the choice of bombarding energy. This t The foils were obtained from the Brush Beryllium Co., Cleveland, Ohio.
102
A . J . F R O E L I C H A N D S. E. D A R D E N
method of determining the proper bombarding energy was checked for one measurement by replacing the 3He cell with an energy-calibrated solid state detector. The operating conditions for the measurement, i.e. bombarding energy, target foil thickness and angle and absorber foils used, were reproduced as accurately as possible, and a foil cut from the same sheet as the 3He cell entrance foil was placed in front of the detector to simulate the 3He cell entrance foil. Although greatly obscured by the 9Be(p, p)9Be elastic-scattering peak, the ground-state deuteron group in the resulting spectrum could be seen to have a m a x i m u m energy of about 630 keV. Once a satisfactory yield curve had been obtained for a given energy and angle, tensor polarizations were measured in a series of runs. The beam current passing through the beryllium target was collected on the beam stop and fed to a current integrator; the duration of each run was chosen to yield at least 100 counts per detector in the peak regions of the detector spectra. Interspersed between these measurements were background runs of comparable duration made with a 25.4/~m tantalum foil intercepting the deuterons incident on the 3I[e cell. A minimum of approximately 1000 proton counts per detector was accumulated for each measurement. To eliminate effects arising from differences in detector solid angles and efficiencies, deuterons elastically scattered from a 9.7 mg/cm z thick gold foil target were used for normalization measurements. For most of these measurements, the reaction chamber was set at a lab observation angle of 50 ° with a foil angle of 25 °, and no absorber foils were used. Yield curves measured under these conditions indicated a deuteron bombarding energy of 2.1 MeV. The deuterons scattered from Au can safely be assumed to be unpolarized, since at this low energy and forward emission angle, Rutherford scattering certainly predominates. This assumption was confirmed by the fact that the relative counting rates for a deuteron-gold scattering angle of 50 ° did not differ from those obtained when the deuteron beam from the accelerator was put directly into the 3He cell. Normalization runs were usually made at the outset of each series of measurements. The high counting rate of about 250 counts per min per detector also made it convenient to use the scattered beam in checking the amplifiers and routing circuitry. It was desired in this investigation to accumulate a set of measurements covering the bombarding energy range of our accelerator. It was also intended that the angular range of the measurements be as great as possible. The rapid energy variation of the 9Be(p, d)SBe cross section below 1.5 MeV made measurements with 300 keV thick targets seem pointless and established at these energies a lower energy limit to the measurements; using significantly thinner targets would have required inordinately long data-accumulation times. The average proton beam current used in this investigation varied from about 3/~A to 7#A. The lower figure was obtained when the accelerator source output was poor; the upper limit was dictated by the inability of the target to dissipate the heat produced by the passage of larger beam currents through it. The counting rate of each proton detector varied from a m a x i m u m of 6 counts/min at a bombarding energy of
9Be(p, d)aBe REACTION
103
3.8 MeV and an observation angle of 10 ° to a minimum of 40 counts/h at 2.8 MeV and 70 ° , respectively. The extremely low counting rates at large observation angles made it impractical to extend the measurements beyond 50 ° for more than a few energies. The average data-taking time at one energy and angle was 10 h.
5. Results of the measurements
The counting rates for the four detectors were converted to the t2~ by use of eq. (1). Normalized measured counting rates in the four detectors were equated to expressions obtained by integrating eq. (1) over the solid angles subtended by the detectors, and the resulting four equations were solved for the t2q. The coefficient p which was used was determined by averaging the measured value 6, z o) of p over the deuteron energies occurring in the 3He cell weighted by the 3He(d, p)4He cross section. The result is
I p(E) o'(E)dE (p) = '
(dE/dx)E
: ~(E)dE
0.89+0.02,
(2)
(dE/dx)~ where the integrals have been approximated by sums. The t2q obtained by this procedure are referred to the outgoing deuteron direction in the lab system as described in sect. 2; the corresponding center-of-mass values are obtained by transforming the measured t2q to a coordinate system in which the z-axis is along the direction of the outgoing deuteron beam in the c.m. system, and the y-axis is unchanged. Geometrical effects involved in the data reduction arise from the uncertainties in the point of origin of the deuteron beam, in the mean position at which the analysing reaction occurs and in the angles at which the protons from the 3He(d, p)4He reaction are observed. Since the incident beam was collimated to a size less than one-tenth that of the entrance aperture of the 3He cell, corrections for the spatial extension of the source of the deuterons can be safely neglected. Calculations were performed to estimate the effect of the displacement of the point at which the 3He(d, p)4He reaction occurs from the geometrical center of the gas cell. This displacement was calculated for the experimental arrangement used for these measurements from the 9Be(p, d) 8Be and Au(d~ d)Au differential cross sections. The displacement is in the direction of smaller scattering or reaction angle and affects chiefly the measured value of The calculated effect was significantly less than the statistical uncertainties, and no correction was made for it. The background counting rates were determined for each measurement by accumulating data for a fraction of the running time with a 25 # m tantalum foil inserted between the beryllium target and the 3He cell. This insured that no deuterons entered the 3He cell, and only background spectra were obtained under these conditions. Typical backgrounds encountered amounted to about 5 ~ of the counting rate for
tzl.
104
A.
J 4
~
J. FROELICH
i
t2o
!
!
~
I
'
i
i
[
_~_ r
i
-}-@
i
t~,
'@'
2
[
2.o
I
I
2.5 .3.o Ep (MeV)
,++ +,
|
3.6
1.5
Fig. 1. The measured tza as functions o f proton bombarding energy for a lab observation angle o f 20 ° . I
i
1
I
I
0.2 Ep = 2.7 MeV
{{{
-0.2
-0.4
0.2
-0.6
t2,
t2, I
-0.2
-O'iI
~
{
{
.... PWaA,D-stote] --
---~---+~
-L__I
DWBA
J
I
20
i
P
I
I
40
I
I
'
I
~
r
60 8e.m. (degrees)
'
I
I
{{
-0°
I
I
I|
I
i
I/
,
-0'2[ I
i
T
-0..' r
3.5
t2o -0.2
-0.4
2.5 5.0 Ep (MeV)
Ep = 3.7 MeV
{
t2o
t2z
2.0
Fig. 2. The measured t2~ as functions o f proton bombarding energy for a lab observation angle o f 50 °.
t
0.4 0.2
I ; I
+4-+_+ 4-
-0.2
J
0"e.rn.= 56.7*
+
o.2
--{-++_{_4__-{ ---{-
h.5
i
-0.4
-o2
-
i
I
-4-! -{-i
i
0.2
0.Z
t~,
S. E. DARDEN
i
8c ~-- 2 5 0 °
0.2
AND
80
I00
Fig. 3. Angular distributions o f the tensor polarization for/~v = 2.7 MeV. The curves are discussed in the text.
i
{{{
I
~ I
2O
40
60
80
Ocm.(degrees) Fig. 4. Angular distributions o f the tensor polarization for/~p = 3.7 MeV.
aBe(p, d)aBe REACTION
105
detector 3 and about half that amount for the other detectors. The background counts appeared to arise from neutrons produced in the 9Be(p, n)gB reaction. The polarization parameters t2q obtained from the counter ratios and corrected for the efficiency of the analysing reaction are presented in figs. 1 and 2 as functions of the average proton bombarding energy for mean c.m. observation angles of 23 ° and 56 °, respectively. Similar data were obtained for angles of 11 °, 34 ° and 45 °. Angular distributions of the t2q measured at average proton bombarding energies of 2.7 and 3.7 MeV are shown in figs. 3 and 4, respectively. The energy dependence of the polari-
0.2
tzo
--+-
+----~
[
,
-0.2
0L,a= 30°
-0.4 0.2
t21
----+ ~---+- ~
-0.2 o present work -OA
Ivonovich et ol Dorden and Froelich
0.2
t2z -0.2 L 2
F
! 4
I
I I 6 E'p ( M e V )
I
I
IO
Fig. 5. Summary of 30° measurements; points labelled Ivanovich et al. are from ref. la), while those labelled Darden and Froehlich are from ref. is).
zations measured at 11 ° is similar to that shown for 23 °, while the 46 ° data resemble the 30 ° data shown in fig. 5. All of the data obtained are given in table 1 with the c.m. angles corresponding to the lab observation angles at each energy. Because of the small Q-value of the reaction, the difference between lab and c.m. angles changes by less than 1° over the proton energy range of the measurements. The t2~ display some variation with bombarding energy, particularly below Ep = 2.7 MeV. Most pronounced is the energy dependence of t z o , which ranges from +0.53_+0.08 atEp = 2.00 MeV to -0.204-0.10 at Ep = 3.16 MeV for 0.... = 11.5°. The values of tzt appear to be generally positive in the energy region below Ep = 2.2 MeV and generally negative from Ep = 2.2 MeV up to the highest energy measured. Essentially zero values of t22 were found below Ep = 2.0 MeV, and generally nega-
106
A. J. FROELICH AND S. E. DARDEN
TABLE 1
Measured tensor polar~ations t~(Oe.m, ) 0 lab (deg.)
0
~p
c.m.
(deg.)
lab (MeV)
10.0
11.4 11.5 11.5 11.5 11.5 11.5 11.5 11.5 11.5 11.6
1.60 2.00 2.27 2.50 2.61 2.78 2.97 3.16 3.55 3.70
0.281 ±0.077 0.531 ±0.078 0.396 ±0.043 0.2644-0.069 --0.155 ±0.082 --0.201 ±0.083 --0.1244-0.075 --0.1994-0.098 --0.148±0.090 0.013±0.057
0.0274-0.030 0.072±0.031 0.020 ±0.016 --0.016±0.025 --0.1984-0.032 --0.128 ±0.031 --0.133±0.028 --0.128±0.032 --0.0944-0.034 --0.103±0.024
0.000±0.044 0.049±0.048 0.044 ±0.026 0.026±0.040 0.0184-0.043 --0.087 ±0.048 --0.0384-0.044 0.013 ±0.046 --0.022±0.049 --0.018±0.034
20.0
22.8 22.9 22.9 22.9 23.0 23.0 23.0 23.0 23.0 23.0
1.78 2.00 2.25 2.45 2.65 2.80 2.95 3.16 3.43 3.66
0.180!0.025 0.217 t0.073 0.322 ±0.068 0.121 ±0.066 --0.026 ±0.067 --0.133±0.088 --0.126±0.086 --0.176±0.040 --0.130±0.083 --0.160±0.089
0.038 ±0.029 O.126 ±0.030 --0.016 ±0.025 --0.109 ±0.028 --0.233 &0.032 --0.206±0.037 --0.222±0.035 --0.207 ~0.018 --0.162±0.033 --0.100±0.031
--0.031 ±0.046 0.083 ±0.047 0.035 ±0.040 --0.020 ±0.040 --0.075 ±0.046 --0.086i0.052 0.034±0.049 --0.005±0.024 --0.090±0.053 0.007 ±0.046
30.0
34.1 34.2 34.3 34.3 34.3 34.4 34.4 34.4 34.4 34.4 34.5
1.66 2.00 2.25 2.52 2.66 2.65 ~) 2.91 3.03 3.26 3.50 3.68
0.220±0.046 0.242 ±0.040 0.138i0.038 0.049 ±0.080 --0.074 ±0.097 0.064±0.055 --0.001 +0.087 --0.090±0.086 --0.233±0.094 --0.166±0.098 --0.087±0.081
0.085±0.018 0.061 ±0.015 --0.007±0.016 --0.161 ±0.036 --0.260 ±0.042 --0.211 ±0.027 --0.244 ±0.041 --0.127±0.035 --0.132±0.035 --0.130±0.038 --0.054&0.030
0.022±0.028 0.106 ±0.025 --0.104±0.025 --0.041 ±0.048 --0.161 ±0.064 --0.090 ±0.036 --0.168 ±0.060 --0.072±0.050 --0.1654-0.056 --0.179 ±0.061 --0.095±0.048
40.0
45.3 45.4 45.5 45.6 45.6 45.7 45.7 45.8
1.72 2.05 2.25 2.70 2.90 3.12 3.58 3.82
0.082 ±0.071 0.266 ±0.066 0.112 ±0.070 0.117±0.053 --0.220 ±0.096 --0.218 ±0.067 --0.085 ±0.086 --0.336±0.101
O.128 I0.031 0.067 ±0.026 0.004±0.027 --0.156±0.023 --0.215 ±0.039 --0.111 ±0.025 --0.198 ±0.038 --0.200±0.038
--0.013 ± 0 . ~ 4 0.107 ±0.043 --0.048 ±0.043 --0.100±0.034 --0.103 ±0.054 --0.095 ±0.037 --0.135 t 0 . 0 5 5 --0.147±0.055
t2o
tz~
107
9Be(p, d)aBe REACTION TABLE 1 (continued)
0
0
~p
lab (deg.)
c.m. (deg.)
lab (MeV)
50.0
56.1 56.4 56.4 56.5 56.6 56.7 56.7 56.8 56.8
1.35 1.73 1.86 2.27 2.50 2.70 2.95 3.30 3.63
--0.1994-0.090 0.002 ±0.072 0.015 4 - 0 . 0 7 5 0.008 4-0.077 0.1044-0.072 0.165 4-0.079 --0.081 4-0.082 --0.1174-0.087 --0.4844-0.120
--0.0544-0.033 0.090 4-0.027 0.1344-0.033 --0.029 3:0.033 --0.121 4-0.032 --0.107 4-0.032 --0.113 4-0.035 --0.1344-0.036 --0.1744-0.040
--0.0904-0.052 --0.045 4-0.048 --0.0265:0.046 --0.2044-0.059 --0.1884-0.053 --0.083 4-0.050 --0.203 4-0.058 --0.0524-0.052 --0.0924-0.060
60.0
67.1 67.5 67.7
1.68 2.70 3.63
0.193 4-0.087 0.147-t-0.046 --0.087 4-0.097
0.186 4-0.040 --0.0024-0.018 --0.220 4-0.040
0.002 -t-0.053 --0.1394-4-0.032 --0.054 4-0.053
65.0
72.9 73.0
2.93 3.67
--0.129 4-0.107 0.110 4-0.087
--0.032 -t-0.040 --0.184 -t-0.038
0.055 4-0.062 -- 0.097 4-0.054
70.0
78.2
2.70
0.3364-0.078
--0.039 4-0.030
--0.083 4-0.049
90.0
98.7
2.68
0.0844-0.073
t2o
t21
0.023 4-0.030
t2e
--0.1074-0.052
The tensor moments are referred to the coordinate system with the z-axis in the direction of the outgoing deuteron in the c.m. system. a) AE~ = 800 keV; AEo = 300 keV otherwise.
tive values were m e a s u r e d at the other energies except near 2.00 MeV, where positive values were o b t a i n e d at all angles investigated. The extreme value of t2~ observed was - 0 . 2 7 - t - 0 . 0 5 at E o = 2.95 MeV a n d 0 .... = 23.0 °, while for t2z the largest value m e a s u r e d was - 0 . 2 0 + 0 . 0 5 at Ep = 2.27 MeV a n d 0 . . . . = 56.5 °. F o r purposes of comparison, the results of Ivanovich et al. between 4.9 a n d 9.8 M e V p r o t o n energies are shown in fig. 5 with the data obtained at this l a b o r a t o r y for a lab angle of 30 °. The variation with b o m b a r d i n g energy is evident for all three tensor parameters.
6. Analysis and discussion The p r o t o n b o m b a r d i n g energies used in this investigation correspond to the region o f excitation of 10B f r o m 7.9 to 10.2 MeV. Since the 8Be(g.s.)+ d system has isospin T = 0, it is expected that levels in 1°B having p r e d o m i n a n t l y T = 0 character will play the m o s t significant role in the reaction. The level scheme of ~°B* near a n excitation energy of 8 MeV is complicated a n d has n o t been clearly established; however,
108
A . J . FROELICH AND S. E. DARDEI~
T = 0 levels in i°B have been tentatively assigned 29, 30) for excitation energies of 7.87, 8.07 and 8.66 MeV corresponding to proton bombarding energies of 1.45, 1.65 and 2.30 MeV, respectively. Weber, Davis and Marion 22) measured excitation curves for the 9Be(p, d)SBe reaction at six observation angles for proton energies between 0.8 and 3.0 MeV. Buccino and Smith 31) reported a time-of-flight study of the 9Be(d, n)l°B reaction and suggested the possibility of two levels near 8.1 MeV in 10B." One notable feature of their spectra is that the neutron group corresponding to the 8.1 MeV level(s) has an experimental width ( F W H M ) near 200 keV, whereas the width reported by Hornyak et al. 32) for the 8.07 MeV level is 800__+200 keV. Since the energy resolution of the present investigation was 300 keV, information on only the broadest of levels could be obtained; thus, spectroscopic information on the 8.07 MeV level could be extracted from the tensor polarization data only if the level width is substantially greater than 300 keV. The 8.66 MeV level of 10B appears as a resonance at Ep = 2.3 MeV in both the 9Be(p, d)SBe and 9Be(p, ~)6Li reactions; these were observed both by Weber et aL 22) and Morita et al. 23), who extended the (p, d) angular distribution measurements of Weber et al. to Ep = 3.30 MeV. If, for low bombarding energies, the 9Be(p, d)SBe reaction proceeds predominantly via one- or two-compound-nucleus resonances at any given energy, the angular distributions of the intensity and the polarization of the emitted deuterons should be expressible as sums of relatively few associated Legendre functions, as given, for example, by the general formula of Welton 33). Once a set of spin-parity assignments is chosen, this formula is parameterized only by the products R~R v of the R-matrix amplitudes, and a fit to the data may be attempted when the appropriate angular momentum coupling coefficients are calculated. If incoming and outgoing partial waves for the 9Be(p, d)SBe reaction are limited g* to I = 0, 1 and 2, the number of possible combinations R~Rv reduces to about 50; omission of a possible 0 - level because of its required d-wave formation and isotropic decay leads to possible spin and parity assignments of 1-, 2 - , 1 +, 2 + or 3 + to the Ep = 1.65 and 2.3 MeV 9Be(p, d)SBe resonances corresponding to the 8.07 and 8.66 MeV levels of ~°B*. Unless the two levels are formed in different incident channel spin states, the lack of odd-order terms in the angular-distribution data indicate that the levels involved have the same parity. Also, the angular-distribution data at the 1.65 MeV resonance have the form da/df2 = (14+ 18P2(cos 0))mb/sr,
(3)
which cannot be obtained for any single J~-value among those discussed above. It follows that two or more combinations R*R~ are required in order to reproduce the angular-distribution data alone. An attempt was made to find spin and parity assignments for the 8.07 and 8.66 MeV levels of l°B* which satisfied both the 9Be(p, d)SBe angular-distribution data and
9Be(p, d)aBe REACTION
109
the tensor polarization measurements. For each possible R~Rv corresponding to a unique set of spins, incident and outgoing orbital angular momenta and channel spins, the coefficients involved in the general formulae for a(0) and atzq were calculated. A subroutine to calculate the latter quantities according to Welton's formula was incorporated into a general search program a4) which varied the products R*Rv until a relative minimum was found in the function defined by
+ £ ((at2q)e(O)--(tTt2a)m(O)]2, O,q \
A(at2q)m(O)
(4)
]
where c and m refer to computed and measurec[ quantities and the A are the experimental uncertainties; the sum is performed over the angles of observation at a given bombarding energy. At least three of the possible R~Rv were used in each calculation. Choices made for possible levels contributing to the Ep = 1.65 MeV resonance were 2+-3 +, 1+-2 +, 1+-3 + and 1 - - 2 - ; attempts were made to reproduce the data at proton energies of 1.6, 1.8 and 2.0 MeV. Although several choices of initial values of the parameters were tried, relatively p o o r values of Z2 were obtained in every case. N o combination of parameters resulted in a value of Z2 per degree of freedom within an order of magnitude of unity. Of the 50 possible products R*R~which could enter the cross section and polarization formulae with the restriction l, l' _-< 2, only four combinations of these products satisfied the requirements that the angular distribution near a proton energy ot 1.6 MeV have approximately the form of eq. (3), and that the calculated t20 be positive at forward angles. As an example, a parameter set corresponding to two levels with spin and parity assignments 3 + and 2 - but formed via separate channel spins was not used, since it results in a negative t2o. No calculations were performed assuming more than two levels to be contributing at a given energy, since the number of parameters required would be excessive. The apparent m a x i m u m of t 2 o at forward angles of observation occurs at an energy between the resonances at Ep = 1.65 and 2.3 MeV in the 9Be(p, d)aBe total cross section, thus suggesting that any analysis in terms of states in 10B will have to include interference terms arising from overlapping resonances. The failure of the calculations to reproduce the angular dependence of the lower-energy data suggests that either several levels are contributing to the reaction, or that a direct reaction mechanism contributes significantly to the cross section below Ep = 2 MeV. In spite of some changes in sign, the measured polarization appears to vary relatively slowly with energy above 2.6 MeV, which would be expected if a direct reaction mechanism predominates at these energies. If, on the other hand, the observed effects in this energy region were to be attributed entirely to a small number of states in 10B. ' these would require widths on the order of 500 keV or more in order to produce the
110
A . J . F R O E L I C H A N D S. E. D A R D E N
observed energy dependence of the data. As pointed out above, the cross section data for bombarding energies above 2.5 MeV are strongly indicative of a direct reaction process. The results shown in figs. 1-5 are not inconsistent with this assumption, as they vary rather gradually with bombarding energy. After initial measurements 18) of the t2q from the 9Be(p, d)aBe reaction were carried out in this laboratory, a preliminary direct reaction calculation of the t2q using the DWBA with a spin-orbit potential added to the central optical-model potentials was performed by Satchler. Since aBe is not available as a target nucleus, 9Be(d, d)gBe data were used to fix the parameters for the deuteron optical potential. For the calculation reported here, the target nucleus was assumed to be described by a p~ neutron moving about a aBe core. The optical potentials used were of the Woods-Saxon type with some surface absorption. The various strength and range parameters were chosen from fits to 9 B e + p scattering at 9 MeV and 9 B e + d scattering at 10 MeV. These calculations yielded values of t2q, which were typically smaller than the measured values by an order of magnitude, as can be seen from the solid curves in fig. 3. Possible weaknesses in the DWBA calculation are, in addition to the absence of D-state effects, the lack of tensor spin-orbit potentials in the deuteron-nucleus optical potential and the spherical symmetry of the deuteron-nucleus potential well. Removal of the latter shortcoming would require a more sophisticated calculation than has been attempted to date. More recently, Johnson 21) investigated the effect of including the D-state of the deuteron on the calculated tensor polarization using a perturbation approach with the plane-wave theory. The results of these calculations for a proton energy of 2.5 MeV are given by the dashed curves in fig. 3. In Johnson's calculations, the tensor parameters are expressed as functions of the ratio of D-state to S-state momentum probability amplitudes as follows: 16n y~ (K) A (K) + 8 - ~A z (K) t2a = - T I+A2(K) '
(5)
where K = ½k~-k~,
A(K) = u2(K)/uo(K), where u o and u 2 are the radial parts of the S- and D-components of the deuteron wave function in momentum space. The data fail to follow even qualitatively the form given in eq. (5), since both Y~ (K) and A (K) are slowly varying functions of proton bombarding energy for any given angle of observation. In particular, the changes in sign of t21 with proton energy at a lab observation angle of 30 ° as shown in fig. 5 are inconsistent with this formula. However, it was pointed out by Johnson that the plane-wave polarization calculations probably underestimate the D-state effects somewhat. The presence of non-negligible tensor polarizations, at angles and energies where the vector polarization measurements described in sect. 1 were made, calls into ques-
9Be(p, d)SBe REACTION
111
tion the validity of the assumptions used in these experiments to obtain the vector polarization from the data. The simple relationship
da/d~2 =
(da/df2)o(1 + 3PpPd)
must be replaced by the general expression 3 5) which includes second-rank polarization effects. Inclusion of the second-rank effects requires knowledge of the tensor polarization produced in the 9Be(p, d)SBe reaction as well as the tensor analysing powers of the 12C(d, p)l 3C and 2H(d, p)3H reactions. Assuming the tensor polarization effects in the above reactions to be comparable in magnitude to those found for the 9Be(p, d)SBe reaction, the contribution of those effects to the measured asymmetries would be of the same order as were observed 12-15).
7. Summary The tensor polarization of deuterons emitted from the 9Be(p, d)SBe reaction has been measured at several angles of observation for proton bombarding energies ranging from 1.6 to 3.8 MeV. Substantial values of the t2q were found. The failure to reproduce even qualitatively the polarization and cross-section data for energies near the cross-section maxima at 1.65 and 2.3 MeV proton energy in terms of simple excitation of one or two levels in 1oB suggests that either several levels are involved, or that appreciable direct reaction is occurring at these energies. The energy and angular dependence of the data above E v = 2.6 MeV appear to be generally consistent with the assumption of a predominantly direct reaction mechanism. However, comparison of the data with the limited direct-reaction calculations available leads to the conclusion that such simplifications as lack of spin-dependent distortion and neglect of the D-state of the deuteron cannot be used in a DWBA calculation, if polarization effects are to be reproduced by the theory. A more complete calculation, which removes both of these restrictions and takes into account tensor terms in the deuteron-nucleus potential as well as the distortion of the initial and final nuclei, may be required to reproduce the data. It might be of interest to investigate other deuteron-producing direct reactions, such as (SHe, d) reactions, to see if significant tensor polarization effects are present. The authors are grateful to Messrs. K. Corrigan, J. Hevezi, J. T. Klopcic and T. G. Sauer for their assistance in taking the data.
References 1) L. J. B. Goldfaxb, Proc. Int. Symp. on polarization phenomena of nucleons (Birkh[iuser Verlag, Basel, 1966) p. 203 2) L. Rosen, ibid., p. 253 3) P. Schwandt and W. Haeberli, Nucl. Phys. A l l 0 (1968) 585 4) J. Raynal, Phys. Lett. 7 (1963) 281 5) L. C. Mclntyre and W. Haeberli, Nucl. Phys. Agl (1967) 382
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A.J. FROELICH AND S. E. D A R D E N
6) H. Meiner, E. Baumgartner, S. E. Darden, P. Huber and G. R. Plattner, Helv. Phys. Acta 40 (1967) 483 7) G. R. Satchler, Nucl. Phys. 55 (1964) 1 8) T. J. Yule and W. Haeberli, Phys. Rev. Lett. 19 (1967) 756 9) Yu. V. Gofman, N. I. Zaika, A. V. Mokhnach, O. F. Nemets, P. L. Shmarin and A. M. Yasnogorodskii, J. Nucl. Phys. (USSR) 5 (1967) 718; Soy. J. Nucl. Phys. 5 (1967) 510 10) G. L. Vysotskii and A. G. Sitenko, ZhETF (USSR) 36 (1959) 1143; JETP (Soy. Phys.) 9 (1959) 812 11) L. J. B. Goldfarb and R. C. Johnson, Nucl. Phys. 18 (1960) 353 12) R. Barloutaud, H. Faraggi, L. Rosen and S. M. Shafroth, J. de Phys. 21 (1960) 369 13) J. M. Lambert, L. Madansky and G. E. Owen, Phys. Rev. 124 (1961) 1959 14) M. S. Bokhari and V. V. Verbinski, Bull. Am. Phys. Soc. 9 (1964) 627 15) V. V. Verbinski and M. S. Bokhari, Phys. Rev. 143 (1966) 688 16) C.L. Petitjean, P. Huber, H. Paetz gen. Schieck and H. R. Striebel, Helv. Phys. Acta, 40 (1967) 401 17) B. P. Ad'yasevich, Yu. P. Polunin and D. E. Fomenka, J. Nucl. Phys. (USSR) 5 (1967) 713; Sov. J. Nucl. Phys. 5 (1967) 507 18) S. E. Darden and A. J. Froelich, Phys. Rev. 140 (1965) B69 19) M. Ivanovich, H. Cords and G. U. Din, Nucl. Phys. A97 (1967) 177 20) L. Brown, H. A. Christ and H. Rudin, Nucl. Phys. 79 (1966) 459 21) R. C. Johnson, Nucl. Phys. A90 (1967) 289 22) G. Weber, L. W. Davis and J. B. Marion, Phys. Rev. 104 (1956) 1307 23) S. Morita, T. Tohei, T. Nakagawa, T. Hasegawa, H. Ueno and Hsu Chu-chtmg, Nucl. Phys. 66 (1965) 17 24) T. Yanabu, S. Yamashita, S. Kakigi, D. Nguyen, K. Takimoto, Y. Yamada and K. Ogino, J. Phys. Soc. Japan 19 (1964) 1818 25) F. H. Read and J. M. Calvert, Proc. Phys. Soc. 77 (1961) 65 26) W. Tr~ichslin, H. Biirgisser, P. Huber, G. Michel and H. R. Striebel, Helv. Phys. Acta 38 (1965) 523 27) L. C. Mclntyre, Ph.D. thesis, University of Wisconsin (1965) available from University Microfilms, Ann. Arbor, Michigan, USA 28) W. A. Schier, Ph.D. thesis, University of Notre Dame (1964) 29) J. D. Purvis, F. Ajzenberg-Selove and L. M. Polsky, Phys. Rev. 162 (1967) 1005 30) T. Lauritsen and F. Ajzenberg-Selove, Nucl. Phys. 69 (1966) 1 31) S. G. Buccino and A.B. Smith, Phys. Lett. 19 (1965) 234 32) W. F. Hornyak, C. A. Ludemann and M. L. Roush, Nucl. Phys. 50 (1964) 424 33) T.A. Welton, in Fast neutron physics, Part II, ed. by J. B. Marion and L. J. Fowler (Interscience, New York, 1963) p. 1349 34) W. D. Davidon, ANL-5990 Rev. (1959) 35) G. R. Satchler, Nucl. Phys. 3 (1958) 67