Polarization of protons from the 9Be(d, p)10Be reaction

Polarization of protons from the 9Be(d, p)10Be reaction

2.B [ Nuclear Physics A90 (1967) 601--611; (~) North-Holland Publishing Co., Amsterdam I Not to be reproduced by photoprint or microfilm without w...

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Nuclear Physics A90 (1967) 601--611; (~) North-Holland Publishing Co., Amsterdam

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Not to be reproduced by photoprint or microfilm without written permission from the publisher

POLARIZATION OF P R O T O N S FROM THE 9Be(d, p)l°Be REACTION R. A. BLUE t , K. J. STOUTtt and G. MARR The Ohio State UniL'ersity, Columbus, Ohio *+~ Received 1 September 1966 Abstract: The polarization of protons from the 9Be(d, p)~°Be reaction has been measured for deuteron energies between 1 and 6 MeV. Angular distributions of the polarization for the ground state proton group (Q - 4.59 MeV) have been measured for laboratory angles between 10' and 135 = at 2.5, 4.0 and 5.5 MeV. The polarization at a laboratory angle of 30° was measured in 0.2 MeV steps between 1 and 6 MeV. In addition the polarization of protons leaving 1°Be in its first excited state (Q - 1.22 MeV) was measured between 10': and 90' for a deuteron bombarding energy of 5.5 MeV. Measurements were made by conventional double-scattering techniques using elastic scattering from helium at 45 ~ as the analyser. The results show a strong energy dependence contrary to what one might expect on the basis of the lack of structure in the cross section. The maximum polarization observed at each energy is about 0.35. E[

NUCLEAR REACTIONS 9Be(d, p), E--: 1-6 MeV; measured polarization (Ep, 0).

1. Introduction M e a s u r e m e n t s o f the p o l a r i z a t i o n f r o m (d, p) reactions have, in general, failed to p r o v i d e the s i m p l e a n d direct m e a n s o f o b t a i n i n g i n f o r m a t i o n a b o u t the s p i n - d e p e n d e n t effects in s t r i p p i n g r e a c t i o n s t h a t the semi-classical pictures such as t h a t p r o p o s e d by N e w n s 1) seemed to p r o m i s e . T h e " s i g n r u l e " for d e t e r m i n i n g the j - v a l u e f r o m the N e w n s m o d e l has p r o v e d to be o f little w o r t h even with v a r i o u s m o d i f i c a t i o n s 2.3). P r o b a b l y the m o s t serious s h o r t c o m i n g o f the t h e o r y 4) u n d e r l y i n g the p r o p o s e d s i m p l e selection rules specifying u p p e r l i m i t s o n the m a g n i t u d e o f the p o l a r i z a t i o n is the neglect o f explicitly s p i n - d e p e n d e n t i n t e r a c t i o n s 5). T h e necessity o f i n c l u d i n g s p i n - d e p e n d e n t t e r m s in the o p t i c a l - m o d e l p o t e n t i a l s used for a D W B A c a l c u l a t i o n has b e e n m o s t s t r o n g l y d e m o n s t r a t e d by the o b s e r v a t i o n o f n o n - z e r o p r o t o n p o l a r i z a t i o n for several cases 3,6) in w h i c h the n e u t r o n is t r a n s f e r r e d with zero o r b i t a l a n g u l a r momentum. P e r h a p s o n e r e a s o n that the p o l a r i z a t i o n f r o m s t r i p p i n g r e a c t i o n s presents a c o n f u s i n g p i c t u r e is that d a t a are still r a t h e r sparse 7), c o n s i s t i n g o f n o m o r e t h a n a few a n g u l a r t Now at the University of Florida, Gainesville, Florida. *t Now at The Harshaw Chemical Company, Cleveland, Ohio. *tt Work supported in part by the National Science Foundation. 601

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distributions for most reactions. Any understanding of the systematics of the polarization will clearly require more extensive measurements as a function of energy and angle. For this reason the present investigation of the polarization of protons from the 9Be(d, p)l°Be reaction was undertaken for deuteron bombarding energies up to 6 McV and over as wide an angular range as possible. This particular reaction was selected because it is experimentally amenable to study, and because previous experimental results 3.8-12) at higher energies are more abundant than for any other reaction 7) except ~2C(d, p)l 3C. An additional reason for selecting 9Be for study is that the cross section for the (d, p) rcaction is quite free from resonant structure above about 2 MeV, at least to the extent that existing excitation curves ~3.14) would reveal any resonances. It was hoped that the lack of resonances could be taken as an indication that the 9Be(d, p)~ °Be reaction proceeds predominantly via a direct process. In the present work the polarization of the ground-state protons from the 9Be(d, p) ~°Be reaction was measured for laboratory angles between 10° and 135 ° at 2.5, 4.0 and 5.5 MeV. An excitation curve of the polarization at a laboratory angle of 30 '~ was measured in 0.2 MeV steps from 1.0 to 6.0 MeV. In addition, the polarization of protons leaving 1°Be in the 3.37 MeV first excited state was measured between IO' and 90 ° for Ea = 5.5 McV. The results of these measurements, with previous measurements at higher energies, provide a rough indication of the energy dependence of the polarization between 1 and 21 MeV as discussed in sect. 4.

Apparatus

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The deuteron beam from the Ohio State University 5.5 MeV Van de Graaff Accelerator was analysed to a resolution of approximately 0.3 ~o by a 90 ° magnet which was

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°Be(d, p)loBe REACTION

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calibrated against the VLi(p, n) threshold at 1.881 MeV. The polarization of protons from the 9Be(d, p)l OBe reaction was measured using the double-scattering apparatus illustrated in fig. 1. Elastic scattering from a 10 atm helium target was used as the polarization analyser. Protons scattered by the helium at an angle of45 ~ were detected in symmetrically placed counter telescopes, each consisting of a proportional counter and a CsI'(TI) scintillation counter operated in coincidence. In addition to the counter telescopes, a silicon surface-barrier detector was used to monitor the spectrum of particles incident upon the helium target. The detector, located behind the helium target, views the first target through a small collimator located on the central axis of the analyser assembly. The incident deuteron beam was defined in direction by an 8 mm aperture 4.6 m from the target and collimated to 1.5 mm by 2.5 mm by insulated slit edges 5 cm from the target. The beam current striking each of the four slit edges was monitored to insure accurate centering of the beam on the target. After passing through the beryllium target, the deuteron beam was stopped on a small gold beam stop insulated from ground so that the beam current could be monitored and integrated for normalizing the data runs. The analyser, consisting of the helium target and detector assembly, is mounted on a 70 cm diameter turntable which rotates about the first target allowing measurements at laboratory angles between 10° and 135 °. The analyser slit geometry is similar to an earlier Wisconsin design is). The slits defining the first-reaction angle are normally 2.5 mm wide by 25 mm high at a distance of 8.7 cm from the first target. The large height-to-width ratio is chosen to optimize the solid angle subtended without serious loss of angular resolution. The rms spread in scattering angle allowed by this geometry is less than 1:: for scattering angles greater than 30 °. To maintain this resolution for scattering angles less than 30 ° it is necessary to reduce the height of the slit opening to 19 mm. The slit design allows this change to be made conveniently and accurately. The apparatus was assembled and aligned using optical alignment techniques such that the mean first-scattering angle is determined to an accuracy of 0.15 ° . Since the height of the analyser slits leads to a shift in the mean scattering angle from the angle measured in the horizontal plane it is necessary to apply a correction to this nominal scattering angle. The correction for each scattering angle was calculated by numerical integration over the slit geometry. The maximum shift of +0.72 ° occurs at 10 ~. Since the polarization in p-4He scattering is well known and varies slowly with angle much poorer angular resolution can safely be used for the second scattering. The overall rms spread in the second-scattering angle is about 4 °. The mean secondscattering angle used for calculating the helium analysing power was also corrected for the shift due to slit heights. An additional effect 1s) of the slit height results from the dependence of the asymmetry observed after the second scattering on the cosine of the azimuthal angle 4~. The measured asymmetries were corrected for the cos 4~ variation using average values

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of cos • calculated by numerical integration for each of the two detectors. The minimum average values, + and - , for the two detectors are 0.859 and 0.851, respectively, for 10 ° scattering. The careful construction and alignment of the apparatus, with a design in which the distances between targets and between the second target and detectors are large compared with the size of the targets, serve to minimize instrumental asymmetries. Estimates of any possible errors due to geometrical effects other than those for which corrections were made show them to be negligible compared with the statistical uncertainties of the measurements. 3. Procedure

The beryllium targets used in the present work were commercial foil * 1.1 mg/cm 2 thick rolled from 99.9 )o pure beryllium. The thickness of the targets was determined to an accuracy of 10 3o both by weighing and by observing the apparent shift in the 7Li(p, n) threshold when the beryllium foil was interposed in the proton beam before the lithium target. The energy lost by deuterons in passing through the target varied from 230 keV at 2.5 McV to 110 keV at 5.5 MeV for normal incidence. It was, hoveever, necessary to orient the target at angles as large as 40 ° to the incident beam direction for measurements near 90 ~ so that the effective target thickness was as much as 1.3 times the value for normal incidence. The deuteron beam energy was varied with target angle to compensate for this increase in energy loss and maintain the same mean energy for all target orientations. The uncertainties in the target thickness and in the deuteron beam energy give an estimated uncertainty in the mean deuteron bombarding energy of about 0.03 MeV. Signals from all counters were amplified using double delay line shaping. The amplified pulses were fed into differential discriminators which drove slow coincidence units using crossover timing. The coincidence resolving time of 2 ,usec resulted in an insignificant accidental coincidence rate. Outputs from discriminators drove sealers to record the singles counts from each counter of the two telescopes and from the detector observing particles passing through the helium target. The coincident events between counters for each telescope were also recorded in sealers. Signals from either the proportional counters or the scintillation counters were routed into quadrants of a multi-channel pulse-height analyser gated by the coincidence outputs. This allowed monitoring of the spectra for purposes of adjusting gains and setting discriminators. The pulse-height analyser was also used to record the spectrum of particles incident upon the helium target during a small portion of the time spent on each measurement. The spectrum recorded at 3.8 MeV for a laboratory angle of 30 ° is shown in fig. 2. In addition to the two proton groups, the prominant triton group from the • Supplied by the Brush Beryllium Company, Cleveland, Ohio.

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9Be(d, t)SBe reaction can readily be identified. The energetic ~t-particles from the 9Be(d, ~)7Li and the 9Be(d, 2~)3H reactions lose too much energy in passing through the helium to be identified, but are probably responsible for the broad peak observed in the lower part of the spectrum. When a similar spectrum is taken with the helium target evacuated it is also possible to identify peaks due to elastically scattered deuterons and two or three additional proton groups which suffer too great an energy loss to be recorded after passing through the 44 atm • cm of helium. It is worth noting that the scattering by helium greatly reduces the energy of more massive particles with respect to the protons, effectively removing ~-particles, tritons and deuterons from the region of interest in the spectrum of particles detected in the counter telescopes.

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CI2(d, p)C 13 reaction from carbon build-up on the beryllium target. No proton groups due to other possible contaminants such as oxygen or nitrogen were ever observed. By substituting carbon for the beryllium target it was possible to show that protons from the carbon contaminant were effectively discriminated against in the counter telescopes and could cause no significant error in the measurements. The coincidence-gated spectrum obtained in the scintillation counters for an angle of 30 ° at 5.0 MeV is shown in fig. 3. The points plotted as open circles showing both the Po and Pl peaks were obtained by operating the proportional counters with only a lower level discriminator requirement. The points plotted as closed circles were obtained with a differential discriminator set on the proportional counter pulses as

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was done for a normal measurement of the polarization of the ground-state proton group. Similarly the proportional counter discriminator could be set to select only protons in the p~ group and thus reduce the background underlying this peak in the coincidence gated scintillation counter spectrum. The full width at half maximum for the scintillator is about 13 },~ of the mean pulse height. With differential discriminators on the proportional counters and the scintillation counters set to select the desired proton group, coincidence yields in the two telescopes were recorded in scalers for runs of a given total integrated beam current. For each measurement the ratio of yields in the two telescopes was measured on both sides of the incident beam direction. The geometric mean of the two measured ratios was Right

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taken to cancel any asymmetries arising from differing coincidence efficiencies for the two telescopes. Backgrounds between I0 oj~ and 50 ~/o of the yield were encountered despite the coincidence requirements set by the counter telescopes. Accidental coincidences accounted for only a small fraction of the background. The observed background was largely independent of the means used to stop charged particles emitted from the beryllium target, whether by placing a tantalum stop before the helium target, after the helium target, or by evacuating the helium target. The background was, however, present only when the deuteron beam was incident upon a beryllium target and was strongly peaked in the forward direction with respect to the incident bcam. It was therefore concluded that the background results from neutron induced reactions in the materials of the counter telescopes themselves, the energetic neutrons responsible

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being produced in the 9Be(d, n)~°B reaction (Q = 4.4 MeV). Later tests showed that stainless steel, when exposed to the counter telescopes in the presence of neutrons from the 9Be(d, n)~°B reaction, emitted charged particles having a spectrum and intensity consistent with the conjecture that the observed background was primarily emitted by the stainless steel at the exit of the helium target and in the proportional counters themselves. Runs for background subtraction were made for an appropriate fraction of the time by evacuating the helium target. The validity of the background subtraction was further checked by observing that there were no net counts remaining in the region of the coincidence-gated pulse height spectra below the proton peak. The energy of protons reaching the center of the helium target was determined by subtracting energy losses in the entrance foil and the helium gas from the calculated energy of protons from the 9Be(d, p)~ °Be reaction. The analysing power for helium scattering at that energy was calculated from p-4He phase shifts provided by Haeberli t. The uncertainty assigned to the calculated analysing power is small enough to be negligible in determining the uncertainty of the present results. The polarization product P~ P2 was calculated from the observed yield ratio with the above mentioned correction for the cos 4) dependence. The statistical uncertainty of P~ P2 was obtained from the recorded yields by the usual rules for propagation of errors. All other known sources of error were much smaller than this statistical uncertainty. 4. Results

The measured angular distributions of the polarization of protons from the 9Be(d, po)~°Be reaction (Q = 4.59 MeV) for deuteron energies of 2.50, 4.00 and 5.50 MeV are shown in fig. 4. The polarization has a positive slope at forward angles for each of the three energies and the position of the first maximum does not change drastically, but the forward half of the curve shifts to more positive values with increasing energy. The polarization at angles greater than 90 ° shows little similarity from one energy to the next. In order to investigate the energy dependence of the polarization in more detail the polarization at a laboratory angle of 30.5 ° was measured in 0.2 MeV steps from 1 to 6 MeV. These results, shown in fig. 5, indicate that the change in the polarization with energy occurs most rapidly in the vicinity of 4 MeV. This transition from negative to positive polarization at forward angles was also observed at 0 ~ = 10.7 ° in mcasuremcnts at 3.40 and 4.40 MeV as indicatcd by the crosses in fig. 5. It should perhaps be noted that Oj, b = 30 ~ is just beyond the main stripping peak in the cross section wherc a "sign rule" for j-dependence might have been expected to apply 2). The comparison of the present results with previous measurements at higher cncrgies shows that for angles lcss than 70 ° the polarization at 5.5, 7.8 (ref. 9)), + The authors are indebted to Professor Haeberli for providing these phase shifts which fit cross section and polarization data between 3 and 20 MeV including the precise polarization values measured by Brown et al. (ref. 1:.)) in the region pertinent to this experiment.

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8.9 (ref. a)) and 10 MeV (ref. 10))is nearly the same. The higher energy results do, however, pass through zero and become negative where the present results at 5.5 MeV 9Be (d,Po)J°Be E d = 2.50MeV

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@c.m. (deg) Fig. 4. The polarization of protons from the 9Be(d, p0)'°Be reaction (Q ~ 4.59 MeV) for incident deuteron energies of 2.50, 4.00 and 5.50 MeV plotted versus center-of-mass angle.

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E d (MeV) Fig. 5. T h e p o l a r i z a t i o n o f p r o t o n s f r o m t h e 9Be(d, p 0 ) ' ° B e r e a c t i o n ( Q = 4 . 5 9 M e V ) p l o t t e d v e r s u s i n c i d e n t d e u t e r o n e n e r g y . T h e d a t a p l o t t e d as c l o s e d circles w e r e m e a s u r e d a t 01ah = 30.5 ° w h i l e t h e t w o p o i n t s a t 3.4 a n d 4 . 4 M e V i n d i c a t e d b y x w e r e m e a s u r e d a t 0tab = 10.7 ° •

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merely dip to a small positive value near 80 °. No comparison can be made at larger angles because none of the previous measurements extends beyond 90 ° . The shape of the polarization at forward angles observed below 10 MeV does not persist at higher energies. Instead the slope of the polarization at forward angles becomes negative, the results at 15 MeV (ref. 3)) and 21 MeV (ref. 11)) showing a negative extremum of about - 0 . 2 near 60 °. Measurements 12) at 13.8 MeV show features somewhat intermediate between the 10 MeV and the 15 MeV results as though a transition similar to the one indicated by the results of this experiment were occurring near that energy.

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1~) c.m. (deg) Fig. 6. The polarization of protons from the °Be(d, p~)l°Be* reaction leaving 1UBein its first excited state (Q = 1.22 MeV) for an incident deuteron energy of 5.50 MeV plotted versus center-of-mass angle. One additional measurement was made in the present experiment. The polarization of protons which leave lOBe in its first excited state (Q = 1.22 MeV) was measured between 10 ° and 90 ° at 5.5 MeV as shown in fig. 6. For this proton group the present results and previous measurements at 7.8 (ref. 9)), 15 (ref. 3)) and 21 MeV (ref. 11)) are all quite similar. Since both the ground state and first excited state reaction involve 1 = 1 neutron transfer the angular distributions of the proton polarization for the two groups might be expected to be similar if the j-values are also the same. In fact, the polarization for the two proton groups are quite similar at 15 and 21 MeV, but the similarity does not remain as the polarization of the ground state protons changes below 15 MeV. 5. Conclusions

Despite the successful fits to the differential cross section for (d, p) reactions using the distorted-wave Born approximation further refinements of the formalism are needed to account for the polarization. Progress toward an understanding of the

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mechanism producing the polarization has been slow due not only to the complexity of the DWBA calculations but also because of the scarcity of experimental data. In the present case the observed energy dependence of the polarization of the ground state protons from the 9Be(d, p)'°Be reaction might appear to make it unsuitable for a DWBA analysis. But first the question must be raised as to whether the observed energy dependence of the polarization can result from a direct reaction mechanism or must be attributed to effects of interfering compound-nucleus formation. The 9Be(d, p)l°Be reaction was selected as a case in which compound-nucleus interfcrencc effects should be least likely to occur. The excitation energies of the compound nucleus ~'B reached by d + 9Be lie above 15.8 MeV. The highest known levels in ~ B, which are best observed in the 7Li(2, n)~°B reaction ~6), correspond to incident deuteron energies of 1.I, 1.3 and 2.1 MeV. Cross-section measuremcnts for reactions induced by deuterons on beryllium at higher cnergies show no structure. However data are rathcr sparse above 3 MeV so that it is possible that additional cross section measurements to supplement the excitation curve measured at 4 0 by Read et al. ~4) might reveal structure related to the change in the polarization at 4 MeV. Comparison of polarization data for (d, p) reactions in other light nuclei with the present results for beryllium may also give some indication of the extent to which the energy dependence of the polarization can be ascribed to a direct reaction mechanism. Some polarization measurements have been made for the ~°B(d, p)l~B and the '2C(d, p)l 3C reactions, both of which also involve transfcr of an / = 1 neutron. As noted by Miller 7), the polarization from the ~°B(d, p)l 1B reaction undergoes a marked change between 10 and 13 MeV similar to the behavior of the 9Be(d, p)1°Be reaction in that energy range. No polarization measurements for the ~°B(d, p)l~B reaction have been made below 7.8 MeV to compare with the present results. By way of contrast the measurements of the polarization of protons from the 12C (d, p)13C reaction at several energies between 4 and 15 MeV as summarized, for example, by Reber and Saladin 3) seem to indicate that the polarization retains the same general shape over this range of energies. The effect on the polarization of the prominent resonances seen in the cross section for the ~2C(d, p)13C reaction has, however, been observed in measurements 17) the present authors have made between 4 and 6 MeV. Even on these resonances the compound-nucleus effects produce no changes in the polarization that are comparable to those observed in the 9Be(d, p)~ °Be reaction. On the basis of the data presently available on the polarization of protons from (d, p) reactions it is difficult to make any firm conclusion concerning the source of the observed variation of the polarization with energy. The three reactions mentioned above are the only cases for which enough measurements have been made to givc a good indication of the energy dependence of the polarization. These results should demonstrate the necessity of measuring angular distributions of the polarization at several energies before serious attempts are made to derive information from DWBA fits to polarization data.

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The authors thank the staffs of the Ohio State Van de Graaff Laboratory and the machine shop of the Ohio State physics department for the many contributions they made to this experiment. The help of Mr. K. A. Kuenhold in taking data is also gratefully acknowledged. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11)

12) 13) 14) 15) 16) 17)

H. C. Newns, Proc. Phys. Soc. A66 (1953) 477 A. Isoya, S. Micheletti and L. Reber, Phys. Rev. 128 (1962) 806 L. H. Reber and J. X. Saladin, Phys. Rev. 133 (1964) B 1155 R. Huby, M. Y. Refai and G. R. Satchler, Nuclear Physics 9 (1958) 94 L. J. B. Goldfarb and R. C. Johnson, Nuclear Physics 18 (1960) 353 A. lsoya and M. J. Marrone, Phys. Rev. 128 (1962) 800 D.W. Miller, Proceedings of the international conference on polarization phenomena of nucleons, Karlsruhe, Germany, 1965 (to be published) B. Hird, J. A. Cookson and M. S. Bokhari, Proc. Phys. Soc. (London) 72 (1958) 489 J. A. Green and W. C. Parkinson, Phys. Roy. 127 (1962) 926 R. G. Alias, R. W. Bercaw and F. B. Shull, Phys. Rev. 127 (1962) 1252 E. Boschitz, Proceedings of the conference on direct interactions and nuclear reaction mechanisms, ed. by E. Clementel and C. Villi (Gordon and Breach Science Publishers Inc., New York, 1963) 13. 640 M. V. Pasechnik, L. S. Saltykov and I). I. Tanbovtsev, ZhETF (USSR) 43 (1962); JETP (Sov. Phys.) 16 (1963) 1111 T. lshimatsu, N. Takano, Y. Hachiya and T. Nakashima, J. Phys. Soc. Japan 16 (1961) 367 F. H. Read, J. M. Calvert and G. Shork, Nuclear Physics 23 (1961) 386 R. 1. Brown, W. Haeberli and J. X. Saladin, Nuclear Physics 47 (1963) 212 M. K. Mehta, W. E. Hunt, H. S. Plendl and R. H. Davis, Nuclear Physics 48 (1963) 90 R. A. Blue, K..I. Stout, G. Marr and K. A. Kuenhold, to be published