Polarization transfer in the 2H(d ,n )3He reaction at θ = 0°

Nuclear Physics A242 (1975) 298--308; (~) North-Holland Publishing Co., Amsterdam

Not to be reproduced by photoprint or microfilmwithout written permission from the publisher

P O L A R I Z A T I O N T R A N S F E R I N T H E ZH(d, fi)aHe R E A C T I O N A T 0 = 0 ° P. W. LISOWSKI and R. L. WALTER Duke University, Durham, North Carolina 27706 and Triangle Universities Nuclear Laboratory, Durham, North Carolina 27706 t

and C. E. BUSCH and T. B. CLEGG University of North Carolina 27514 and TUNL t

Received 13 September 1974 (Revised 27 December 1974) Abstract: The vector polarization transfer coefficient K / ' and the tensor analyzing power A~z have been measured for the 2H(~, fi)aHe reaction at 0 = 0 ° over an incident deuteron energy range from 1 to 15 MeV in 0.5 MeV steps. The results agree with the previous 2H(~, fi)aHe measurements of Simmons et aL and are nearly identical to the 2H(~, ~)3H measurements of Clegg et aL in the region of overlap. The present results provide an accurate and complete set of the observables necessary to use the 2H(~, fi)3He reaction as a source of polarized neutrons.

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NUCLEAR REACTION 2H(a, n), 1 MeV < E < 15 MeV; measured transverse polarization transfer coefficient Kyy' and tensor analyzing power A~z.

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1. Introduction I n recent years the most important advance in the technique for neutron polarization measurements has been the observation that there are large vector polarization transfer coefficients for certain charged particle induced reactions. This result was f o u n d a b o u t the same time at Los A l a m o s 1) and at Birmingham 2 ) for the 2H(d, n)aI-Ie reaction. In the more t h o r o u g h measurement 1) Simmons et aL reported seven values for the polarization transfer coefficient K~" (0 °) which indicated that beams o f neutrons could be obtained with very large polarizations over the energy range f r o m 7 to 18 M e V when highly polarized deuteron beams were available. I n a successive set o f experiments 3) we have used the polarization transfer capability o f this reaction to investigate the scattering o f polarized neutrons f r o m aHe and 4He. Attempts to analyze those data, however, required that more detailed and accurate knowledge be available for the transfer polarization for 2H(d, n)3He. A comparison o f the 2H(d, ~ ) 3 H and 2H(d, fi)3He values o f K~'(0 °) has been reported by Clegg et al. 4). These authors show that the values for b o t h reactions are nearly identical to within the accuracy o f the data over the region f r o m 6 to 15 MeV. * Work supported in part by the US Atomic Energy Commission. 298

2H(~, ~)3He

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From a theoretical viewpoint, transfer polarization coefficients for neither the 2H(d, n)3He nor the 2H(d, p)3H have been predictable. A simple picture of the reaction suggests that the neutrons produced at 0 ° retain the magnitude of polarization that they "possessed" as nucleons in the polarized deuteron beam. This might be expected since the reaction exhibits a very pronounced l --- 0 stripping peak at 0 n. To obtain more accurate data for calibrating the 2H(d, fi)3He reaction as a source of polarized neutrons, to extend the measurements over a wider energy range than was previously available, and to provide additional data for testing theoretical predictions for the four-nucleon system, a new study of K~' (0 °) was undertaken at our laboratory. Data were obtained at 0.5 MeV intervals from 1 to 15 MeV. As will be discussed in the next section, in the general case the transferred neutron polarization py, depends not only on the vector, but also on the tensor polarization of the incident deuteron beam. Under the most favorable conditions for producing highly polarized neutrons beams (such as those used in the present measurements) the dependence of py, on the deuteron tensor polarization is manifested in the tensor analyzing power Azz. We therefore report values of Az~ at a reaction angle of 0 ° as a function of incident deuteron energy along with the values for K y' . In sect. 2 we present a brief discussion of the polarization transfer formalism for 0 = 0 ° studies. Sect. 3 describes the experimental techniques used in measuring A~z and in determining the outgoing neutron polarization. Finally, sects. 4 and 5 deal with the experimental results and a comparison with similar 2H + d measurements. 2. Formalism for polarization transfer measurements

Several authors 5) have recently presented discussions of the equations relating the observables of any reaction with the spin structure I A + I - - , ½ + I B, where I A and 13 are arbitrary spin values. We shall adopt the Cartesian coordinate representation presented by Ohlsen 5). In this notation, the expressions for the differential cross section and the outgoing nucleon polarization at a reaction angle of 0 ° may be written as" I(0) = Io(0)[1 +½p=A~(O)], (1) px,(0)I(0) = Io(0) [½pxK~'(0) + ~p,zKr~(0)],

(2)

p,,(0)i(0) =

(3)

+

= Io(0) [½p~K~(0) + ]-pxyKxy(O)],

(4)

where I(0) and Io(0) are the polarized and unpolarized differential cross sections; the p~ and pfj are the Cartesian vector and tensor spin moments of the beam. The K are polarization transfer coefficients and Azz is a tensor analyzing power, the only one which is non-zero at 0 = 0 °. The subscripted unprimed variables refer to a righthanded coordinate system in which the z-axis is taken along ~in and the y-axis is denoted by ~, (the usual choice of ~ along ~in x ~out is arbitrary, since at 0 = 0 °

P.w. LISOWSKI et al.

300

i~in X ~out is undefined). The primed quantities refer to a right-handed coordinate system based on the outgoing momenta, in which the z' axis is along ~o,t and the y' axis is parallel to the y-axis. If fl and tk describe the orientation of the deuteron spin quantization axis S on target, such that fl^measures the angle between S and ~in and ~b is the angle between the projection of S on the x, y plane and the y-axis, then the quantities involved in these measurements may be expressed in terms of two equations I(0) = Io(0)[I +¼(3 cos 2 f l - 1)p33.4z:(0)], p¢(0)I(0) = Io(0)[~ sin fl cos ~bpaK~'(0 ) - s i n fl cos ~b sin ~bp3aK~(0)],

(5) (6)

where Pa and Pa3 are the vector and tensor polarizations of the beam with respect to its quantization axis at the polarized ion source. For a deuteron beam with the quantization axis on target chosen such that fl = 90 ° and ~b = 0 ° or 180 °, the neutron polarization p/(0) is given by __.½p3K~'(0)

(7)

p,,(o) = I

where the plus sign corresponds to a choice of q~= 0 ° (spin "up"), the negative sign to a choice of ~ = 180 ° (spin "down"). Clearly, for these choices of fl and ~ a knowledge of py,(O), A::(O) and the beam polarization is necessary to determine K~'(0). Conversely, when using the 2H(d, n)3He reaction (with these values of fl and 4) as a source of polarized neutrons, both K~'(0) and Az:(0) must be known in order to calculate the outgoing neutron polarization from the deuteron polarization. It may be noted that the choice of fl = 54.74 °, ~ = 0 ° or 180 ° gives a value ofpy,(0) which does not depend on A:: or K ~ (see eq. (5)); this arrangement, however, does not give the largest possible value ofpy,(0).

3. Experimental procedure 3.1. POLARIZED BEAM The measurements were carried out using a polarized deuteron beam produced by the Lamb-shift ion source 6) of the T U N L tandem accelerator facility. For these measurements the beam had vector and tensor polarizations Pa and P33 which were typically 0.75 as measured by the quench-ratio method 7). The spin quantization axis of the deuteron beam was along the beam direction at the ion source and could be precessed by a mirror-solenoid combination into an orientation transverse to the beam direction and in the vertical plane (fl = 90 °, ~b = 0 ° or 180°). The beam intensity on target ranged from 20 to 60 nA. 3.2. TARGET AND POLARIMETER The polarized beam entered a low mass cylindrical gas cell approximately 7 cm long through a Havar entrance foil and stopped at the rear of the cell on a tantalum

2H(a, ~)3He

301

beam stop. The Havar foils employed were of 2.9 and 6.2/~m for beam energies ranging over 1 to 7 MeV and 7.5 to 15 MeV, respectively. Deuterium pressures in the gas cell were adjusted to give an average energy spread of about 200 keV. Neutrons from the target which passed through a 40 cm long collimator of 2.5 cm diameter were incident on a high-pressure He gas scintillator. The scintillator was filled with 165 atm 4He and 9 arm Xe and was located 90 cm from the deuterium target. For the Az~ determinations, values were deduced from ratios of the neutron intensity in the helium cell for incident deuteron beams with transverse spin to the intensity with longitudinal spin. For the longitudinal spin measurements the spin quantization axis was actually set at an angle of fl = 8.5 °, ~ = 270 °. This orientation arises from a combination of deflection and Larmour precession of the deuterons in the postacceleration momentum analyzing magnet with the spin precession solenoid at the ion source turned off. Determinations of the neutron polarization were made by scattering from 4He into a left-right pair of NE 102 plastic side detectors positioned at 0lab = 120°. The neutron polarizations py, were deduced from the expression e = py,P, where e is the observed left-right asymmetry and P is the n-4He analyzing power. The general experimental technique has been described in detail in previous papers s) so only the features pertinent to this experiment will be presented here. Backgrounds were minimized by accepting only those 4He(n, n)4He events which satisfied energy and timecoincidence requirements placed on both the central and side detector pulses. Detection efficiency effects were cancelled by taking geometric means of data collected in successive runs with the deuteron quantization axis at the polarized ion source oriented to give neutron spin up or down. Background counts originating from the Havar foil and tantalum beam stop were measured at several energies by taking runs with the cell evacuated. An off-line analysis indicated that a subtraction procedure could be used to estimate this relatively small, but polarized, contribution. 3.3. DATA REDUCTION FOR THE p/ MEASUREMENT Helium recoil spectra taken in coincidence with neutrons scattered at 0~ab = 120° are shown for several deuteron energies in the upper half of fig. 1. For all but the lowest energy measurements the spectra had tails of background extending under the peak. The portion of this background which originated in the breakup of deuterons on the deuterium target, Havar foil, and tantalum beam stopwas found to be polarized. Another part, which was unpolarized and remained after a gas-out subtraction, presumably originated from ~-rays and room-scattered neutrons. Both types of background were subtracted in an off-line analysis using information about the regions above and below the 2H(d, n)aHe peak and information from an analysis of the asymmetry values calculated for each channel as illustrated in the lower half of fig. 1. A typical change in the asymmetry value for a maximum and a minimum estimate of the background extending under the peak was 0.004. The average analyzing power of the polarimeter was calculated using the Monte

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Carlo program MOCCASINS 9). Both finite geometry and multiple scattering corrections were calculated using the new set of 4He(n, n)4He phase shifts obtained recently at this laboratory t o). 3.4. DATA REDUCTIONS FOR THE A,z MEASUREMENT Values for A~ below 6 MeV were independent of the fraction of the recoil spectra employed in the calculation since deuteron breakup and other sources of background gave negligible contribution to the counting rate. For energies above 6 MeV it was obvious from analysis of the channel-by-channel values for A~ that a contribution to the lower region of the spectrum existed which had a lower value of A~. This produced a gradual decrease in magnitude for the low channels; therefore, only those portions of the spectra which were clearly above the region where this background effect set in were used to evaluate A=.

4. Results and comparison with related data 4.1. THE Azz RESULTS

The results from the 2H(d, n)3He zero-degree analyzing power measurements are shown in fig. 2 and are listed in table 1. The deuteron energies listed are the mean energies in the target; the uncertainties given for A~, are statistical only.I n addition, errors may result from incorrect beam polarization determinations as provided by the quench-ratio method. This diiticultyhas been recently discussed by Ohlsen et al. ~ ~) and found t o arise primarily from two effects. The first effectis a depolarization resulting from two-step charge exchange of the beam in the residual gas in the tandem Van de Graaff terminal. The second effect is a polarization enhancement which occurs -0.2

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because the unpolarized component of the b e a m has a poorer emittance than the polarized component and is thus partially removed or "scraped o f f " in passing f r o m the ion source to the target. We have found that under normal operating conditions these two effects largely cancel in a manner similar to that discovered at Los Alamos. Further investigations of the absolute accuracy of the quench-ratio method of determining the beam polarization are under way at our laboratory. To date, our best estimate is that the correction to the magnitude o f the beam polarization P33 is less than +0.02 at deuteron energies below 10 MeV and less than +0.01 above this energy x2). The correction to P3 is expected to be less than that to Pa3 [ref. 11)]. The comparison of the present results with the earlier data of Simmons et al. 1) and Salzman et aL x 5) in fig. 2 shows very good agreement. The data are well described by a constant value ofAz,(0 °) = - 0 . 4 6 1 for deuteron energies above 3 MeV. Below 3 MeV the values of Az, show an increase in magnitude, reaching - 0 . 6 8 at Eo = 1 MeV. The energy dependence below 3 MeV can be described by a third-order least-squares parametrization as A,,(0 °, Ed) = --0.8838+0.3218 Ee--0.0776 E~+0.0055 E 3. The decrease of A,, at low energies is too large to attribute to any of several possible experimental effects. F o r instance, in addition to the beam depolarization mentioned above, depolarization can occur as the deuteron beam traverses the target gas 13). However, in this experiment the target gas pressure was kept sufficiently high to prevent depolarization of the deuterons 13). Also, at the lowest energies multiple scattering effects in the H a v a r entrance foil of the gas target m a y cause an angular

Deuteron energy (MeV)

Analyzing power

0.93 1.28 1.54 1.64 1.84 2.10 2.56 3.11 3.59 4.12 4.65 5.18 5.68 6.20 6.48 7.07

--0.637 --0.597 --0.554 --0.535 --0.520 --0.499 -- 0.480 --0.475 --0.474 --0.475 --0.438 --0.456 --0.465 --0.434 --0.461 -- 0.454

A~

TABLE 1 Zero-degree analyzing power Uncertainty Deuteron energy AA:~ (MeV) 0.021 0.012 0.030 0.011 0.024 0.019 0.018 0.010 0.007 0.011 0.013 0.011 0.013 0.010 0.009 0.008

7.54 8.06 8.58 9.10 9.61 10.12 10.64 11.15 11.78 12.17 12.68 13.19 13.70 14.21 14.82 15.22

Analyzing power A:~

Uncertainty

--0.448 --0.457 --0.451 --0.477 --0.466 --0.473 -- 0.459 --0.458 --0.438 --0.470 --0.468 --0.458 --0.468 --0.470 --0.486 -- 0.468

0.008 0.009 0.009 0.009 0.013 0.010 0.013 0.016 0.014 0.011 0.011 0.016 0.016 0.016 0.016 0.016

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spreading of several degrees for the deuteron beam. However, unless Az= is strongly forward-peaked as a function of 0 (which is not the case at higher energies is)), corrections for such multiple scattering effects would be small in comparison to the sizeable statistical uncertainties at lower energies. 4.2. T H E Kyy' RESULTS

Polarization transfer coefficients were calculated at 28 energies using the previously discussed Az= values, the measured neutron polarizations and the beam polarizations. The results are given in table 2. The uncertainties listed as AK~" contain the statistical contribution from the A=~ measurement. As discussed in subsect. 4.1, there is an additional beam polarization uncertainty which has not been included in the tabulated values. The Kf(0) data of Simmons et aL 1) used the set of phase shifts reported by Satchler et al. 1~) to calculate the average analyzing power of 4He. In the present experiment a more recent set of phase shifts ~o) derived at our laboratory were used. In order to eliminate any differences in K~'(O) resulting from different 4He analyzing powers and to allow us to compare our results directly with those of Simmons et al. 1), we have adjusted their K~'(0), compensating for the difference of the 115° lab analyzing powers calculated from each set of phase shifts. The data adjusted by these ratios, which ranged from 1.00 to 1.06, are listed in table 3 and are compared to the present results in fig. 3. The agreement for the two sets of experiments is quite good. From 1 to 3 MeV the values of K~" show an increase from 0.4 to nearly 0.66. From about 3 to 15 MeV the data appear to be nearly constant, but a very gradual decline with increasing energy is present. For deuteron energies above 4 MeV a least squares TAnLE 2 Zero-degree transverse vector polarization transfer coefficients Deuteron energy (MoV)

Neutron energy (MeV)

0.91 1.40 2.01 2.47 2.96 3.59 4.11 4.65 5.08 5.64 6.12 6.59 7.10 7.50

3.92 4.56 5.24 5.70 6.27 6.85 7.37 7.90 8.32 8.86 9.33 9.78 10.27 10.65

Transfer Uncertainty coefficient /IKy'y K"~, 0.425 0.510 0,577 0.598 0.610 0.638 0.632 0.655 0.650 0.663 0.634 0.631 0.648 0.644

0,054 0.033 0.017 0.020 0,035 0.008 0.012 0.009 0.010 0.008 0.008 0.008 0.009 0.010

Deuteron energy (MeV)

Neutron energy (MeV)

7.97 8.50 8.97 9.54 10.06 I0.57 11.09 11.56 12.11 12.59 13.14 13.67 14.12 14.64

I I.I0 11.60 12.07 12.59 13.08 13.57 14.06 14.50 14.98 15.47 15.99 16.44 16.92 17.41

Transfer Uncertainty coefficient dKY'~ K", 0.642 0.626 0.627 0.652 0.636 0.639 0.624 0.628 0.630 0.61.6 0.615 0.605 0.605 0.615

0.005 0.010 0.011 0,010 0,008 0.010 0.008 0.011 0.013 0.010 0.007 0.012 0.012 0.012

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Results of Simmons et aL and adjustment factor Deuteron energy (MeV)

Neutron energy (MeV)

Analyzing power ratio a)

Adjusted K~'y

Adjusted uncertainty AKr,y

4.06 6.04 8.04 10.02 11.97 13.50 15.08

7.3 9.2 11.2 13.0 14.9 16.3 17.8

1.001 1.006 1.007 1.013 1.026 1.038 1.056

0.630 0.653 0.620 0.660 0.640 0.600 0.642

0.018 0.116 0.011 0.014 0.011 0.013 0.023

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polynomial fit parametrizes the data as

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and below 4 MeV as K~y' (0 o , Ed) = 0.2475+0.2604 Ed--0.0588 EaZ+0.0046 Eda. In fig. 1 an increase in the number of counts in the lower channels with increasing deuteron energy is apparent. These counts are associated with the production of neutrons through the breakup reaction 2H(d, n)pd. At the two highest energies illustrated in fig. 1, these neutrons exhibit a large asymmetry, indicating high polarization transfer coefficient. Since Az= was not determined for these neutrons, it is not yet possible to extract K~' values from these data. However, in a successive study (to be reported in a later publication) the present authors measured K~' for neutrons pro-

2H(~, ~)aHe

307

duced in deuteron breakup on a number of light nuclei, one of which was deuterium. In this case the deuteron beam was prepared in a pure vector polarized state, which permits K~' to be determined without knowledge of ,4z~, as can be readily seen from eq. (7). Values of K y' were found to be slightly lower for the breakup neutrons than for the monoenergetic 2H(d, n)aHe neutrons. This feature agrees with the indications reported by Simmons et al. 1), who also conclude that the polarization is lower for the breakup neutrons than for the monoenergetic ones. 5. Discussion

The current experiment has provided an accurate determination of the 0 ° transverse vector polarization transfer characteristics for the 2H(d, n)aHe reaction for deuteron energies above 1 MeV. Below 3 MeV both A= and K~' show a monotonically varying structure. No rapid energy dependences were exhibited in either K f or Az~ above 3 MeV, a fact which enhances the usefulness of the reaction as a source of polarized neutrons. In fact, this feature, along with the accurate results reported here, emphasizes the fact that the 2H(d, n)aHe reaction is the best polarized neutron source for energies above 4 MeV if a reliable source of at least 15 nA of polarized deuterons is available. The present data also strengthen the previously reported similarity between the values of K~' for the 2H(d, p)aH and 2H(d, n)aI-Ie mirror reactions. To emphasize this agreement, a new comparison is shown in fig. 4 where the 2H(d, p)3H values of Clegg 0.8

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et al. 4) are shown plotted along with the curve which was used in fig. 3 to represent the present 2H(d, n)aHe transfer coefficient data. It would be interesting to make this comparison at lower energies where Coulomb effects in the outgoing p-all channel will enter in more strongly. However, such measurements are extremely difficult to

308

P.W. LISOWSKI e t al.

p e r f o r m a c c u r a t e l y at a l a b o r a t o r y (like o u r s ) where one is restricted to the use o f a large t a n d e m V a n de G r a a f f accelerator. C o m p a r i s o n s o f these d a t a to accurate theoretical predictions are n o t possible yet. Several simplified pictures have a p p e a r e d in recent papers w h i ch can explain the large p o l a r i z a t i o n transfer as well as the feature that the coefficient K~' falls 4 % to 10 % below that naively anticipated f r o m a pure stripping reaction. H o w e v e r , until a m o r e exact reaction calculation is possible, it does n o t seem wise to suggest, for example, that the d e u t e r o n D-state effects are totally responsible for this difference. T h e au t h o rs w o u l d like to gratefully a c k n o w l e d g e the assistance o f Dr. G. M a c k , R. Byrd a n d R. H e n n e c k in the later stages o f this experiment.

References 1) J. E. Simmons, W. B. Broste, G. P. Lawrence and G. G. Ohlsen, Polarization phenomena in

2) 3) 4) 5) 6) 7)

8)

9) 10)

11) 12) 13) 14) 15) 16)

nuclear reactions, ed. H. H. Barschall and W. Haeberli (University of Wisconsin Press, Madison, 1971) p. 469; J. E. Simmons, W. B. Broste, G. P. Lawrence, J. L. McKibben and G. G. Ohlsen, Phys. Rev. Lett. 27 (1971) 113 C. O. Blythe, P. B. Dunscombe, J. S. C. McKee and C. Pope, Phys. Lett. 33B (1970) 211 P. W. Lisowski, T. C. Rhea, R. L. Walter, T. B. Clegg and C. E. Busch, Bull. Am. Phys. Soc. 17 (1972) 922; 18 (1973) 697 T. B. Clegg, D. D. Armstrong, R. A. Hardekopfand P. W. Keaton, Jr., Phys. Rev. C8 (1973) 922 G. G. Ohisen, Rep. Prog. Phys. 35 (1972) 717, and references therein T. B. Clegg, G. A. Bissinger and T. A. Trainer, Nucl. Instr. 120 (1974) 445 G. G. Ohlsen, J. L. McKibben, G. P. Lawrence, P. W. Keaton and D. D. Armstrong, Phys. Rev. Lett. 27 (1971) 599; G. G. Ohlsen, G. P. Lawrence, P. W. Keaton, Jr., J. L. McKibben and D. D. Armstrong, Phys. Lett. 33B (1970) 842; G. G. Ohlsen, Los Alamos Scientific Laboratory Report, LA4451 (1970); P. W. Lisowski, T. A. Trainer, C. E. Busch and T. B. Clegg, Bull. Am. Phys. Soc. 18 (1973) 699 J. R. Sawers, F. O. Purser and R. L. Walter, Phys. Rev. 141 (1966) 825; J. Taylor, G. Spalek, Th. Stammbach and R. L. Walter, Phys. Rev. C1 (1970) 803; G. L. Morgan and R. L. Walter, Nucl. Instr. 58 (1968) 22 J. R. Sawers, Ph.D. dissertation, Duke University, 1966; Th. Stammbach, unpublished TUNL report P. W. Lisowski, Ph.D. dissertation, Duke University, 1973 (available from University Microfilms, Ann Arbor, Michigan); P. W. Lisowski and R. L. Walter, to be published G. G. Ohlsen, P. A. Lovoi, G. C. Salzman, U. Meyer-Berkhout, C. K. Mitchell and W. Gri~ebler, Phys. Rev. C8 (1973) 1262 T. A. Trainer, P. W. Lisowski and T. B. Clegg, Nucl. Phys. A220 (1974) 533 W. W. Lindstrom, R. Garrett and U. Von Mollendorff, Nucl. Instr. 93 (1971) 385 G. C. Salzman, J. C. Martin, J. J. Jarmer, J. E. Simmons and G. G. Ohlsen, Phys. Lett. 45B (1973) 123 G. C. Salzman, G. G. Ohlsen, J. C. Martin, J. J. Jarmer and T. R. Donoghue, to be published G. R. Satchler, L. W. Owen, A. J. Elwyn, G. L. Morgan and R. L. Walter, Nucl. Phys. A l l 2 (1968) 1