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Neutron polarization studies with low-energy accelerators
NUCLEAR
INSTRUMENTS
AND METHODS
537-546; ©
92 ( I 9 7 I )
NORTH-HOLLAND
PUBLISHING
CO.
N E U T R O N POLARIZATION STUDIES WITH LOW-ENERGY ACCELERATORS* R. B. G A L L O W A Y
Dept. of Natural Philosophy, University of Edinburgh, Scotland The role of low-energy accelerators in fast-neutron polarization studies is assessed in the light of a review of the value of information on polarization, the techniques available for the measurement of the polarization of a fast neutron beam and of the
available data on neutron polarization resulting from elastic scattering and from nuclear reactions. Data on the principal neutron producing reactions is summarised for incident particle energies of up to 10 MeV.
1. Introduction
In a typical situation, fig. 1, a beam of unpolarized charged particles of energy E are incident on a target T1 and produce, at an angle 01 neutrons of energy En and polarization P,. The neutrons are then scattered by a sample T 2 through an angle 02 and azimuthal angle 4~ so that the number of neutrons moving in this direction in a given time is
Nucleon polarization resulting from scattering and from nuclear reactions has been the subject of much study, both experimental and theoretical1). The motivation has been and continues to be the possibility of extracting spin and parity information concerning unbound nuclear states 2'3) and of investigating the importance of spin dependent interactions in elastic scattering and in nuclear reactions. Data on elastic scattering may be discussed in the framework of the optical model*' 5). While differential cross-section data (for unpolarised neutrons) can be fitted satisfactorily with an optical potential without spin-orbit term and the model predictions are insensitive to the spin-orbit term if included6), polarization data should be related more directly to the spin-orbit term in the optical potential. Again in the description of direct reactions 7) the polarization of emitted nucleons is sensitive to the spin-orbit term in the nuclear potential. A striking example is provided in the DWBA calculations by Robson and Weigold a) on the 11B(d,p)12C reaction which show (their fig. 10) alternative spin-orbit terms with which differential cross-section data may be fitted but which predict substantially different polarization of the emitted protons to the extent of a change of sign. From a practical point of view an accurate knowledge of polarization of neutrons emitted in the principle neutron producing reactions is important for their use in experiments on the scattering of polarized neutrons. In what follows the present state of experimental fast neutron polarization studies is reviewed. The comprehensive review by Haeberli 9) of the subject up to 1961 and the shorter review by Alekseev et al. 1°) published in 1964 should be noted. 2. The principle of neutron polarization measurement
The principle of polarization measurement for nucleons is well known 9) and need only be outlined here. * Proofread by the Publisher.
U(02,~b) oc a2(E.,02) [-1 + Pn(E,Oo)A2(E,,O2)cos4)],
(1)
where a2(E.,02) is the differential scattering cross section and mz(En,02) is the analysing power of the scatterer T 2. For elastic scattering A2(En,O2) is just equal to the polarization Ps(En,02)that would result if unpolarized incident neutrons of energy En were scattered through an angle 02. Usually in an experiment the numbers of neutrons scattered to "right" (~b --0) and to "left" (q~ = n) are obtained, say N R and NL respectively and then
(NR--NL)/(NR+NL) = Pn(E,01) Ps(En,02).
(2)
Thus if Ps is known the system forms a polarimeter for measuring the polarization of neutrons from reactions and if P, is known the system may be used to study the polarization produced by elastic scattering. The established procedure to determine neutron polarization is to employ elastic scattering by spin zero nuclei since in this case Ps may be calculated if the neutron scattering phase shifts are known. Thus, for elastic scattering by 4He11), the most used polarization analyser, the neutron scattering phase shifts have been deduced from the more accurate proton scattering phase shifts which, supported by neutron scattering experiments, are used to calculate Pne(E,,O). Scattering by 12C and, more rarely other spin zero light nuclei, has been employed in neutron polarimeters9). Once the polarization of neutrons from a reaction has been determined in this way, these neutrons may be used to study the polarization resulting from elastic scattering from a range of nucleiS). Of course, the direct method of obtaining P~(E,O) would seem to be by double scattering experiments. If
537 IV. A P P L I C A T I O N S TO N U C L E A R P H Y S I C S
538 unpol,
R.B. GALLOWAY
>
T, --
~,-----
anal. power A~t,
t
right S
Fig. 1. The basic outline of a neutron polarization experiment. unpolarised neutrons of energy E, were elastically scattered by a sample through an angle 0, neutrons of energy E~ and polarization Ps(En,01) would result and if these neutrons were in turn scattered through an angle 02 to right and to left, P~(En,01)Ps(E~,Oz) could be determined. Consideration of likely counting rates shows why this approach has only been attempted when appropriate phase shift data was not availablel2). White et al. 13) have recently discussed particular cases in which double scattering by liquid He samples might be used. The proposal exploits the fact that due to symmetry, the polarization Pn(E,j) of neutrons emitted from the 2H(d,n)gHe reaction at a centre of mass angle of c~ is equal and opposite to that for angle (Tt-:0, although the neutron energies will differ in the laboratory system, E n and E~ say. If scattering asymmetries are determined for these neutrons, we may obtain, enes(En,O1) (3) and P,P~(En,02). (4) Now, if unpolarized neutrons of energy E, are scattered through an angle 01, chosen so that the scattered neutrons have energy E,~, and they are again scattered through an angle 02 to right and to left then the product
es(En,Oa)e(En,02)
(5)
may be determined. Thus Po,Ps(En,00 and e (E;,o2) may all be found from (3), (4) and (5). The choice of energies and angles to give counting rates worth considering is discussed in ref. 13. The small angle Mott-Schwinger scattering 9' 14), due to the interaction between the magnetic moment of the neutron and the Coulomb field of a nucleus, provides a process whose polarization analysing power is more simply and more directly calculated than in the case of the phase shift analyses of elastic scattering referred to above, although the practical difficulties of making
measurements on scattering though angles of only a few degrees have discouraged its use. A possible alternative in some cases to elastic scattering for polarization analysis could be to employ the inverse reaction to that producing the neutrons 9'15), i.e., if neutrons are produced in a reaction A(x,n)E then p2 is obtained from the asymmetry in the emission of x from B(n,x)A with the same energies and angles in the centre of mass system in both cases. Practical polarimeters will be discussed in section 3 the polarization produced by elastic scattering in section 4 and the polarization of neutrons emitted from nuclear reactions in section 5.
3. Neutron polarimeter systems To measure the right-left scattering asymmetry in the type of system outlined in fig. 1 requires two neutron detectors. Either one "side" detector with which to measure successively the counting rate of neutrons scattered in the direction (02,0) and then the counting rate in the direction (02,~) along with a detector to monitor the neutron yield from the reaction, or more usually two "side" detectors so that the two counting rates of interest can be determined simultaneously and a more efficient system results. The side detectors must at least be shielded from neutrons coming directly from the target T 1. A false asymmetry may be introduced by instrumental imperfections, e.g. if the two side detectors are not of equal detection efficiency or are not quite equidistant from the scatterer. However, instrumental asymmetry may be compensated by making successive measurements with the roles of the "right" and "left" detectors interchanged 9' 16), and for this reason the side detectors are often fitted to a mounting which can rotate about an axis passing through the scatterer. Clearly from eq. (1) the extent of any instrumental asymmetry may be determined by a measurement of asymmetry with the side detectors rotated into a plane normal to the reaction plane, i.e. with scattering angles (02,½~) and (02,3n). Alternatively the instrumental asymmetry may be found from an asymmetry measurement for a reaction angle 01 = 0 since the polarization Pn(E,O)=0. Another way of averaging out instrumental asymmetry is to make successive measurements with the neutron spin direction inverted, thereby effectively interchanging the roles of the "right" and "left" side detectors. This may be done by making successive measurements on neutrons emitted from the target T 1 in directions which differ in azimuth by rr, say (01,0) and (01,n)9'16). Inversion of the neutron spin direction may be achieved by precession in a magnetic field between the target and
NEUTRON
POLARIZATION
STUDIES WITH LOW-ENERGY
scatterer and this effect has been exploited in order to cancel instrumental asymmetry2~) by using a solenoid 17'~8) and by using an electromagnet19). With a solenoid, instead of processing the neutron spin through 7r and 0 alternately, the usual procedure is to process the neutron spin through ½7z and -½7z by reversing the current through the solenoid and therefore to determine Pr,Ps from asymmetry measurements in the plane normal to the reaction plane 18). Fringing fields may depolarize the neutron beam, e.g. it has been calculated 2°) that for a solenoid of length ten times its radius a depolarization of 1% should result and if the length and radius are equal the depolarization becomes 21%. Also, since scintillation counters are usually employed, the photomultipliers must be protected from stray magnetic fields lest changing the magnetic field should introduce rather than cancel instrumental asymmetry. To obtain an acceptable counting rate in a practical polarimeter the scatterer and side detectors are usually sufficiently close to require that account be taken of the finite geometry and that an equation analogous to (2) be developed from eq. (1) taking account of the spread in 01, 02 and ~b and possibly also taking account of multiple scattering in the scattering sample22'23). Elastic scattering by 4He is the most used process for determining fast neutron polarization. One attraction is that for a wide range of neutron energies an analysing power close to 1 may be obtained by using a scattering angle 02 of about 120 ° (fig. 2). A contour plot of the analysing power as a function of scattering angle and neutron energy (up to 30 MeV) is given by Hoop and Barschall 11). The analysing powers deduced from various sets of phase shifts describing n-4He scattering are compared in ref. 24. A second advantage of helium as scatterer is that both as a gas25'26), and
aMgle 120"
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Fig. 2. T h e n e u t r o n polarization p r o d u c e d by elastic scattering by 4He, f r o m H o o p a n d Barschal111).
ACCELERATORS
539
as a liquid 2s) it can be used as a scintillation detector of the recoiling 4He nuclei involved in neutron scattering. Thus the inevitable problem of background neutrons and y-rays registered in the side detectors may be reduced by recording only events in which a pulse from a side detector is coincident with a pulse from the helium scatterer-scintillator. Side detectors with pulseshape discrimination against y-rays 19) can also help reduce the background counting rate. Many 4He gas scintillators, contained in a stainless steel shell with AI and MgO reflective lining, have been used at pressures up to 175 arm with, typically about 5% Xe and a coating of diphenyl stilbene as wavelength shifter to improve light output26). The energy resolution for recoil 4He nuclei is about 10% although it depends on the uniformity and efficiency of light collection from the scintillator volume and on the gas pressure and purity. Neutron polarimeters employing a He gas scintillator are described in refs. 24, 30, 31. The use of a strong electric field to improve the light output and energy resolution of noble gas scintillators at pressures close to l arm has been reported27). The greater density of liquid He offers the possibility of a more efficient scatterer-scintillator 2s) but with the complication of the need for multiple scattering corrections which may well be larger than the corrections for finite geometryZZ'23). The higher detection efficiency of the liquid scintillator is particularly attractive when a neutron polarimeter is incorporated in a pulsed beam time-of-flight system32- 34). A different approach to neutron polarimetry based on elastic scattering by 4He has been to obtain the scattering asymmetry by detecting the 4He recoils in directions (Oz,rr) and (02,0) rather than the associated neutrons scattered in directions (02,0) and (02,r0. Small diameter He filled proportional counters primarily sensitive to recoil nuclei moving approximately axially have been used 35) as have other forms of direction sensitive proportional counters 36) and counter telescopea7). With parallel plate avalanche counters 37'3s) pulses of sufficiently fast rise time have been obtained to allow the 4He recoil polarimeter to be used in a neutron time-of-flight system. Helium filled cloud chambers have been used for polarization measurement and the possibility of using semiconductor detectors in a helium filled container to detect recoil nuclei has been investigated39). Elastic scattering by 12C is much less used than scattering by 4He as a polarization analyser for fast neutrons because the analysing power is less well established and is much more energy dependent. In most 12C polarimeters to date a graphite cylinder has IV. A P P L I C A T I O N S
TO NUCLEAR
PHYSICS
540
R. B. G A L L O W A Y
served as scatterer so loosing the advantage of the standard 4He polarimeter of discriminating against background neutrons by requiring the detection in coincidence of both the recoil nucleus and the scattered neutron. A large diamond has been employed as scatterer-scintillator to detect the recoil lZC nuclei 4°) while a less expensive method has been to use an organic scintillator and to distinguish between l zC recoil nuclei and recoil protons by a pulse-shape discrimination technique41'68). With a simple graphite scatterer a time-of-flight system may be used to distinguish the neutrons of interest from the general background as in the arrangement described by Finlayg2), in which the time of emission of a neutron from the 2H(d,n)aHe reaction is indicated by detecting the associated recoiling 3He nucleus. This associated particle time-of-flight technique has received attention recently as a promising method to use more generally when exploiting the ZH(d,n)3He reaction as a source of partially polarized neutrons for scattering experiments42'4a). Some of the work has been encouraged by developments in the preparation of thin deuterated polythene targets44), since it is desirable that the relationship expected from reaction kinematics between the directions of the incident beam, recoil nuclei and emitted neutrons should not be upset by significant scattering of the incident deuterons or the 3He recoil nuclei within the target. The most accurate measurement of this kind on the angular dependence of P.e(En,O) is by Sawers et ai. 31) who used polarized neutrons of 1.01 MeV energy from the 7Li(p,n)TBe reaction and 2.44 MeV energy from lZC(d,n)l aN. Measurements have also been made with neutrons of 12.0 MeV from 15N(d,n)160 and 16.2 MeV from 3H(d,n)4HeSZ), 23.1 MeV from 3H(d,n)4He along with a double scattering experiment using initially unpolarized neutrons12), 2.0 and 6.0 MeV from 3H(p,n)3He, 10.0 MeV from ZH(d,n)3He, 16.4 and 23.7 MeV from 3H(d,n)4He53) and 20 MeV from 3H(d,n)4He54). A double scattering experiment, inevitably of low accuracy, using 15 MeV initially unpolarized neutrons scattered by 4He in direction sensitive proportional counters has been reportedSS). PHe (90 ° c.m.) has been determined using 262 keV polarized neutrons from ZH(y,n)1H56). The general behaviour of Pr~e(En,O) is illustrated in fig. 2. The most recent discussion of the data on n-4He scattering is in terms of the optimal model in ref. 57. Two sets of phase shifts for n-~ZC elastic scattering due to Meier et al. 58) and to Wills et al. 59) are traditionally used to determine Pc in the 2 ~ MeV neutron energy range within which ~zC has been used as a
polarization analyser. Measurements of Pc made by scattering neutrons whose polarization is known (from ~He scattering asymmetry) 66) incline towards the values found from the phase shifts of Wills et al.59). The data available five years ago for neutrons of energies less than 10 MeV is reviewed by Darden3). Since then measurements have been reported of Pc (135 °) for E. =3.2-4.2 MeV using a diamond scatterer-scintillator 66) and of Pc(0) for En=15.85 MeV 67) using pulse shape selection of carbon recoil nuclei in a plastic scintillator along with neutron timeof-flight measurement68). With the latter system measurements were also made of the asymmetry in the inelastic scattering of neutrons by 12C with excitation to the 4.43 MeV state. The data on n-t2C elastic scattering through 50 ° is summarised in fig. 3. Data on scattering through 135 ° is summarised in ref. 66. The polarization measurements on scattering by other light nuclei have not been so extensive. In addition to the pre-1965 work on polarization of neutrons scattered by 2H, 3H and 3He summarised by Barschal169), a study of 22 MeV neutrons scattered by liquid 3H has been reported recently 7°) while in n-3He scattering a maximum polarization of about 40% is found for E, = 16 and 12 MeV 71) and E, = 7.9 and 3.3 MeV72). Measurements on some other light nuclei, Li, Be, B, O, M g 3 ' 7 9 ' 9 ) and Si 74) have been the subject of phase shift analyses and interpretation in relation to the states of the compound system. The optical model has inspired many measurements of neutron polarization resulting from elastic scattering. The earlier measurements on a wide range of +1 " ~
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Fig. 3. The neutron polarization produced by elastic scattering by 12C, for a scattering angle of 50 °. a. Bucherer et al.~°); b. Granberg61); c. Elwyn and Lane62); d. Gorlov et al.63); e. Kelsey et al.65); solid line from phase shifts of Wills et al.49); dashed line Meier et a1.48).
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Steuer et al. ~2) Baicker and Jones 9z)
Avignon et al. °4)
Boersma et al. 9s)
Dubbeldam and Walter ~)
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Trostin and Smotryaev 2s)
Babenko et al. ~9)
Bondarenko and Ot-Stavnov ~2o) Rogers and Bond TM)
Hangsen et al. ~°2)
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Miller zz)
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Reference
a b c
Symbol
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Ea (MeV)
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Target
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40 ° lab.
20 °, 30 °, 40 ° lab. 45 ° c.m.
45 ° c.m.
32 ° lab.
several
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40 ° lab.
53 ° c.m. 40 ° lab.
46 °, 56 ° lab. 150 ° lab.
47 °, 59 ° c.m.
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several 53 ° c.m. 49 ° lab.
Angles
5a, b, c
5b, c
5a, c
5c
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-
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5a
5a, b, c 5a
5c
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5b
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5a
5a
5a, b, c
5a, b, c
5b
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5b, c -
5a, b
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Figs.
aHe
4He lzC
4He
4He
4He
~zC
4He 4He
4He
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4He
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Analyser
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H ÷ B 11)
H + B 11)
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Meier et al. 58) D G S 49)
Meier et al. 58) Levintov et al. 35)
see 25) for D G S 49) evaluation
Meier et al. 58) Meier et al. 52) DGS42, 35)
Phase shifts
TABLE 1 N e u t r o n polarization in the 2H(d,n)aHe reaction for deuteron energies up to l0 MeV.
He recoil detection in triple proportional counter expansion cloud chamber associated 3He coincidence, 1 neutron side detector He gas scint., 2 neutron detectors with rejection o f 7__coincidences by timing
He gas scint., 2 neutron detectors Schwinger 12) scattering through 2 °, 4o, 6 o pulsed beam time-of-flight, liquid He scint., 2 interchangeable n e u t r o n detectors diffusion cloud chamber He gas scint., 2 interchangeable n e u t r o n detectors with _F-rejection by timing associated 3He time-of-flight solenoid, finds 0.10 < Pn < 0.15 pulsed beam time-of-flight, liquid He scint., 2 interchangeable neutron detectors with P.S.D., simultaneous real and r a n d o m coincidences He gas scint., 2 neutron detectors
He gas scint., 2 interchangeable neutron detectors He recoil in directional p r o p o r t i o n a l counter accelerated beam not analysed, 2 neutron detectors 2 neutron detectors with P.S.D.
pulsed beam time-of-flight, liquid He scatterer, 1 neutron side detector He gas scint., 2 interchangeable neutron detectors solenoid, He gas scint., 2 neutron detectors with P.S.D. solenoid, He gas scint., 2 neutron detectors solenoid, He gas scint., 2 n e u t r o n detectors He gas scint., 2 interchangeable n e u t r o n detectors
2 neutron detectors 2 neutron detectors He recoil in directional p r o p o r t i o n a l counters He gas scint., 2 interchangeable neutron detectors 2 He proportional counters, a scatterer, 2 interchangeable neutron detectors 1 neutron side detector He recoil in directional p r o p o r t i o n a l counter
Experimental details
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542
R.B.
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L
GALLOWAY
mately inversely as the angle. The scattering process and its use for polarization analysis has long been established for neutrons of energy about 100 MeV9). The scattering process has been studied for neutrons of energy 18-120 MeV 8z) and used recently to determine the polarization of 49 MeV neutrons from the lZC(d,n)13N reaction83). There have been only two studies of the polarization resulting from M o t t Schwinger scattering at more modest neutron energies. Gorlov et al. 84) obtained both the differential cross section and the polarization for 4 MeV neutrons scattered through angles of between 2 ° and 21 ° (with an angular resolution ~ 1°) from samples of Cu, In Sn, Pb, Bi and U, while in a similar experiment Kuchnir et al. 8s) used neutrons of energies ranging from 0.6 to 1.6 MeV, scattering angles from 1.75 ° to 15 ° with an angular resolution ~ 1° and samples of Cd, W, Au, Pb, Th and U. In both cases the results were consistent with the Schwinger theory. The incorporation of the Coulomb interaction responsible for Mott-Schwinger scattering into an optical model has been discussed recently86).
t
, det. ~ , __t . . . . .
Fig. 4. The annular neutron polarimeter. nuclei with E, < 3.5 MeV (and a few for En = 2 4 MeV) are summarised by RosenS). Polarization measurements on neutrons of 0.4, 0.7 and 1.0 MeV energy scattered through 55 ° by 31 elements are reported by Ferguson et al.V6). Olness et al. 75) report on 1.5 MeV neutrons scattered through 51 ° by 18 elements while Korzh et al. vg) also studied 1.5 MeV neutrons scattered by Mg, A1 and Si. The angular dependence of polarization due to scattering by a wide range of nuclei is reported for neutrons of 3.5 MeVS°'81), 4 MeV 78) and 4.4, 5.0 and 5.5 MeVTV). We may note, however, that there are few cases where independent measurements can be compared and that the statistical accuracy of some of the measurements puts them in the category of a preliminary survey. There is clearly scope for additional measurements of higher accuracy and for measurements which extend the range of neutron energies studied. In the case of Mott-Schwinger scattering 14) the m a x i m u m polarization should occur at a scattering angle of less than 1° and should be greater than 0.8, decreasing with increasing scattering angle approxi-
I
(a)
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4. The polarization of neutrons from reactions The 2H(d,n)aHe reaction is a convenient source of polarized neutrons and the most studied reaction so far as neutron polarization is concerned. It is therefore a convenient illustration of the different techniques that have been employed, of the statistical accuracy typical of polarization measurements and of the diffit
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NEUTRON
POLARIZATION
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STUDIES WITH LOW-ENERGY
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ACCELERATORS
543
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Fig. 5. Polarization o f n e u t r o n s f r o m the ZH(d,n)aHe reaction as a function of incident deuteron energy for laboratory angles o f a b o u t (a) 35 °, (b) 45 °, (c) 55 °. T h e s y m b o l s are explained in table 1.
culty of polarization work as shown up by the substantial discrepancies between different measurements at the same deuteron energy and angle of neutron emission. Measurements made at laboratory angles of approximately 35 °, 45 ° and 55 ° are compared in figs. 5a, b and c respectively and the key to the symbols and brief details of the experiments are listed in table 1. Where 12C has been used as analyser, the points (a, b, f, q, r, e) are based on the analysing power deduced from the phase shifts of Meier et al.SS). The use
of the Wills et al. 59) phase shifts would lead to larger numerical values of polarization, typically by about 20%. However, even if data based on scattering by 12C be ignored, substantial discrepancies remain and they cannot be attributed to differences in 4He analysing power used by different workers. The most recent account of the theory of neutron polarization in the 2H(d,n)aHe reaction at low energies is by Boersma 112) who attributes the peak in polarization, fig. 5c points r, to a resonance in n-12C scattering. IV. A P P L I C A T I O N S
TO N U C L E A R
PHYSICS
544
R.B. GALLOWAY
F e w e r p o l a r i z a t i o n m e a s u r e m e n t s , a dozen or less, have been m a d e on each o f the other p r i n c i p a l reactions used as n e u t r o n sources, 3H(p,n)3He, 3H(d,n)4He a n d 7Li(p,n)VBe. C o n c e r n i n g the first o f these, for a l a b o r a t o r y angle o f a b o u t 35 ° the p o l a r i z a t i o n is negligible j u s t a b o v e the r e a c t i o n t h r e s h o l d (Ep = 1.02 MeV), rises to 0.4 for E v a b o u t 2 M e V a n d falls to 0.1 for E p ~ 4 MeV113), while for Ep r a n g i n g f r o m 6 to 10 M e V the n e u t r o n p o l a r i z a t i o n I P , I is f o u n d f r o m an inverse reaction e x p e r i m e n t to vary s m o o t h l y f r o m 0.15 to 0.3~14). It is u n f o r t u n a t e t h a t significant neut r o n p o l a r i z a t i o n is n o t o b t a i n e d with the 3H(d,n)4He r e a c t i o n for d e u t e r o n energies b e l o w a few MeV. A t 30 ° lab. the n e u t r o n p o l a r i z a t i o n rises a l m o s t linearly f r o m zero at a b o u t 2.5 M e V d e u t e r o n energy to 0.6 at a b o u t 8 M e V while similarly large negative values o f p o l a r i z a t i o n are f o u n d between 70 ° a n d 90°115'116). W i t h the 7Li(p,n)TBe reaction a n d a n e u t r o n emission angle o f 50 ° a n e u t r o n p o l a r i z a t i o n o f a b o u t 0.3 can be o b t a i n e d for p r o t o n energies f r o m a b o u t 2.6 to 4.5 M e V a b o v e which the p o l a r i z a t i o n falls a n d changes sign at a b o u t 5 MeV, see ref. 117 and earlier w o r k listed there. A precision m e a s u r e m e n t for E p = 2 . 9 1 M e V is r e p o r t e d in ref. 31 o f Pn = 0.304 + 0.008. M o r e limited studies have been r e p o r t e d on some o t h e r reactions, either as investigations o f the r e a c t i o n m e c h a n i s m or as possible sources o f p o l a r i z e d n e u t r o n s for scattering experiments. M e a s u r e m e n t s o f significant p o l a r i z a t i o n have been m a d e on neutrons f r o m (p,n) reactions on 9Be for E p = 3 . 7 - 8 . 5 M e r i t s ) , on b o t h 9Be a n d l i B for E p = 7 - 1 1 M e v I I g ) , a n d on I a c a n d 15 N for Ep = 6.9-12.3 M e W 2o). P o l a r i z a t i o n measurements on (d,n) reactions have been m a d e on X°B E a = 1.2-2.9 MeVX2~), a~B E d = 1.35-2.0 MeV31'~22), 1zC E a = 1.7-7.5 MeV31'123), 14N E a = 1.32-3.7 MeV~24), aSN E a = 2 . 0 - 5 . 5 MeV125), /8Si E d = 5 . 0 M e V 126) a n d 4°Ca E d = 6 . 0 MeV127). T w o (aHem) reactions, on ~zC and ~3C, have been studied in the 2 - 4 M e V energy range, as have the 9Be a n d ~3C (c~,n) reactionsa3°'a3~). Thus relatively few r e a c t i o n s have been studied to date, generally over a very limited energy range, while m e a s u r e m e n t o f p o l a r i z a t i o n of n e u t r o n groups leading to different states o f the final nucleus are few. 5. Conclusion A n a c c e l e r a t o r o f less t h a n 1 M e V energy can p r o v i d e a useful source o f p o l a r i z e d n e u t r o n s ( P , - 0.15) f r o m the 2H(d,n)3He reaction, while increasing the m a c h i n e energy increases the accessible range o f p o l a r i z e d n e u t r o n p r o d u c i n g reactions so p r o v i d i n g the possibility o f higher n e u t r o n p o l a r i z a t i o n a n d a
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INSTRUMENTS
AND METHODS
537-546; ©
92 ( I 9 7 I )
NORTH-HOLLAND
PUBLISHING
CO.
N E U T R O N POLARIZATION STUDIES WITH LOW-ENERGY ACCELERATORS* R. B. G A L L O W A Y
Dept. of Natural Philosophy, University of Edinburgh, Scotland The role of low-energy accelerators in fast-neutron polarization studies is assessed in the light of a review of the value of information on polarization, the techniques available for the measurement of the polarization of a fast neutron beam and of the
available data on neutron polarization resulting from elastic scattering and from nuclear reactions. Data on the principal neutron producing reactions is summarised for incident particle energies of up to 10 MeV.
1. Introduction
In a typical situation, fig. 1, a beam of unpolarized charged particles of energy E are incident on a target T1 and produce, at an angle 01 neutrons of energy En and polarization P,. The neutrons are then scattered by a sample T 2 through an angle 02 and azimuthal angle 4~ so that the number of neutrons moving in this direction in a given time is
Nucleon polarization resulting from scattering and from nuclear reactions has been the subject of much study, both experimental and theoretical1). The motivation has been and continues to be the possibility of extracting spin and parity information concerning unbound nuclear states 2'3) and of investigating the importance of spin dependent interactions in elastic scattering and in nuclear reactions. Data on elastic scattering may be discussed in the framework of the optical model*' 5). While differential cross-section data (for unpolarised neutrons) can be fitted satisfactorily with an optical potential without spin-orbit term and the model predictions are insensitive to the spin-orbit term if included6), polarization data should be related more directly to the spin-orbit term in the optical potential. Again in the description of direct reactions 7) the polarization of emitted nucleons is sensitive to the spin-orbit term in the nuclear potential. A striking example is provided in the DWBA calculations by Robson and Weigold a) on the 11B(d,p)12C reaction which show (their fig. 10) alternative spin-orbit terms with which differential cross-section data may be fitted but which predict substantially different polarization of the emitted protons to the extent of a change of sign. From a practical point of view an accurate knowledge of polarization of neutrons emitted in the principle neutron producing reactions is important for their use in experiments on the scattering of polarized neutrons. In what follows the present state of experimental fast neutron polarization studies is reviewed. The comprehensive review by Haeberli 9) of the subject up to 1961 and the shorter review by Alekseev et al. 1°) published in 1964 should be noted. 2. The principle of neutron polarization measurement
The principle of polarization measurement for nucleons is well known 9) and need only be outlined here. * Proofread by the Publisher.
U(02,~b) oc a2(E.,02) [-1 + Pn(E,Oo)A2(E,,O2)cos4)],
(1)
where a2(E.,02) is the differential scattering cross section and mz(En,02) is the analysing power of the scatterer T 2. For elastic scattering A2(En,O2) is just equal to the polarization Ps(En,02)that would result if unpolarized incident neutrons of energy En were scattered through an angle 02. Usually in an experiment the numbers of neutrons scattered to "right" (~b --0) and to "left" (q~ = n) are obtained, say N R and NL respectively and then
(NR--NL)/(NR+NL) = Pn(E,01) Ps(En,02).
(2)
Thus if Ps is known the system forms a polarimeter for measuring the polarization of neutrons from reactions and if P, is known the system may be used to study the polarization produced by elastic scattering. The established procedure to determine neutron polarization is to employ elastic scattering by spin zero nuclei since in this case Ps may be calculated if the neutron scattering phase shifts are known. Thus, for elastic scattering by 4He11), the most used polarization analyser, the neutron scattering phase shifts have been deduced from the more accurate proton scattering phase shifts which, supported by neutron scattering experiments, are used to calculate Pne(E,,O). Scattering by 12C and, more rarely other spin zero light nuclei, has been employed in neutron polarimeters9). Once the polarization of neutrons from a reaction has been determined in this way, these neutrons may be used to study the polarization resulting from elastic scattering from a range of nucleiS). Of course, the direct method of obtaining P~(E,O) would seem to be by double scattering experiments. If
537 IV. A P P L I C A T I O N S TO N U C L E A R P H Y S I C S
538 unpol,
R.B. GALLOWAY
>
T, --
~,-----
anal. power A~t,
t
right S
Fig. 1. The basic outline of a neutron polarization experiment. unpolarised neutrons of energy E, were elastically scattered by a sample through an angle 0, neutrons of energy E~ and polarization Ps(En,01) would result and if these neutrons were in turn scattered through an angle 02 to right and to left, P~(En,01)Ps(E~,Oz) could be determined. Consideration of likely counting rates shows why this approach has only been attempted when appropriate phase shift data was not availablel2). White et al. 13) have recently discussed particular cases in which double scattering by liquid He samples might be used. The proposal exploits the fact that due to symmetry, the polarization Pn(E,j) of neutrons emitted from the 2H(d,n)gHe reaction at a centre of mass angle of c~ is equal and opposite to that for angle (Tt-:0, although the neutron energies will differ in the laboratory system, E n and E~ say. If scattering asymmetries are determined for these neutrons, we may obtain, enes(En,O1) (3) and P,P~(En,02). (4) Now, if unpolarized neutrons of energy E, are scattered through an angle 01, chosen so that the scattered neutrons have energy E,~, and they are again scattered through an angle 02 to right and to left then the product
es(En,Oa)e(En,02)
(5)
may be determined. Thus Po,Ps(En,00 and e (E;,o2) may all be found from (3), (4) and (5). The choice of energies and angles to give counting rates worth considering is discussed in ref. 13. The small angle Mott-Schwinger scattering 9' 14), due to the interaction between the magnetic moment of the neutron and the Coulomb field of a nucleus, provides a process whose polarization analysing power is more simply and more directly calculated than in the case of the phase shift analyses of elastic scattering referred to above, although the practical difficulties of making
measurements on scattering though angles of only a few degrees have discouraged its use. A possible alternative in some cases to elastic scattering for polarization analysis could be to employ the inverse reaction to that producing the neutrons 9'15), i.e., if neutrons are produced in a reaction A(x,n)E then p2 is obtained from the asymmetry in the emission of x from B(n,x)A with the same energies and angles in the centre of mass system in both cases. Practical polarimeters will be discussed in section 3 the polarization produced by elastic scattering in section 4 and the polarization of neutrons emitted from nuclear reactions in section 5.
3. Neutron polarimeter systems To measure the right-left scattering asymmetry in the type of system outlined in fig. 1 requires two neutron detectors. Either one "side" detector with which to measure successively the counting rate of neutrons scattered in the direction (02,0) and then the counting rate in the direction (02,~) along with a detector to monitor the neutron yield from the reaction, or more usually two "side" detectors so that the two counting rates of interest can be determined simultaneously and a more efficient system results. The side detectors must at least be shielded from neutrons coming directly from the target T 1. A false asymmetry may be introduced by instrumental imperfections, e.g. if the two side detectors are not of equal detection efficiency or are not quite equidistant from the scatterer. However, instrumental asymmetry may be compensated by making successive measurements with the roles of the "right" and "left" detectors interchanged 9' 16), and for this reason the side detectors are often fitted to a mounting which can rotate about an axis passing through the scatterer. Clearly from eq. (1) the extent of any instrumental asymmetry may be determined by a measurement of asymmetry with the side detectors rotated into a plane normal to the reaction plane, i.e. with scattering angles (02,½~) and (02,3n). Alternatively the instrumental asymmetry may be found from an asymmetry measurement for a reaction angle 01 = 0 since the polarization Pn(E,O)=0. Another way of averaging out instrumental asymmetry is to make successive measurements with the neutron spin direction inverted, thereby effectively interchanging the roles of the "right" and "left" side detectors. This may be done by making successive measurements on neutrons emitted from the target T 1 in directions which differ in azimuth by rr, say (01,0) and (01,n)9'16). Inversion of the neutron spin direction may be achieved by precession in a magnetic field between the target and
NEUTRON
POLARIZATION
STUDIES WITH LOW-ENERGY
scatterer and this effect has been exploited in order to cancel instrumental asymmetry2~) by using a solenoid 17'~8) and by using an electromagnet19). With a solenoid, instead of processing the neutron spin through 7r and 0 alternately, the usual procedure is to process the neutron spin through ½7z and -½7z by reversing the current through the solenoid and therefore to determine Pr,Ps from asymmetry measurements in the plane normal to the reaction plane 18). Fringing fields may depolarize the neutron beam, e.g. it has been calculated 2°) that for a solenoid of length ten times its radius a depolarization of 1% should result and if the length and radius are equal the depolarization becomes 21%. Also, since scintillation counters are usually employed, the photomultipliers must be protected from stray magnetic fields lest changing the magnetic field should introduce rather than cancel instrumental asymmetry. To obtain an acceptable counting rate in a practical polarimeter the scatterer and side detectors are usually sufficiently close to require that account be taken of the finite geometry and that an equation analogous to (2) be developed from eq. (1) taking account of the spread in 01, 02 and ~b and possibly also taking account of multiple scattering in the scattering sample22'23). Elastic scattering by 4He is the most used process for determining fast neutron polarization. One attraction is that for a wide range of neutron energies an analysing power close to 1 may be obtained by using a scattering angle 02 of about 120 ° (fig. 2). A contour plot of the analysing power as a function of scattering angle and neutron energy (up to 30 MeV) is given by Hoop and Barschall 11). The analysing powers deduced from various sets of phase shifts describing n-4He scattering are compared in ref. 24. A second advantage of helium as scatterer is that both as a gas25'26), and
aMgle 120"
IOO" 140"
%e 0
•
,
-
,
.
• •
8 •
, ,
1,0 .
, .
.
12 .
, .
14
,.
~
, E n
MeV
.
60 °
~
aO°
-I
Fig. 2. T h e n e u t r o n polarization p r o d u c e d by elastic scattering by 4He, f r o m H o o p a n d Barschal111).
ACCELERATORS
539
as a liquid 2s) it can be used as a scintillation detector of the recoiling 4He nuclei involved in neutron scattering. Thus the inevitable problem of background neutrons and y-rays registered in the side detectors may be reduced by recording only events in which a pulse from a side detector is coincident with a pulse from the helium scatterer-scintillator. Side detectors with pulseshape discrimination against y-rays 19) can also help reduce the background counting rate. Many 4He gas scintillators, contained in a stainless steel shell with AI and MgO reflective lining, have been used at pressures up to 175 arm with, typically about 5% Xe and a coating of diphenyl stilbene as wavelength shifter to improve light output26). The energy resolution for recoil 4He nuclei is about 10% although it depends on the uniformity and efficiency of light collection from the scintillator volume and on the gas pressure and purity. Neutron polarimeters employing a He gas scintillator are described in refs. 24, 30, 31. The use of a strong electric field to improve the light output and energy resolution of noble gas scintillators at pressures close to l arm has been reported27). The greater density of liquid He offers the possibility of a more efficient scatterer-scintillator 2s) but with the complication of the need for multiple scattering corrections which may well be larger than the corrections for finite geometryZZ'23). The higher detection efficiency of the liquid scintillator is particularly attractive when a neutron polarimeter is incorporated in a pulsed beam time-of-flight system32- 34). A different approach to neutron polarimetry based on elastic scattering by 4He has been to obtain the scattering asymmetry by detecting the 4He recoils in directions (Oz,rr) and (02,0) rather than the associated neutrons scattered in directions (02,0) and (02,r0. Small diameter He filled proportional counters primarily sensitive to recoil nuclei moving approximately axially have been used 35) as have other forms of direction sensitive proportional counters 36) and counter telescopea7). With parallel plate avalanche counters 37'3s) pulses of sufficiently fast rise time have been obtained to allow the 4He recoil polarimeter to be used in a neutron time-of-flight system. Helium filled cloud chambers have been used for polarization measurement and the possibility of using semiconductor detectors in a helium filled container to detect recoil nuclei has been investigated39). Elastic scattering by 12C is much less used than scattering by 4He as a polarization analyser for fast neutrons because the analysing power is less well established and is much more energy dependent. In most 12C polarimeters to date a graphite cylinder has IV. A P P L I C A T I O N S
TO NUCLEAR
PHYSICS
540
R. B. G A L L O W A Y
served as scatterer so loosing the advantage of the standard 4He polarimeter of discriminating against background neutrons by requiring the detection in coincidence of both the recoil nucleus and the scattered neutron. A large diamond has been employed as scatterer-scintillator to detect the recoil lZC nuclei 4°) while a less expensive method has been to use an organic scintillator and to distinguish between l zC recoil nuclei and recoil protons by a pulse-shape discrimination technique41'68). With a simple graphite scatterer a time-of-flight system may be used to distinguish the neutrons of interest from the general background as in the arrangement described by Finlayg2), in which the time of emission of a neutron from the 2H(d,n)aHe reaction is indicated by detecting the associated recoiling 3He nucleus. This associated particle time-of-flight technique has received attention recently as a promising method to use more generally when exploiting the ZH(d,n)3He reaction as a source of partially polarized neutrons for scattering experiments42'4a). Some of the work has been encouraged by developments in the preparation of thin deuterated polythene targets44), since it is desirable that the relationship expected from reaction kinematics between the directions of the incident beam, recoil nuclei and emitted neutrons should not be upset by significant scattering of the incident deuterons or the 3He recoil nuclei within the target. The most accurate measurement of this kind on the angular dependence of P.e(En,O) is by Sawers et ai. 31) who used polarized neutrons of 1.01 MeV energy from the 7Li(p,n)TBe reaction and 2.44 MeV energy from lZC(d,n)l aN. Measurements have also been made with neutrons of 12.0 MeV from 15N(d,n)160 and 16.2 MeV from 3H(d,n)4HeSZ), 23.1 MeV from 3H(d,n)4He along with a double scattering experiment using initially unpolarized neutrons12), 2.0 and 6.0 MeV from 3H(p,n)3He, 10.0 MeV from ZH(d,n)3He, 16.4 and 23.7 MeV from 3H(d,n)4He53) and 20 MeV from 3H(d,n)4He54). A double scattering experiment, inevitably of low accuracy, using 15 MeV initially unpolarized neutrons scattered by 4He in direction sensitive proportional counters has been reportedSS). PHe (90 ° c.m.) has been determined using 262 keV polarized neutrons from ZH(y,n)1H56). The general behaviour of Pr~e(En,O) is illustrated in fig. 2. The most recent discussion of the data on n-4He scattering is in terms of the optimal model in ref. 57. Two sets of phase shifts for n-~ZC elastic scattering due to Meier et al. 58) and to Wills et al. 59) are traditionally used to determine Pc in the 2 ~ MeV neutron energy range within which ~zC has been used as a
polarization analyser. Measurements of Pc made by scattering neutrons whose polarization is known (from ~He scattering asymmetry) 66) incline towards the values found from the phase shifts of Wills et al.59). The data available five years ago for neutrons of energies less than 10 MeV is reviewed by Darden3). Since then measurements have been reported of Pc (135 °) for E. =3.2-4.2 MeV using a diamond scatterer-scintillator 66) and of Pc(0) for En=15.85 MeV 67) using pulse shape selection of carbon recoil nuclei in a plastic scintillator along with neutron timeof-flight measurement68). With the latter system measurements were also made of the asymmetry in the inelastic scattering of neutrons by 12C with excitation to the 4.43 MeV state. The data on n-t2C elastic scattering through 50 ° is summarised in fig. 3. Data on scattering through 135 ° is summarised in ref. 66. The polarization measurements on scattering by other light nuclei have not been so extensive. In addition to the pre-1965 work on polarization of neutrons scattered by 2H, 3H and 3He summarised by Barschal169), a study of 22 MeV neutrons scattered by liquid 3H has been reported recently 7°) while in n-3He scattering a maximum polarization of about 40% is found for E, = 16 and 12 MeV 71) and E, = 7.9 and 3.3 MeV72). Measurements on some other light nuclei, Li, Be, B, O, M g 3 ' 7 9 ' 9 ) and Si 74) have been the subject of phase shift analyses and interpretation in relation to the states of the compound system. The optical model has inspired many measurements of neutron polarization resulting from elastic scattering. The earlier measurements on a wide range of +1 " ~
~
T
r
t
3 ~
I
q
l
x T
% &
ra l
L
r
a~
2
t
,t'",'," ta 4
6
8 En
MeV
Fig. 3. The neutron polarization produced by elastic scattering by 12C, for a scattering angle of 50 °. a. Bucherer et al.~°); b. Granberg61); c. Elwyn and Lane62); d. Gorlov et al.63); e. Kelsey et al.65); solid line from phase shifts of Wills et al.49); dashed line Meier et a1.48).
f3
,<
©
Steuer et al. ~2) Baicker and Jones 9z)
Avignon et al. °4)
Boersma et al. 9s)
Dubbeldam and Walter ~)
May et al. ~3)
Niewodniczanski et al. 97)
Trostin and Smotryaev 2s)
Babenko et al. ~9)
Bondarenko and Ot-Stavnov ~2o) Rogers and Bond TM)
Hangsen et al. ~°2)
Purser et al. ~°z) Gorlov et al.a°a)
Miller zz)
Mulder ~2~) Behof et al. ~°s)
Stoppenhagen and Finlay ~87) Lam et al. 3~)
T h o m a s and H o f m a n n l°s)
Drigo et al. a°9)
Prade and Csikai 1 1 ° )
g h
i
j
k
1
m
n
0
p
r
s t
u
v w
-
x
y
z
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q
Roding and Scholermannl 11)
Kane 9°) Ot-Stavnov 91)
f
-
Pasma 25)
Dachnick 89)
d
e
Meier et al. 58) McCormac et al. 87) Levintov et al. 82)
Reference
a b c
Symbol
0.53-2.0
0.124).23
1.09-3.14
0.08~0.14
3.0-6.0
0.375 0.064).38, 0.34 0.084).12
1.5-1.9
1.9-3.7 1.2
0.074). 15
0.115-0.17
2.97
4.7, 5.6
9.0, 12.0
5.9-11.3
8.4
1.9-11.0
0.2754).45
5.5
0.75 2.0-4.5
0.12 0.4-1.0
8.2
0.2-0.5
0.6 0.7 0.4-1.8
Ea (MeV)
Ti-D 186/~g/cm 2
Ti-D 400/~g/cm 2 Ti-D 1.5 m g / c m z T i - D thick
T i - D thick
D20 50 keV DzO thick
gas D20
D20 thick
D20 thick
Zr-D 19 m g / c m z gas
gas
gas, 175-350 keV gas
T i - D 50 keV
gas
D~O thick gas
"drive in" AI D20
gas
D20 "drive in" Cu Zr-D 150 keV and thick D20 50 keV
Target
several
49 ° 54 ° lab.
35 °, 55 ° lab.
50 ° lab.
45° c.m.
46.5 ° lab. 47 ° lab., several 50 ° lab.
35 ° lab.
several 37 ° lab.
50 ° lab.
45 ° lab.
40 ° lab.
20 °, 30 °, 40 ° lab. 45 ° c.m.
45 ° c.m.
32 ° lab.
several
several
40 ° lab.
53 ° c.m. 40 ° lab.
46 °, 56 ° lab. 150 ° lab.
47 °, 59 ° c.m.
47 ° lab.
several 53 ° c.m. 49 ° lab.
Angles
5a, b, c
5b, c
5a, c
5c
5a
-
5b 5b, c
5a
5a, b, c 5a
5c
5b
5b
5a
5a, b
5a
5a
5a, b, c
5a, b, c
5b
5b 5b
5b, c -
5a, b
5b
5b, c 5b 5b
Figs.
aHe
4He lzC
4He
4He
4He
~zC
4He 4He
4He
4He U
a~C
I2C
4He
4He
4He
4He
4He
4He
4He
4He
12C 4He
12C 4He
aHe
4He
12C 12C 4He
Analyser
ABS 5°) Meier et al. s8) Wills et al. 59) H ÷ B H)
H ÷ B 11)
H + B 11)
H-~B H)
ABS 5°) D G S 42)
Meier et al. ~8) Wills et al. 52) Meier et al. ~8) Wills et al. 59) D G S 49) -
Levintov et al. ~5)
D G S 4~)
D G S 49)
D G S 49)
D G S 42)
ABS ~°)
D G S 49)
Meier et al. 58) D G S 49)
Meier et al. 58) Levintov et al. 35)
see 25) for D G S 49) evaluation
Meier et al. 58) Meier et al. 52) DGS42, 35)
Phase shifts
TABLE 1 N e u t r o n polarization in the 2H(d,n)aHe reaction for deuteron energies up to l0 MeV.
He recoil detection in triple proportional counter expansion cloud chamber associated 3He coincidence, 1 neutron side detector He gas scint., 2 neutron detectors with rejection o f 7__coincidences by timing
He gas scint., 2 neutron detectors Schwinger 12) scattering through 2 °, 4o, 6 o pulsed beam time-of-flight, liquid He scint., 2 interchangeable n e u t r o n detectors diffusion cloud chamber He gas scint., 2 interchangeable n e u t r o n detectors with _F-rejection by timing associated 3He time-of-flight solenoid, finds 0.10 < Pn < 0.15 pulsed beam time-of-flight, liquid He scint., 2 interchangeable neutron detectors with P.S.D., simultaneous real and r a n d o m coincidences He gas scint., 2 neutron detectors
He gas scint., 2 interchangeable neutron detectors He recoil in directional p r o p o r t i o n a l counter accelerated beam not analysed, 2 neutron detectors 2 neutron detectors with P.S.D.
pulsed beam time-of-flight, liquid He scatterer, 1 neutron side detector He gas scint., 2 interchangeable neutron detectors solenoid, He gas scint., 2 neutron detectors with P.S.D. solenoid, He gas scint., 2 neutron detectors solenoid, He gas scint., 2 n e u t r o n detectors He gas scint., 2 interchangeable n e u t r o n detectors
2 neutron detectors 2 neutron detectors He recoil in directional p r o p o r t i o n a l counters He gas scint., 2 interchangeable neutron detectors 2 He proportional counters, a scatterer, 2 interchangeable neutron detectors 1 neutron side detector He recoil in directional p r o p o r t i o n a l counter
Experimental details
Z
r~
©
t~
m
i t~
©
m
Z
N
0
o Z
Z
542
R.B.
)
det.
~
s s i 0~ ,
L
GALLOWAY
mately inversely as the angle. The scattering process and its use for polarization analysis has long been established for neutrons of energy about 100 MeV9). The scattering process has been studied for neutrons of energy 18-120 MeV 8z) and used recently to determine the polarization of 49 MeV neutrons from the lZC(d,n)13N reaction83). There have been only two studies of the polarization resulting from M o t t Schwinger scattering at more modest neutron energies. Gorlov et al. 84) obtained both the differential cross section and the polarization for 4 MeV neutrons scattered through angles of between 2 ° and 21 ° (with an angular resolution ~ 1°) from samples of Cu, In Sn, Pb, Bi and U, while in a similar experiment Kuchnir et al. 8s) used neutrons of energies ranging from 0.6 to 1.6 MeV, scattering angles from 1.75 ° to 15 ° with an angular resolution ~ 1° and samples of Cd, W, Au, Pb, Th and U. In both cases the results were consistent with the Schwinger theory. The incorporation of the Coulomb interaction responsible for Mott-Schwinger scattering into an optical model has been discussed recently86).
t
, det. ~ , __t . . . . .
Fig. 4. The annular neutron polarimeter. nuclei with E, < 3.5 MeV (and a few for En = 2 4 MeV) are summarised by RosenS). Polarization measurements on neutrons of 0.4, 0.7 and 1.0 MeV energy scattered through 55 ° by 31 elements are reported by Ferguson et al.V6). Olness et al. 75) report on 1.5 MeV neutrons scattered through 51 ° by 18 elements while Korzh et al. vg) also studied 1.5 MeV neutrons scattered by Mg, A1 and Si. The angular dependence of polarization due to scattering by a wide range of nuclei is reported for neutrons of 3.5 MeVS°'81), 4 MeV 78) and 4.4, 5.0 and 5.5 MeVTV). We may note, however, that there are few cases where independent measurements can be compared and that the statistical accuracy of some of the measurements puts them in the category of a preliminary survey. There is clearly scope for additional measurements of higher accuracy and for measurements which extend the range of neutron energies studied. In the case of Mott-Schwinger scattering 14) the m a x i m u m polarization should occur at a scattering angle of less than 1° and should be greater than 0.8, decreasing with increasing scattering angle approxi-
I
(a)
I
I
I J llll
4. The polarization of neutrons from reactions The 2H(d,n)aHe reaction is a convenient source of polarized neutrons and the most studied reaction so far as neutron polarization is concerned. It is therefore a convenient illustration of the different techniques that have been employed, of the statistical accuracy typical of polarization measurements and of the diffit
I
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NEUTRON
POLARIZATION
0"3
I
(b)
STUDIES WITH LOW-ENERGY
II
I
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I ]111
I
i
ACCELERATORS
543
I I I
£
r T
~ q Z
d
.L
T
r
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,L
,w
~
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.L
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TT
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i
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(c)
I
I°O
O.I
0.3
.L
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i
i I I
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i-
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w w wWWT~, w
-
l
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I
'!i
JJ'z
T -rf~
T13 It 1
1 llll
--
I
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Ed
MeV
Fig. 5. Polarization o f n e u t r o n s f r o m the ZH(d,n)aHe reaction as a function of incident deuteron energy for laboratory angles o f a b o u t (a) 35 °, (b) 45 °, (c) 55 °. T h e s y m b o l s are explained in table 1.
culty of polarization work as shown up by the substantial discrepancies between different measurements at the same deuteron energy and angle of neutron emission. Measurements made at laboratory angles of approximately 35 °, 45 ° and 55 ° are compared in figs. 5a, b and c respectively and the key to the symbols and brief details of the experiments are listed in table 1. Where 12C has been used as analyser, the points (a, b, f, q, r, e) are based on the analysing power deduced from the phase shifts of Meier et al.SS). The use
of the Wills et al. 59) phase shifts would lead to larger numerical values of polarization, typically by about 20%. However, even if data based on scattering by 12C be ignored, substantial discrepancies remain and they cannot be attributed to differences in 4He analysing power used by different workers. The most recent account of the theory of neutron polarization in the 2H(d,n)aHe reaction at low energies is by Boersma 112) who attributes the peak in polarization, fig. 5c points r, to a resonance in n-12C scattering. IV. A P P L I C A T I O N S
TO N U C L E A R
PHYSICS
544
R.B. GALLOWAY
F e w e r p o l a r i z a t i o n m e a s u r e m e n t s , a dozen or less, have been m a d e on each o f the other p r i n c i p a l reactions used as n e u t r o n sources, 3H(p,n)3He, 3H(d,n)4He a n d 7Li(p,n)VBe. C o n c e r n i n g the first o f these, for a l a b o r a t o r y angle o f a b o u t 35 ° the p o l a r i z a t i o n is negligible j u s t a b o v e the r e a c t i o n t h r e s h o l d (Ep = 1.02 MeV), rises to 0.4 for E v a b o u t 2 M e V a n d falls to 0.1 for E p ~ 4 MeV113), while for Ep r a n g i n g f r o m 6 to 10 M e V the n e u t r o n p o l a r i z a t i o n I P , I is f o u n d f r o m an inverse reaction e x p e r i m e n t to vary s m o o t h l y f r o m 0.15 to 0.3~14). It is u n f o r t u n a t e t h a t significant neut r o n p o l a r i z a t i o n is n o t o b t a i n e d with the 3H(d,n)4He r e a c t i o n for d e u t e r o n energies b e l o w a few MeV. A t 30 ° lab. the n e u t r o n p o l a r i z a t i o n rises a l m o s t linearly f r o m zero at a b o u t 2.5 M e V d e u t e r o n energy to 0.6 at a b o u t 8 M e V while similarly large negative values o f p o l a r i z a t i o n are f o u n d between 70 ° a n d 90°115'116). W i t h the 7Li(p,n)TBe reaction a n d a n e u t r o n emission angle o f 50 ° a n e u t r o n p o l a r i z a t i o n o f a b o u t 0.3 can be o b t a i n e d for p r o t o n energies f r o m a b o u t 2.6 to 4.5 M e V a b o v e which the p o l a r i z a t i o n falls a n d changes sign at a b o u t 5 MeV, see ref. 117 and earlier w o r k listed there. A precision m e a s u r e m e n t for E p = 2 . 9 1 M e V is r e p o r t e d in ref. 31 o f Pn = 0.304 + 0.008. M o r e limited studies have been r e p o r t e d on some o t h e r reactions, either as investigations o f the r e a c t i o n m e c h a n i s m or as possible sources o f p o l a r i z e d n e u t r o n s for scattering experiments. M e a s u r e m e n t s o f significant p o l a r i z a t i o n have been m a d e on neutrons f r o m (p,n) reactions on 9Be for E p = 3 . 7 - 8 . 5 M e r i t s ) , on b o t h 9Be a n d l i B for E p = 7 - 1 1 M e v I I g ) , a n d on I a c a n d 15 N for Ep = 6.9-12.3 M e W 2o). P o l a r i z a t i o n measurements on (d,n) reactions have been m a d e on X°B E a = 1.2-2.9 MeVX2~), a~B E d = 1.35-2.0 MeV31'~22), 1zC E a = 1.7-7.5 MeV31'123), 14N E a = 1.32-3.7 MeV~24), aSN E a = 2 . 0 - 5 . 5 MeV125), /8Si E d = 5 . 0 M e V 126) a n d 4°Ca E d = 6 . 0 MeV127). T w o (aHem) reactions, on ~zC and ~3C, have been studied in the 2 - 4 M e V energy range, as have the 9Be a n d ~3C (c~,n) reactionsa3°'a3~). Thus relatively few r e a c t i o n s have been studied to date, generally over a very limited energy range, while m e a s u r e m e n t o f p o l a r i z a t i o n of n e u t r o n groups leading to different states o f the final nucleus are few. 5. Conclusion A n a c c e l e r a t o r o f less t h a n 1 M e V energy can p r o v i d e a useful source o f p o l a r i z e d n e u t r o n s ( P , - 0.15) f r o m the 2H(d,n)3He reaction, while increasing the m a c h i n e energy increases the accessible range o f p o l a r i z e d n e u t r o n p r o d u c i n g reactions so p r o v i d i n g the possibility o f higher n e u t r o n p o l a r i z a t i o n a n d a
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