Polarization of protons elastically scattered from deuterons

I

1.B:

Nuclear Physws 62 (1965) 497--510, (~) North-Holland Pubhshmg Co, Amsterdam

2 B

N o t to be reproduced by p h o t o p r m t or microfilm without written permission from the pubhsher

POLARIZATION ELASTICALLY

OF PROTONS

SCATTERED

FROM

DEUTERONS

R A C H A L M E R S t , R S COX, K K SETH a n d E N STRAIT Northwestern University, Evanston, Ilhnom tt Received 10 July 1964

Abstract: The polarization of protons elastically scattered from deuterons has been measured by a double scattering experiment Partially polarized protons of energy 1 50, 2 02 and 2 52 MeV were obtained by scattering a 4 1 MeV proton beam from carbon and by subsequent energy degradation m suitable foils The scattering chamber was filled with a mixture of deuterium, helium and xenon, and the proton groups corresponding to elastic scattering from the individual gases were resolved in two symmetrically located semi-conductor detectors The simultaneous measurement of right-left asymmetries for xenon, helium and deuterium permitted a continuous monitoring of false asymmetries, proton beam polarization and the p-d polarization, respectively The measurements yield positive polarizations, relatively independent of energy, for p-d scattering at angles (c m ) between 45 ° and 120 ° with maxima of about (8±2)% near 90 °, and near zero values at 45 ° and 120 ° These results are consistent with recent n-d polarmatxon experiments of comparable accuracy E I

I

N U C L E A R REACTIONS H2(p, p), E = 1 5, 2 0, 2 5 MeV, measured polarization (0)

1. Introduction T h e r o l e o f s p i n - o r b i t a n d s p i n - s p i n d e p e n d e n t f o r c e s an n u c l e a r r e a c t i o n s is u s u a l l y i n v e s t i g a t e d b y s t u d y i n g t h e s p i n p o l a r i z a t i o n o f e m i t t e d p a r t i c l e s 1) A l a r g e b o d y of data on nucleon-nucleon scattering and polarization has been analysed m terms o f v a r i o u s p h e n o m e n o l o g l c a l n u c l e o n - n u c l e o n p o t e n t m l s w h i c h a t t e m p t to t a k e i n t o a c c o u n t s u c h i n t e r a c t i o n s 2) S~mxlarly a l a r g e b o d y o f d a t a o n t h e s c a t t e r i n g a n d p o l a r i z a t i o n o f n e u t r o n s a n d p r o t o n s (up to tens o f M e V o f e n e r g y ) f r o m r e l a t w e l y h e a v i e r n u c l e i has b e e n successfully a n a l y s e d m t e r m s o f a n o p t i c a l p o t e n t i a l w h i c h i n c l u d e s a s p i n - o r b i t p a r t a) T h e s c a t t e r i n g o f n u c l e o n s f r o m d e u t e r o n s , t r i t o n s a n d H e a h a s r e c e i v e d a t t e n t i o n o n l y r e c e n t l y A t e n e r g i e s less t h a n a f e w M e V e s s e n t i a l l y n o p o l a r i z a t i o n h a s b e e n e i t h e r p r e d i c a t e d 4 ) o r o b s e r v e d 5) in n u c l e o n - n u c l e o n scattering

F o r elastic s c a t t e r i n g o f 1 M e V n e u t r o n s f r o m H 3, S e a g r a v e et al 6)

report a maximum

p o l a r i z a t i o n o f (10___7)% at 0 c m = 80 ° F o r t h e s c a t t e r i n g o f

t Present address Lockheed Mxssdes and Space Company, Palo Alto, Cahforma tt This research was supported in part by the U S Office of Naval Research, National Science Foundation and the U S Army Research Office (Durham), and is based on a thesis submitted by R A C in partial fulfillment of the requirements for the degree of Doctor of Philosophy at Northwestern University, Evanston, Ilhnols 497

498

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CHALMERS e t al

protons of energies between 4 and 13 MeV from He 3, McDonald, Heaberh and Morrow 7) report rather large polarizations Even at 4 MeV polarization as large as (40_ 4)9/o were found in these experiments From these experiments it has become obvious that even at low energies a proper description of scattering of nucleons by hght nuclei must include the effect of spin-orbit forces Elastic scattering of protons from deuterons was first studied by Sherr et a l , Brown et al. and Rosen and Allred s) Neutron scattering was studied by Hamouda et al, Wantauch 9) and Allred et al 9) The angular distributions in the energy region I to 5 MeV were adequately fitted by the calculations of Buckingham and Massey 1o) and of Christian and Gammel 11), both calculations employing purely central potentials, and thus implying zero polarization. Recently a number of experiments attempting to measure polarization of neutrons scattered from deuterium have been made Discounting the first measurements of White, Chisholm and Brown 12) which yielded large (..m 40 7o) polarization, the consensus of results 13-22) indicates a small positive polarization for n-d scattering up to a few MeV. The only measurement of p-d scattering polarization reported so far is the one made at this laboratory 23) which Indicated a small positive polarlzatmn which was not inconsistent with zero. The present investigation was prompted by the desire to measure p-d scattering polarization with greater accuracy and to compare It with the n-d scattering polarization of comparable precision

2. Experimental Method Spin polarlzatmn P is a vector quantity defined as the statistical average (over all o f the spin states) o f the expectation value o f the vector Pauh spin operator a, 1 e , P = ( a ) . For spin ½ particles, this definition is equivalent to P=

(N+-N_)/(N++N_),

- 1 < P<= +1,

(1)

where N+ and N_ are numbers of particles whose spins are in the " u p " and " d o w n " directions, respectively, the words up and down being defined with respect to the plane of the polarization producing (or analysing) Interaction In a typical scattering experiment, illustrated by fig 1, an unpolarJzed primary particle beam, with linear momentum kl produces a beam of secondary particles, with linear momentum k2 and polarization P. According to the Basle convention 1), the positive polarization (or the up directions m eq (1)) is taken in the direction of the vector product kl x k 2 . The cross section ap for the scattering of the polarized particle beam by the second target at angle 02 (fig 1) can be written in terms of the same cross section a u for an unpolarxzed beam without making any specific assumption about the reactton mechamsm O'p(02,~b) ---- O'u(02)[1 +PI(01)

A2(02)],

(2)

where A2(02) is the "analysmgpower" of the second Interaction and is equal to the

499

p--d POLARIZATION

polarizing power of the reverse reaction, 49 is the azimuthal angle between P1 and A 2. For elastic scattering t, A2(02) = P2(02).

Thus ap(02, E2, 49) = a.(02, E2)[1 +P1(01, E1)P2(O2, E2) cos 49]

(3)

If two measurements are made at 49 = 0 (left, looking in the direction k2) and 49 = n (right, looking m the direction k2), then the ratio R _ ap(02, Ez, 49 = n) = 1 - P I ( O x, E1)P2(O2, Ez) L

0"p(02,

E2, 49 = 0)

1 +PI(O 1 , Ex)P2(O2, E2) '

from which It follows that P2(E2, 02) - PI(E1 01) -x V1 - - ( R / L ) I '

[.1 + ( R / L ) . ]

"

(4)

The usual method o f measuring P2 consists of measunng the right/left ratio and the mmal beam polarization P , , the accuracy in the value of P2 bemg determined by the accuracy in the measurement of these two quantmes

Fig. 1 S c h e m a t m o f a typical double scattering expertment

IfP~ is not known, it must be experimentally determined in an auxiliary experiment by replacing the second scatterer with one of known analysing power Further, the right/left ratio must be corrected for false asymmetries which may arise from geometrical inaccuracies (e g , the angle 0 may not be exactly the same for both left and right scatters) or instrumental effects (e g , the efficlences or solid angles of the left and right detectors may not be the same) This can best be done by doing another auxdxary experiment with the second scatterer replaced by one with P2 = 0 In this case any departure of R / L from umty must be due to these undestrable effects The ¢ This is strictly true only when the reverse a n d the dxrect reactions are exactly the same, 1 e , for elastic scattering f r o m an mfimtely heavy nucleus Th~s is hardly the case for scattering f r o m d e u t e r m m A s such, eq (2) is true only to the extent o f this a p p r o x i m a t i o n

500

R. A CHALMERSe t al.

two auxlhary experiments would of course be of dubious value if they were not performed under conditions exactly identical with those of the main experiment This statement essentially implies that all three experiments must be done simultaneously, and in the same geometry with the same detectors. The design of our experiment for the determination o f p - d elastic scattering polarization was governed by this consideration Instead o f a pure deuterium target, our target consisted of a gaseous mixture o f deuterium, helium and xenon, and the proton groups corresponding to elastic scattering from these different gases were resolved in the solid-state detectors located within the gas chamber. Since the analysing power of helium is known with sufficient accuracy for several energies and angles, helium was a natural choice for the original beam polarization analyser Xenon has a Coulomb barrier of about 9 3 MeV and scattering of protons of energy below 3 MeV is essentially all Coulomblc. Thus the analysing power of xenon is zero, and it offers a good gaseous target for momtoring false asymmetries. The sohd state detectors offer adequate resolution for most scattering angles and incident proton energies to permit resolution of the elastically scattered proton groups from the three different gases with such large ratios o f atomic weights.

3. The Experimental Apparatus Fig. 2 shows the schematic arrangement of the experimental apparatus except for the gas handhng apparatus The proton beam from the Northwestern Umverslty 5 MeV electrostatic accelerator was incident on a thick carbon foil at the centre of the first Monitor

Faraday

C u p ~

Wmdow Fo,,

Beom

/~//~\ ~,~CQrbon Tar,et

Ro,t~cto,~ ~,~~~

LDetector

Fig 2. Schematic of the arrangement of the experimental apparatus

scattering chamber The partially polarized protons elastically scattered at 50 ° passed through an energy degrading foil and entered a second scattering chamber which was filled with the mixture of gases under investigation Two collimated solid

p-d POLARIZATION

501

state detectors which could be posmoned symmetrically on the two sides of this beam at angles between 45 ° and 120 ° detected the protons scattered by the gases Monitor detectors were located in both scattering chambers

Proton beam The polarization of p-carbon scattering at 50 ° increases with energy from 3 MeV to 4 7 MeV However, in order to achieve stable operation o f the accelerator over long periods of time with a 5-6 ~A d c beam, an energy of 4 1 MeV was selected The resultant beam polarization 2,) was expected to be about 30 ~ However, since this polarization is not very accurately known and calculation of the effective polarization for a thick carbon target introduces further errors, tills value of P1 was not used Instead PI was determined by analysing the hehum asymmetry. As will be seen later, P1 = 0 28_+0 01 was obtained experimentally. Carbon target. The self-supporting carbon targets used had thicknesses of about 10 mg/cm 2 These were made by repeatedly dipping a glass plate in a colloidal graphite alcohol suspension, anddrylng The peeled-offcarbon targets were conditioned m a diffuse proton beam before being submitted to a focussed 6 #A beam over a 3 m m x 1 m m area This treatment was found to make the targets less subject to brittleness and disintegration due to beam heating. Beam posttton momtor During a run it was important to make sure that the proton b e a m hit the same spot on the carbon target, and that this spot was indeed on the symmetry axis of the second scattering chamber An accurately collimated monitor using a sohd state detector was mounted in the first chamber directly opposite the entrance to the second chamber and was carefully aligned to look along the symmetry axis of the second chamber thru a pair of micrometer mounted slits At approximately 10 min intervals during each experimental run a 60 cycle transverse sweep was periodically applied to the proton beam incident on the carbon foil and the beam steering adjusted so that the burst of impulses seen by the monitor detector occurred as the sweep field passed thru its zeros The steering adjustment required was seldom large and its direction seemed to vary randomly. A rotating shaft carrying a number of nickel foils of various thicknesses was also provided m the first scattering chamber such that any particular foil could be interposed m the scattered beam to reduce its energy The chamber also contained a simple Faraday cup with an air-cooled tungsten beam stopper for approximate beam integration Gas target chamber. Since the second (gas) target chamber was designed to be used with semiconductor detectors, its dimensions could be kept small and particle path lengths from the scattering chamber to the detectors could be a minimum The vertical section through the chamber is illustrated m fig 3 The chamber consists of a cylindrical body and Identical rotatable top and bottom lids Each hd carries one of the detectors used to measure the right-left scattering asymmetry The hds carry the angular scales and are held m place by clamping rings and are sealed with O rings

502

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CHALMERS et al

A

A s o h d state m o m t o r d e t e c t o r Is m o u n t e d o p p o s i t e the b e a m t u b e a n d is shown r e t r a c t e d into its h o u s i n g in fig 3 It c o u l d also be inserted to the centre o f the c h a m b e r to m e a s u r e the energy o f the p r o t o n s at the exact p o i n t at whlch the s e c o n d scattering

Well of

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Fig 3 Detailed view o f gas target chamber U p p e r lid is s h o w n with detector at 90 ° scattering position (for clarity the collimating shts are not shown) Lower hd detector is s h o w n in the 0 ° p o s m o n I

I

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Fig 4 Typical pulse-height spectra for a mixture of D2, He and Xe m the chamber The pulse-height spectra for the left and the right detectors occupy the separate halves of the memory of the multichannel analyser takes place. T h e pulse-height s p e c t r u m o f this d e t e c t o r also p r o w d e d a m e a s u r e o f the s p r e a d o f p r o t o n energy at this point. The response o f this m o n i t o r d e t e c t o r a n d also t h a t o f b o t h side-detectors as a function o f p r o t o n energy was c a l i b r a t e d w~th a precision v a r i a b l e pulse g e n e r a t o r against p r o t o n s o f k n o w n energy.

p-d POLARIZATION

503

The housing of the monitor detector served as the mechanical support for the far end of the chamber. It rested in a vee-shaped bracket thus permitting the whole gas target chamber to be readily rotated about the direction of the incident beam The bracket was provided with adjustments in vertical and horizontal directions In order to compromise between countmg rate and resolution requirements a vertical sht geometry and detectors, 1 m m x 14 ram, were employed For different scattering energies or gas mixtures the energy at the scattering point was monitored while adjustments were made in the thickness of the energy degrading foil, the gas pressure in the chamber or the operating energy of the accelerator The latter means o f adjusting the energy was used only when use of the other two was insufficient, since changing the energy of the unpolarlzed beam scattered by carbon changes the polarization o f the once-scattered beam However, such changes were kept to within 100 kV and were compensated for by use of the known variation of carbon polar~zatlon w~th energy The polarization data at any particular energy and angle were taken m a number of runs each of about 2 h duration with the chamber alternating between the up and over posmons A typical spectrum of a single run at 2 25 MeV, 60 ° with three gases in the chamber is shown in fig 4 The actual number of runs per data point vaned from two to twenty depending on the energy, angle and gas mixture. The combined counts in the deuterium peaks had statlstlcal errors of 0 5 % at 2 0 and 2 5 MeV and 0 7 % at 15 MeV Backgrounds runs were made to determine the presence or absence of particle counts due to neutrons or g a m m a rays Above the low-energy noise of the detector amplifier system a neghglbly small number o f counts with random pulse-height were detected However, these events, being most likely due to power line transients, occurred in both detectors at the same time Such signals were blocked by the multi-channel analyser which, when used in a selective storage mode, rejected all comcident signals. 4. Results Counts from all runs at a gtven energy and angle were summed to gwe a total number of particles scattered to the right and left for each peak (due to different gases in the mixture) m the spectrum. Totals for the up runs and the over runs differed only shghtly and required a 0 2 % correction only m two instances The right-left ratio R / L was then found for each peak When the detectors were at 30 °, recoil deuteron pulses were also well resolved at two of the energies included. The R / L ratio of the recoil deuterons could therefore be used to obtain the equivalent R / L ratio for 90 ° proton scattering. For the xenon peaks, the R / L ratio differed from umty due to r a n d o m and systematic errors m location of the beam spot on the carbon target. This systematic error could arise if the monitor collimation were not exactly on the symmetry axis

504

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A

C H A L M E R S et al

of the gas target c h a m b e r F o r those d e u t e r m m a n d h e h u m data that were o b t a i n e d s i m u l t a n e o u s l y with x e n o n data, a c o r r e c t m n is made for the x e n o n a s y m m e t r y observed m the same r u n F o r the data obtained with only d e u t e r i u m in the chamber, however, a n average departure o f the x e n o n ratio f r o m u m t y is a p p h e d to the d e u t e r m m asymmetry. The fluctuation o f the x e n o n r a t m f r o m angle to angle and energy to energy is t a k e n Into a c c o u n t as a n a d d i t i o n a l c o n t m b u t l o n to the final error in the results o f this experiment The correction for false a s y m m e t r y is m a d e b y calculating the a n g u l a r displacement of the once-scattered b e a m which w o u l d yield the observed x e n o n a s y m m e t r y o n the basis o f the k n o w n slope o f the x e n o n cross sectmn, d~r(O)/dO Thls a n g u l a r displacement together with the knowledge of the slope o f the cross section o f d e u t e r i u m (or h e l i u m ) yields a correction factor to be a p p h e d to the observed R / L ratio o f d e u t e r i u m (or helium) T o o b t a i n the correction factor for the data p o i n t s t a k e n w i t h o u t x e n o n in the chamber, the a n g u l a r dmplacements calculated f r o m the various x e n o n asymmetries were averaged to o b t a i n a m e a n dmplacement o f 0 0 9 8 ° + 0 098 ° (wlth a distance between the two scattermgs o f 21 7 cm, this corresponds to a t r a n s l a t i o n of the b e a m spot by 0 38 ram), a n d this value was used to d e t e r m i n e the systematic correction U s i n g the corrected R / L ratms, P1P2 values were o b t a i n e d f r o m eq (4) These values and the values o f c a r b o n , helium a n d d e u t e r i u m polarization are given in table 1 TABLE 1 Data and results E (MeV)

0lab (deg)

0e m (deg)

Range of 0o m (deg)

P1 = Pc

P~= Pa

1 504-0 15

30 45

44 5 65 7 85 7

38 7-55 2 60 2-74 5 80 5-92 6

+ 0 0015 --0 0182 --00182

--29 34-0 6 --28 7+0 6 --27 2+0 6

--0 5+3 3 + 6 3+2 8 + 6 7+2 8

202+015

30 45 60 70 90 a)

445 657 857 98 0 1200 a)

387-552 602-745 805-926 93 2-103 9 1050-1281

+00040 --00138 --00230 --0 0143 +00015 a)

--275+06 --289+06 --28 2 + 0 6 --28 9+0 6 - - 2 7 5 ± 0 6 a)

--15+21 +48+1 7 +82i19 +5 0±1 9 - - 0 5 + 1 4 a)

2 52±0 15

30 45 60 75 90 a)

445 657 857 1039 1200 a)

387- 552 602- 745 805- 926 992-1095 1050-128 1

--00239 --00143 --00234 --00153 --00010

--297i06 --275+06 --282±06 --302+06 - - 2 9 7 ± 0 6 a)

+8 1 ± 2 0 +52+19 +83120 +51+16 + 0 3 + 1 3 a)

202i015 252t0.15

60 60

--02395 --01543

- - 2 8 2 i 0 6 b) --282+06

+ 8 5 0 ± 3 0 c) + 5 4 8 ~ 1 6 d)

P1P2

(%)

(%)

jD 2 ~

725 725

iDne

a) Data obtained from recod deuterons b) Thin value of Pc was determmed experimentally Other values m this column were obtained by adjustment of --2 ~o per + 100 keV change m beam energy e) Assumed value of PHe at 2 02 MeV a) Calculated value of fine at 2 52 MeV

p-d POLARIZATION

505

F r o m the P1P2product for hehum at 2 MeV and 60 °, the polarlzatton of the oncescattered beam was calculated using Scott's 25) value o f (85__+3)~ for the hehum polanzataon The mean value of polarization for the 4 1 MeV protons scattered at 50 ° by the thick carbon target was found to be Px = (-28__+ 1)~ This agrees well wxth the expected value assuming a target thickness o f about 1 MeV. The actual value of carbon polarization used was obtained by adjusting the above measured value to compensate for the shght varlatmns of proton beam energy from the nominal 4 1 MeV by using a value dPI(E)/dE = - 0 02 per 100 keV Values of the deutermm polarlzatxon found in this experiment are plotted as a funct|on o f centre-of-mass scattering angle in fig 5 I0 I 50:t: 15MeV 5 0 -5 -I0

÷+

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i

0

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Q.

2 0 2 k 15MeV

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30

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i

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150

180

0t" M Fag 5 Polarizations measured m this experiment

The spread m energy observed by the m o m t o r detector at the centre of the gas scattering chamber was about __ 150 keV The spread m angle of scattering as calculated from the eolhmatmn geometry was about +_4° in the medmn plane of the geometry A small addltmnal angular uncertainty favouring larger effecttve angles results from the poss]bdlty of scattering out of the medmn plane. As a test of the stabd~ty of the experimental condmons the reproducibility of the measurement of the carbon polarization from the hehum data at 2 MeV and 60 °

R A CHALMERS et al

506

was examined For these data a large number of ldenncal runs were made, each having a relanvely small number of counts per peak These data also took the longest overall period of time (3 d) and they may be expected to show the worst effect o f external variables The polarization of the once scattered beam was calculated from each of eight successive pairs of runs and it was found that five of the eight measurements fall within the standard error + a, and all fall within + 2 2 a of the average as would be expected in absence of any larger systematic deviations or lnstabdit~es in the system

5. Discussion of Results The analogue states of the n-d and p-d systems differ m energy by a couple of hundred kilovolts only Thus as far as the polarization phenomena are concerned n-d and p-d scattering can be compared at roughly the same energy As mentioned in sect 1, only one p-d polarization measurement, made m 1960 at this laboratory, has been reported in published literature for Ep __< 5 MeV On the other hand a large number of measurements of comparable accuracy have been made for n-d scattering m the past five years To bring these various results m proper perspective we have summarized them in table 2. In fig 6 we have plotted our results for p-d scattering polarization together w~th results for n-d scattering polarization at energies between 1 9 and 2 1 MeV. We have omitted the 2 MeV point o f Darden e t al. 16), since later measurement by these same authors 2~) indicate that the earher value may be m considerable error. It is obwous that the general trend of all available n-d and p-d data indicates posmve polarization with a maximum of about 3 to 5 % at 0~ m = 90°In fig 6 the dashed curve, P = 0 03 sin 0, has been drawn to indicate the general trend of the data The solid curve refers to the results of the original calculations of Delves and Brown 26) We shall refer to these calculations later. TABLE 2

Summary of other n-d and p-d polarmatlon measurements below 3 MeV Ref White et al 12) (1958) n-d Cranberg 18) (1959) n-d Bucher et al 1~) (1959) n-d

Energy (MeV)

0c m (deg)

(%)

Pa

Remarks

2 26 31

90 90

484-5 404-2

defimtely m error

214-005

445 72 5 98 120 138 90 60 90 135 60 90 135

2+2 3q-2 04-3 44-2 24-3 --25:7 24-5 94-8 10-/-7 14-5 --2±6 45:8

2 3±0 2 3 14-0 2 394-01

507

p-d POLARIZATION TABLE 2 (continued)

Ref Brullmann et al 12) (1959) n-d

Darden et al x6) (1960) n-d Donohue x~) (19619 ) n-d Fergnson et al is) (1962) n-d

Elwyn et aL 19) (1962) n-d

Energy (MeV) 3 27

1 04-0 14

204-0 1 0 41

0 53 0 60 0 75 0 87 1 00 0 54-0 1

1 04-0 1

1 954-0 1

0e m (deg) 53 72 91 120 135 161 70 110 140 110 70 110 140 80q- 15 804-15 804-15 804-15 804-15 33 70 110 130 165 33 70 110 130 165 33 70 110 130 165 85

Beghian et al 2o) (1963) n-d Behof et al 31) (1963) n-d Walter et al 22) (1963) n-d

1 154-0 05

19

59 73 86 98 110 120 130 138

Shafroth et al 23) (1960) p-d

3 34 3 45 3 74

45 90 45

104-007

110

Pa

(%)

Remarks

34-6 14- 6 34-6 --54-6 0q-6 74-10 9 24-5 superceded by their 7 4- 5 own remeasurement 20) 10 7 ± 5 --84-6 14- 5 14-5 44-5 74- 5 doubtful See refs 17, 19) 15±7 134-5 124-6 104-3 3 24-2 4 0 84-1 8 --0 74-1 8 244-1 8 0 64-2 6 0 54-1 4 0 94-1 4 --0 5q-1 5 0 8q-1 4 --1 14-2 1 0 0~0 9 1 64-1 1 results in the second 1 8 ~: 1 1 4 1 4-1 7 colunm are expected 374-1 5 484-23 to be better 2 14-1 4 2 14-2 2 51~22 --094-38 4 8q-4 0

134-21

044-1 6 1 6±2 0 04-20 2 94-2 0 1 64-2 0 0 4q-2 4 --0 8q-2 0 1 6i2 0 6 q-5 --2 4-5 4 4-5

508

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al

T h e e n e r g y v a r m t m n o f p o l a r i z a t i o n is b r o u g h t o u t m o r e clearly in fig. 7 w h e r e we h a v e p l o t t e d n - d a n d p - d p o l a r i z a t i o n s f o r a n g l e s 70 ° __< 0c m =< 1 10 ° as a f u n c t i o n T

log-

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180

ecM

Fig 6 Measured p-d and n-d polarizations vs scattering angle for energtes between 1 9 and 2 1 MeV Key to symbols 0 - t h i s experiment, + - C r a n b e r g 18), I~,- Elwyn et al 19), ~, _ Walter and Kelsey ~) Sohd curve is result of Delves and Brown's 36) theory Dotted curve, P = 0 03 sm 0, is merely an attempt to g,ve a simple representation to the trend of the data /

20

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'

/

I

'

/

I

'

10

#

I tt

o

-10

-20

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I I

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I 2

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El) or E n ( M e V )

Fig 7 Measured p-d and n-d polarizations (70 ° ~ 0e m ~-- 110°) energy Key to symbols , - this experiment, ~, - Cranberg la), ~X- Bucher et al 1,), + _ Brulhnann et al xB), ½ _ Donohue aT), I

iI

[~ - Ferguson and White is), i _ Elwyn et al ~'>, * - Beghlan et al s0>, + _ Shaffroth et a, ~3) The curve drawn xs the prediction of Delves and Brown 2G) at 00 in = 90° o f e n e r g y A g a i n results o f r e f 16) h a v e b e e n o m i t t e d T h e t h e o r e t i c a l c u r v e d r a w n is a g a i n t h a t d u e to D e l v e s a n d B r o w n 26). F r o m the g e n e r a l t r e n d o f t h e d a t a , it is

p-d POLARIZATION

509

obvious that over the entire energy range polarazatlon ~s about 5__+2~o, and the results of ref is) are suspect as being too large In any case the theoretical curve misses the data trend completely In summarizing the experimental results, it appears that n-d and p-d polarlzatmns m the energy region 0 5 to 3 5 MeV are defimtely non-zero and posmve. The maximum near 0c,. = 90 ° is P = 5___2~ , and there is httle indication of any sharp energy varmtmn m the measured values The theoretical knowledge of the three-body problem is meagre Buckingham, Hubbard and Massey 10) and Christian and Gammel 11) have made analyses of p-d and n-d angular distribution data m the energy region 0 to l0 MeV Christian and Gammel a 1) calculated phase shifts for l > 1 m Born approximation with eight d~fferent two body central potentmls and determined the l = 0 phase shifts as the only free parameter m least-squares fitting of the angular d~strlbutlon data Wxth shght re-adjustment of the quartet p-phase shift (from that calculated m Born approximation) they were able to obtain fits to the data well within the clmmed accuracy (error+ 3 ~ ) of the data and concluded that no evidence existed for inclusion of noncentral forces They also gave plausibdxty arguments for this result The existence of small but defimte polanzatmns as obtained in the p-d and n-d scattering experiments summarized above, however, mdlcates that the phase shifts for l ____1 are split This is not necessarily m contradiction with Chnstxan and Gammel's conclusmn With as many phase shifts involved (2 for l = 0, 5 for l = 1 and 6 for l > 2) the angular distribution data need to have a extremely high degree of accuracy t before any conclusions can really be drawn about the need for non-central forces In order to develop a vahd theory the three body problem must be formulated with proper spin-orbit and tensor forces The basic formulatmn of the problem was done a number of years ago by Bransden, Smith and Tare 2s) but the calculations mvolwng numerical solutions of coupled second-order mtegro-&fferentml equatmns are reported z9) to be so tedmus that no results are avadable, as yet In the meantime Delves and Brown 26) have attempted to solve the tensor force problem by making rather drastic approxlmatmns Their calculations y~eld negative n-d polarizations for all angles over the entire range of energies from 0 to 5 MeV As we have already seen the measured polanzatmns are positive and at 1 MeV their magmtude is much smaller than predicted Delves 30) ascribed the incorrect s~gn of the theoretical predlctmns to a purported sxgn error m Simon and Welton's 3~) polarlzatmn formahsm However, as Elwyn et al x9) point out, th~s fads to remove the sign d~screpancy between the experimental and theoretical polarizations This is so because if the sign of Delves and Brown's 26) prediction is to be changed so should the sign * Experiments have been started m this laboratory to improve the accuracy of p-d angular dlsmbutlon data Prehmmary experiments with a much extended angular range and with error ~ 2 indicate ~7) that the older data s) may be in error as much as 5 to 7 ~ The measurements in progress are intended to have errors of the order of ½~ over the entire energy range from 0 8 MeV to 5 MeV

510

R A CHALMERSet aL

o f p - H e an d n - H e p o la r iz a t io n s and t h e r e f o r e the signs o f the measured p-d and n-d p o l a r i z a t i o n s (which always refer directly to p - H e o r n - H e polarizations)

The

discrepancy between experimental results a n d theoretical p r e d l c h o n s r em ai n s u n explained. T h e a u t h o r s wish to a c k n o w l e d g e the help o f M r H H a g e l a u e r with the e q u i p m e n t a n d Miss G M m n e m a in the p r e p a r a t i o n o f this p ap er T h e a u t h o r s are also i n d e b t e d to Dr s

S M

Shafroth and R

E

Segel w h o s e w o r k d r e w o u r interest to this

p r o b l e m T h a n k s are also due to the T e c h n ic a l M e a s u r e m e n t C o r p o r a t i o n , N e w H a v e n , C o n n e c t i c u t , f o r their c o o p e r a t i o n during the execution o f th~s experiment.

References 1) Proc Int Symposmm on Polarization Phenomena of Nucleons, Helv Phys Acta Suppl 6 (1961), L Wolfenstem, Ann Rev Nucl Scl 6 (1956)43, E J Sqmres, Progr Nucl Phys 8 (1960)47 2) G Brelt, Revs Mod Phys 34 (1962) 766 and references therem 3) Rosen et a l , Phys Rev 124 (1961) 199, 121 (1961) 1423, H H Barschall, Helv Phys Acta, Suppl 6 (1961) 529, Elwyn, Lane, Langsdorf and Monahan, Phys Rev 133 (1964) B80 4) G Brelt, prwate commumcatlon (1963) 5) I Alexeff and W Haeberh, Nuclear Physics 15 (1960) 609 6) J D Seagrave, L Cranberg and J E Simmons, Phys Rev 119 (1960) 1981 7) D G McDonald, W Haeberh and L W Morrow, Phys Rev 133 (1964) Bl178 8) R Sherr et a l , Phys Rev 72 (1947) 662, R J S Brown et a l , Phys Rev 88 (1952) 253, L Rosen and J C Allred, Phys Rev 82 (1951) 777 9) Hamouda et a l , Phys Rev 79 (1950) 539, 83 (1951) 1277, E Wantauch, Phys Rev 86 (1952) 679, Allred et a l , Phys Rev 91 (1953) 90 10) R A Buckingham, S J Hubbard and H S W Massey, Proc Roy Soc A211 (1952) 183 11) R S Christian a n d J L Gammel, Phys Rev 91 (1953) 100 12) R E White, A Chisholm and D Brown, Nuclear Physics 7 (1958) 233 13) L Cranberg, Phys Rev 114 (1959)174 14) W P Bucher, W B Beverly, G C Cobb and F L Hereford, Nuclear Physics 13 (1959)164 15) M Brullmann, H J Gerber, D Meier and P Scherrer, Helv Phys Acta 32 (1959) 511 16) S E Darden, C A Kelsey and T R Donoghue, Nuclear Physics 16 (1960) 351 17) T R Donoghue and S E Darden, unpubhshed (1961), S E Darden, prwate commumcanon (1963) 18) A T G Ferguson and R E White, Nuclear Physms 33 (1962) 477 19) A J Elwyn, R O Lane and A Langsdorf, Jr ,Phys Rev 128 (1962) 779 20) L E Beghlan, K Suglmato, M Wachter, and J Weber, Nuclear Physics 42 (1963) 1 21) A E Behof, G P Lletz, S F Trevmo and S E Darden, Nuclear Physics 45 (1963)253 22) R L Walter and C A Kelsey, Nuclear Physics 46 (1963) 66 23) S M Shafroth, R A Chalmers, E N Strait and R E Segel, Phys Rev 118 (1960) 1054 24) T A Tombrello, R Barloutand and G C Phdhps, Phys Rev 119 (1960) 761 25) M J Scott, Phys Rev 110 (1958)1398 26) L M Delves and D Brown, Nuclear Physics 11 (1959) 432 27) K K Seth, R A Chalmers, E N Strait and R S Cox, Bull Am Phys Soc 8 (1963)38 28) B H Bransden, K Smith and C Tate, Proc Roy Soc A247 (1958)73 29) H S W Massey, in Nuclear forces and the few nucleon problem, Proc Int Conf London (1959) Vol 2 (Pergamon Press, New York, 1960), p 345 30) L M Delves, Nuclear Physics 33 (1962) 482 31) A Simon and R A Welton, Phys Rev 90 (1953) 1036