Neutron polarization in the 1 MeV region by elastic scattering on C, O and D

Nuclear Physics 42 (1963) 1 - - 2 0 ; @

North-Holland Publishing Co., Amsterdam

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

NEUTRON

POLARIZATION

IN THE

BY E L A S T I C S C A T I ' E R I N G

1 MeV REGION

O N C, O A N D D

LEON E. BEGHIAN, KENZO SUGIMOTO t, MANFRED H. W)kCHTER ¢t, and JACQUES WEBER ttt Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge 39, Massachusetts Received 24 September 1962 Abstract: The polarization product PxP2 for low energy ( ~ 1 MeV) neutron elastic scattering has

been measured for carbon, oxygen and deuterium by the time-of-flight method. The LF(p, n) reaction has been used as a neutron source. Multiple scattering corrections have been estimated by Monte Carlo calculation. The results are Element Neutron energy (MeV) Pt(30°L) -P~(60°L) carbon

0.830:0.075 --0.00264-0.0041 1.15 :t0.05 +0.019 -t:0.015 oxygen 0.830±0.075 --0.181 ±0.012 deuterium 1.15 i0.05 -t-0.015 -t-0.012 A method for measuring the lithium target thickness by examination of time-of-flight profiles is described.

1. I n t r o d u c t i o n

T h e elastic scattering o f nucleons by d e u t e r i u m in the region below 10 M e V is the simplest interaction that can be studied for the p u r p o s e o f investigating nuclear forces involving a n g u l a r m o m e n t a l > 0. A n u m b e r o f theoretical investigations have been m a d e on the basis o f p u r e l y central forces between nucleons including the c u s t o m a r y forms o f exchange interactions. Central forces between nucleons, on the o t h e r hand, c a n n o t lead to a p o l a r i z a t i o n o f scattered particles (for an u n p o l a r i z e d incident b e a m ) ; Massey 1) has p o i n t e d o u t that m e a s u r e m e n t s o f the p o l a r i z a t i o n in n u c l e o n - d e u t e r o n elastic scattering s h o u l d lead to i n f o r m a t i o n on possible t e n s o r force c o m p o n e n t s in the nucleon-nucleon interaction. N o exact t h e o r y on n-d scattering yet exists, a l t h o u g h it has been r e p o r t e d t h a t Bransden et al. 2) plan to solve the c o u p l e d e q u a t i o n s o f the three b o d y p r o b l e m t Present address: Department of Physics, Faculty of Science, Osaka University, Osaka, Japan. tt Present address: General Electric Company, APED, San Jose, California. ttt Present address: Physics Institute, University of Neuch,~tel, Switzerland. This work is supported in part through funds provided by the U.S. Atomic Energy Commission under AEC Contract AT (30-1)-2098. 1 April 1963

2

L. E. B E G H I A N

el

aL

by numerical methods. Delves and Brown 3) have given an approximate calculation (including polarization effects) which takes into account tensor forces; their prediction is compared with experiments in sect. 5.3 of this paper. A number of experiments have been performed on the polarization of neutrons scattered from deuterium in the range 500 keV-3 MeV. The most recent results indicate that the effect, if it exists, is small and in the few percent range. The object of the present experiment was to obtain a reliable value of the degree of polarization in scattering from deuterium, using techniques which would obviate as much as possible the difficulties inherent in most polarization experiments. Scattering from carbon and oxygen has also been studied, chiefly for calibration purposes. The main difficulties and the steps taken to overcome them are enumerated below. (1) The presence of more than one neutron group in the primary neutron beam. The neutron time-of-flight technique has been used to investigate the scattering of a single neutron group. (2) False asymmetries due to background, scatterer size and other causes, in rightleft polarization asymmetry measurements. Magnetic precession of the neutrons is used here to eliminate systematic errors of this kind. This method was first suggested by R. Wilson and first used by Hiilman et al. 4). (3) "Smearing out" of the polarization effect due to multiple scattering in the scattering sample. Monte Carlo calculations have been made to take account of any order of scattering. It has been possible to calculate the distribution in time of scattered neutrons at the detector and to obtain good agreement with the measured time profile; hence, the contribution due to singly scattered neutrons could be calculated. (4) For deuterium it is either necessary to use a solid scattering sample (e.g. CD2) or high pressure gas in a container. In either case, neutrons will b~ scattered from the carbon in the CD2 or from the material of the container. The time-of-flight technique makes it possible to separate the neutron groups scattered from deuterium and carbon, owing to the difference in recoil energy.

2. Equipment The pulsed proton beam from the Rockefeller generator 5) was used to produce neutron bursts of short duration (2-6 nsec) via the reaction LiT(p, n)Be 7, see fig. 1. The time reference signal (time zero) is generated before the proton bursts strike the lithium target, by means o f an induction tube 5). A description of the target and of the method we have used to measure its thickness is given in appendix A. Neutrons emitted at 30 ° (lab.) to the left (the Basel convention is used throughout this paper) with respect to the proton beam strike a small scattering sample after having travelled about 47 cm through a transverse magnetic field. This field is used to reverse the relative populations of the two spin states defined with respect to the

NEUTRON

POLARIZATION

3

4

L. E. BEGHIAN el a[.

LiV(p, n) reaction plane 4). Both the magnet yoke and pole pieces are made of ordinary soft iron (Armco magnetic ingot iron). The DC power supply for the magnet is automatically regulated: Variations in the magnetic field strength are less than -t-0.5 ~ . The maximum integrated field strength is (1.901-t-0.030)103 Gauss meter, not quite sufficient to produce a precession angle of 180 ° at the maximum energy considered in this experiment (1.25 MeV). However, this is of no major consequence with regards the measurement of polarization. This limit in maximum field strength is dictated by geometrical requirements and by the magnet design itself. The influence of inhomogeneities of the magnetic field and of its longitudinal component outside the pole region is negligible with regards the angle of precession. The displacement of the proton beam due to the magnetic field strength at the target is also negligible. Effects of the magnetic field on the detectors and the consequent necessary corrections to the detector efficiencies are described in appendix B. Neutrons scattered in the LiV(p, n) reaction plane, at an angle of 60 ° in the laboratory system, are detected by a liquid scintillation counter (NE 211 liquid scintillator 10.2 cm diameter, 2.5 cm thick, coupled to a RCA-7046 photomultiplier), referred to as "main detector", placed at a distance of about 80 cm from the scatterer. The counting rates of scattered neutrons are observed when the magnetic field is switched on (R) and off (L). If PI is the degree of polarization of the primary beam, P2 the polarizing power of the scatterer, then R/L = (1 +P~ P2 cos Z)/(I +P1P2), where X is the angle of precession of the neutron. Particular attention is given to data normalization, i.e. monitoring of the neutron source strength. A separate neutron counter (pilot B plastic scintillator coupled to a RCA 7264 photomultiplier), referred to as "monitor counter", is used for this purpose. With both detectors, the time-of-flight technique is used to isolate neutrons of different energies and to reduce background radiation. Fig. 2 shows a block diagram of both time-of-flight spectrometers. The fast outputs (anodes) of the photomultipliers are processed by voltage limiters and are used to operate the start input of the timeto-pulse height converters; the stop signals are supplied by the time reference monitor 5). The usual side channels (slow output) are also featured. The "beam discriminator" has the following purpose: It analyses the signal level of the zero-time reference. Whenever the level drops below a preset value, the pulse-height discriminators (one-channel analysers) s) in both time-of-flight systems are blocked entirely, thereby inhibiting the accumulation of all data (the gates in both systems are closed). These window discriminators are freed again as soon as the zero-time signal reaches sufficient amplitude. This data processing logic was found very essential to obtain adequate time-of-flight spectra. The "walk" compensation was found necessary (for the main detector system) to correct the time-of-flight spectrum generated by signals of low but variable amplitude. A detailed description of the circuitry is given elsewhere 2t). The geometrical arrangement of the experimental setup is chosen so that the axis of the incident proton beam and emitted and scattered neutrons are coplanar.

I

OUTPUT

-

SELECTOR

RCL Model 2603 Mark 20

256 CHANNEL

IBM.

COUNTER

DISCRIMINATOR

MONITOR

’

m,

Fig. 2. Block diagram of the electronic

nwdllred

024

PUNCH

Target

I /i

1

equipment.

-IBM

0

Control

PREAMP

Room

Mochlne

,Inc. Hewlett Packard Co. lnternotmnal Bustness

Electromcs

, Inc Lobs

Dumont Franklin

Code

c_____________

MONITOR

Monufoclurers

4EOA

F

Model

COMPUTER 709

Hp.

Beam

DETECTOR

7090

Proton

MAIN

Co.

_I

6

L. E. BEGHIANet

al.

The monitor counter is placed so that it has a direct view of the target, in the plane perpendicular to the scattering plane containing both the target and scatterer axis. Its elevation as seen from the target is 30 to 55 degrees, and its distance from the latter is 1.5 m. The analysis of the measurements has been performed largely with the aid of the IBM 709-7090 computer systems of the M.I.T. Computation Center and of the M.I.T. Cooperative Computation Laboratory; the punched cards served directly as the data input medium (see fig. 2). Details of the data analysis procedure are given below. The following scatterers have been used: Carbon: A right circular cylinder (4.45 cm height, 3.80 cm diameter) was machined from reactor grade graphite (AGOT). None of the impurities it contained are significant for the present experiments. Oxygen: Liquid oxygen (commercial brand) has been used as a scattering sample enclosed in a Styrofoam Dewar; the cylindrical scattering volume was 4.45 cm high and 1.82 cm in diameter. It was not possible to secure accurate information on the composition of the liquid oxygen but no significant impurities are expected to be present. Deuterium: A set of eight slabs of deuterated polyethylene (CD2) has been prepared (molded) from CD2 powder. The slabs have been assembled in a parallelepiped of dimensions 3.65 x 4.29 x 2.70 cm. The deuterium concentration is given by the manufacturer as 99~o. The chief impurity is probably hydrogen since the sample was manufactured from C H z by atom exchange.

3. Experiment Description 3.1. EXPERIMENT PROCEDURE It has been indicated in sect. 2 that the product PI P2 can be inferred from the measurement of neutron scattering intensities for a known value of the angle •. The experimental ratio R / L (magnetic field on and off, respectively) is determined from a series of cycles of three runs each: scatterer in, magnetic field off; scatterer in, field on; scatterer removed, field off, by making the reasonable assumption that the time dependent background is independent of the field situation. The observed asymmetries have been corrected for multiple scattering (see sect. 4). 3.2. DATA ANALYSIS

The accumulation of large quantities of data requires that a high speed digital computer be used for the analysis of these data in order that the ultimate amount of information contained in the measured quantities can be obtained. As has been outlined in sect. 2, the time-spectra obtained from the 256-channel analyser have been punched automatically on IBM cards and processed by the M.I.T. 709 and 7090 computers. In this section we shall describe briefly the procedure followed for this data analysis. The entire analysis, except for the application of multiple scattering corrections,

NEUTRON

POLARIZATION

'7

is contained in a single IBM 709-7090 program 21). Multiple scattering processes are studied in a separate program 6' 2t) (see also sect. 4), and they are finally combined with the results of the present analysis as will be shown later. The essential operations of the program are the following: For each cycle the time-independent backgrounds are computed and subtracted from the data. Also, a small correction to account for systematic variations in counter efficiencies is applied (see appendix B). For the purpose of a timing correction, the 0 th, first and second moments of the peaks are computed (also for the background-run), as well as their statistical errors. When this is done for all cycles, the average values of the peak centroids (for the monitor and detector) are computed for the runs field on-scatterer in, field offscatterer in, field off-scatterer out. Subsequently all monitor measurements are lined up with respect to their centroid by means of a translation of the time scale. This is required for correcting for any zero-time shifts. For the main detector a similar correction is applied, but the three types of measurements are treated independently: All measurements of the same type are lined up with respect to their centroid (as with monitor measurements), but provision is made in the program for relating the time scales of the three types in one of two ways; either all measurements are lined up with respect to their centroid, irrespective of the type, or any possible (non-statistical) differences in the average peak centroids for the three types are taken into account. As an example, the second procedure is appropriate when the differences in average centroids are caused by multiple scattering effects rather than by a purely instrumental phenomenon. The selection of the scheme to be used in a particular case can usually be made by investigating the time-of-flight distributions and the behaviour of first and second moments. All data are then normalized with respect to their respective total monitor count; corresponding data for all cycles are averaged and the time-dependent background is subtracted, yielding the net average number of counts per time channel (new coordinates) for field-off measurements (L) and field-on measurements (R); also the ratio V = R / L is computed for each channel as well as the statistical errors of these quantities. As a first approximation (before any multiple scattering correction is made), the total "right-to-left" ratio V* for each cycle is computed (after integration over the peak to obtain the total counts for field on and field off measurements). The mean value F*, the standard deviation of an individual measurement V*, and the standard deviation of the mean are computed. The analysis of a typical run (about 20000 input quantities) requires 15 minutes of IBM-7090 time. 4. Multiple Scattering Corrections Let R(t), L(t), Ms(t), ML(t) represent the time-of-flight spectra for single scatteringfield on, single scattering-field off and multiple scattering-field on and off, respectively.

8

L. E. BEGHIAN e l

aL

The true V(t) = R(t)/L(t) can then be obtained from the measured ratio

V.(t) = R(t) + M.(t)

L(t)+M,.(t) by the relation

R(,)_ V(t) = V,,(t)

R(t)+MR(t)I

L(t) 1

- Vm(t)f(t ).

(4.1)

L(t)+ ML(t i) A Monte Carlo program has been written to evaluate the function f(t). A detailed description o f the program will be published elsewhere 6). The results of the computation are discussed in sect. 5. 5. Results

In this section we shall give the results of the experiments on carbon (which was used essentially as a "null" calibration of our experimental setup), oxygen and deuterium. Preliminary results have been reported previously 2s). 5.1. CARBON The scatterer we have used has been described in sect. 2. The relevant parameters for the measurement are maximum proton energy, 2.7 MeV; target thickness, (152 + [

06,

~

oi 0 ~ -~2

/

Fletd off

\

/ 1 -)0

I -8

1 -6

1 .4

\ 1 1 1 ~ .2 0 2 4 d' [ C h o n n e l Number]

' 6

' 8

L)0

_~.-~£?-J )2

Fig. 3. Main detector total time-of-flight distributions in their new coordinate system, before multiple scattering correction (carbon scatterer). 15) keV; average neutron energy (ct = 30D, (830+ 15) keV; beam burst width: 2 to 2.5 nsec and angle of scattering q)L,b ----60°. The total time-of-flight spectra after data analysis are shown in fig. 3. The difference in shape of the two profiles is statisti-

NEUTRON POLARIZATION

9

cally significant and is probably caused by an instrumental effect. This is of no major consequence for the asymmetry I'm if one integrates from ? = - 11 to ~ = + 13; the result is Vm = 1.005+0.008. The stated error combines statistical, estimated multiple scattering and instrumental errors. No detailed calculation of multiple scattering phenomena has been performed in this case. The effect is expected to be much smaller than the overall error of 0.008. The calculated spin rotation is (2.762-1-0.050) rad so that = PI(30~)P2(60~.) = - 0.0026 + 0.0041.

(5.1)

Assuming further that Pt(30~.) = 0.31 4-0.06 (see subsect. 5.2) as an average value over our range of neutron energies, P2 is given by P2(60~.) = - 0.008 4- 0.013.

(5.2)

This is an average value over the neutron energy range E, = (0.8304-0.075) MeV. N o correction has been made for the variation of PI and the LiV(p, n) reaction cross section with emission angle. Also the variation of the Ct2(n, n) cross section with neutron energy is neglected. The result 5.1 is in excellent agreement with recent data of A. J. Elwin and R. O. Lane 7) obtained at different scattering angles, incident neutron energies, and for an emission angle ~L ---- 51°. This comparison suggests that our technique is presently limited to the determination of an asymmetry V with a relative uncertainty of 1 to

1.5%. The carbon polarization Pz has been calculated on the basis of measured phase shifts for elastic neutron scattering by Wills et al. 8). These authors point out that calculated P2 values are extremely sensitive with respect to some phase shifts, but the latter are not well-known at a neutron energy of about 1 MeV or less. In view of this situation one can only make the qualitative statement that the polarization P2 is expected to be small. 5.2. OXYGEN The scatterer has been described in sect. 2. The relevant parameters characterizing the condition of the equipment are the same as for carbon. In the analysis of the data, it has been assumed that the polarizing power of carbon was negligible, which is well justified in view of the relatively large statistical error in the final result for Pt (30~-)P2(60~.). Fig. 4 shows the oxygen scattered neutron peaks as obtained after analysis but before any multiple scattering correction. By graphic integration Vm = 1.360+0.035. The quoted error contains statistical and instrumental errors.

|0

L . E . BEGHIAN e l

al.

06

i

__ ---

,e,Oo°

F~eld off

~OaL

',2

'

0!~

! I

l

-8

-6

,__, -4

-2

,

,

l

l

ix--_]

0

2

4

6

8

,

~0

i¢ [ Channel Number ]

Fig. 4. Main detector total time-of, flight distributions in their new coordinate system, before multiple scattering correction (oxygen scatterer). ~0.5

:~

.... 04

Theoretical Spectrum ,Single Scotlerlng Theoreticol Spectrum,Total

~

o~c 0 32

0

~- 0

--~-~'!~ ~1

16

/'-, Deri

m

14

t2

!

e

n

o

l

~0 8 Time t(nsec I

6

I

t

I

~

I

t

I

4

2

--

0

Fig, 5. Time-of-flight distributions for oxygen (field off (Left) scattering). 06

~---- Theorehcol Spectrum, Single Scottering -Theorehcol Spectrum, Totol

F

t~

~o4 g. 03

,3o2 ~o~ i

o

18

16

~4

I~

10 8 Time t(nsec)

6

4

2

Fig. 6. Time-of-flight distributions for oxygen (field on (Right) scattering).

NEUTRON POLARIZATION

1|

The Monte Carlo program (see sect. 4 and ref. 6)) has been used to evaluate the function f(t) of eq. (4.1) in the following way. The calculated time-of-flight profiles for field off and field on scattering, after the instrumental resolution has been taken into account, are shown in figs. 5 and 6, respectively. The theoretical curves have been normalized to the experimental profiles at t = 4.8 nsec and the time scale was translated so that the right tails overlap most closely. One observes a marked discrepancy in both figs. 5 and 6 on the late time side of the peaks. We believe that this effect is caused by the fact that the calculation assumes a uniform lithium target of constant density. The instrumental resolution correction might also have some influence although the resolution function should be modified rather drastically with respect to the one used for the C D 2 experiment (subsect. 5.3), to obtain better agreement.

1.5

1.4 cc 1.3 +

1.2t 12

J I0

I 8

CorrectedRotio

I 6

I 4

I 2

0

Timet [nsec) Fig. 7. "Right-Left" ratios for oxygen experiment. Fig. 7 shows a comparison of tion can be made:

Vm(t ) with V(t) (see eq. (4.1)). The following observa-

(a) The measured ratio Vm(t ) decreases with increasing arrival time because of the growing influence of multiple events. This trend is expected. Correspondingly the multiple scattering correction becomes stronger as t increases. (b) If the multiple scattering analysis were entirely correct it would have transformed all measured data points to about the same value of V. In the present analysis this is not the case, although the correction procedure does flatten the function V(t) to some extent. This failure is not inherent in the Monte Carlo method per se, but it directly reflects the discrepancy noted in figs. 5 and 6 which we have ascribed to an

12

L . E . BEGHIAN e t aL

incorrect treatment of the lithium target. In fact the correction function f ( t ) increases rapidly for times t > 12 nsec and if the influence o f the lithium target had been represented correctly this increase would set in at earlier times. (c) The " b u m p " in fig. 7 at 7 < t < 10 nsec is believed to be caused by a difference in instrumental resolution for "field on" and "field off" profiles. Summarizing this situation we can say that the accurate determination of the true ratio V is not limited by the method of analysis but rather by experimental difficulties. From fig. 7 we can conclude that the true value of V is in the vicinity of the five data points between t -- 2.3 nsec and t = 5.5 nsec. Using their average value we obtain V = 1.425-t-0.035. (5.3) The error is a combination from all sources. By means of the calculated spin rotation one obtains = PI(30~.)P2(60~.) = - 0.181 + 0.012.

(5.4)

This measurement can be used to determine the polarization P~ (30~.) if an effective value of P2(60~.) is computed. This has been done by using the values of P2 given by Austin et aL ~7) and the values of the elastic differential cross section given by Fowler and Cohn 9) P2(60~) = - 0 . 5 8 6 + 0 . 1 (the error is due to the uncertainties in the scattering phase shifts). Finally P~(30~.) = 0.31-t-0.06,

(5.5)

where the error is largely caused by the uncertainty in Pz. The value of Pt(30~.) should be compared with the data shown in fig. 12. Our result is in disagreement with the measurement of Austin et aL ~7). 5.3. D E U T E R A T E D

POLYETHYLENE

The important parameters of the experiment are the following: maximum proton energy, 3 MeV; beam burst width (estimated): 4 to 6 nsec, lithium target thickness (estimated), 100 keV, average neutron energy (~ = 30~.): 1.15 MeV, nominal scattering angle: (59.3+0.5)j°,b . A typical time-of-flight spectrum is depicted in fig. 8. It exhibits the characteristic peaks from neutrons scattered from carbon and deuterium. The arrows ;.5 through 2 a indicate ranges o f integration. The range 25 to 26 is used for the determination of peak moments and the range )-7 to 28 serves to calculate an average timeindependent background level (see sect. 3). Fig. 9 shows the total time-of-flight profiles as obtained after the data analysis (without multiple scattering correction). The time-dependent background distribution is also given independently. Fig. 9 clearly shows a polarization effect, both for scattering from carbon and deuterium. In either case the sign of P2 is opposite to that found for oxygen.

l

1

1

1

~.~

),6

X7

ke

50~

0

C

ooo

oo

o°

o

%

-6 4 0 C E c o L.>

o

o cp o

o~ oooo

o v~ E

13

POLARIZATION

NEUTRON

o

°o°

o o o

o° o o

a~oO ao~

o

o

o ° oeo Oo o °o° cb o ~° q ~ o o ¢o

o

o 200

I00 o [ 140

I

I 160

I 180

I

I

I 200

I

I 220

I

I 240

k " Channel Number

Fig. 8. Typical main detector time-of-flight profile (CDz scatterer).

505

--~'-.... ~ ....

Field Off Field On Background

'/~"~'~X

~o4

/

{o~ 7 gO _'2' ~3

*o

E

:~ -zo

a

78

Ooo

I -IO

'=~©_?.,o.o.a~-9"o"

~g,q;

I

1 I 0 -r : Charmer tJumber

I I0

[

la 20

Fig. 9. Main detector total time-of-flight profiles, before multiple scattering correction (CD, scatterer).

i C

i --.,.o.,c0 um o Ex.per~ment31s0.c SpeCtrum °

°

01 35

I 30

°

I 25

I 20 Time

L.- / 15 Hnsec)

[ iO

"~'~L

--

5

I 0

Fig. 10. CDs experiment Monte Carlo analysis. Time-of-flight distributions. Cl'h¢ calculated spectra for single scattering from carbon and deuterium are shown as dashed curves.)

14

L.E. BEGH1AN e l aL

In order to find the true "field on, field off" ratios, both for C and D, the relative intensities (as a function of arrival time t) must be estimated. The Monte Carlo technique has been used again to this end. Fig. 10 shows the result of this analysis. No distinction has been made in the calculation between "field on" and "field off" scattering. The multiple scattering corrections for this experiment can be evaluated from a single theoretical analysis, in view of the relatively small polarization effects. The experimental spectrum given in fig. 10 represents the "field off" case. The calculated spectra for single scattering from carbon and deuterium are shown as dashed curves. One sees that the agreement between theory and experiment is very satisfactory. Using the calculated distributions the following ratios are formed:

ro(t ) = ND(t)/Nx(t),

rc(/) = Nc(t)/Nx(t),

where ND(t ) and Nc(t ) are the single scattering spectra for D and C, respectively, and Nr(t ) is the total scattering spectrum. The experimental distributions of fig. 9, both for field on and field off measurements, are then multiplied with rD(t ) and rc(t) to yield the corrected experimental single scattering intensities. The results are shown in fig. 11.

~ 0.4

~,,I

Deulerium

~0.3

~ O.t D E z

0

I

I

20

I

I

I0

"~L,X,

4x"

Time ,~(nsec)

I

I0

1

1

0

\

Fig. 11. CDz experiment Monte Carlo analysis. Time-of-flight distributions (single scattering).

By integration one finds deuterium: V = 0.975+0.020;

carbon: V = 0.968+0.026.

The quoted errors include all sources but are mainly statistical and from background asymmetries. With the calculated spin rotation one further obtains: deuterium: e = P~(30~.)P2(60~) = + 0.015 + 0.012, carbon:

e = Pl(30[)P2(60~) = +0.019+0.015.

NEUTRON POLARIZATION

15

Finally with the value of P1(30~.) obtained above deuterium: P2(60~.) = + 0.048 + 0.040, carbon:

P2(60~.) = +0.061-t-0.049.

The results constitute average values over the range of incident neutron energies E, = (1.15___0.05) MeV. No correction has been made for the variation of P1 and the LiT(p, n) reaction cross section with emission angle. Also, the variation of the Ct2(n, n) and D(n, n) cross sections with neutron energy has been neglected. Recent measurements of P2 for deutermm near 1 MeV and for similar scattering angles have been made by Lane et al. 23) [(0.05-2.0)%] and Darden 1o) [(9+5)%]. Our result with the quoted error overlaps both these measurements. Delves and Brown a) have calculated P 2 o n a semi-classical model taking account of the distortion of the deuteron and including tensor forces between nucleons. They calculate a value of P 2 ~ + 12 % at 1 MeV neutron energy for a laboratory scattering angle of 60 °. In the original paper P 2 w a s given as a negative. However, the sign was incorrect 22). 5.4. S U M M A R Y

OF THE RESULTS

The results of the present experiments are given in table 1. TABLE 1 Results Element

N e u t r o n energy (MeV)

Pt(30°L)P,(60°L)

Carbon

0 . 8 3 0 t 0.075

- 0.0026 + 0.004 I

Carbon Oxygen

1.15 =t=0.05 0.830±0.075

+0.019 +0.015 --0.181 -+-0.012

Deuterium

1.15 ___0.05

-t-0.015 -t-0.012

The authors express their gratitude to Professor G. H. R. Kegel for stimulating discussion and to the staff of the Rockefeller Generator Laboratory and the High Voltage Laboratory at M.I.T. for their collaboration. J. Weber expresses his gratitude to the CSA of the Swiss Scientific Foundation for its partial support and to the D.S.R. at M.I.T. for the opportunity to contribute to this work. This work has been supported by the Atomic Energy Commission, The Office of Naval Research and the Air Force Office of Scientific Research through contracts with the MIT Laboratory for Nuclear Science.

Appendix A AI. THE LITHIUM TARGET

In the last few years, the LiT(p, n)Be ~ reaction has been investigated extensively 11--20). The ratio of neutron intensities of the two groups (LiT(p, n)Be 7., Be 7 reactions) increases with proton energy, varying from ~ 5 % to ~ 13 % for Ep = 2.7

16

L.E. BEGHIAN

e ! al.

MeV and Ep = 3.0 MeV, respectively ~5). The presence of the second neutron group is of no consequence for our polarization measurements since it is clearly resolved by the time-of-flight technique. The polarization of emitted neutrons has been the subject of detailed experimental investigation 14-2o). Among all these data, few are pertinent to an angle of emission of 30°(lab)(fig. 12). In fig. 12, the solid curve has been drawn somewhat arbitrarily, considering however, the general trend at an emission angle of 50°(lab). 0

4

m

PI(L '7(c n',SeT).~ :50 o

T

O3

P,

02

o

x

ST 5 8 Au O!

1 1 0 i :.-. 24

I 2~

[ 2.8

I 30

I 3.2

..J 34

36

Cp t ~ e V )

Fig. 12. LiT(p, n) reaction (main group); Neutron polarization at 30° Lab emission angle. (See text.) ST 58: H. R. Striebel e t al. ~6); AU 61 : S. M. Austin et al. tT); CR 59: L. Cranberg 20). A.2. TARGET PREPARATION After metallic lithium has been evaporated onto a tantalum disk, a thin film of silicon diffusion pump fluid D C 704 is evaporated onto the target. This oil effectively protects the lithium from contamination when exposed to air for about l0 minutes, which is sufficient to mount the target at the accelerator. It has been estimated that the oil layer is less than about 10 keV thick and consequently of very little importance for the present application. The target is water-cooled and insulated from the accelerator by a short lucite pipe, see fig. 1. A.3. TARGET THICKNESS MEASUREMENTS For practical reasons, we did not use the usual rise method to estimate the thickness of our targets. In the technique adopted here, neutrons emitted at ~ = 30 ° are detected by the monitor counter, placed in the same plane as the main detector, using the time-of-flight method. The analysis of time-of-flight profiles observed at different target-to-counter distances yields an estimate of the target thickness and of the mean neutron energy, as will be shown below. The shift of the centroid of the neutron peak,

NEUTRON

POLARIZATION

17

as the target-to-counter distance increases, gives an independent measurement of the neutron mean energy. If we consider a time-of-flight peak due to a single neutron group, the shape of the profile is determined by a number of phenomena, (a) the finite temporal extent of the proton beam burst, (b) the spread in neutron arrival time at the counter for a fixed emission time from the target. This spread is a complex function of (1) neutron energy spread due to the finite target thickness, (2) neutron energy spread due to the spread in incident proton energy (neglected here), (3) neutron energy spread due to the varying emission angle (finite detector dimensions), (4) neutron transit time spread due to varying path length. (c) The finite temporal resolution of the detector. (This includes time spreads due to the finite thickness of the scintillator.) Each of the three causes (a), (b) and (c) is characterized by a probability distribution

P,(t), Pb(t), Pc(t). The resolution profile Pro(t) is the combination of these three factors. One can show that the second moment/a m of Pm(t), referred to the centroid of Pro(t) is the sum of the individual second moments of Pa, Pb and Pc (simultaneous events): ~m = ~ . + ~ b + ~ c .

(A.0

If we consider n o w two timc-of-flightprofiles,measured at two target-to-counter distances L (I) and L (2),it follows for thc corresponding moments/~
=

, (2) - - ~.(1) 'm

t~m

~

.(2)- - }.(1) a'b "

~Mb

(A.2)

We assume here that the proton burst profile and the detector resolution do not depend on the spatial coordinates of the latter. The moments/~(0 (i = 1, 2) can be determined from the measured profiles. Consequently the target thickness AEp can be obtained, provided that a simple relation exists between AEp and/a b. Such is the case only, however, if the process b(1) is solely responsible for a non-vanishing value of/a b. In our case, fortunately, b(2, 3, 4) are negligible. By making suitable assumptions about the neutron emission process (in particular a uniform target), we can now seek a relation between gb and AEp. The neutlon energy spread AE, due to the target thickness AEp is given by

0-t~LB +

-2,

1

(A3)

where Eo ----maximum neutron energy at ~ = 30 °, B--- x/m/2 (m = neutron mass), Atr = t2--tl (tt and t2 are the transit times for neutrons of maximum and minimum energy respectively), L -- target-to-detector distance. By using the following approx-

18

t.E. B[GH1AN el

aL

imation for the differential cross section for the LiT(p, n) reaction (for the pertinent neutron energy range) do "E "

a

(A.4)

d-~ C °~ - [ e . - b]~'

one finds for the probability distribution N(t)dt for a neutron to arrive at the detector at time t after emission from the source: N(t)dt -

2au 2 dt, [u 2 - bt2]'}

(A.5)

where a, u and b are constants. Then /z b ---- M t2)- [ M " ) ]

(A.6)

2,

where M tz> and M tl) are the second and first normalized moments of N(t), respectively. By Taylor expansion of eq. (A5) and integration one finds St,--

12

'

,i-~'--~)(Atr)2+

.''}

(A.7)

where ? and ~ are related to the first and second derivative of N(t) at t ,= t~, respectively. For our experimental conditions the correction terms were negligible so that

(at.r) ~

Sb ~ - 12

(A.8)

Further At T is proportional to the distance L. Hence ZJSb = S(2)--S (1) = 1-~-(2c 2 -

1XAt(I)) 2,

(A.9)

where C .~ D2)/L (1). The quantity ASh can be measured by virtue of eq. (A.2) (the moment S . is easily found if the peak profile is Gaussian); eq. (A.9) yields At~ t) from which AE. follows by eq. (A.3) for L = L m. Finally AEp can be found from the graph of E,(Ep, ~). (Practically dEp -- AE,.) Once the target tickness is known, the average neutron energy E. at the angle can be found by using the approximation formula (A.5). From the difference between this result and/~, measured by the peak centroid shift one can in principle deduce some information on the carbon build-up on the target.

Appendix B Although both the main detector and the monitor counter have been shielded carefully, small effects on the gain of the multipliers, due to the precession magnetic field, could not be avoided. Changes in gain modify the pulse-height spectra (side

NEUTRON POLARIZATION

19

channels in fig. 2) and consequently the counter efficiencies, which in turn introduce systematic errors in the measured field on-field off ratios. Correction factors have been estimated in the following way: Let N ( x ) d x be the observed pulse-height spectrum and n _- ( g 2 - - g l ) / g t the relative gain (g) change. Also let $1 and $2 denote the counting rates before and after the gain change, respectively, when a window (one-channel pulse-height discriminator of fig. 2) from x = x t to x = x2 is placed on the pulse-height spectrum; then the relative change in counting rate (or detection efficiency) is, if N ( x ) d x represents a flat spectrum, AS

__ S12 - -_S

St

Sx

_

o~

,"

S =

(x)dx.

(A.10)

1+~

This equation enables us to determine n for any particular gain change. (A fiat spectrum is easily realized for this purpose by considering a portion of the Compton recoil spectrum from a mono-energetic gamma-ray source.) In the case of mono-energetic neutrons, the pulse-height spectrum is not flat 24). Generally it was found that the pulse-height window of the main detector had to be placed on the decreasing portion at large pulse-height in order to obtain maximum signal-to-noise ratio. In this region the spectrum is well described by the function N ( x ) d x = A exp (-- ax)dx.

(A. 11 )

The relative change in detection efficiency is then found to be AS _ e -°ax ( 1 - e -*¢~'2) + (e - * ~ ' - 1) St (1 - e -°4x) ' Ax

(A.12)

= x2DxI,

or, as in our case, by the approximation AS _ ( x t - x 2 e -*~x)

St

a~.

(A.13)

(1 - e -*~x)

It is interesting to note that depending on the values of a, xt and x2, AS/S~ can be equal to zero even if the gain change is not equal to zero. A small gain change can thus be taken into account by multiplying all counting rates $2 by a factor Cr = 1/(1 + AS~St). In all cases we found 0.994 ~ Cr < 1.006 although ~ may have been as large as 3 %. References

1) Proc. Int. Conf. on Nuclear Forces and the Few Nucleon Problem, Vol. II, ed. by T. C. Griffith and E. A. Power (Pergamon Press, London, 1960) p. 345 2) K. Smith and M. Peshkin, ANL Report 5910 (1959) 3) L. M. Delves and D. Brown, Nuclear Physics 11 (1959) 432 4) Hillman, Stafford and Whitehead, Nuovo Cim. 4 (1956) 67

20

5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25)

L.E.

BEGHIAN e t al.

L. E. Beghian and M. K. Salomaa, Nucl. Instr., 17 (1962) 181 W1ichter, Weber and Bcghian, Nucl. Instr., to be published A. J. Elwin and R. O. Lane, Nuclear Physics 31 (1962) 78, also private communication Wills, Bair, Cohn and Willard, Phys. Rev. 109 (1958) 891 J. L. Fowler and H. O. Cohn, Phys. Rev. 109 (1958) 89 Darden, Kelsoy and Donoghue, Nuclear Physics 16 (1960) 351 Fast neutron physics, Vol. I, ed. by J. B. Marion and J. L. Fowler (lnterscience Publishers, New York, 1960) chapt. I.E. Hanson, Taschek and Williams, Revs. Mod. Phys. 21 (1949) 635 Bcvington, Rolland and Lewis, Phys. Rev. 121 (1961) 871 W. Haeberli, Heir. Phys. Acta Suppl. 6 (1961) 149 S. M. Austin, Heir. Phys. Acta Suppl. 6 (1961) 214 Sriebel, Darden and Haeberli, Nuclear Physics 6 (1958) 188 Austin, Darden, Okazaki and Wilhelmi, Nuclear Physics 22 (1961) 451 A. J. Elwyn and R. O. Lane, A N L Report 6358 (1961); also private communication J. A. Baicker and K. W. Jones, Nuclear Physics 17 (1960) 424 L. Cranberg, Phys. Roy. 114 (1959) 174 M. H. Witchter, P h . D . Thesis (Department of Physics, M.I.T., 1962) L. M. Delves, Nuclear Physics 33 (1962) 482, also private communication Lane, Elwyn and Langsdorf, Jr., Bull. Am. Phys. Soc. 7 (1962) TA1 Witchter, Weber and Beghian, Nucl. Instr., to be published B¢ghian, Sugimoto, Witchter and Weber, Bull. Am. Phys. Soc. 7 TA2