A multiwire proportional chamber as a polarimeter for fast neutrons

NUCLEAR

INSTRUMENTS

AND

METHODS

I22

(1974) 415-43~; ©

NORTH-HOLLAND

PUBLISHING

CO.

A MULTIWIRE P R O P O R T I O N A L CHAMBER AS A POLARIMETER FOR FAST N E U T R O N S C. P. S I K K E M A

Laboratorium voor Algemene Natuurkunde der Rijksuniversiteit Groningen, Groningen, The Netherlands Received 11 September 1974 T h e azimuthal a s y m m e t r y o f the scattering o f polarized n e u t r o n s by helium nuclei is m e a s u r e d by detecting the recoil alpha particles in a multiwire proportional chamber. The required i n f o r m a t i o n on the direction o f the particles is obtained from the particle energy, from the spread in the drift time o f the collected electrons a n d from the difference in discharge position o n successive collecting wires. This difference is determined in a direct way by m e a n s o f a newly developed electronic system. Since with the present m e t h o d no d i a p h r a g m s are used for the

direction determination o f the recoil particles, the associated geometrical asymmetries a n d limitations o f the sensitive v o l u m e are avoided. The scattering a s y m m e t r y is determined simultaneously for a range o f scattering angles. Results obtained with polarized d - d - n e u t r o n s are presented. T h e y show good agreement with k n o w n n--~ scattering phase shifts and polarization values obtained recently by other techniques.

1. Introduction

helium gas must be smaller than the range of the recoil particles. Also geometrical asymmetries are readily introduced. Secondly, cloud chambers have been applied to determine the directions of the recoil particle tracks14-16). Although geometrical asymmetries do not occur with this method, if suffers from a low duty cycle and the elaborate measurement of the photographed tracks. To avoid the specific disadvantages of the abovementioned polarimeter systems, we considered applying the recoil particle method using an ionization chamber without geometrical apertures to define solid angles for the alpha particles. Such a system should be based on electronic direction-sensitive detection methods. The uniform motion of electrons created by a particle in a parallel-plate (gridded) ionization chamber may be utilized to obtain information on the spatial orientation of a particle track. Firstly, there is a spread in the time of arrival of the electrons at the collecting electrode, depending on the inclination of the track with respect to the plane of the electrodes. This inclination may be inferred from the shape of the charge pulse on the collector. Secondly, the electrons arrive at the collector on a line which is the projection of the particle track on the plane of the electrodes. The direction of this projection may be determined by a suitable position analysis of the arriving electrons. So far only the first method has been applied (cf. e.g. ref. 17). However, for adequately determining the direction of a recoil particle, both methods should be combined. The second method involves recording charge pulses from the electrons on a large number of small insulated parts of the collecting electrode. With

Elastic scattering by helium nuclei is most generally used as the analyzing process for measuring the polarization of fast neutrons (cf. for instance ref. 2). The analyzing properties of helium are well known up to about 22 MeV neutron energy 3) and quite suitable for polarization analysis. The methods involve measurement of the azimuthal scattering asymmetry either by detection of the scattered neutrons or the recoil alpha particles. The former technique has been used predominantly in recent years, in a way originated by Pasma4). The scattering helium gas is contained at high pressure in a gas scintillation chamber. To eliminate background events, coincidences are recorded between pulses from one or more neutron scintillation counters and the gas scintillator detecting the recoil alpha particles. A problem is presented by coincidences due to neutrons scattered both from the helium gas and from the gas scintillator envelope, before entering the neutron detectors (cf. e.g. refs 5 and 6). Recently also liquid helium scintillators have been used and time-offlight techniques employed to reduce background effects (cf. e.g. ref. 7). However, the background problems which are specific to neutron detecting devices are entirely avoided if the scattering asymmetry is determined by means of the charged recoil particles only. This involves some way of confining or determining the direction of these particles. So far, the recoil particle method has chiefly been applied in two ways. Firstly, proportional or avalanche counters have been used and the directions of the particles confined with tubes or slits 8-13). Such systems have a low efficiency since at least one dimension of the sensitive volume of 415

416

c . p . SIKKEMA TARGET

k a X k n

" ~ /

~

/

Fig. 1. G e o m e t r y o f fast n e u t r o n polarization m e a s u r e m e n t by the helium recoil particle m e t h o d . Measured are the n u m b e r s of particles scattered at given angles 0 in equal azimuthal intervals centered at ¢ = 0 and ~ = ~ (cf. section 2).

the ordinary (gridded) ionization chamber this would lead to serious electronic noise problems. We therefore introduced gas multiplication, replacing the plane collecting electrode of the gridded ionization chamber by a row of parallel collecting wires. The resulting instrument was described in a previous papeP). A similar type of chamber has been independently developed at C E R N by Bressani et al. for locating the passage of high-energy particles by means of the collection time of the electrons. They called their instrument a drift chambeP s). In our new proportional chamber, the direction of the particle track projection on the plane of the wires can be deduced from the difference in position of discharges on successive wires. In our chamber differences of only a few millimetres should be reliably recorded. This would be difficult to achieve with current linear position-sensitive systems because of the required high absolute accuracy in the determination of the discharge position on each wire. Instead we developed a system for directly recording the relative position of discharges on successive wires, irrespective of the absolute position of the discharges. The polarimeter operation and performance is described in section 3. Concluding remarks are contained in section 4.

The neutrons are elastically scattered by helium nuclei. If the neutrons are initially unpolarized, the polarization of the scattered neutrons is analogously to eq. (1) represented as k, x k,,, Pne = PHc Ik. x k.,I

k, x k~ PHe [k. x k=l

(2)

k., and k~ being the unit direction vectors of the scattered neutron and the helium recoil respectively. If polarized neutrons are scattered, the process becomes asymmetric, the differential scattering cross section depending on the azimuthal angle 4' according to o'(0, 4') = 6(0)(1 +Pn 'Pne) = 0"(0)(1 -PnPHeCOS4').

(3) Here the angles 0 and 4' pertain to the recoil particle, 0 being the angle between k. and k~ and 4' between k~ x k, and k, x k~. The cross section ~(0) is the value averaged over ¢ or the differential cross section for unpolarized neutrons. Since the azimuthal variation, described by eq. (3), is proportional to P. PHe, this product is called the asymmetry, and PHe the analyzing power of the n - H e scattering process. PHo is a function of the scattering angle 0. It follows from eq. (3) that

~(0, ~)- ~(0, O) P, PHe(0) = a(0, ~Z)+Cr(0, 0)"

2. Principle of polarization measurement For a general discussion of the principle of neutron polarization measurements we may refer to an article by HaeberlP 9). The situation in our case is sketched in fig. 1. Unpolarized particles (a) directed along the unit vector k~ strike a target, in which neutrons are produced by a nuclear reaction. The transverse polarization of neutrons emitted from the target in a direction kn can be expressed as

ka x k.

P"

=

P° I/,~ x ~.1

(1)

(4)

The asymmetry may therefore be determined by detecting recoil particles scattered at a given angle 0 " t o the right" ( 4 , = 0 ) and " t o the left" (4' =Tz). In practice we measure the numbers of particles scattered within a small interval of 0 and equal intervals 25 o f ~ , centered at 4} = 0 and 4' = ~. These numbers are proportional to the cross section ~(0, +) integrated over the intervals of 4). Denoting the integrated cross sections by a o and a~ respectively we obtain: cro = 2~(0) ( ~ - P,,PH~ sin 6) , a~ = 2a(0) (6+P, PHe sin 6) .

(5)

POLARIMETER FOR FAST NEUTRONS It follows that the a s y m m e t r y m a y be expressed as pnpH e =(a~--ao / 5 \ a ~ + ao/sin 5

(6)

I f the m e a s u r e d n u m b e r s o f particles scattered in the two intervals centered at q~ = 0 and q~ = n are d e n o t e d by R and L respectively, we define the measured asymmetry a as:

a

(7)

It has been shown that the statistical r o o t - m e a n - s q u a r e deviation o r e is a m i n i m u m i f 5 is a b o u t 60-70 degrees. W i t h our p o l a r i m e t e r , 5 typically lies between 3 0 ~ and 60 ° . In this region the statistical error only slightly exceeds the m i n i m u m value2°). Obviously, when e~ is measured at one scattering angle O, the neutron p o l a r i z a t i o n P , can only be d e t e r m i n e d if Pne is known. Pne is a function o f 0 and the scattering phase shifts, which depend on the

417

neutron energy. The phase shifts must be determined experimentally. F a i r l y accurate values have been deduced from total and differential n-c~ cross sections3'21). W i t h our instrument e is measured simultaneously for a range o f scattering angles 0. These d a t a m a y be analyzed by calculating Pl_le(O) with a predetermined set of phase shifts and fitting the measured values o f e with PnPHe(O) by only a d j u s t i a g P , . This fit provides a check on the assumed phase shifts. On the other h a n d the phase shifts m a y be independently determined along with P , in a p r o c e d u r e t o fit the measured asymmetries together with the value o f the total cross section22). W e applied b o t h m e t h o d s to analyse our measured d a t a and c o m p a r e d the results. This is described in section 3.9.

3. The ionization polarimeter The neutron p o l a r i z a t i o n is measured according to the principle outlined in the previous section. The a s y m m e t r y g, defined by eq. (7), is determined by

ne

Fig. 2. Schematical view of the electrode system of the polarimeter chamber. The ionization or drift volume is confined between the fiat cathode A, the grid C and the field electrodes B. In the gas multiplication volume between the grid C and the cathode F are stretched the collecting wires D and the intermediate wires E. Also shown are the direction of the neutron beam, the envelope of recoil alpha particle tracks originating at O, and a cone of tracks corresponding to a given scattering angle 0 defined by the pulse height t,D. A pair of azimuthal intervals 26 centered at ¢ = 0 and ¢ = ~ is selected by discriminating the differentiated pulse height v'~. The intervals are distinguished by the pulse height vF derived from the electrode structure F. Further explanation is given in section 3.1.

418

C. P. SIKKEMA

recording the numbers R and L of recoil alpha particles scattered at given angles 0 into equal azimuthal intervals 26, centered at ¢ = 0 and ¢ = ~z. The instrument and the principle of its operation are described in section 3.1, referring for various details to subsequent sections. The experimental procedure is described in section 3.8 and an example of evaluating the result in terms of neutron polarization and scattering phase shifts is discussed in section 3.9. 3.1. PRINCIPLE OF OPERATION The basic instrument is a helium-filled multiwire proportional chamber which has been described in detail in ref. 1, except for the structure of the lower electrode F which was introduced later on. The electrode system is shown schematically in fig. 2. The neutrons enter the chamber as a beam directed parallel to the electrodes and perpendicular to the wires. In the helium gas recoil alpha particles are produced anywhere along the neutron beam. The electrons, liberated in the gas by ionization, move uniformly along the lines of force in the homogeneous electric field between the top electrode A and the grid C. This field is maintained with the aid of the field electrodes B. After passing the grid, the electrons are collected on the wires D where gas multiplication occurs. The wires E and the flat cathode F serve to symmetrize the electric field around the collecting wires1). However, they also are used to pick up positive pulses from the discharges around the collecting wires for purposes discussed later on. A survey of the chamber dimensions and operating data is given in section 3.10. From the proportional chamber three types of pulses are derived, which contain information on the direction of a recoil particle. We call these pulses the D-pulse, the D'-pulse and the F-pulse, and denote the " and VF respective pulse heights by VD, VD The D-pulse and the D'-pulse are derived from the charge pulse on the collecting wires D, which are connected in parallel to a charge sensitive amplifier. From the. output pulse the D-pulse is obtained by integration and the D'-pulse by differentiation. The pulse height vo is proportional to the total collected charge, which is approximately proportional to the energy E, of the recoil particle. E, depends on the neutron energy En and the scattering angle 0 of the recoil particle (in the laboratory system) according to E~ E~o cos 2 0, (8) =

with E~o = 4m,~m~(rnn+m~)-2En, mn and m~ being the masses of the neutron and the alpha particle, re-

spectively. Hence, there is a well-defined relation between v D and 0, which is discussed in detail in section 3.2. With our chamber a collimated monoenergetic beam of neutrons is used which is directed along the Y-axis (fig. 2). A given pulse height VD corresponds to a cone of recoil particle tracks which have the same length R. The axis of the cone is parallel to the Y-axis and the half top angle is 0. The top may be located anywhere within the neutron beam. Such a cone has been sketched in fig. 2. Information on the azimuthal position of a particle track on the cone is obtained from the D'-pulse, which depends on the component R. of the track in the electric field direction. R= is the maximum path difference of the electrons in the drift space between the electrodes A and C. The rise time of the charge pulse on the collecting wires is approximately IRzl/w, w being the electron drift velocity. The height ~D"of the D'-pulse, which is obtained by differentiating the charge pulse, therefore is approximately proportional to l/[Rz[. A measured relation between t'~ and R= (at a given particle energy) is shown in fig. 3 (taken from ref. 1). By accepting only D'-pulses exceeding a given threshold for a given pulse height vt~, an upper limit is set on LR..I, which is denoted by IR=[0. Fig. 2 shows that in this way recoil particles are selected which are scattered at a fixed angle 0 into a pair of equal azimuthal intervals centered at ¢ = 0 and ¢ = n. The half interval width is denoted by 6. The sharpness of definition of 6 by a W-threshold is discussed in section 3.3. There also a direct method is described to determine 6 from the data collected during the polarization measurement. Obviously the recoil particles selected in the above

1.0

0.8 {9 D Ld 2:

0.6 bJ I.,9 _]

G. LI.I > I'-<

d

0.4

0.2

Ld rY

O

o

I

I

I

I

5

1o

15

20

R z (ram)

Fig. 3. Dependence of the pulse height v'D on Rz, the particle track component in the electric field direction.

419

P O L A R I M E T E R FOR FAST N E U T R O N S

The relation between vD and E, we express as

way by means of the pulse heights vo and v~, may be scattered in either of the two intervals to the right and to the left. These two cases are distinguished by means of the F-pulse. The height VF of this pulse is approximately proportional to x , + ~ - - x , , the position difference of the discharges produced by a particle on two successive wires n and n + 1. It appears from fig. 2 that x , + , - x , has the opposite sign for recoil particles scattered to the right and to the left. The system for producing the F-pulse, called the left-right discriminating system, is described in section 3.4. An asymmetry measurement is performed by recording the three-parameter correlation between the pulse heights vo, t~ and vv. An example is given in section 3.7. The method of evaluation is described in section 3.8.

vD = kE~.

(9)

The relation between vD and 0 may accordingly be written cos 2 0 vo/C, (10) =

with C = k m E , . The factor k depends on the ionization, electron collection and gas multiplication processes i n the proportional chamber, as well as on the amplifier gain. Pulse height fluctuations mainly arise from electron loss in the drift space (electron attachment) and variation in the gas multiplication factor caused by wire irregularities. Statistical fluctuations in the ionization and gas multiplication and amplifier noise are of minor importance in the present case. The fluctuations are expressed by the relative standard deviation a k in k, which is approximately constant for the particle energy range of interest here. The average value of k is constant to a first approximation, but deviations may originate in the ionization and gas multiplication processes which will be discussed later in this section. The factor C in eq. (10) fluctuates with a relative standard deviation•

3.2. THE DEFINITION OF 0 BY THE PULSE HEIGHT UD Eq. (8), which is used to determine the scattering angle 0 of the recoil particle, may be written cos20 = E~,/E,,o, with E,o = mEn. Here E, is the particle energy and E~0 the maximum value corresponding to a head-on collision (0 = 0). E, is the neutron energy and m a constant determined by the neutron and alpha particle masses according to m = mnm~,(m,, + m , ) - 2. It was mentioned in the preceding section that vo, the height of the D-pulse, is proportional to the total charge collected on the wires D. The D-pulse is obtained from the charge pulse on the wires by means of a differentiating and an integrating RC-filter, both with time constant 5/ts. In this way the influence of the rise time variations, discussed in the previous section, on the pulse height is virtually eliminated. The maximum rise time in our case is 3 ~ts.

~

~ , = (.~ + ~r)

(11)

~ being the relative standard deviation in E,. To determine 0 from vD by means of eq. (10), C and ~c are deduced from the pulse height spectrum N0,v). A typical example is given in fig. 4. The distribution of cos 20 for the recoil particles of course cuts off sharply at c o s 2 0 - - 1 . Eq. (10) implies that at a given 0, co fluctuates with a relative standard deviation ~c. The

N(VDJ 2000

°~,

,,,, •.,

1000

V o

D

O rv

"'" .... """ ........ 1415~

Ld N I

CHANNEL

NO. ( 1 )

1 2 3

I O

CHANNEL

NO. ( 2 )

I 100

I

I

I

I

I

l

F

I

I

I

IiI 200

I

Ili~

NO

,'-

IN°

I

\ vD

Fig. 4. Typical distribution of the pulse height cD. Tile scattering angle 0 is deduced from the ratio between t'D and the upper edge cOD as described in section 3.2. The wide channels (no. 1) are used in the polarization measurement (cf sections 3.7 and 3.8).

420

c.P.

SIKKEMA

spectrum N(vD) accordingly shows an upper edge with a gradual slope, from which % may be deduced by means of the expression No

ac

\/(2n)vO N,(vg ) .

(12)

Here N o is the full height of the spectrum just below the upper edge, and v° and N' (v°) are the values of vD and the derivative N'(vD) at half-height of the edge, respectively. These values were determined by leastsquares fitting a straight line to the measured points in this region. The procedure is illustrated in fig. 4. It is correct if N(vD) is constant below the upper edge and the distribution of C is Gaussian. Otherwise it may be used as an approximation. For cos 2 0 = 1 (0 = 0), v° is the average value of YD. Hence, according to eq. (10), for 0 = 0 also v° = ( C ) . At first we assume that ( C ) is the same for other values of 0. Then at a given VD the average value of cos 2 0 is (COS 2 0)

=

U'-~D

vo'

(I

3)

and the relative standard deviation in cos 2 0 is % . For the example of fig. 4, the above procedure yields a value a c = 0.017. Then, according to eq. (l 1), crk <0.017 and the chamber resolution corresponds to a full width at half maximum less than 4%. Higher values of trc, up to about 0.03 were observed a few weeks after filling the chamber with the gas mixture. This increase may be ascribed to electron attachment by impurities released inside the chamber. Eq. (13) was obtained from eq. (10), assuming that ( C ) = ( k m E , ) is constant throughout the range of 0 and YD. Actually, ( k ) may not be constant. Firstly, there is evidence that the ionization by alpha particles is not precisely proportional to the energy23). Probably this should require a relatively small correction on eq. (13), for which, however, no adequate data are available. Secondly, the space charge caused by the positive ions created in the avalanches may appreciably reduce the gas amplification factor. The space charge density is greatest for discharges caused by particles crossing the wires at right angles.In our geometry these are the forward scattered alpha particles (0 = 0), since the neutron beam normally is directed along the Y-aris which is perpendicular to the wires. The space charge effect was investigated by determining v° for various directions of the neutron beam in the X - Y plane. In fig. 5, VD ° is plotted as a function of q/, the angle between the neutron beam and the Y-axis, for gas amplification factors designated by A ( ~ I 0 0 ) and 2 A ( ~ 2 0 0 ) .

At the gas amplification 2A, which was originally used, an appreciable space charge effect is present. The effect decreases when the gas amplification is reduced, the maximum variation of v° being about 1.5% at the gas amplification A. A further decrease to about 0.5% was attained at a gas amplification ½A. Since in this case the signal-to-noise ratio in the pulse channels of the left-right discriminating system decreased too much, a gas amplification factor A ~ 100 was chosen for normal use. The space charge effect was taken into account, assuming that the gas amplification is constant for 0 exceeding about 20 ° and lowered due to the space charge effect by 1.5% at 0 = 0. The tracks of particles used for the asymmetry determination lie approximately in the X - Y plane and have ~ > 20 °. The only correction applied on eq. (13) therefore is an increase of co° by 1.5%. Eq. (13) accordingly was replaced by (cos 2 0) = CD/(I.OI5 C°). 3.3. THE DEFINITION OF AZIMUTHAL ANGLE I N T E R V A L S

BY THE PULSE HEIGHT t'~)

The D'-pulse is obtained by differentiating the charge pulse on the collecting wires. For this purpose we use a closed delay line with transit time z = 1/~s. The rise time t of the charge pulse approximately is [RzJ/w (cf. section 3.1) and the pulse height is vo (apart from approximately constant electronic amplification and attenuation factors which are assumed unity for the present discussion). Then the charge pulse rises at a rate vDw/IR~I and the height of the differentiated pulse is r -OD

UDW"~,

(14)

IR_.I

~

190

v; (arb

units)

185

2A

-A

(

1800

I 10

I 20

I 30

L 40

[

qr 5 0 °

Fig. 5. Space charge effect. T h e m e a n pulse height V0D for forward scattered alpha particles is m e a s u r e d with neutrons entering the c h a m b e r in the X - Y - p l a n e at various angles ~bwith respect to the Y-axis. G a s multiplication factors are A and 2 A ( A ~ 1 0 0 ) .

421

P O L A R I M E T E R FOR FAST NEUTRONS

provided t > r or JR=[ > tcr. R~ is related to the particle range R and the angles 0 and 49 by R: = R sin 0 sin 49 (cf. fig. 2). Hence the relation between ~o ,' and 49 may be expressed as K

t,~

(1 5)

[sin 49[' with K = t'ou~z/(R sin 0). This relation is approximately valid if Isin 491 > wr/(R sin 0). Since at a given ct~, R and 0 are fixed, K is also fixed. However, fluctuations occur in u' (electron diffusion), R (energy spread and range straggling) and 0 (cf. section 3.2). The resulting spread in K is expressed by the relative standard deviation ~rK. This spread may be determined experimentally from the distribution of pulse heights t'g at a given vD. Since the distribution of Isin qSI cuts off sharply at sin 49 = 0 (q5 = 0 and 7r) and at Isin 491 = 1 (49 = ½rr and 3zt), the v~ spectra show an upper and a lower edge with a gradual slope due to the above fluctuations. Typical examples are shown in fig. 6 for rD-channels indicated in the

N(v;)

t;D--t'~ correlation diagram. F o r the lower part of the v~ spectra eq. (1 5) is applicable and crK may be determined from the slope of the lower edge analogously to the method described in section 3.2 for the vD-spectrum. F r o m the spectra shown in fig. 6 a value of about 0.07 is obtained. According to eq. (15), Isin 491 is defined by a ,' with a relative standard deviation a t . The given ~D corresponding standard deviation in ~b is Itg 491 crK. This also applies to 6, the half width of the azimuthal intervals selected by applying a threshold to the D'-pulses. Hence cro = Itg 61 crK. F o r the asymmetry determination 6 usually was chosen between 30 ° and 60 °. We assume the value crK = 0.07, determined for Isin~bl = 1(49=½7r or ~rr), to be valid in the range 49 = 30%90 ° . Then we find cro = 2.4 ° at 3 = 30 ° and % = 7 ° at 6 = 6 0 ° . A calculation showed that such fluctuations in 3 cause a negligible error in the determination of e by means of eq. (7), provided the correct average value of 6 is inserted. It is not necessary to determine this value from the D'-bias and the relation between t,b and 49, which is not easily established. Instead, a simple statistical method is available. We denote the total number of pulses counted in the ro-channel by N and the number exceeding the @-bias by M. M is proportional to the sum of the cross sections a 0 and a~ expressed by equations (5). It follows that M is proportional to 6. Since N is the number of pulses recorded for all values ofqS, that is for 6 = ½~z, we have the relation M / N = 26/7r.

(16)

With this relation the average value of ~ is determined with good statistical accuracy.

I

t

1

t_

t

I

v D

3.4. THE LEFT-RIGHT DISCRIMINATING SYSTEM; THE F-PULSE

This system serves to distinguish between recoil particles scattered into the azimuthal intervals centered at 49 = 0 and 49 = rr which are selected by means of the pulse heights c o and c~ (cf. section 3.1). These particles have the opposite sign of track c o m p o n e n t R x (fig. 2). N o w we have the relation Rx/R r = tg ~ = (x,+ 1 - x , ) / d . Here ~ is the angle between the track projection on the X-Y-plane and the Y-axis; x, is the position of the centre of the discharge on the nth wire and d is the distance between the wires. For a given pulse height vo, Ry = R cos 0 is fixed and R x is directly proportional to Xn+

Fig. 6. Bottom: correlation between pulse heights VD and v'r~ for recoil alpha particles produced in the geometry of fig. 2. Top: v't)-spectra for two r D - c h a n n e l s indicated by arrows.

1 -- Xn •

To determine x , , + l - X , , use is made of pulses, induced by the positive ions created in discharges on the wires, on rectangular insulated sections of the flat cathode F (fig. 2). The positions of the rectangles with

422

c . P . SIKKEMA

respect to the wires and the interconnections are shown in fig. 7. A discharge on the nth wire gives rise to pulses on three periodic sequences of interconnected rectangles which are indicated by A., B. and C., respectively. The pulses are amplified by charge sensitive amplifiers. The output pulse heights, denoted by a., b. and c. are periodic functions of the position coordinate x. of the discharge as shown at the top of fig. 7. The curves in the figure were obtained by producing concentrated discharges on a wire with a narrow beam of alpha particles which traversed the volume between the grid C and the plate F perpendicular to the plane of the wires. The beam, from an 241Am source, passed near to the wire and could be moved in the wire direction. The measured curves may be approximately represented by the functions a. = ~.q.[cos 2n x./2 + p . ] , b. = ~.q.[cos 2n(x.12-½) + p . ] , c. = ~,,q.[cos 2n(x.12 - z ) + p . ] .

(17)

The pulse heights are proportional to the collected

charge q. and the electronic amplification factor ~., which should be equal for all amplifiers. The constantp is greater than unity. The period 2 is the period of the systems of rectangles A., B. and C.. If discharges are produced by a particle on two successive collecting wires n and n + 1, the difference between the discharge positions x. and x.+ l may be deduced from the output pulse heights a., b., c. and a.+ 1, b.+ l, cn+ 1 by means of the expression

F.,n+ 1 = a.b.+ l -bna.+ 1+b.c,,+ l -c.bn+ l +c,,a.+ 1 --

-

(18)

anc.+l.

It may be shown by inserting eqs. (17) that 3 F,,,.+ 1 = ~\,3o~.o~.+lq~q.+ 1sin

2n x"+

x~ . (19)

To determine x , , + l - x , for particles occurring anywhere within the sensitive volume of the chamber, expressions F.,.+~ may be summed for all pairs of collecting wires. Since x.+ l - x , is the same for any pair of wires, this yields F = ~ F.,.+ 1 = ~,,/3~2 ( ~ q.q.+l)sin(2nx"+~----x"].

RELATIVE PULSE

.

,

\

2

)

(20)

i

Qn,

-50

,'

0

50

x~(rnrn)

c 1 ~

Here we have assumed ~. =c~ for all values of n. Eq. (20) may be further simplified if the ionization density is assumed to be constant along the particle tracks and charge is collected on three or more wires. In this case we may write

-

03

q,,q,,+l = q ( q - q ' ) = flE~,(E~,-E'a).

(21)

rl

Here q is the total collected charge and q' is the greatest charge collected on a single wire. E. is the particle energy and E" is equal to E~,q'/q, which is the energy corresponding to the charge q'. The factor fl is a constant. Combining eqs. (20) and (21) we obtain

F = ,E~,(E~,-E'~)sin(2nx"+~-x'~), -

.

.

.

.

.

.

°

•

,

°

•

•

,

°

,

.

.

.

.

.

.

.

.

.

.

.

°

.

.

.

.

.

.

Fig, 7. The left-right discriminating system. Top: pulse heights an, bn and Cn measured as functions of the discharge position xn.

Bottom: configuration and connection of the insulated parts of the electrode F. Further explanation is given in section 3.4.

(22)

T being a constant, In the actual case, the discharges are spread over some distance along the wires. This merely causes a slight reduction of the factor ~ in eq. (20), x, referring to the centre of the discharge on the nth wire. Also the actual response functions deviate slightly from the cosine functions eqs. (17). This may cause F not to be quite independent on the location of the particle track within the sensitive chamber volume. However, as was mentioned before, the system principally

POLARIMETER

FOR FAST NEUTRONS

serves to reveal the sign of x , + t - x .. According to eq. (20) this requirement is fulfilled if [x,,+~-x,,I does not exceed ~11. It may be shown by symmetry considerations that also in the actual case Fchanges sign at x,+ ~- x , = 0. The system therefore should be adequate for our purpose. The quantity F = ~ , F,,,+~ is determined from the output pulse heights a,, b,, e, by means of an analog operation according to eq. (18). In principle this involves processing a number of output pulses which is three times the number of collecting wires, that is 45 pulses in our case. However, this number may be considerably reduced because of the limited range of the recoil particles. In our case, discharges are produced by a particle on no more than 5 successive wires. Hence, the systems of rectangles A~, B~ and C, in the first row may be connected in parallel to the corresponding systems in the 6th and the l lth row, etc. In this way only 15 patterns of interconnected rectangles remain, which are indicated in fig. 7 by A~, B~, C 1 . . , A s, B 5, Cs. From the 15 pulse heights on these systems, a~,b~, cj , . . . , a s , b s , cs, the quantity F i s calculated according to F = F l , 2 -1- F 2 , 3 + -.. + F s , 1, w i t h F~, 2 = (11 D 2 - - b l a2 + bl c 2 - c l b2 + ci a 2 - a l c2, etc. The electronic analog computer used to calculate F produces a pulse which in height is proportional to F. This pulse height we denote by vv. The operation of the system was investigated by means of collimated alpha particles from an Amsource mounted within the ionization volume. The alpha particle collimator was parallel to the X-Y-plane (fig. 2) and could be adjusted at various angle ~ with respect to the Y-axis. The measured pulse height vv is plotted in fig. 8 for various values o f t g tp which is equal to (x,+ l - x,,)/d, d being the distance between the wires.

VF

Oil

(orb units

/1"

U

£y

-~!o

-(~.5

u

H"

llO

/

/

/ i

d~ tg g,

y/ // / /O . . "~

Fig. 8. Performance o f the left right discriminating system: the o u t p u t pulse height el,' plotted vs tg ~b = Rx/Rv, the ratio o f the track c o m p o n e n t s in the X- and Y-directions.

423

The result approximately agrees with the dashed line, calculated by means of eq. (22). This curve is not sineshaped since in this experiment E ( E - E ' ) depended on due to a diaphragm mounted above the screening grid C to limit the sensitive volume and thereby the effective length of the alpha particles tracks. The constant 7 was adjusted to fit the measured data. The dependence of q,- on the position of the alpha particle source was investigated by moving the source in a direction parallel to the X-axis at a constant angle ~9 = 24". The maximum deviation of F from the mean value amounted to about 10%. The system operates satisfactorily in the polarimeter. This appears from the measured correlation between the pulse heights t'D, t'~ and rv shown in fig. 11. With the pulse heights t'o and t:~ alpha particles are selected, which are scattered into equal solid angles to the left and to the right. These particles originate in an extended volume in the chamber. The corresponding distributions of~, v properly show the two groups to be expected. These spectra will be discussed in detail in section 3.8. 3.5. DEFINITION O f THE SENSITIVE VOLUME

The polarimeter chamber is designed to be used with a collimated neutron beam directed along the Y-axis (fig. 2). In the X- and Z-directions the sensitive volume therefore is confined by the diameter of the neutron beam. However, near the entrance and exit of the beam, recoil alpha particles cross the boundary of the ioniziation volume. These particles are prevented from being recorded by utilizing the partial sensitive volumes associated with individual wires. From the shape of the electric field it follows that the sensitive volume associated with one single collecting wire is confined by the symmetry planes between this wire and the two adjacent collecting wires (cf. fig. 2 of ref. 1). The sensitive volume associated with one of the intermediate wires E, which are stretched midway between the collecting wires (fig. 2), consists of the sensitive volumes associated with the two adjacent collecting wires, since it picks up pulses from discharges on these two wires. From intermediate wires, located near the boundaries of the sensitive chamber volume, anticoincidence pulses were derived, blocking the main output pulses of the chamber. These wires are indicateJ in figs. 2 and 9 by E~ and E'j. The associated sensitive volumes are indicated in fig. 9 by V 1 and V] respectively. Let us suppose that recoil particles with a given energy and orientation have to penetrate at least to the depths t~ and t'1 into the volumes V 1 and V'1 respectively, to produce a blocking pulse. These two extreme track positions are mutually shifted in the

424

c . P . SIKKEMA

/ / , ) . 1 ',,

."

~

r

/ ~r; . . . . .',t . . . . .

i

I

I

I

/

i

I

I

I/

I K

D

,

"/"

,I

_

/"2-7-~[-. • / /

~r

I

I

,,4

I /

2"

-,L . ~

- 4.

~.////,,r/////>,'//~/

z,

....

suitable for determining scattering cross sections by the recoil particle method becaus', of the accurate elimination of wall and end effects.

-I!

i

,

t

I

I

I

I ; D I ml

////

//.

-'.2"- -LL/ ~__Zj~j.

Sd'/"

2 ~2 E 2 ['1 Fig. 9. Definition o f the sensitive volume in the Y-direction w i t h gating pulses f r o m the wires E2 and blocking pulses f r o m the wires E t and E ' I . Partial sensitive volumes associated with these wires are indicated by Vs, Vz and V ' t respectively.

Y-direction by s, + t, + tj - R r, s I being the distance between the volumes V, and V~ and R~ the track component in the Y-direction. Since all particles with tracks located between the extreme positions are recorded, the above expression represents the depth of the sensitive volume measured in the Y-direction. Obviously, this depth depends on the length and orientation of the particle tracks. A well-defined sensitive volume was obtained by a modification of this system. It involved the additional use of gating pulses from a series of intermediate wires, indicated in fig. 9 by E2. These wires are connected in parallel to an amplifier followed by a discriminator and a univibrator. The discriminator bias is adjusted to the same level as that used for the wires E, and E~. The pulses on the wires E 2 are due to electrons created in the volume V2, which partly overlaps V~. Between V 2 and V~ there is a spacing about equal to the maximum range of the recoil particles. With this system gating pulses occur when the track penetrates into V: to a depth t~ or more, and blocking pulses are produced when V~ is penetrated to at least the same depth. Since these two limiting track positions are shifted in the Y-direction by a distance s2, being the distance between the front faces of V2 and V~, the depth of the sensitive volume is s2, independent on R r and ;~. It should be noted that the sensitive volume is shifted with respect to the volume between the front faces of V2 and V~ by a distance R r - t ~ . This shift, which depends on the range and orientation of the recoils, does not affect the detection efficiency when a collimated neutron beam is used. The present system therefore is

3.6. THE ELECTRONIC SYSTEM The electronic system used with the ionization polarimeter is shown schematically in fig. 10. From the pulses on the collecting wires, the D- and D'-pulses are derived by integration and differentiation respectively as discussed in sections 3.1, 3.2 and 3.3. From the insulated parts of the cathode plate F, 15 pulses are obtained which are processed to yield the F-pulse as described in section 3.4. This pulse may be negative or positive. Since the analog-to-digital conversion requires positive pulses, a uniform rectangular positive pulse is added. The start of the pulses is marked by feeding the pulses from the collecting wires to a discriminator which is operated at a low bias. The output pulse from COLE. WIRES

WIRES E2

WIRES E1 E 1'

SECTIONS OF c

T.oDE F

I

l e CHANNI i i:

"6 ~

~

-~-~ v0

40(59

- CHANNEL

MEMORY

Fig. 10. Block diagram o f the electronic equipment

POLARIMETER FOR FAST NEUTRONS the discriminator is delayed by 4.7/~s and, after passing a multiple gate opens linear gates for the D-, D ' - and F-pulses during 1 Its. At this time the D- and F-pulses have reached their m a x i m u m height. The D'-pulse, which is much shorter, is first stretched. On the multiple gate also gating pulses from the wires E2 and blocking pulses from the wires E, and E'1 operate. These pulses serve to define the active chamber volume as described in section 3.5. Small pulses from the collecting wires are rejected by a discriminator which also acts on the multiple gate. After analog-to-digital conversion the pulse heights VD, V~ and t:v are stored in a 4096-channel memory in a three-dimensional mode as shown below in fig. 10.

losing essential information. The 16 channels used for analyzing the D-pulses were adjusted to cover about the upper half of the Vo-spectrum, corresponding to a range of 0 between 0 ° and about 45 ° . Only in this region the scattering asymmetry can be determined. This also is the most useful region for the neutron polarization analysis since here the analyzing power

16 15 14

3.7. THE D - D ' - F CORRELATION

13

The three types of pulses D, D' and F generated with the polarimeter system were discussed in sections 3.2, 3.3 and 3.4 respectively. The pulse heights depend on the direction of the recoil alpha particles according to the following simplified expressions: L'D =

12 11

0 l) D COS 2 0 ,

l

VD ~ VD/IR:I,

425

10

(23)

v v ,-~ (vD)2 Rx/Ry. Here 0 is the scattering angle of the particle. The track components Rx, Ry and R= refer to the coordinate system shown in fig. 2. The lower expression is derived from eq. (22), using the relation ( x , + t - x , ) / d = R,,/R~,. During the polarimeter operation the three-parameter tD-t . . . . D - - I F correlation is recorded. The result is displayed on the oscilloscope screen of the m e m o r y unit as shown in fig. 1 l. For 16 Vo-channels, the t:'D-Vv correlation is shown by an 8 x 32 dot diagram, 8 channels used to analyze tD " being plotted vertically and 32 channels for vv horizontally. Since the pulse height VD fixes the scattering angle 0, single cD-channels correspond to cones of recoil particle tracks with the axis parallel to the neutron beam and half top angle 0. The half-circular or U-shaped t'b-v v correlation patterns may be considered as images of both the lower and upper half of the cones (cf. fig. 2). These images coincide because t •o' only depends on the absolute magnitude of the track c o m p o n e n t R=. For the highest Vo-channels, that is near the upper limit t,g, the patterns shrink together, since here 0 approaches zero. They also reduce a the lower values of vD due to the factors t:D and (Vv)2 occurring in the expressions for v~ and vv respectively. The VD-@--V v correlation is recorded with a minimum n u m b e r of channels for e c o n o m y of m e m o r y space and ease of survey of the result, without

C)

z9

_J bJ 8 Z Z < 7- 7 (D i

r,,6 5

v~I

N(VF) vF

vF

Fig. 11. Correlation between the pulse heights t,•, UZD and v~. To the left: ~/b-vF correlations for individual vD-channels, i.e. for fixed scattering angles 0 of the recoil particles. To the right: VF-spectra summed for the e'l>ehannels exceeding a threshold indicated by the brackets. The two groups represent particles scattered to the left and to the right (¢ = n and 0).

426

c.P.

SIKKEMA

PH~ is largest. Since in the evaluation only a threshold is applied to c~, depending on the VD-channel , a detailed multichannel analysis of this pulse is not required. Only 8 channels were used, combined with a "saturating'" system consisting of a simple circuit for adding all D'-pulses with height exceeding the 8th channel to this channel, h! this way, the cD-r~,-cr correlation could be recorded in a 4096-channel memory. 3.8. DI:IERMINATION OF ~: AS A FUNCTION OF 0 F r o m the VD C'V-CV correlation the scattering asymmetry e is deduced as a function of the scattering angle 0 of the recoil alpha particle. For the various rD-channels 0 is determined as described in section 3.2. and c is derived from the corresponding tD" Zv' correlalion. The determination of 0 involves determining c °, the upper edge o f the cD-spectrum. For this purpose the t'D C~--l'~, correlation is not adequate if a small number of channels is used to analyze the rD-pulse. Therefore in a separate run ~e analyzed z:p simultaneously with the

16-channel analog-to-digital converter used for the VD-@--VV correlation and a 256-channel A D C , and recorded the correlation between both analyzers. In this way, the position of the 16 channels is determined in the 256-channel spectrum. In this spectrum c ° and the standard deviation a c are determined by the method described in section 3.2. A typical example was shown in fig. 4. For the 16 rD-channels the values of 0 are then deduced by applying the modified form of eq. (13)given at the end of section 3.2. To deduce ~; from the zo-t " 'v correlations, a threshold is set on l "D in such a way that the W-spectra summed for the channels above the threshold show two welldefined groups. These groups represent the recoil particles scattered to the left and to the right in two equal azimuthal intervals selected by the @-threshold (cf. section 3. I). Hence, ~: may be determined according to eq. (7), inserting for L and R the numbers of pulses in the two groups. The value of (5 is obtained by applying eq. (16). Fig. 11 shows typical examples of

9

12

-

7

J i

[: !I

1000 _1

Ld Z Z I U

500

W a-

.

I

l

I

uO W uO

¼

3

-2

o_ m

©

2000

Fr

ii

w co z

1OO0

\

% PULSE

HEIGHT

O 10 v F ( C H A N N E L NO.)

20

30

Fig. 12. Histograms of the rv-di~tributiOns sho',~n in fig. 11 (full lines), l)ashcd lines: corresponding distributions recorded vdth reversed neutron polarization. The ,'l~-channel numbers are indicated on the diagrams. The spectra '~ere cut at the arrows in the evaluation procedure described in section 3.8.

POLARIMETER

FOR FAST N E U T R O N S

or-spectra obtained in the above-mentioned way. These spectra are given more quantitatively by the histograms in fig. 12. The histograms show that L and R cannot be unambiguously determined, since some pulses are recorded between the peaks. The origin of these pulses has not been clarified. The spectra were obtained by irradiating the chamber with neutrons from the d-d-reaction as described in the next section. fhey have already been corrected for neutrons originating in the target backing and for scattered neutrons penetrating the shielding, by performing separate runs with a blank target and with a normal target with closed collimator, respectively. One could think of a contribution of neutrons deviating in energy and direction by scattering at the inside of the collimator, which cannot be measured separately. The presence of intermediate pulses necessitates the application of a cut-off in determining the numbers of pulses in the peaks. For the examples of fig. 12 the cut-off is indicated by arrows. This implies a possible loss of genuine pulses and inclusion of false pulses. These effects may be taken into account by expressing the numbers of pulses in the two peaks as:

Nl

= fi

R+nt,

N2 = f 2 L + i12 .

(24)

Here R and L are the true numbers of particles scattered in the selected solid angles. The loss of true events is accounted for by the factors J'~ and f2, and n 1 and rt 2 represent contributions of false pulses which are assumed to be proportional to the neutron flux only. To minimize the errors in 8, we also took runs with reversed polarization. The numbers of pulses counted in the same groups of channels during a run with reversed polarization may be expressed as N', = ~(J'l

L+nl),

N2 = 0{(f2 R_]_H2),

(25)

:~ being the ratio of the neutron flux in the "reversed" run to that in the " n o r m a l " run. The asymmetry e is calculated from: [ 1 - S \ <5 e =[=, , (26) \ 1 + 5 7 sin c5 with

S =(N1N2~ ~.

\sv; sv~) If we assume that for N1, N . , N[ and N~ eqs. (24) and '25) are valid,f~ and f2 being nearly unity and n~ andn2 mall as compared to L and R, the relative error in

427

obtained by the above procedure is approximately equal to d~,/e = - 0 1 1 +n2)/(L+R). The negative sign implies that the absolute magnitude of e is always lowered by the background contributions #71 and t/2. No direct means to determine the ratio (nl 4-112)/(L4- R) is available, although the histograms in fig. 12 suggest that it should not exceed a few percent for the higher cD-channels. The %-v~-v v correlation, shown as an example in fig. II, was obtained by irradiating the polarimeter with neutrons from the reaction 2H(d,n)3He at a deuteron bombarding energy of 400keV and a neutron emission angle of 47 ° . The experimental arrangement is shown by the photograph in fig. 13. The polarimeter chamber with neutron collimator and shielding is mounted on a turntable which can be rotated around a vertical axis intersecting the neutron source. To reverse the neutron polarization the polarimeter set-up was moved to the opposite side of the deuteron beam, which was directed horizontally. The angle between the neutron collimator and the beam was again adjusted at 4 7 . Distributions of cv obtained with inversed polarization for the same cD-channels and r~-threshold are shown in fig. 12 by the dashed histograms. From the spectra corresponding to " n o r m a l " and "inversed" polarization, asymmetries were determined according to the above procedure for I1 CD-channels corresponding to 11 scattering angles 0. The result is shown in fig. 14. Here instead of 0, the scattering angle of the recoil alpha particle in the laboratory system, 0,, is used: the scattering angle of the neutron in the centre-of-mass system, which is related to 0 by 0 , , = 7 r - 2 0 or cos 0,, = l - 2 cos 20. The values of ~ have been corrected for the spread in 0 due to the finite CD-channel width and the fluctuations in 0 characterized by the standard deviation % (section 3.2) after fitting an analytical function to the data as described in the next section. 3.9. NEUTRON POLARIZATION AND SCATTERING PHASE SHIFTS

From the asymmetry ~ measured as a function of the scattering angle 0, the neutron polarization and the n-:~ scattering phase shifts may be deduced as indicated in section 2. We shall here describe the result for the example shown in fig. 14, which was obtained with neutrons from the d-d reaction at an incident deuteron energy of 400 keV and a neutron emission angle of 47 '~ in the laboratory system. The neutron energy was about 3 MeV. The measured values of e were fitted with a function Pn Plte(COS On, ilk), Pn being the neutron

428

c.P. SIKKEMA

Fig. 13, Experimental arrangement for measuring the polarization o f neutrons from the reaction ~H(d,n)3He. (1). beam tube from the Cockcroft-Walton accelerator, (2) target, (3) polarimeter chamber, (4, 5) housing for connections and amplifiers, (6, 7) lead and paraffin shielding, partly removed, (8) neutron collimator hole.

-0.2

E d = 3 3 0 - 4 0 0 keV

-0.2

On=47 ° Pn=-0166z0.005

-OJ

- o."

Fi"

>.re" I-" I..#

" '

o

0

/ .

/ / -.

J

*01

.0.1

o:5

i

o COS

-05

-1

On

Fig. 14. Asymmetries in n-c~ scattering for various neutron scattering angles On (centre-of-mass). Neutrons from the d - d reaction at Ea = 330~t00keV and neutron emission angle On = 47 °. Dashed line: asymmetry calculated with phase shifts o f Hoop and Barschall and the indicated value o f the neutron polarization Pn.

polarization and PHe the analyzing power of helium, expressed as a function of 0,,, the scattering angle of the neutron in the centre-of-mass system, and the scattering phase shifts 5k. At the present neutron energy only the s- and p-wave phase shifts 50, ~- and g + are important. The analysis was performed in two different ways. Firstly, fixed values of the phase shifts were used, P, being the only adjustable parameter. The phase shifts were obtained by interpolating the values given by Hoop and Barschall3), for our neutron energy of 3.03 MeV. These phase shifts are deduced from measured differential and total n - H e cross sections. Secondly, the three phase shifts were used as variables as well as P, in a search program to fit the measured asymmetries together with the value of the total cross section crx = 2.77 _+0.06 b taken from reference 24). The results of both methods are given in table 1. The function P. PHcobtained ~ ith the first method is represented by the dashed line in fig. 14. It appears that with the H o o p and Barschall phase shifts a quite satisfactory fit to the measured asymmetries is attained, which is indi-

POLARIMETER

429

FOR FAST NEUTRONS TABLE 1

P o l a r i z a t i o n o f n e u t r o n s f r o m the d + d r e a c t i o n for Eo = 365 k e V a n d On = 47 ° a n d n - H e s c a t t e r i n g p h a s e shifts for E n = 3.03 M e V .

H o o p a n d B a r s c h a l l p h a s e shifts P h a s e shifts frona p r e s e n t a n a l y s i s

6o

67

6+

P~

X2

137.9 137.4-'

25.2: 24.1"

122.0 ° 122.2'

-0.1664+0.0045 -0.1683 t0.0045

12.4 12.0

cated by fig. 14 and the value X2= 12.4 obtained in fitting 11 data points with one free parameter. This fit is not significantly improved by the procedure with variable phase shifts, uhich yields nearly the same parameter values. It may be concluded that the measured asymmetries are in good agreement with the properties of n - H e scattering previously established by cross section measurements. The values of P, also agree well with other recent measurements carried out for about the same deuteron energy and neutron emission angle. This appears from the survey given in table 2. The diffusion cloud chamber method used by Mulder should essentially be free of systematic errors. Because of the agreement of the present result with that obtained by this method, we may assume that the systematic error in our result does not exceed the statistical error in the cloud chamber measurement. This, however, does not necessarily include a possible error caused by neutrons scattered from the neutron collimator, since a collimator is also used in the cloud chamber experiment, as well as in all

other experiments referred to in the table except that of Levintov et al. The polarimeter is being used at present to measure the polarization of d-d neutrons at other deuteron energies. The results are to be published in due timeZS). 3.10.

G E O M E T R I C A L AND OPERATIONAL DATA OF THE P R O P O R T I O N A L CHAMBER

Referring to fig. 2, the chamber dimensions were as follows: Ionization volume between the electrodes A and C: 90 m m along the X-axis, 155 m m along the Y-axis and 85 mm along the Z-axis. Gas amplification volume between the electrodes C and F: height 20 mm. Number of collecting wires: 15, 10 m m apart. Thickness of all wires 0.1 mm. Structure of the electrode F: insulated rectangles 11 x 9 mmZ; period in the X-direction 33 mm, in the Y-direction 50 mm. Total number of rectangles 9 x 15 = 135. For these dimensions, the maximum range of the recoil alpha particles should be about 4 cm. For

TABLE 2 P o l a r i z a t i o n o f d - d n e u t r o n s m e a s u r e d for E a ~ 350 k e V a n d On ~ 47 °. Authors, year

Ea (keY)

On (lab)

M u l d e r , 1968 15)

400 a 375 b 350 ~ 360 a 380 a 350 )'

49 ° 47 ° 45.8 ° 47 ° 47 ° 46,5 °

D a v i e a n d G a l l o w a y , 1973 6) P r e s e n t exp., 1973

385 )~ 365 b

47 ° 47 °

L e v i n t o v et al., 1957 25) P a s m a , 1958 4) E o e r s m a et al., 1963 26) B e h o f et al., 1968 27)

Pn

- 0.105 + 0.020 -0.086±0.011 -0.127 ±0.006 -0.170±0.010 -0.166+0.011 -0.169+0.014 --0.1674-0.012 e -0.166+0.011 -0.166+0.005

Method d

2 1 1 1 1 3 1 4

a M a x i m u m d e u t e r o n e n e r g y o n t h i c k target. b M e a n d e u t e r o n e n e r g y in t h i n target. c R e s u l t s r e c a l c u l a t e d w i t h p h a s e shifts o f H o o p a n d B a r s c h a l l . M e t h o d 1: N e u t r o n - r e c o i l c o i n c i d e n c e m e t h o d ; h e l i u m gas s c i n t i l l a t o r . M e t h o d 2: R e c o i l p a r t i c l e m e t h o d ; p r o p o r t i o n a l c o u n t e r t u b e c o l l i m a t i o n . M e t h o d 3: R e c o i l p a r t i c l e m e t h o d ; d i f f u s i o n c l o u d c h a m b e r . M e t h o d 4: R e c o i l p a r t i c l e m e t h o d ; m u l t i p l e w i r e proportional chamber.

430

c . P . SIKKEMA

neutrons from the d-d reaction with an energy of about 3 MeV a gas filling of 90 cm Hg of helium and 2 cm of CO2 was used. The voltage applied to the ionization volume was about 800 V and the electron drift velocity about 6 mrn/l~s. The maximum of the particle track component R, in the direction of the electric field is about 20 ram, the maximum pulse rise time being about 3 ps. With the above gas tilling the gas amplification system was operated at about 1000 V, applied between the collecting wires and the surrounding electrodes. Since the maximum alpha particle range is approximately fixed by the chamber dimensions, the gas pressure depends on the neutron energy. At 14 MeV for instance, the helium pressure should be increased to about 12 atm, or a gas with higher stopping power should be added. With the present chamber dimensions the diameter of the neutron beam should not exceed 40 mm.

4. Conclusion With the present fast neutron polarimeter, based on the n-ct scattering process, statistical and systematical errors in the determination of the azimuthal scattering asymmetry should be reduced by: 1) Application of the recoil alpha particle method, to avoid background problems associated with the detection of the scattered neutrons (cf. section 1). 2) Electronic solid angle definition for the alpha particles instead of geometrical apertures, to obtain a high efficiency and to avoid geometrical asymmetries. Actually, a good statistical accuracy is obtained, but the systematic error could not be definitely assessed from the instrumental characteristics (cE section 3.8). However, comparison with a cloud chamber measurement did not indicate any appreciable systematic error (section 3.9). It may be concluded that the present method compares favourably with other polarimeter systems. It can be used for a monoenergetic group of neutrons if no other neutrons are present with energies exceeding about half the energy of the main group. This work, carried out at the Laboratorium voor Algemene Natuurkunde of the University of Groningen, is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (F.O.M.) supported by the Netherlands Organization for Pure Scientific Research (Z.W.O.). It could not have been performed without the skillful technical support of

many members of the mechanical and electronical workshops of this laboratory. The experimental arrangement was set up and the data were taken in close cooperation with Mr S.P. Steendam, who also assembled and tested much auxiliary equipment and took care of the Cockcroft--Walton accelerator. The author also is indebted to Mr J. V. Jansen of the University Computing Centre for performing the data fitting procedures described in section 3.9 and to Prof. H. de Waard for his comments on the manuscript.

Appendix The mathematical relation expressed by eqs. (17), (18) and (19) (section 3.4) may be extended to the following proposition: If a~ = p t c o s x ,

+ql, bl = Pl COS (X 1 -~0{) 2f_ ql, cl = Pt cos (xl +fl) + ql, and

(27) a2 = P2 c o s x 2

+q2,

b2 = P2 c o s ( x 2 + ~ ) + q 2 , C2 = P2 COS(X 2 + f l ) + q 2 ,

Pl, P2, ql and q2 being arbitrary real quantities, the following relation holds: a I b 2 -a2b

1 +b~ c 2 -b2c

I +cla2 -cza

l =

= 4 p i p 2 sin ½~ sin½fi s i n ½ ( a - f l ) s i n ( x z - x 0 .

(28)

This extension is due to Prof. P.C. Sikkema, Dept. of Mathematics, Technische Hogeschool, Delft, Netherlands. The original relation used in the present work is the special case for :~ = - 2 n and fi = - 4 n, the righthand side ofeq. (28) becoming equal to p i p 2 ( 3 ,,/3)x × s i n ( x z - x l ) . It may be shown that in this case the product sin ½~ sin ½fl sin ½(~-fl) has the maximum absolute value for all values of ce and ft.

References 1) 2) 3) 4) 5)

C. P. Sikkema, Nuc.l. Instr. and Meth. 81 (1970) 189. R. B. Galloway, Nucl. Instr. and Meth. 92 (1971) 537. B. Hoop and H. H. Barschall, Nucl. Phys. 83 (1966) 65. p. j. Pasma, Nucl. Phys. 6 (1958) 141. H. Davie and R. B. Galloway, Nucl. Instr. and Meth. 92 (1971) 547. 0) H. Davie and R. B. Galloway, Nucl. Instr. and Meth. 108 (1973) 581. 7) j. R. Smith and S. T. Thornton, Nucl. Phys. A187 (1972) 433. 8) I. I. Levintov, A. V. Miller and V. N. Shamshev, Zh. Eksp. Teor. Fiz. 32 (1957) 274; Soy. Phys. JETP 5 (1957) 258; Nucl. Phys. 3 (1957) 221. 9) p. S. Ot-Stavnov, Zh. Eksp. Teor. Fiz. 37 (1959) 1815; Sov. Phys. JETP 10 (1960) 1281.

POLARIMETER

FOR FAST N E U T R O N S

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