Experimental apparatus for the study of small angle neutron-proton elastic scattering at intermediate energies

Experimental apparatus for the study of small angle neutron-proton elastic scattering at intermediate energies

Nuclear Instruments and Methods in Physics Research A270 (1988) 419-430 North-Holland, Amsterdam 419 EXPERIMENTAL A P P A R A T U S FOR THE S T U D ...

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Nuclear Instruments and Methods in Physics Research A270 (1988) 419-430 North-Holland, Amsterdam

419

EXPERIMENTAL A P P A R A T U S FOR THE S T U D Y OF S M A L L ANGLE N E U T R O N - P R O T O N ELASTIC SCATrERING AT INTERMEDIATE ENERGIES

A.A. VOROBYOV, G.A. KOROLEV, and E.M. SPIRIDENKOV

A.V. D O B R O V O L S K Y ,

A.V. KHANZADEEV,

G.E. PETROV

Leningrad Nuclear Physics Institute, Gatchina, Leningrad district, 188350, USSR

Y. T E R R I E N ,

J.C. L U G O L , J. S A U D I N O S ,

B.H. SILVERMAN

a n d F. W E L L E R S

Service de Physique Nucl$aire, Moyenne Energie, CEN Saclay, 91191 Gif-sur-Yvette Cedex, France Received 25 January 1988

An experimental setup for measurements of absolute differential cross sections and analyzing powers in small angle elastic np scattering is described. The main part of the apparatus consists of a multielectrode ionization chamber IKAR filled with methane, serving as both a gas target and a recoil detector. The apparatus was used in measurements with a polarized neutron beam from the Saturne synchrotron (Saclay, France) in the energy range from 378 to 1135 MeV.

1. Introduction One of the main subjects in physics at intermediate energies is the study of the two nucleon system. In particular the search for dibaryon resonances is a topic of great interest. Phase shift analyses (PSA) of data for pp elastic scattering [1-3] indicate the possible existence of resonances in the ID2, 3F3, and 3P2 partial waves, although the evidence is by no means conclusive. For the isospin I = 0 channel, the situation is even more unclear because of a lack of data for the n + p process, especially at small transfers (forward scattering). The rarity of good monoenergetic neutron beams at these energies, and the experimental difficulties of the detection of neutral particles, make such experiments especially difficult. A detailed study of np elastic scattering at small transfers has been performed in the energy range 100-400 GeV [4]. At intermediate energies, only one experiment at small t was performed until recently, for the measurement of absolute differential cross sections at 790 MeV [5]. In this article, we present an experimental setup which was used to measure the asymmetry A00n0 and absolute differential cross section d o / d t in np elastic scattering at small angles with a polarized neutron beam of 378-1135 MeV produced at the Saturne synchrotron at Saclay. This information is needed for PSA of the n u c l e o n - n u c l e o n system at intermediate energies. The 0168-9002/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

results will also help provide the amplitudes used in multiple scattering calculations of nucleon-nucleus scattering. The main part of the experimental apparatus, the I K A R recoil detector, was developed at the Leningrad Nuclear Physics Institute (LNPI). Different versions of I K A R have already been used and successfully in a series of measurements of small angle elastic scattering of charged hadrons at Gatchina [6], Serpukhov [7], and C E R N [8]. In these experiments, I K A R was used together with an auxilliary spectrometer of fast scattered particles, which made it possible to eliminate the unscattered beam particles and provided an external trigger for I K A R . The correlation between the recoil energy and the forward scattering angle was also very helpful for the elimination of the background events. For the experiment using a neutron beam, described here, it would have been difficult to provide a reliable external trigger. To do so would have required a large neutron detector with a very uniform efficiency, or one for which the variation of detection efficiency with position was known very accurately. We decided instead to use I K A R without an external trigger. This required more rapid operation of I K A R , as well as a more reliable identification of elastic events using information only from I K A R . With these objectives, a new version of I K A R was constructed, having greater complexity and using methane instead of hydrogen. The new detector I K A R is described in detail in this article.

A.A. Vorobyov et al, / Small angle np elastic scattering at intermediate energies

420

O u r results for n p elastic scattering have already been p u b l i s h e d in two letters [9,10] a n d will soon be p u b lished in a more complete form [11].

2. Experimental setup and neutron beam T h e experiment was performed using a n e u t r o n b e a m at the Saturne s y n c h r o t r o n in Saclay, France. F o r the first series of m e a s u r e m e n t s a n unpolarized b e a m was used a n d absolute differential cross sections for free n p elastic scattering at forward angles were measured. In later m e a s u r e m e n t s a polarized b e a m was used a n d the a s y m m e t r y was m e a s u r e d as well. A schematic view of the b e a m line a n d experimental setup are s h o w n in fig. 1. A collimated n e u t r o n b e a m was incident o n the I K A R ionization c h a m b e r filled with pure C H 4 at a pressure of 14.5 atm. The gas in I K A R served as b o t h the target a n d as ionizing m e d i u m for recoil protons. C h a r g e d particles in the incident b e a m were vetoed b y the scintillators A1 a n d A2. F o r m e a s u r e m e n t s with a polarized beam, the forward scattered n e u t r o n s were

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Fig. 1. Schematic of the beam line and experimental layout (not to scale).

detected in two l e f t - r i g h t symmetrical sets of scintillators. Each set was c o m p o s e d of two counters 26 X 80 x 80 cm 3 a n d 2 6 x 6 0 x 6 0 cm 3 in size. The detection efficiency for scattered n e u t r o n s which hit the scintillators was = 70%. T h e relative intensity of the n e u t r o n b e a m was m o n i t o r e d with a 10 cm thick c a r b o n target viewed b y two scintillator telescopes placed at 5 o to the left a n d right of the beam. Each telescope was composed of three counters, with d i m e n s i o n s 36 x 36 x 5 m m 3, 7 0 x 7 0 x 1 0 m m 3, a n d 1 0 0 x l 0 0 x l 0 m m 3, placed at distances of 800, 1000, a n d 1200 m m from the center of the c a r b o n target. T h e c o u n t e r pulse heights for three-fold coincidences were recorded, a n d the high voltages a n d thresholds were chosen to place the peaks well above threshold. A l t h o u g h n o o t h e r special precautions were t a k e n to ensure counter stability, the calibration of the m o n i t o r was identical for two d a t a runs taken one year apart. This suggests t h a t a similar monitor could b e used w i t h o u t calibration to provide an absolute n e u t r o n b e a m n o r m a l i z a t i o n (see section 7). T h e polarized n e u t r o n b e a m was p r o d u c e d b y breakup of a vector polarized d e u t r o n b e a m o n a 20 cm beryllium target. T h e p r o d u c t i o n of this type of m o n o energetic n e u t r o n b e a m is discussed in detail in [12]. The m e a n n e u t r o n b e a m energy was t a k e n to b e one-half the d e u t e r o n energy after the m e a n energy loss in the beryllium target. The energy w i d t h of the n e u t r o n b e a m arises mainly from the F e r m i m o m e n t u m of the p r o t o n b o u n d inside the deuteron, a n d was m u c h greater t h a n the u n c e r t a i n t y in the m e a n b e a m energy. T h e w i d t h d e p e n d e d o n energy a n d varied from a b o u t 60 to 120 MeV, F W H M , for energies between 378 a n d 1135 MeV, respectively. N o n - i n t e r a c t i n g deuterons in the b e a m a n d o t h e r charged particles p r o d u c e d in the beryllium target were removed from the n e u t r o n b e a m with a sweeping magnet. The size of the n e u t r o n b e a m was d e t e r m i n e d b y two steel collimators. T h e first h a d a d i a m e t e r of 25 m m a n d a length of 2 m, starting 5.65 m d o w n s t r e a m of the Be target; the second h a d a d i a m e t e r of 15 mm, a length of 4.5 m, a n d b e g a n 9.35 m d o w n s t r e a m of the target. T h e center of the active volume of I K A R was 14.87 m d o w n s t r e a m of the Be target. A t this position the b e a m spot was s h a r p edged with a d i a m e t e r of a b o u t 16 m m a n d a n angular divergence of a b o u t + 0.8 mrad. T h e extracted d e u t e r o n b e a m from Saturne was m o n i t o r e d with a secondary emission c h a m b e r . T h e absolute normalization of this c h a m b e r was calibrated to - 2 0 % via the use of 12C(d,x)llc activation as explained in [12]. T h e absolute calibration of the neutron b e a m monitor, p r o v i d i n g a n overall n o r m a l i z a t i o n u n c e r t a i n t y for n p elastic differential cross sections of 4 - 7 % , was done b y c o m p a r i n g the differential cross sections of n - a H e elastic scattering, m e a s u r e d with the same b e a m conditions, with those for the nuclear part of p - 4 H e . T h e validity of this c o m p a r i s o n was dis-

421

A.A. Vorobyoo et al. / Small angle np elastic scattering at intermediate energies

cussed in [13]. More details about the absolute calibration are given in section 7. The intensity of the neutron beam was about 105/cycle (1 cycle = 1.3-3.6 s depending on energy). With the polarized beam the spin direction was flipped (up or down) every cycle. During the experiment the polarization of the deuteron beam was continuously monitored with a polarimeter measuring pp quasi-elastic scattering at 17 °(lab). In using this technique we assume that the polarization of the proton bound in the deuteron before break-up is equal to that of the neutron at 0 ° after break-up. This has been shown to be true at the 2% level by integrating over the appropriate regions of phase space and deuteron wave function [14]. Our measured value for the polarization of the neutron beam is 0.59 + 0.02.

3. The recoil detector IKAR I K A R served as a target for the incident neutron beam. At the same time recoil protons were detected in I K A R . Elastic scattering events are selected with information provided by I K A R about the recoil energy TR, the energy loss A E in each of several regions, and the recoil angle 8 R. I K A R is an ionization chamber with a grounded grid operating with electron collection. The principles of operation as a recoil detector are discussed in [15,16]. In previous experiments I K A R was filled with hydrogen as a proton target [6,8]. For the present work the chamber was filled with methane (CH4) to increase the counting

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rate and the speed of operation: for a given pressure there are twice as many protons with C H 4 as with H2, and the drift speed in C H 4 is several times nigher (fig. 2). A further advantage is that with C H 4 the range of recoil protons is shorter, allowing measurements to be made to higher T R. The disadvantage of C H 4 is the background produced by scattering from carbon. The construction of I K A R as used in this experiment is shown in fig. 3. I K A R was filled with C H 4 at 14.5 atm. Two spherical steel windows were used for entrance (thickness 0.27 mm, radius 40 mm) and exit (thickness 1.2 mm, radius 100 mm) of the beam. Inside I K A R were a cathode, a grounded grid, and five concentric anodes, all perpendicular to the beam direction. The outer radii of the anodes were 10, 20, 100, 210 and 250 mm. The g r i d - c a t h o d e distance was (149.7 ___0.1) mm. A precise determination of this distance was important for determining the effective target thickness. The g r i d - a n o d e distance was 20 mm. Ring electrodes connected to a resistance chain were put in the g r i d - c a t h o d e space, as was an annular electrode around the cathode, to provide a more uniform electric field in the active volume. Two guard electrodes were set outside the a n o d e - c a t h o d e space to prevent detection of the ionization produced outside the active volume. The central parts of the electrodes were made of 25 /~m A1 foil to reduce the thickness of material in the beam. To reduce electronegative impurities, methane of very high purity (N55 from Air Liquide) was used. Before filling, I K A R was pumped while being heated for several days.

4. Operation of IKAR

torr

Fig. 2. Electron drift velocity W in methane as a function of c / P (c = electric field, P = gas pressure). Experimental data

were taken from [17] for CH 4 and from [18] for H 2.

Neutrons incident on I K A R scatter from near the axis of the chamber. For events of interest, in which the neutron is scattered forward at small angle, the recoil

422

.4..4. Vorobyov et aL / Small angle np elastic scattering at intermediate energies

p r o t o n track is almost parallel to the a n o d e plane. As the p r o t o n ionizes the gas along its track a signal appears on the cathode b y induction as soon as electrons begin to drift toward the anodes. The a n o d e signals, however, a p p e a r only after electrons have crossed the grid. The drift time from the cathode to the anodes is a b o u t 8/zs. The amplitudes of the a n o d e signals d e p e n d on the recoil energy T R. In fig. 4 is shown the energy loss in the volume corresponding to each a n o d e as a function of T R. The calculation was m a d e for the working pressure of I K A R , assuming a n infinitely n a r r o w b e a m perfectly aligned along the c h a m b e r axis. Values for range a n d energy loss in C H 4 were t a k e n from [19]. Relations between the a n o d e amplitudes can be used to help separate elastic events. F o r recoil p r o t o n s that stop in the working volume, the recoil energy Tg is j u s t equal to the sum S of the energy loss in the four volumes A, B, C, a n d D. F o r p r o t o n s for which the projection of the track to the a n o d e p l a n e is greater t h a n the radius of a n o d e D ( T R > 15 MeV), T R can be determined from S which is now the energy loss A E in the active volume. This corresponds to region 3 in fig. 4. The time difference between the arrival of signals on the anodes a n d cathode determines the Z R position (along the b e a m axis) of the interaction vertex in the g r i d - c a t h o d e volume. Suitable software windows are placed on Z R to reject b a c k r o u n d arising from b e a m interaction with the electrodes, a n d to eliminate tracks which are close to the grid (for which the signal induced on the cathode is too small) or the cathode (the recoil track can pass t h r o u g h the cathode a n d leave the active volume). A n o t h e r source of b a c k g r o u n d is interaction of the b e a m with c a r b o n in C H 4. As the range of recoil c a r b o n nuclei from elastic n - C scattering is very short, AE, MeV 16 14

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90 OR,deg

Fig. 5. The relation between the energy TR and the angle OR of recoil protons (OR is determined relative to the chamber axis). The shaded area corresponds to inelastic reactions. The beam energy is 1000 MeV. we selected with the trigger electronics only events for which the C a n o d e furnished a signal. I n f o r m a t i o n a b o u t the recoil angle was used for selection of n p elastic scattering events. This m e a s u r e m e n t of recoil angle came from the difference in time of arrival of the a n o d e signals. In fig. 5 we show the kinematical relation between p r o t o n recoil energy T R a n d angle OR for n + p processes at a n incident energy of 1000 MeV. T h e shaded region corresponds to inelastic interactions. F o r T R < 40 MeV, elastic scattering can be easily separated using the recoil angle. The most difficult p r o b l e m is separation of quasi-elastic scattering from p r o t o n s in the c a r b o n in C H 4. T h e distribution of recoil angles for a given recoil energy is wider for quasi-elastic scattering t h a n for elastic scattering because of F e r m i m o t i o n of the b o u n d protons. In the d a t a analysis this quasi-elastic b a c k g r o u n d was subtracted from the m a i n peak for each data point. D u r i n g d a t a taking, the c a t h o d e signal VK was required in the trigger, a n d the scintillators A1 a n d A2 were used to veto charged particles in the beam. As m e n t i o n e d above, we required a signal from a n o d e C in order to eliminate heavy particles with very short range. I n addition, at least one of the anodes A, B, or D was required. The overall trigger was thus: VK-A1 - A 2 . V¢. ( VA V VB V VD).

6

70

(1)

F o r each event, we recorded o n tape the amplitudes of all five anodes a n d of the cathode, a n d the analog sum Vs = VA + VB + Vc + VD. The time of arrival of each a n o d e signal relative to the c a t h o d e was recorded. F o r runs with the polarized beam, for which the n e u t r o n detectors were present, we also recorded the signal time relative to the c a t h o d e for each of the four blocks. The time distribution of the I K A R - n e u t r o n coincidence h a d a f w h m of a b o u t 300 ns, which is consistent with the time resolution of I K A R . B a c k g r o u n d from r a n d o m coincidences was less t h a n 2%.

423

A.A. Vorobyoo et al. / Small angle np elastic scattering at intermediate energies

A c o m p u t e r controlled generator system was used to simulate physical events b y sending signals to the I K A R electronics. T h e signal amplitudes a n d arrival times could b e varied as desired. A m p l i t u d e s were set to b e consistent with the curves in fig. 4. This generator system p e r m i t t e d frequent checks of the stability a n d linearity of the electronics. G e n e r a t o r events were also used during off-line d a t a analysis to calculate corrections for inefficiencies arising from the analysis procedure (see section 6).

700 60O

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5. Calibration experiment using a proton beam 100 T h e operation of I K A R with H2, D2, a n d 4He gases has b e e n extensively studied in previous experiments [6-8,16,20]. T h e current work with C H 4 required additional investigations. A t the L N P I synchrocyclotron a n auxilliary calibration experiment was p e r f o r m e d with a 991 MeV p r o t o n beam. T h e aim was to clarify the conditions a n d possibilities of using I K A R with CH4, to choose optimal operating conditions, a n d to p e r f o r m a n energy calibration. The version of I K A R used was s o m e w h a t different from the one used in the n p experiment. Only three anodes were present, with external radii of 100, 210, a n d 250 m m (the same as anodes C, D, a n d E of the above described version). In m e a s u r e m e n t s of d o / d t with I K A R the value of the f o u r - m o m e n t u m transfer t is d e t e r m i n e d from the recoil energy using the relation: (2)

It[ = 2 m T R,

where m is the recoil (proton) mass. The aim of the energy calibration is to d e t e r m i n e the relationship between T R a n d the a m p l i t u d e sum Vs m e a s u r e d with IKAR. M e a s u r e m e n t s with the p r o t o n b e a m were p e r f o r m e d for three different gas pressures a n d several different electric fields. A system of multiwire p r o p o r t i o n a l c h a m b e r s was used to measure the angle 0 s of the forward scattered proton. The recoil energy T R is related to 0 s b y the formula: T. =

To(Zm + To) sin 2 0 s

,

(3)

2 m + TO sin 2 0 s where To is the i n c i d e n t p r o t o n energy. ( F o r m u l a 3 is valid for elastic scattering where the b e a m a n d target particles have the same mass m.) F o r selected p p elastic scattering events, T R was d e t e r m i n e d from the measured 0 s. T h e data was b i n n e d into small intervals of Vs, a n d for each one the m e a n energy T R was calculated. (The w i d t h A T R was a b o u t 60 keV.) A fit was then m a d e to give a f u n c t i o n f such that T R = f ( V s ) . F o r events with T R _< 15 M e V (for which the p r o t o n

0

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Fig. 6. Experimental relation between the anode amplitude Vs and recoil energy TR (in the region TR < 15 MeV) as measured in the pp calibration experiment. The recoil energy was calculated from the measured scattering angle 0s. Experimental points are fitted with formula [4]. This leads to the value E 0 = 400 keV. Beam energy TO= 991 MeV; methane pressure in the chamber P =14.48 atm at temperature 18.5 °. The electric field is c = 1.5 kV/cm.

stops within the active volume defined b y anodes A, B, C, a n d D) we fit the data with the form (see fig. 6): (4)

T R = kV s + Eo,

where k a n d E o are parameters that d e p e n d o n the type of gas, pressure, a n d electric field. T h e value of k also depends o n the gain of the amplifiers. For events with T R > 15 MeV (for which the p r o t o n s do not stop in the active volume) we used the formula TR = ao + a 1 e x p ( -

fllkVs) + a 2 exp(-fl2kVs),

(5)

where k is the same as in eq. (4), a n d a0, a l, a2, fix, a n d r2 were d e t e r m i n e d by a least squares fit - see fig. 7. In the calibration experiment, we d e t e r m i n e d the value of the " b o u n d a r y energy" T c D for which the projection of the track to the a n o d e p l a n e lies at the b o u n d a r y between anodes C a n d D. In the n p experiment, I K A R was operated at almost identical conditions, a n d the value of TRcD m e a s u r e d in the calibration experiment could b e used as a reference point. T h e value of T c ° can also be calculated using energy-range curves. This was d o n e for the three pressures of the calibration experiment with the range curves of [19]. The calculated a n d m e a s u r e d values agree to within 1%. We were also able to p e r f o r m a preliminary, less precise calibration using a particles from Z41Am sources

424

A.,4. Vorobyov et al. / Small angle np elastic scattering at intermediate energies

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Fig. 7. The same as in fig. 6 but for TR > 15 MeV, i.e. for recoil protons which leave the working volume. Experimental points are approximated with formula (5). The best fit .parameters are:a 0 =14.505 MeV, cq = 264.76 MeV, a 2 = 79.327 MeV, fll = 1.0384 MeV -1, f12 = 0.32731 MeV -1.

(E~ = 5.486 MeV) placed inside I K A R . This was essential for p r e p a r a t i o n of the experiment a n d for on-line checks. Complications arise, however, because p r o t o n s a n d a ' s of the same energy produce different a m o u n t s of ionization in methane. They have very different ranges a n d recombination. T h e d e p e n d e n c e of a-source amplitude as a function of electric field e, for several different pressures, is shown in fig. 8. The decrease in amplitude at low fields a n d high pressures is due to

U/Umax 2atm

10 09

recombination. A t a pressure of 2 a t m r e c o m b i n a t i o n is practically absent, therefore at this pressure a preliminary calibration from the a-sources c a n be performed. Analysis of our p p elastic scattering d a t a has s h o w n that r e c o m b i n a t i o n for p r o t o n s is m u c h less t h a n for a ' s (only 4% at 14.48 a t m a n d ( = 1.5 k V / c m , while it is a b o u t 45% for a ' s u n d e r the same conditions). As a result of the calibration experiment we chose the operating conditions with m e t h a n e to be used for the np m e a s u r e m e n t s (14.48 a t m at a t e m p e r a t u r e at 18.5 ° C, giving a p r o t o n density of 1.499 × 102t c m - 3 ) . The d e p e n d e n c e of a n o d e amplitudes o n Tg was then determined for these conditions. T h e density of target p r o t o n s was consistent to within 0.2% for the three series of useful np m e a s u r e m e n t s ( J a n u a r y 1984, F e b r u a r y a n d D e c e m b e r 1985). As m e n t i o n e d a b o v e the energy-range d e p e n d e n c e of J a n n i [19] was tested a n d verified to within 1%. This d e p e n d e n c e was then used to d e t e r m i n e the o p e r a t i o n of the generator test system a n d to fix the amplifier gains. To d e m o n s t r a t e the possibility of using I K A R with methane, we d e t e r m i n e d d o / d t for the p p elastic scattering events at the energy of 991 M e V used in the calibration experiment. Correlations between I K A R a n d the M W P C system were used to select good events. Our cross sections o b t a i n e d in this way agree well with those o b t a i n e d using I K A R filled with h y d r o g e n [6]. To test the principle of using I K A R without a n external trigger, d o / d t was also d e t e r m i n e d in a separate analysis using I K A R alone. The procedure discussed in the following section was used to select good events. It should b e n o t e d that for this d a t a we can only use events for which the p r o t o n stopped in the region of a n o d e D (10 ~ T R _< 15 MeV, region 2 in fig. 4) because this version of I K A R h a d only three anodes instead of five. T h e cross sections o b t a i n e d in this way agree well with the other results, showing that quasi-elastic b a c k g r o u n d can be correctly d e t e r m i n e d with this method.

0.8

6. Analysis of np data 0.7

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0.2

The procedure used to d e t e r m i n e absolute differencross sections consisted of the following steps: Selection of elastic scattering events. Calibration of the [t[-scale. D e t e r m i n a t i o n of the n u m b e r of target p r o t o n s N TA b s o l u t e normalization of the relative b e a m monitor using d a t a from the n4He measurements. Using ampfitudes Vc a n d VD we d e t e r m i n e d for each event the region (1, 2, or 3 in fig. 4) to which it belonged. The a m p l i t u d e s u m Vs m u s t b e corrected for a b s o r p t i o n of electrons b y electronegative impurities in the gas [21]. The p r o b a b i l i t y of electron loss is p r o p o r tional to the drift length in the gas, so the m e a s u r e d

tial (1) (2) (3) (4)

/ i 1

i

i

2

3 ~.

kV/cm

Fig. 8. The ionization produced by a particles in methane as a function of the electric field and gas pressure.

A.A. Vorobyoo et al. / Small angle np elastic scattering at intermediate energies

425

c)

i, a) t I, IF i, j,



# dr

i,

II ir 6.

-.~...--ll,~-, ! . . .

.i

b)

d) ,%-,.

>~

I ~vc

--%

Fig. 9. Bidimensional correlations of anode signals: (a) Vo versus V¢ without event selection, (b) same as (a) after selection of good events, (c) VD versus Vc for generator signals which simulate the physical events, (d) Vs versus Vc after selection of good events.

amplitude depends on the coordinate Z R of the position of the track in the grid-cathode space. As already mentioned, Z R was determined using the arrival time on the C anode ~c relative to the cathode time ~K- The maximum amplitude loss due to absorption was determined by the difference of the peak positions for tracks produced by a-sources placed on the grid and on the cathode. Only c~ tracks almost parallel to the electrodes were selected. The absorption correction made for each event takes into account both the position of the track vertex in the g r i d - c a t h o d e space and the observed variation of gas purity with time. To help select elastic scattering events, windows were placed on bidimensional correlations between amplitudes V B / V c , V c / V D, V c / V s, and V D / V s. Examples are shown in fig. 9. Figs. 9(a) and (b) show the correlation V c / V o without and with the windows. The positions of the generator signals that simulate physical events are shown in fig. 9(c). The regions 1, 2, and 3 referred to in figs. 9(b) and 9(d) correspond to regions of increasing T R shown in fig. 4. Cuts are also placed on the differences of arrival times of anode signals *c - % and ~ - ~c to reject neutrons scattered at large angles.

The recoil energy T R was calibrated using elastic scattering events for which the projection of the recoil track to the anode plane lies near the boundary between anodes C and D. At our working conditions and (for

example) for an incident neutron energy of 985 MeV, this range corresponds to a recoil energy TRcD= 10.270 MeV. To determine the corresponding amplitude Vsc ° at the C - D boundary we look at the ratio ND x = ND + ~/~ (6) as a function of amplitude Vs. Here N o is the number of good elastic scattering events for which a signal from anode D is present, and -No is the same but for D absent. The value of Vs at which t¢ = 0.5 is taken to be the boundary amplitude VscD. The value of the calibration parameter k in eqs. (4) and (5) is then given by k = ( T c o - E o ) / V s c o . For each event this value of k is used to calculate T R. Eq. (4) is used for regions 1 and 2 (fig. 4) and equation 5 for region 3. Background from np quasi-elastic scattering from carbon is subtracted using the time difference ~cB ~ ~c - ~ B - The value of rcB characterizes the recoil angle with respect to the anode plane. As an example, the histogram of fig. 10 shows the number of scattering as a function of rcB for the interval 20.0 _< T R < 20.5 MeV. The background under the elastic peak is about 20% of the signal. Absolute differential cross sections are calculated from do AN dt - AtNTNB(I - 8)' (7)

A.A. Vorobyov et al. / Small angle np elastic scattering at intermediate energies

426

using elastic events in a small fixed energy range. F o r (~'C)m~x, corresponding to the c a t h o d e position, we exa m i n e d a histogram of ~'c- T h e position at which the distribution has descended to half-height, after corrections due to the non-zero angle of the tracks with respect to the a n o d e plane, is defined as (~'C)m~" TO find the grid position (~'c)min we have used the c a t h o d e signals. F o r a fixed energy T R the c a t h o d e a m p l i t u d e VK is p r o p o r t i o n a l to the distance from the grid to the center-of-mass of the charge d i s t r i b u t i o n of positive ions [16,22]. After application of small corrections due to the finite size of the c a t h o d e a n d the imperfect shielding of the grid, a plot of the ratio IrK/Vs versus ~'c gives a straight line which intersects the abscissa at the point (~'c)min" A second m e t h o d of d e t e r m i n i n g ( ~'c ) m a x - - ( ' 7 " C ) min is to measure the drift time for tracks from a-sources placed on the cathode. F o r this m e t h o d tracks almost parallel to the cathode are selected. T h e two m e t h o d s agree to within the precision of the m e a s u r e m e n t s ( a b o u t 0.5%).

T O = 1085 MeV TR : 20.25 MeV

400

A T R = 0.5 MeV

300

Fz Lo

200

IJA rn Z

loo

4

8

12 16 20 (q~C-q~8), CHANNELS

7. Absolute normalization

Fig. 10. Distribution of np scattering events, for a given interval ATR, as a function of the difference of arrival times of signals from anodes C and B (related to the recoil angle). The shaded area is the quasi-elastic scattering background. Beam energy To =1085 Mev; the mean recoil energy TR= 20.25 MeV; 1 channel = 80 ns.

where A N is the n u m b e r of elastic scattering events in the interval of f o u r - m o m e n t u m transfer At, N x is the n u m b e r of p r o t o n s / c m 2 in the target, N B is the n u m b e r of b e a m n e u t r o n s incident o n the target, a n d 8 is a correction factor related to loss of good events in analysis. The correction 8 ( - - 3 % ) was d e t e r m i n e d from a n analysis of simulated generator events o n which we placed the same cuts as for the physical data. The m a i n source of loss of good events in I K A R is pile-up. T h e n u m b e r of target p r o t o n s is N T = nl, where n is the p r o t o n d e n s i t y / c m 3 a n d l is the thickness of the useful working volume. G a s pressure a n d t e m p e r a t u r e were measured such that n was determined with a precision of +0.2%. Effective target thickness l was f o u n d from

To d e t e r m i n e absolute differential cross sections we need to k n o w the n u m b e r of b e a m n e u t r o n s N B incident o n the target. In our n p scattering experiment only a relative m o n i t o r i n g of the b e a m was d o n e with high accuracy. The relation between the m e a s u r e d m o n i t o r counts M a n d N B is simply N B =)~M, where ~ is a c o n s t a n t that, for a fixed m o n i t o r geometry, depends only o n the n e u t r o n energy. To d e t e r m i n e the absolute m o n i t o r calibration we have m e a s u r e d n - 4 H e elastic scattering at the same energies a n d b e a m intensities as for np. This permits a c o m p a r i s o n with p - 4 H e elastic scattering at small angles, for w h i c h the absolute differential cross section in this energy region has been precisely measured. It has been s h o w n [13] that in the region of small I t I( I t I ~< 0.07 ( G e V / c ) 2) the nuclear parts of the n - 4 H e a n d p - 4 H e differential cross sections are equal to within 1.5%. W e can thus write: do (n_4He) =

dt

A~-d

AN

AtNTM)~(1 - 8)

_ donUC1 ( p _ a H e )

dt

(8)

(9)

where d is the g r i d - c a t h o d e distance, (rc)m~ x a n d ( r c ) ~an are c h a n n e l s of the arrival time of signals on the a n o d e C for tracks at the cathode a n d grid, respectively, a n d A~- is the n u m b e r of time c h a n n e l s used. The value of d/[(~'C)m~x - (ZC)r~n] gives the drift velocity of electrons in the gas. We determined (~'c)m~ a n d (Z¢)min

(with the same n o t a t i o n as in eq. (7)) a n d so d e t e r m i n e

l = ('/'C)rnax -- ('/'C)min '

The n - 4 H e experiment was carried out using a gas mixture of H e (5 atm) a n d H 2 (1 atm) (pure h e l i u m c a n n o t s u p p o r t the necessary high voltage). A similar mixture was used earlier in the p - 4 H e experiments at

427

A.A. Vorobyou et aL / Small angle np elastic scattering at intermediate energies

4He 3He o

o - p4He 793MeV

1000

• - n4He 784 MeV

v 400 200

,,

5

100 40 i

o.o~

i

i

,

~o4

~&

,

,

o,68

o,io

- t , (GeV/c) 2

Fig. 12. The relative differential cross section for n-4 He elastic scattering at 784 MeV, normalized to the nuclear part of the absolute differential cross section for p-4He elastic scattering taken from [23].

Fig. 11. Correlation of anode signals VD versus Vc for n - H e scattering.

L N P I [20]. Elastic scattering events were selected in the same way as for the np measurements (section 6). Background from recoil nuclei 3He, 3H, 2H, and 1H was easily eliminated by using the correlations between anode amplitudes (fig. 11). N o t e that this technique works only for region 2 of fig. 4, where the recoil 4He stops in the volume corresponding to anode D. Tracks from the 241Am a-sources inside I K A R were used to calibrate TR, and the pedestal value E 0 = 40 keV was known from the electric field and pressure used and from previous measurements [20]. Comparison with the nuclear part of the p - 4 H e differential cross sections via eq. (9) was made in two ways. At 683, 784, 884 and 985 MeV the n - 4 H e data were compared directly to p - 4 He results measured with I K A R at Gatchina [23]. Small corrections (0.5-1.5%) were made for the slight differences in incident energy. An example of the comparison is shown in fig. 12. A fitting technique was also used to provide an absolute normalization at all energies measured in our data runs. This method used all available p - 4 H e data in this energy range and will be explained in more detail in [11]. The values of the normalization coefficient determined by the two methods are in good agreement at the energies where both methods can be used. Our final values for the number of incident neutrons per monitor count are shown in fig. 13. The uncertainty varies between 3% and 6% depending on energy. At 683, 784 and 884, normalization runs were performed in both January 1984 and February 1985. The results of the two calibrations agree to within the precision of the measurements. A further check on monitor stability was provided by the ratio of left to right monitor counts, which was constant to within about _+2%. We believe that for a similar, uncalibrated monitor with the same

dimensions (see section 2), the values given in fig. 13 should be valid to within _+ 10%. This provides a relatively simple and reliable method of monitoring neutron beams in this energy range. Adding in quadrature the uncertainty in absolute beam normalization and a 2.8% uncertainty in relative differential cross sections, we obtain overall systematic uncertainties of 4-7% for np elastic scattering. An example of our results is shown in fig. 14, where we compare our absolute differential cross sections at 784 MeV from two separate series of measurements with those measured at Los Alamos at 790 MeV [5]. The agreement is good. We have already published absolute differential cross sections at seven energies between 378

5000 O- DIRECT NORMALIZATION TO GATCHI NA DATA

4000

O-NORMALIZATION TO THE AVERAGE WORLD DATA

3000

£ Z 0

÷÷

200C Z 0

S

15ooi

w Z

0 I00C 80C I

400

I

I

600

I

I

800

I

l

1000

To, MeV Fig. 13. Number of incident neutrons per monitor count as a function of energy.

A.A. Vorobyov et al. / Small angle np elastic scattering at intermediate energies

428

o-

120

np 800 HeV ~-

OUR

1978

DATA:

o- 1984(FIRSTSERIES)

1oo

0,0B~;~o~o,..%o~,

CARLINI el at

.

~- 1985(SECONDSER,ES~

80



8

8,

i

o

6o

o

0

,

o, 0

o

O

g 5O l

I

I

I

I

0.01

002

0.03

0.04

0.05

I

-t,

i

0.06 (GeV/c) 2

007

0.08

Fig. 14. Absolute differential cross sections for np elastic scattering at 784 MeV obtained in two independent series of measurements together with the data from [5].

and 1085 MeV. More results and details will be given in [11].

In principle, systematic uncertainties would be minimized by calculating a using the geometric mean [24] ~]VL~ N~ -- ~

N.,

8. Calculation of np analyzing powers In addition to the measurement of d a / d t as described in the preceding sections, for runs with a polarized beam we also measured the analyzing power Aoo,0 for np elastic scattering. As explained in section 2, two sets of scintillation counters were placed symmetrically to the left and right of the beam axis downstream of I K A R . Each set consisted of two counters, and each counter was viewed by three photomultiplier tubes (top, bottom, and back of the counter). For each counter a coincidence among the three photomultipliers was required, and the time-of-flight for each of the four counters was recorded for each event, with the cathode signal from I K A R used as the START. The neutron counters were not placed in the trigger. This eliminated dependence of the d o / d t yields on neutron counter efficiencies. Data analysis for the asymmetry measurements followed all of the steps outlined in sections 4 and 6 for selection of elastic scattering events. Windows were then placed on the I K A R - n e u t r o n T O F peaks, and events were binned according to the state of polarization of the beam. Four conditions are of interest: (1) neutron to the left, beam up (yield NLr ), (2) neutron to the right, beam up ( N ~ ) , (3) neutron to the left, beam down ( N ~ ) , (4) neutron to the right, beam down ( N ~ ) . The yields N were determined from histograms of the time difference ~'cB (related to recoil angle) as explained in section 6. The experimental asymmetry a for each bin of AT R = 2.5 MeV was then calculated from the formula: a=

(NL~ + N ~ ) - (NL~ + U ~ ) (NL~ + N ~ ) + ( N L *

+ N R~ ) "

Nt

(I0)

instead of the arithmetic mean of eq. (10). We used the arithmetic mean, however, because it reduced by half the number of spectra to be analyzed. The effect on systematic uncertainties is negligible in our case, as will be discussed below. The analyzing power A0o,0 is related to the asymmetry a by: (11)

Aoono = R a l P h ,

where PB is the beam polarization and R is a geometrical factor arising from the integration over the azimuthal acceptance. PB was determined to be 0.59_+ 0.02 by measuring the asymmetry in quasi-elastic pp scattering as explained in section 2. The factor R was determined as follows. For a number of good elastic events No(O ) with laboratory polar angle 0 detected in I K A R the number

LEFT DETECTOR

YT

ct RIGHT DETECTOR

po~RGLARIZED ET NEUTRONBEAM Fig. 15. Definition of angles and parameters used in asymmetry measurements (see text).

A.A. Vorobyovet aL / Small angle np elastic scattering at intermediate energies of n e u t r o n s detected in the left side n e u t r o n counter will be (see fig. 15)

( ( O ) N ° ( 8 ) fq' (1 + P n A o o n o ( 0 ) cos f l ) dfl

NL(0 )

2~r



_ .(0)N0(0),

1+ e.A0o°o(0)--

.

where ~(0) is the detection efficiency, Aoo,o(O ) is analyzing power, a n d PB is b e a m polarization. Likewise:

for the n e u t r o n counter o n the right. T h e asymmetry a = ( N L - N R ) / ( N L + NR) is t h e n a ( 0 ) = PBAoo~o(O) sin ~ / ~ a n d so:

A°°"°(O)

,) sinq~q, a (PB

(12)

C o m p a r i n g with eq. (11) we see that R = ¢ / s i n ¢, where

ck = c o s - ' ( a / 2 L t a n O). In this expression, a is the distance between the two n e u t r o n counters, L is the distance of the n e u t r o n counters from the target along the b e a m axis, a n d 0 is the n e u t r o n scattering angle in the lab ( d e t e r m i n e d from TR). F o r most of o u r data, a = 7.0 cm. W e have t a k e n the distance L to b e the distance from the center of the active volume of I K A R to the center of the n e u t r o n counters (132.1 cm). T h e validity of this simplification was checked by integrating the detection p r o b a b i l i t y over the geometry of our n e u t r o n counters for a few angles. The results agree to within 1% with those obtained using eq. (12) with L = 132.1 cm. A n o t h e r check was m a d e by p e r f o r m i n g m e a s u r e m e n t s at one energy (784 MeV) for two different positions of the n e u t r o n counters ( a = 7 a n d 11 cm), thus c h a n g i n g the value of R b y 4-10%. T h e results of the two m e a s u r e m e n t s are in good agreement. T h e data were analysed in bins of A T R = 2.5 M e V which were then s u m m e d together to give a final bin w i d t h of A T R = 10 MeV (corresponding to A0 .... __ 2.7-5.2 ° ). This procedure reduced the u n c e r t a i n t y arising from b a c k g r o u n d subtraction. Statistical errors were calculated in the usual way, b u t with the errors increased to account for the u n c e r t a i n t y in b a c k g r o u n d subtraction. W e write for the u n c e r t a i n t y Aa in the experimental a s y m m e t r y (see eq. (10)):

429

a n d Nbg is the n u m b e r of b a c k g r o u n d counts subtracted (thus N = Ntot - Nbg). This m e a n s that we have assigned a n u n c e r t a i n t y of 10% of b a c k g r o u n d to each yield, a n d a d d e d it in q u a d r a t u r e with the statistical uncertainty. T h e internal consistency of the d a t a is good, confirming that the assigned uncertainties are reasonable. Systematic uncertainties in the analyzing powers were evaluated considering the following e x p e r i m e n t a l errors: (1) Difference in b e a m n o r m a l i z a t i o n between the polarization states " u p " a n d " d o w n " . A " w o r s t case" estimate of this effect was a 10% difference, a n d 4% is considered realistic. (2) Difference in polarization b e t w e e n the two spin states. W o r s t case error = 7%, realistic error = 3%. (3) Difference in solid angle between the left a n d right n e u t r o n counters. W o r s t case error = 10%, reahstic error = 4%. (4) M i s a l i g n m e n t of the beam. Besides the purely geometrical effect of causing a difference in solid angle (considered in (3) just above) this c a n b e a n effect o n the calculated recoil energy T R for tracks which leave the active volume ( T R > 15 MeV). W o r s t case error = 10 m m , realistic error = 3 ram. T h e c o m b i n e d effect of the worst case errors cited above is to introduce a n overall systematic error A A ~< 0.008. The realistic errors give AA = 0.001. Both of these are small c o m p a r e d to the uncertainties arising from c o u n t i n g statistics a n d b a c k g r o u n d s u b t r a c t i o n (AA = 0.024 to 0.046). F o r this reason we are justified in using arithmetic rather t h a n geometric mean. N o t e that in our experiment all of the systematic errors considered above cancel in first order d u e to the use of b o t h u p - d o w n spin states a n d a l e f t - r i g h t detection symmetry. F u r t h e r m o r e , all b u t one of the nine second order terms d e p e n d o n two different effects, m a k i n g precise estimations of the errors even less i m p o r t a n t .

t++

0.3

++

++

8

<

~o 0.2 &

++

< 0.1

ON, ]

+

o-THIS EXPERIMENT 834MeV

(aN2)2'

where N l = g [ +N~ and N2 = N ~ uncertainties A N we have t a k e n

O-LENAR et ol. 85OMeV quasi elost ic

+ N R T. F o r the

( A N ) 2 = Nto ' + ( N b g / 1 0 ) 1, where Ntot is the total n u m b e r of counts in the peak

110

210

310

410 Oncm •

510 DEG

Fig. 16. Analyzing powers Aoon0 for np elastic scattering measured in this experiment compared with those from [25].

430

A.A. Vorobyov et al. / Small angle np elastic scattering at intermediate energies

As m e n t i o n e d earlier, our m e a s u r e d b e a m polarization was 0.59 ± 0.02. This leads to a systematic uncertainty of a b o u t 3% in our m e a s u r e d analyzing powers. O u r results for the analyzing power A00~0 at five energies (633, 784, 834, 934 a n d 985 MeV) have already b e e n published [9]. In fig. 16 we c o m p a r e our data at 834 M e V to those o b t a i n e d by the nucleon-nucleon group at Saturne with a similar n e u t r o n b e a m [25]. A l t h o u g h the angular regions of the two m e a s u r e m e n t s do not overlap, there seems to b e good consistency between them. This gives a d d e d confidence in the validity of our method.

9. Conclusions Use of the I K A R recoil detector with the free polarized n e u t r o n b e a m from Saturne permitted us to measure analyzing powers a n d absolute differential cross sections for n p elastic scattering in the small angle region at intermediate energies. Such m e a s u r e m e n t s would be extremely difficult with other experimental methods. Our results fill a gap in the experimental d a t a at small transfers over a wide range of energies. The use of m e t h a n e in I K A R allowed an increase in counting rate a n d an extended I t I range as c o m p a r e d with earlier work with hydrogen. Use of I K A R without an external trigger was m a d e possible by a more complicated internal structure which permitted reliable selection of elastic scattering events using i n f o r m a t i o n from I K A R alone. C o m p a r i s o n of n - 4 H e m e a s u r e m e n t s with existing absolute differential cross sections for p - 4 He has p r o v i d e d a n absolute systematic uncertainty of 4-7%.

Acknowledgements W e would like to t h a n k J. Arvieux, A. B o u d a r d a n d F. L e h a r for help with the d e t e r m i n a t i o n of the b e a m polarization. W e also t h a n k G.N. Velichko, N.I. Timoshuk, Y.S. Grigoriev, V.I. Medvedev, a n d G.L. Sokolov, who helped at different stages of construction of the apparatus.

References [1] R.A. Amdt, J.S. Hyslop III and L.D. Roper, Phys. Rev. D35 (1987) 128. [2] J. Bystricky, C. Lechanoine-Leluc and F. Lehar, J. Phys. (Paris) 48 (1987) 199.

[3] R. Dubois, D. Axen, R. Keeler, M. Comyn, G.A. Ludgate, J.R. Richardson, N.M. Stewart, A.S. Clough, D.V. Bugg and J.A. Edgington, Nucl. Phys. A377(1982) 554. [4] A. Arefiev et al., Nucl. Phys. B232 (1984) 365. [5] R. Carlini, B. Dieterle, J. Donahue, C. Leavitt, T. Rupp, W. Thomas, D. Wolfe, UB. Auerbach, V.L. Highland, K.F. Johnson, W.K. Mcfarlane, J. Pratt and R. Bentley, Phys. Rev. Lett. 41 (1978) 1341. [6] A.V. Dobrovolsky, A.V. Khanzadeev, G.A. Korolev, E.M. Maev, V.I. Medvedev, G.L. Sokolov, N.K. Terentiev, Y. Terrien, G.N. Velichko, A.A. Vorobyov and Yu.K. Zalite, Nucl. Phys. B214 (1983) 1. [7] V.G. Ableev et al., Sov. J. Nucl. Phys. 34 (1981) 428. [8] J.P. Burq et al., Nucl. Phys. B217 (1983) 285. [9] G.A. Korolev, A.V. Khanzadeev, G.E. Petrov, E.M. Spiridenkov, A.A. Vorobyov, Y. Terrien, J.C. Lugol, J. Saudinos, B.H. Silverman and F. Wellers, Phys. Lett. 165B (1985) 262. [10] Y. Terrien, J.C. Lugol, J. Saudinos, B.H. Silverman, F. Wellers, G.A. Korolev, A.V. Dobrovolsky, A.V. Khanzadeev, G.E. Petrov, E.M. Spiridenkov and A.A. Vorobyov, Phys. Rev. Lett. 59 (1987) 1534. [11] To be submitted to Nucl. Phys. B. [12] G. Bizard, F. Bonthonneau, J.L. Laville, F. Lefebvres, J.C. Malherbe, R. Regimbart, J. Duflo and F. Plouin, Nucl. Instr. and Meth. 111 (1973) 645; Nucl. Instr. and Meth. 111 (1973) 451. [13] Y. Terrien and F. Wellers, J. Phys. (Paris) 46 (1985) 1873. [14] A. Boudard, Private communication. [15] A.A. Vorobyov et al., Preprint FTI-429 (Leningrad, 1972). [16] A.A. Vorobyov, G.A. Korolev, V.A. Schegelsky, G.Ye. Solyakin, G.L. Sokolov and Yu.K. Zalite, Nucl. Instr. and Meth. 119 (1974) 509. [17] B. Jean-Marie, V. Lepeltier and D. L'Hote, Nucl. Instr. and Meth. 159 (1979) 213. [18] E.B. Wagner, F.J. Davis and G.S. Hurst, J. Chem. Phys. 47 (1967) 3138. [19] J.F. Janni, Atomic Data and Nucl. Data Tables 27 (1982) 147. [20] G.N. Velichko, A.A. Vorobyov, Yu.K. Zalite, G.A. Korolev, E.M. Maev, N.K. Terentiev, Y. Terrien and A.V. Khanzadeev, Preprint LNPI-665 (Leningrad, 1981); Sov. J. Nucl. Phys. 35 (1982) 154. [21] G.N. Velichko, A.A. Vorobyov, G.A. Korolev, E.M. Maev, N.K. Terentiev and A.V. Khmazadeev, Preprint LNPI-549 (Leningrad, 1980). [22] G.N. Velichko, A.A. Vorobyov, Yu.K. Zalite, G.A. Korolev, E.M. Maev, N.K. Terentiev, A.V. Khanzadeev and V.A. Schegelsky, Preprint LNPI-655 (Leningrad, 1981). [23] G.N. Velichko, A.A. Vorobyov, A.V. Dobrovolsky, G.A. Korolev, S.I. Manaenkov, J. Saudinos and. A.V. Khanzadeev, Sov. J. Nucl. Phys. 42 (1985) 837. [24] G.G. Ohlsen and P.W. Keaton Jr, Nucl. Instr. and Meth. 109 (1973) 41. [25] J. Bystricky et al., Nucl. Phys. A444 (1985) 597.