Nuclear bremsstrahlung from 140 MeV protons

t 2.A.l:

Nuclear Physics 89 (1966) 523--552; (~) North-Holland Publishing Co., Amsterdam

•

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

3.A

N U C L E A R B R E M S S T R A H L U N G F R O M 140 MeV P R O T O N S J. A. E D G I N G T O N

Cambridge University, Cambridge, England t and B. ROSE

AERE Harwell, Berks., England Received 26 May 1966 Abstract: Differential cross sections and rough energy spectra for bremsstrahlung production have been measured under 140 MeV proton b o m b a r d m e n t o f H, D, Be, C, N, O, A1, Cu and Pb. The total cross section per neutron in the target nuclei for photons above 40 MeV varied from 4.5/tb to ~ 2/~b from D to Pb. The observed cross section for the p - p system was -- 0.06 ± 0.05 ¢tb. The data from nuclei are in reasonable agreement with the limited experimental data available and with the theory o f Beckham. The p - p value is much lower than any theoretical estimate.

E

N U C L E A R R E A C T I O N S : H, D, Be, C, N, O, AI, Cu, Pb(p, x)z(bremsstrahlung)), E ~ 140 MeV; measured a(E~, 0).

1

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1. Introduction

Nucleon-nucleon elastic scattering experiments give information only about the diagonal elements of the scattering matrix; the existence of consistent phase-shift analyses at several energies indicates that this interaction is, phenomenologically at least, fairly well understood. As yet, however, little is known about the elements of the scattering matrix lying "off-the-mass shell". It is in principle possible to study these off-diagonal elements directly by the use of electromagnetic interactions, which are assumed to be completely understood. Experiments, such as photodisintegration and n-p capture, which involve a coupling between the electromagnetic field and the deuteron suffer from ambiguous interpretations, in that the precise choice of the deuteron wave function affects the calculated two-nucleon potential. One interaction where this difficulty does not arise is that producing nuclear bremsstrahlung, where the deuteron appears in neither the initial nor the final state. In 1949 Ashkin and Marshak 1) (and also, independently, Krook 2) and Pomeranchuk and Shmushkevich a)) noted the possibility of bremsstrahlung in nucleonnucleon scattering. Their calculations, refined by Simon 4), indicated a cross section o f the order of the elastic scattering cross section multiplied by the square of the fine-structure constant. Further work 5) predicted the n-p cross sections more exactly t Present address: Queen Mary College, London, England. 523

524

J. A. E D G I N G T O N AND B. ROSE

and confirmed 6) Ashkin and Marshak's prediction that p - p bremsstrahlung should occur only in second order. The experimental work of Wilson 7) and of Cohen 8) confirmed the order of magnitude of these cross sections for proton-nucleus bremsstrahlung. Their work was carried out using internal cyclotron targets viewed at a small number of angles. The purpose of the present work was to extend their cross-section measurements over a wide range of targets and angles with accurate normalization and to investigate bremsstrablung in proton-proton scattering.

2. Method

2.1. PRINCIPLE A total-absorption (~erenkov counter in combination with a scintillation counter telescope was used to detect and energy-analyse gamma rays produced when the external proton beam of the A E R E 279 cm synchrocyclotron struck thin targets of various materials ranging from hydrogen to lead. This photon detection system gave excellent discrimination against background protons and neutrons; the effect of spurious events such as cosmic rays was much reduced by the coincidence and gating system employed. The scattered proton was not observed separately; at the higher photon energies it does not escape from the target. 2.2. LAYOUT AND BEAM The proton beam was deflected into the experimental area by a single bending magnet, thereby avoiding the flux of fast neutrons present in the undeflected beam. The positioning of the apparatus in the experimental area is shown in fig. 1. The ,/ / ,Y ;:" ,/ ,,j ,;

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counters were mounted on the scattering table which was rotated by hand to the required angle. Targets were clamped to the rigid centre column of the table. At the target position the beam was found by radiography to be about 15 m m in diam., and its energy was determined by range measurements in aluminium to be 146.0 MeV with a spread (base width) of 3.0 MeV. Paraffin wax beam-stoppers downstream of the target were used when it was essential to reduce the background radiation to a minimum, as when using a liquid hydrogen target; otherwise the beam was allowed to strike the concrete wall. The beam intensity was monitored continuously by an air ionization chamber. This was calibrated by the usual technique of scattering from a thin target in the direct beam. Copper absorber in both direct and scattered beam counter telescopes eliminated possible contamination by low-energy particles; a correction was applied for the proton attenuation in this absorber. The results were consistent and reproducible. The beam intensity throughout the experiment averaged about 1.5 x 108 protons per sec; there was a negligibly small ( < 1 ~o) variation with duty cycle. The total calculated error in the absolute intensity was _+5 ~ . 2.3. T A R G E T S

Table 1 lists the targets, their thicknesses and the energy loss of a 146 MeV proton passing perpendicularly through them. The solid targets were machined to 7.5 cm diam. discs; these were generally clamped at 45 ° to the beam line to minimise the probability of photon conversion in the target. The water targets, which were also usually inclined at 45 ° to the beam line, were contained in identical dural annuli with 0.13 m m mylar windows "araldited" to both sides. The light water target was emptied and used as a d u m m y during background runs. The liquid hydrogen and liquid nitrogen target was a 7.5 cm diam. vacuum insulated cylinder with mylar windows. When using this target a square brass collimator of side 2.5 cm was reTABLE 1 List of targets used Composition

Be C AI Cu Cu Pb polyethylene H20 D20 liquid hydrogen liquid nitrogen

Thickness (g- cm 2) 2.38 2.53 3.41 2.51 5.67 3.52 2.31 2.54 2.81 0.54 6.16

Energy loss of 146 MeV proton (MeV) 11.2 12.8 15.1 9.4 21.2 9.5 14.0 14.3 14.0 6.4 30.0

526

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quired upstream of the entry port to prevent the "wings" of the beam from striking the brass walls of the vacuum vessel. Beam loss by this collimator was measured and corrected for. 2.4. C O U N T E R

TELESCOPE

This is shown in fig. 2. Photons from the target produced electron pairs in the thin lead converter, these pairs giving pulses in counters 2 and 3 before entering the Cerenkov counter. Counter 1 was 15 cm square and was put in anticoincidence with counters 2 and 3 (each 10 cm in diam.) to veto events in which the photon converted before

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the lead sheet. Thus the electron-photon cascade was initiated at a fixed distance from the target and was in effect confined to the central region of the (~erenkov counter by counter 3. The graphite absorber (18.0 g- cm -2 thick) prevented counter 1 from being blocked by the high flux of scattered protons. The distance between counters 2 and 3 was ~ 15 cm, so that electron pairs of large divergence, which might produce anomalously small pulses in the ('erenkov counter, were not accepted. The acceptance angle, defined by counter 3, was __6} ° at the target centre, and the converter and counters 1 and 2 extended well outside this acceptance cone.

NUCLEAR

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527

Counters 1, 2 and 3 were of 0.25 cm thick NE102 scintillator cemented to perspex light guides in optical contact with EMI6097 photomultipliers. Since the lightcollection efficiency was neither high nor uniform, and since the required triggering pulses were produced by either one member or both of the electron pair, the phototubes were selected with care; typically, dark currents were of the order of 0.1 /~A when operated at a photocathode sensitivity of 60/2A 1n - 1. The triggering signal (]23) was used to open a linear gate and allow pulses from the Cerenkov counter to pass through. The Qerenkov counter was made of Chance lead glass, type E D F 653335 of refractive index 1.689 at 4047 A. It was in the form of a 20 cm deep frustum of a circular cone, with basal diam. 15 cm and 22.5 cm, with its smaller face towards the target. This was identical in material and form with a counter used in an experiment at Liverpool on the Panofsky ratio 9). The size was sufficient to contain the cascade shower produced by a 146 MeV photon (but see subsect. 2.6 below), the ~erenkov light produced by the shower particles being concentrated by total internal reflection onto the larger face. This was viewed through a 2.5 cm perspex light guide by a 57 AVP photomultiplier, a tube with a very low noise level in spite of its size (20 cm photocathode diam.). The counter and phototube were mounted inside a mumetal magnetic shield within an outer steel canister; on the front of this was bolted the scintillation counter telescope, and the entire assembly could be moved so that its axis was vertical for cosmic ray calibration. 2.5. E L E C T R O N I C S

The electronic system was entirely conventional. The (123) coincidences triggered a fast proportional gate through which a pulse from the anode of the ~erenkov counter phototube passed. The gate length was set to a nominal 150 ns and the phototube pulses, which had a base width of 40 ns, were centred within this by observation of the monitor output and by drawing delay plateaux. The output of the linear gate was displayed on a 99-channel pulse-height analyser. All discriminators, coincidence circuits and scalers were A E R E "2000" series unitised equipment. The scalers and pulse-height analyser were part of an automatic read-out system controlled by information from the proton monitor; thus all experimental runs were normalized to a known proton flux. To reduce the cosmic-ray background, the scalers and analyser were gated by a frequency pick-off pulse from the synchrocyclotron r.f. sweep. Typically, using a l0 ~ duty cycle, cosmic-ray counts were reduced from 50 to 5 counts per 1000 sec (compared with a machine-associated rate of about 15 per 1000 sec using the liquid hydrogen target). Gated and non-gated scalers were run in parallel to detect any loss of efficiency, and the use of scaling circuits of different dead times enabled the duty cycle to be monitored continuously. The counters were set on delay plateaux in the direct proton beam. Resolving times were 19 ns for the coincidence circuits and 26 ns for the anti-coincidence circuits. Because of the wide variation referred to above in the pulse height produced by the

528

J. A. E D G I N G T O N

A N D B. ROSE

electron pairs, discriminators were used to saturate the input circuits of the coincidence units; the counters were swung out of the direct beam, the lead converter inserted and the phototube voltages adjusted so as to obtain plateaux of kicksorter counting rates as a function of discriminator bias level. Finally the anticoincidence efficiency of counter 1 was optimised at better than 99.9 ~o in the direct proton beam; the gain of this counter was then raised by a factor of three to ensure at least this efficiency in counting minimum-ionizing electrons. An accurate knowledge of random coincidences was essential in this low counting rate experiment. The estimated randoms counting rate on the kicksorter was given by Nestimate d =

-cN]-z3Nc,

where z is the length of the proportional gate, N123 the rate of gate opening and Nc the rate of occurrence of Cerenkov counter pulses above the kicksorter threshold. The N~2 a and r were measured directly, and Nc was found by feeding the discriminated Cerenkov counter pulse both to the proportional gate and directly to a scaler; the scaler rate, at a discriminator bias level such that the kicksorter rate remained unchanged, was equal to Nc. The randoms counting rate Nob . . . . . d was also found directly by delaying the (~erenkov counter pulse by 200 ns, which was equal to four r.f. cycles. The N~tlm,~ted and Nob...... d values agreed well; using a 10 ~o duty cycle the randoms rate was less than 1 ~o of the real counting rate. 2.6. ENERGY CALIBRATION OF CERENKOV COUNTER The (;erenkov counter was calibrated at the University of Liverpool synchrocyclotron using a collimated beam of mono-energetic positons. This was done after the bremsstrahlung work had been completed and comparison with the experimental runs was effected by observation of the pulse heights produced by cosmic-ray llmesons passing vertically downwards through the counter. This technique also afforded a day-to-day check on the performance and gain of the counter and associated equipment. First, a semiconductor light pulser was used to check the absolute efficiency and pulse-height resolution of the counter. A pair of rotatable crossed-polaroid end windows provided an accurate and reproducible calibration of the light pulser. The operating voltage was adjusted to match the phototube output with the maximum pulse heights encountered in the experiment, and typical output spectra are shown in fig. 3i. The integrated counting rate was the same for each polaroid setting, showing the counting efficiency to be 100 ~o. The square of the full width at half height is plotted against the corresponding pulse height in fig. 3ii, the linear relationship indicating that the observed pulse-height variation was principally due to a Poisson distribution of photoelectrons. The absolute zero level of the counter and its associated circuitry was also found by extrapolating the linear relationship obtained between pulse height and polaroid transmission (fig. 3iii).

529

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The counter assembly was then placed in the positon beam; its m o m e n t u m was known to +_3 %. The proportional gate was in general triggered by a coincidence between scintillation counters 2 and 3 placed as in fig. 2, but this arrangement was altered several times to study the calibration in more detail. Pulse-height spectra obtained are shown in fig. 4 together with a typical cosmic-ray spectrum. A 0.6 cm 500

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wide defining counter was also scanned across the Cerenkov counter face. An observed fall in response at the edges was the reason for the choice of a 10 cm defining counter in the bremsstrahlung work. The measurements were repeated with the 0.6 cm defining counter in the position previously occupied by the bremsstrahlung target, thus simulating exactly the

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geometry of this work. N o difference was observed from the results using the two large counters alone. Finally the effect on the counter of the fringing field of the synchrocyclotron magnet (about 14 Oe at the counter position) was measured, using cosmic rays passing through the horizontal counter to provide a peaked spectrum. The field was found to reduce the pulse height by 5 4- 1 ~o, and this was allowed for in comparing cosmicray and positon spectra. The calibration curve obtained in this way is shown in fig. 5i. The non-linearity

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implied at the low-pulse end is due to 10) a pulse-shape dependent effect on the linear gate at low levels, but is of no consequence, being outside the range of interest. The slight departure from linearity at the highest energy recorded is due to the inability of the counter completely to contain the most energetic cascade showers 11). This "containment factor" may be calculated using the "similarity rule" tl) and is essentially 100 % for electron energies of less than 80 MeV. Thus the peaks found for positons of a given energy occur at constant fractions of the cosmic-ray pulse height, and since this response is essentially the same as the response to a number of electrons

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of the same total energy, the incident photon energy corresponding to a particular fraction of the cosmic-ray pulse height can be calculated. A comparison 10) of the observed number of photoelectrons with that expected by consideration of the Cerenkov process, the optics of the counter and the photocathode quantum efficiencies showed good agreement with experiment. +-I J

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PHOTONS

The technique used for each target and angle was to count both with the converter inserted between counters 1 and 2 and with it removed. The resulting energy spectra were normalized to the same incident proton flux and subtracted to obtain the counts due to bremsstrahlung photons produced in the target. A typical pair of spectra are shown in fig. 6; the monotonic decrease with energy and the corresponding decrease in the ratio (converter " o u t " - converter " i n " ) are features characteristic of all targets and angles. For the liquid targets a "target empty" subtraction was necessary but for the solid targets this effect was small and, at larger angles, negligible. The graphite absorber blocked all charged particles from the target. Proof of the photon origin of the observed counts rested, therefore, on showing that their variation with converter and absorber thickness was incompatible with that expected for neutrons (which could, via conversion protons, simulate photons in the Cerenkov counter) but agreed with that predicted for photons. It should be noted that the (~erenkov counter had a small but non-zero efficiency for detecting charged particles (see later in this section).

532

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The conversion efficiency was observed for various thicknesses of material, as described in the next section. It was found, for example, that the ratio counting rate using 1.0 g . cm - z of lead converter counting rate using 1.1 g

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Similarly, various thicknesses of lead absorber were interposed between the graphite and counter 1, and the observed attenuations were strong evidence for the photon origin. For instance, observing at 55 ° to a carbon target, we found reductions in counting rate by factors of 0.33+0.07 and 0.12+0.06 for 14.3 and 28.9 g • cm -2 of lead, respectively. The calculated attenuation factors for photons are 0.30 and 0.10 and for neutrons 0.82 and 0.66, respectively. [The photon factors are calculated at 65 MeV, the median photon energy as deduced by the methods of the previous section, and the neutron factors assume an average total cross section of 5 b for neutron energies from 15 to 120 MeV, ref. 1 6 ) . ]

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These direct indications of the photon origin were supplemented by calculations of counting rates due to the three following processes which could simulate targetassociated photons in the (~erenkov counter telescope: (i) (p, n) reactions in the target followed by (n, p) reactions in the converter; (ii) (p, p') reactions in the target followed by (p, n) reactions in the absorber followed by (n, p) reactions in the converter and (iii) (p, p') reactions followed by scattering to escape the geometrical veto. The proton detection efficiency was measured in the direct proton beam and found to be 5 • 10 -4 for protons of 90 MeV simulating photons of > 30/VfeV. Substituting this figure together with known data on the (p, p') and (p, n) cross sections, the rate for the first process was determined to be, typically, 6.5 counts for every 2 • 1011 protons incident on the carbon target. The observed count rate under the same conditions (carbon target viewed at 45 ° ) was 641_+26 counts per 2" 10 ll protons. The rate for the second process is lower still since an additional nuclear reaction is involved, and the third process, though difficult to estimate, is independent of the converter position and so does not contribute to the observed count rate. A constant check of the (123) coincidence rates showed that these estimates of nonphoton counts were, if anything, too high and it is deduced that the observed count rate is almost entirely due to target-associated photons, with a limit of 1 ~ on counts due to other processes. 2.8. CONVERSION EFFICIENCY OF COUNTER TELESCOPE No source of m o n o kinetic g a m m a rays was available so a direct efficiency determination was not possible; instead the relative efficiency of the counter telescope for detection of the bremsstrahlung spectlum was determined using converters of various elements and thicknesses, and these results were compared with the efficiency calculated for the particular geometry employed. Relative counting rates obtained using converters of lead, copper and aluminium are shown in fig. 7. Photons from the thick copper target were observed at 54 ° to the beam line, and total kicksorter counts were noted with and without the converter in position. Counts with target out were negligible. There was no detectable difference between runs with the converter holder alone inserted in the counter arm, and runs with it removed. Using the position of the cosmic-ray peak as a calibration, as described in subsect. 2.6, the median energy of the photon spectrum was found to be 55 MeV. The exact theory of the conversion efficiency is complicated, and approximations were introduced where appropriate. We require the probability that the photon undergoes conversion and that at least one of the electrons passes through the defining scintillator, that is, emerges from the converter inside a cone of given semiangle. Using known results for the energy spectra in pair production 12), the energy loss of electrons 13) and the multiple scattering probability 14) it was possible to calculate 10) the conversion efficiency for a given incident photon energy. The relevant integrals were evaluated numerically at 10 MeV intervals. The results, evaluated at 50 MeV for lead, copper and aluminium are shown in fig. 7. The calculated curves

534

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have been n o r m a l i s e d to the initial slope o f the experimental points for lead; agreem e n t is excellent up to at least 3.5 g ' cm -2. Since a b s o r p t i o n a n d scattering losses b e c o m e significant for thicknesses greater t h a n a b o u t 1.5 g . cm -2, the converter used for the m a j o r i t y o f d a t a - t a k i n g runs was 1.45 g • cm - 2 o f lead. The calculated efficiency is shown in fig. 5(ii). The total error is estimated f r o m the spread o f observed c o u n t i n g rates a n d from k n o w n errors in the various calculational p a r a m e t e r s to be a b o u t + 10 ~ . The assertion in subsect. 2.4 that counter 3 was the defining element was tested by c o m p a r i n g count rates with the counter assembly subtending different solid angles

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535

to p r o d u c e the c o u n t i n g rate observed fewer t h a n one in a t h o u s a n d p r o t o n s scattered into 1 sr t o w a r d s the counters, w o u l d be required to rescatter a n d evade the geometrical veto. I n this process also, the p r o t o n detection efficiency o f the C e r e n k o v c o u n t e r decreased very r a p i d l y with energy.

3. Results 3.1. DATA TAKING The d a t a presented below were o b t a i n e d in four separate runs, in each o f which the overall p r o c e d u r e was the same. T h e electronics settings were checked a n d d a t a a c c u m u l a t e d at the several angles for each target. M e a s u r e m e n t s with converter in a n d o u t a n d with target present a n d r e m o v e d were a l t e r n a t e d as usual, each cycle t a k i n g a b o u t 1 h. Before a n d after each r u n the c o u n t e r assembly was tilted to the vertical to r e c o r d cosmic rays. A t intervals t h r o u g h o u t each run the p o s i t i o n o f the k i c k s o r t e r zero level was checked; i n d i v i d u a l m e a s u r e m e n t s varied b y up to one channel b u t no systematic change in the m e a n p o s i t i o n was observed. Consistency between the runs was excellent. T y p i c a l counting rates are given in table 2. The p o o r duty-cycle b e a m was used for runs with the liquid h y d r o g e n target TABLE 2 Typical counting rates at 54° (lab) Target

C AI Cu Pb (no target)

Kick-sorter counts per 10I1 protons incident converter in

converter out

531± 9 594~10 782-~ 11 334-~ 7 11± 3

140 ± 7 175 ± 7 274 ±10 102 ± 6 1.3± 0.7

The mean incident proton rate was 1.5 x l0 s protons, sec 1. when the m a x i m u m intensity was required; otherwise the slow e x t r a c t i o n system was used, a n d t h r o u g h o u t the r a n d o m c o u n t i n g rate was less t h a n 1 ~ o f the " r e a l " rate. A t each angle, k i c k s o r t e r channels were c o m b i n e d in blocks c o r r e s p o n d i n g to p h o t o n energy intervals o f 10 MeV. T o convert these d a t a to p h o t o n spectra, the very p o o r energy r e s o l u t i o n o f the system was i g n o r e d a n d the efficiency for p r o d u c t i o n o f a c o u n t in a p a r t i c u l a r channel was t a k e n directly f r o m the curves o f fig. 5. The justification for this p r o c e d u r e will be a p p a r e n t later (subsect. 4.1) when o u r results are c o m p a r e d with those o f C o h e n 8) w h o used a p a i r spectrometer. C o r r e c t i o n s were a p p l i e d where necessary for a b s o r p t i o n in the g r a p h i t e a b s o r b e r a n d in the various targets. F i n a l l y for h y d r o g e n a n d d e u t e r i u m the angles, energies a n d cross sections were c o n v e r t e d to the centre-of-mass system.

536

J, A. E D G I N G T O N A N D

B. ROSE

3.2. HYDROGEN RESULTS NO bremsstrahlung was observed; the results are given in table 3. The data are plotted in fig. 8 as differential cross sections for p r o d u c t i o n of p h o t o n s of energy > 49 MeV. If the cross section is assumed to be isotropic in the centre-of-mass, the estimated total cross section above 30 MeV is - 0 . 0 1 + _ 0 . 0 6 /~b. For a threshold of 40 MeV, the corresponding isotropic total cross section is - 0 . 0 6 _ + 0.05 I~b. TABLE 3 Centre-of-mass p - p b r e m s s t r a h l u n g p r o d u c t i o n cross section in n b . s r

Total (nb • sr ~)

Photon energy (MeV) 0~.m. 45.8 53.1 67.3 80.7 93.6 134.4

30-40

40-50

50 60

0 . 5 _ ' - 0 . 9 0.9±0.5 --0.2±0.3 1.5~0.8 0.0--0.4 0.2~0.3 --0.5±0.9 --0.740.5 0.7:!-0.4 0.2±0.8 --0.3~-0.5 0.2~0.4 0.1±1.0 --0.7z 0.6 0.2~0.4 --1.2-!1.1 0.0__--0.7 0.9--0.5

~. MeV

60 70

> 70

--0.2L0.2 7~3 0.1--0.2 5±3 0.2~0.4 8 4 0.0-}-0.3 --9--4 0 . 3 ~ z 0 . 4 --3--5 0.2- 0.4 6±6

> 40

~-'~30

-- 2"~ 8 --- 4 : 6 .... 10~ 8 --10-- 7 -- 5-- 8 17±12

3"_12 11~-10 --15--12 -- 8±11 -- 4--13 5--16

The errors, as elsewhere in this paper, are standard errors, here dominated by the statistical component. 3.3. DEUTERIUM RESULTS The p - p bremsstrahlung being essentially zero, the (D z O - H z O) difference gave the p - d c o n t r i b u t i o n directly. The derived centre-of-mass cross sections depend u p o n whether the interaction producing the p h o t o n s is treated as a p r o t o n - d e u t e r o n collision or as a quasi-free p r o t o n - n e u t r o n collision. The differential cross sections for p r o d u c t i o n of p h o t o n s of energy > 40 MeV derived u n d e r both assumptions are listed in table 4 together with the laboratory distribution. It will be observed that there is in fact not a great difference between the c.m. values. The c.m. results are also shown graphically in fig. 8, the lines t h r o u g h the points being visual aids. The energy spectra were not significantly different at the different scattering angles. To derive a differential energy spectrum for the total p h o t o n production, the data were integrated numerically, m a k i n g reasonable assumptions as to the shape of the differential cross-section curve beyond the region of measurement. Typically a b o u t 23 ~,, of the total cross section was c o n t r i b u t e d by the extrapolation. The c.m. results are listed in table 5 (columns I and I l I ) where the statistical errors only are quoted. To derive the full absolute errors one should c o m b i n e quadratically with the above another 12 ~ as an allowance for errors in the extrapolation procedure a n d l 1 for the absolute errors in the efficiency of the converter a n d the p r o t o n beam intensity. It is a p p a r e n t that if there is a " c a p t u r e " peak at 70 MeV, corresponding to the quasi-free process n(p, ?)d, it does not exceed ~ 1 /tb. This is to be compared with

NUCLEAR

537

BREMSSTRAHLUNG

a value of 11 pb calculated from detailed balance. Alternatively the data would be consistent with the presence of a small amount of ~ 90 MeV radiation coming from the radiative capture process d(p, 7)3He. If one assumed that the total contribution above 90 MeV (the limit set by the available centre-of-mass energy) is due to the higher half of the distribution produced by such a capture process (and of course implicity PROTON - PROTON AND PROTON-DEUTERON BREMSSTRAHLUNG AT 140 MeV 0.8

T //

'

~'

I-oZ0.6

iT [17 I

p-p_['~i p-n KINEMATICS. p-a,~L~ p-d K, NEMAT,CS

~

[-EI~">

40

McV]

U

/

on- 0.4 L)

1[

,

.

I-Z w r,e

uJ 0.2

7,

FROM

U

A '

I

I

,

o L~

0°

~ q

~ ~ 90lo PHOTON ANGLE IN C.M. SYSTEM

180°

Fig. 8. Differential cross section for p - p and p - d bremsstrahlung (E~ > 40 MeV). Lines are drawn to guide the eye t h r o u g h the deuterium data. The p - p line is derived from Ueda (see text). TABLE 4 The lab and centre-of-mass p - d p h o t o n production cross sections E~ > 40 MeV in/~b • sr -t Cross section lab

Cross section c.m. ( p - d kinematics)

01ab

dtr/df2

0c.m.

30 42 54 66 78 90 102 114 126

1.09,0.20 1.07±0.09 1.00±0.09 0.50±0.13 0.45,0.09 0.23 ~0.05 0.18i0.06 0.12±0.06 0.22-}:0.06

35.7 49.3 62.8 75.6 88.2 100.5 112.0 123.2 134.0

da/dO 0.63--0.11 0.56- -0.05 0.70- -0.06 0.40- -0.10 0.41 - -0.09 0.255-0.05 0.23 - -0.08 0.18 0.08 0.285-0.08

Cross section c.m. ( p - n kinematics) 0c.m.

da/d.Q

38.7 53.1 67.3 80.7 93.6 105.6 117.0 127.7 137.9

0.45,0.09 0.48±0.04 0.66--0.06 0.39--0.10 0.42,0.09 0.27,0.05 0.25--0.08 0.20±0.09 0.32i0.09

538

J. A. E D G I N G T O N A N D B. ROSE

ignoring the poor energy resolution of the system) then the cross section for radiative capture is 0.5_+0.2 l~b. This is in adequate agreement with a calculation giving 1 -+ 1 /~b based on a recent m e a s u r e m e n t of the inverse process 17). C o l u m n s II and IV in table 5 give the spectra with the c o n t r i b u t i o n for this presumed capture process subtracted. The total differential cross section for the p - d case ( c o l u m n II) is plotted in fig. 9. D a t a which were available only at two angles were used to derive the point at 35 MeV. TABLE 5

p-d photon production cross sections in nb- MeV-1 Photon energy (MeV)

Cross sections (nb. MeV 1) assuming proton-nucleon kinematics proton-deuteron kinematics lI

IIl

IV

195,20 121,17 70,11 28± 9 94_ 7 6-- 6 --2, 5 --24 4

185+19 104~13 784 11 334 7 21, 6 16, 5 4+ 4 2! 3

185,19 1031 13 74£11 25A 7 10:t- 6 5, 5 --4£- 4 --22. 3

--0.01.÷O.05 4.25£0.33

0.05,0.03 4.48,0.28

0.04 !0.03 4.00,0.28

I

40- 50 50 60 60 70 70- 80 80-90 90-100 100-110 110-120 total cross section qub) > 120 MeV > 40 MeV

195±20 122,17 74,11 36, 9 20-- 7 17-- 6 6i 5 2." 4 0.00 ~=0.05 4.73~0.33

Columns II and IV have been corrected for the calculated cross section for the d(p. 7)aHe radiative capture process (see text). The errors are statistical only. Additional common absolute errors are 12 % for extrapolation and 11% for uncertainty in knowledge of the converter efficiency and beam intensity (see text). 3.4. RESULTS WITH HEAVIER NUCLEI The energy spectra are given in tables 6-8. There are indications that for the lighter nuclei they are somewhat " h a r d e r " for forward than for backward production, though there is no clear i n d i c a t i o n for the heavier nuclei. Similarly, the spectra for a heavy element are somewhat "softer" t h a n for a light element. This is illustrated in fig. 10(i), where the ratio is shown of the double differential cross sections for several other elements to those for c a r b o n at 54 ° p r o d u c t i o n angle. The spectra, which follow an exponential law up to the highest energies we were able to measure (though clearly they must deviate from this near the m a x i m u m kinematically allowed energy), may be characterized by a q u a n t i t y Eo where tr ~ e x p ( - E , . / E o ) . The derived quantities Eo for various p r o d u c t i o n angles are listed in table 9, which gives a q u a n t i t a t i v e evaluation of the above statements a b o u t the relative hardness a n d softness of the spectra, and some of these data are plotted in fig. 10(ii). These effects are clearly not very p r o n o u n c e d .

539

NUCLEAR BREMSSTRAHLUNG

The only really significantly different value is for deuterium in either centre-ofmass system for which E o = 13+_2 MeV, whereas all the other values were near 20 MeV. The differential cross sections for production of photons of energy greater than 30 and 40 MeV are illustrated in fig. I1 and show preferential production in the forward hemisphere. With the limited data available there are no significant differences between the angular distributions of any of the nuclei studied (apart from deuterium),

LEAD

\

_ I0.0

~\

co.°E.,~ ALUMINIUM

~\ T

.

%

~__ t,

CAR~ON\\~ '>

I.O

-

\\t

[

t

\t \t\ \@\ \t,

z O F-

O O.I

0

I 50

I

I0 0

I

150

PHOTON ENERGY (MeV)

Fig. 9. Total energy spectra for p-d and p-nucleus bremsstrahlung. The straight-line fits have a slope characterised by the parameter Eo which is listed in table 9. as is indicated in table 10 where the ratios of a (54 °) and a (90 °) to a (126 °) are seen to be independent of the nucleus. The total energy spectra and the total cross sections were obtained for carbon and oxygen by numerical integration, as for the deuteron case outlined in subsect. 3.3. For these elements the extrapolation over the unmeasured angular region contributed only ~ 10 ~ of the total. The resultant spectra are included in tables 6 and 7.

540

J. A. EDGINGTON A N D B. ROSE

The energy spectra for the total photon production for nuclei other than carbon and oxygen were estimated by assuming that their differential cross sections had the same shape as these two elements, and the corresponding energy spectra are also included in table 8 and also illustrated in fig, 9. Finally in table 11 we list the total 01a b = 5 4 °

(0 z

I

O

T

~ LEAD

" ~ 1 - 1 ._

,~

I "~

. IO'u

T

" " '-

I ~

T

COPPER

_

~:

ALUMINIUtV,

'

~

OXYGEN

t

.i. /-~

! i

5i

,_

"x~ /

±

O 50

O

IOO

PHOTON 0.08

ENERGY

150 (.M~:V)

,l i

006

T

5 }

0.04

To Ld CARBON

002

O. O ; b . . . . .

LEAD

~ ...... PHOTON

:

-

-

-

ANGLE

----90- o ----L

IN

LABORATORY

180o

SYSTEM

Fig. 10, (i) Variation with energy of the cross sections of several elements normalised to carbon. Full: lines correspond to the various fitted values of E0 (see text). (ii) Illustration of the hardening of the spectra in the forward direction (see text). The curve is that expected on the assumption that t h e bremsstrahlung is produced by free p - n collisions within the nucleus (see subsect. 4.2).

NUCLEAR BREMSSTRAHLUNG

541

cross sections and the total cross sections per neutron in the target, which will be discussed later. It is perhaps worth remarking that at the energy of the experiment, the incident protons were above the threshold for no production only in the case of aluminium. However, there was no evidence for the presence of more photons of about 70 MeV energy from the aluminium than from the other targets. At 180 MeV, Cohen 8) had abundant evidence of their presence. f

8F i

a • o

7

6--

5

\

-x\

5i[

J

~T

\\I

[

-I

/'\

! o

4 ~3

PREDICTION OF BECKHAM : FOR CARBON,ABOVE 30 MeV PREDICTION

~ ~ ~

/

OF

S I M P L E P-N

REACTION MODEL (.NORMALIZED TO CARBON

/ /

CARBON, ABOVE 3 0 MeV CARBON. ABOVE 4 0 MeV OXYGEN, ABOVE 4 0 MeV

ABOVE 4O M,V, AT 90°7 ~

~

~

"

WILSON (RE-NORMALIZED)

/',,%, \

2

30 PHOTON

60 ANGLE

~

~

90 IN

LABORATORY

,

120

150

180

SYSTEM (DEGREES)

Fig. 11. Differential cross sections for p-carbon and p-oxygen bremsstrahlung, integrated above p h o t o n energies o f 30 MeV and 40 MeV. Also shown are the normalised experimental points o f Wilson, curves representing the predictions o f a simple p-free neutron production process (normalised to carbon datum at 90 °) and the prediction o f Beckham (see text).

4. Discussion 4.1. C O M P A R I S O N W I T H E A R L I E R D A T A

We can compare our data directly with those of Cohen 8) only in the case of Be at 90 ° . The comparison in fig. 12 shows that the spectra are the same shape, (thus justifying our method of evaluating the data outlined in subsect. 3.1) though our cross sections are approximately a factor of 2 higher than his. This probably lies within the combined errors of absolute normalization. We may make a further comparison with his 95 MeV data on A1 and Cu by observing a "proportionality rule" in comparing Cohen's data at 100 and 140 MeV

183i16 1274`12 834- 8 65± 6 384- 5 28 I 4 19-- 3 15 5 3 4 L 2

0.09 4 0.02 3.87:] 0.17 5.704`0.23

30-. 40 4 0 - 50 50- 60 60- 70 70- 80 80-90 90 100 100 l l 0 110-120

120 40 30

0.09±0.01 3.62~0.12 5.254_0.20

1634-16 1134- 8 86-]: 6 53-2:4 38± 3 28± 3 19-- 2 104` 1 71 l

54 1244-13 814` 9 54± 6 41± 5 194- 3 124- 2 94- 2 4:k 1 3j 1

78 96±11 574-- 5 38t: 3 21:z 2 154- 2 94- 1 44- 1 34` 1 2 L 1

90

0.06±0.01 2.544-0.11 3.894`0.15

0.02i0.01 2.244`0.12 3.484`0.18

0.01 4`0.01 1.50±0.07 2.464`0.13

1)

lab p r o d u c t i o n angle (deg)

Integrated cross section (/tb. sr

135±10 91!: 7 574` 5 394- 4 284- 3 184- 2 94- 2 44- l 44- 1

66

0.01 i 0 . 0 1 1.144-0.09 2.024`0.13

88±10 464` 6 30± 4 214- 3 104- 2 34- 2 14- 1 2± 1 14- I

102

0.00±0.01 0.92_+.0.08 1.51+0.11

594`8 364`5 254`4 154-3 9±2 34-2 44-1 1±1 04`1

114

0.00i0.01 0.69i0.06 1.28±0.09

584`7 354`4 14±3 84-2 54-2 3±1 24-1 1~ 1 1±1

126

0.6 4`0.4 23.24-2.8 36.04`4.3

Total cross section @b)

1.285-0.05 0.82±0.03 0.544`0.02 0.374-0.02 0.22±0.01 0.144-0.01 0.094-0.01 0.054-0.01 0.034`0.00

Integrated cross section (t~b. MeV J)

The totals above 120 MeV probably only reflect the p o o r energy resolution. Extrapolation errors have been included in the total cross sections; olherwise errors arc statistical only. There is an additional 11 o~ absolute crror (see text).

> 2.

42

(MeV)

Photon energy

Bremsstrahltmg production cross sections of C in n b • s r - a . M e V ~ a n d integrated cross sections above 30 MeV, 40 MeV a n d 120 MeV

TABLE 6

0

© Z

89±10 652- 8 50± 7 35± 5 152- 5 182- 4 62- 3

40- 50 50- 60 60- 70 70- 80 80- 90 90-100 100 110 110-120

0.112-0.04

30

Photon energy (MeV)

>120 > 40

TABLE 7

0.15~0.02 4.36~0.15

1512-13 902- 5 58+ 4 46± 3 32± 2 20± 2 13~ 2 112- 1

42

0.132-0.02 3.652-0.18

125±14 812- 7 522- 6 26:k 4 272- 3 20± 3 14± 2 62- 2

54 872-10 632- 7 37± 4 242- 3 15± 3 10± 2 8± 2 4± 2

78 77±7 362-4 282-3 13±2 122-2 5±2 62-1 22-1

90

0.102-0.03

0.032-0.02 2.512-0.14

0.042-0.01 1.82~0.09

Integrated cross section Q~b. sr -])

492-9 28±8 262-6 182-5 10~5 102-4 82-3

66

lab production angle (deg)

0.022-0.01 1.37±0.10

612-7 252-4 222-4 13±3 62-2 3±2 5±2 12-2

102

0.032-0.02 0.92±0.10

37±7 162-5 13±3 10±2 72-2 32-2 3±2 1±1

114

0.01±0.02 0.982-0.08

372-5 242-4 162-2 9±3 4±2 4:k2 22-2 0±1

126

0.62-0.2 25.82-3.1

Total cross section ~ b )

1.012_0.14 0.57±0.06 0.412-0.05 0.172-0.02 0.16±0.02 0.112-0.02 0.09-k0.03 0.032-0.01

Integrated cross section Q~b- MeV 1)

Bremsstrahlung production cross sections of O in nb • sr -~ • MeV -1 and integrated cross sections above 40 MeV and 120 MeV

z

z

r~

a:

(3

544

J. A. E D G I N G T O N

AND

B.

ROSE

on Be. We can test the assumption that the total radiation above an energy E~, is proportional to the ratio (E,./Ep), where Ep is the proton energy, but is otherwise independent of Ep and E~, by multiplying the energy scale for the 100 MeV data by (140_~ and dividing the double differential cross sections by the same factor. This 1001 test also is shown in fig. 12 and the agreement is excellent. We now use this assumption to compare his limited 95 MeV data on A1 and Cu with ours. The shapes are again in good agreement; for the A1 data the magnitudes require the same factor of 1.9 as for Be but the ratio for Cu cannot exceed 1.5. Equally meagre data are available on the angular distribution. Wilson 7) obtained some data for photon production above about 20 MeV, and he presents ratios of count rates at 30 °, 45 ° and 180 ° to that at 90 ° for Be at 140 MeV proton energy. These points, normalized to our 30 TABLE

Bremsstrahlung production cross sections of Be, N, Al, Cu and Pb in nb • sr -Z • MeVPhoton energy (MeV) 30- 40 40- 50 50-60 60- 70 70- 80 80-90 90-100 100-110 110 120

Be . 90 ~

472-5 332-4 202-3 112.2 82-2 62.1 42.1 12.1

N .

66 ~

54 °

A1 . 90 °

1392.21 952.14 612. 9 42, 6 272- 5 102. 3 72- 2 42- 2 2~ 1

3572_32 2232.21 1592.16 101,11 71~ 8 41, 6 28-- 4 20 ~'- 4 8-= 2

177~2l 1192-14 80i10 52~ 7 362- 5 19, 3 12, 3 62- 2 12. 1

.

.

.

.

.

Cu .

. 126 ° 126£: 63, 32± 15, 122. 92522, 12.

14 9 6 4 3 2 2 1 I

.

. 54 °

. 90 °

8032-72 4362-42 290-z29 1752-20 1282.15 612,10 452- 8 19, 5 162. 4

3872-40 207£=24 109,18 72,11 51± 9 22-~ 6 194- 4 172. 4 82- 3

Integrated cross section ( # b - s r > 120 > 40 > 30

0.02±0.01 1.312.0.08

0.04±0.01 2.512.0.19 3.90,0.28

0.10i0.03 6.62::[-0.31 10.192.0.45

0.02±0.02 3.272,0.19 5.04,0.29

0.012.0.01 1.382.0.12 2.64,0.19

0.182.0.05 11.88::i_0.58 19.91,0.92

1

0.062-0.03 5.11,0.34 8.982-0.53

MeV carbon point at 90 °, are shown in fig. 11 and are in adequate agreement with our results. The total cross section is plotted against ( A - Z ) A - " in fig. 13. The latter function represents a product of the normal A~ variation observed in proton reaction cross sections ~~) with a factor (A - Z)/A representing the fraction of nucleons in the nucleus which are neutrons. The straight line relationship is in good agreement with the data of Wilson v), which are given in table 11. Wilson's data were taken at 90 ° only and we have normalized them to the carbon total cross section. 4.2. C O M P A R I S O N O F p - N U C L E U S R E S U L T S W I T H B E C K H A M ' S T H E O R Y

The only quantitative theoretical work with which we can make comparison is

NUCLEAR BREMSSTRAHLUNG

545

t h a t by B e c k h a m 19). H e considers two possible sources for nuclear b r e m s s t r a h l u n g . The first assumes the interaction to t a k e place between the incident p r o t o n a n d the target nucleus as a whole. The second assumes t h a t the p r i m a r y i n t e r a c t i o n is between the incident p r o t o n a n d the i n d i v i d u a l target neutrons, p r o t o n - p r o t o n b r e m s s t r a h l u n g being a s s u m e d to be negligible. The first a p p r o a c h B e c k h a m considers less satisf a c t o r y because o f the size o f the nucleus c o m p a r e d with the p r o t o n wavelength, a n d he m a k e s calculations only at one p r o d u c t i o n angle (90 ° lab). However, a c o m p a r i s o n between his calculations a n d o u r results divided by a factor o f 3.5 shows that this a p p r o a c h gives a respectable qualitative fit b o t h to the energy s p e c t r u m a n d to the relative cross sections for different nuclei. This is ill u s t r a t e d in fig. 14, where a c o m p a r i s o n is m a d e with fig. 14 o f B e c k h a m ' s paper.

and integrated cross sections above 30 MeV, 40 MeV and 120 MeV Integrated cross section ~ b • MeV -1)

Pb 126°

54°

90°

126'~

AI

Cu

Pb

197,23 121±14 74± 9 52, 7 26, 5 14± 3 7, 3 4, 2 1, 1

1735,144 1135± 97 7 8 6 , 70 4 3 1 , 51 2 7 7 , 37 2 3 1 , 31 9 1 , 17 6 9 , 18 5 2 , 16

908,173 643,113 4 1 0 , 87 1 8 2 , 69 1 4 7 , 48 1 1 5 , 32 9 0 , 28 6 1 , 23 22± 16

547±127 2 4 9 , 82 2 3 1 , 60 161± 43 106, 32 49± 22 2 7 , 17 11± 13 5 , 15

2.83,0.36 1.64,0.19 1.01--0.12 0.71,0.09 0.43±0.06 0.22,0.04 0.14,0.03 0.12,0.03 0.04,0.01

6.13--0.80 3.09,0.37 1.79,0.22 1.20,0.17 0.76,0.10 0.31,0.06 0.21--0.04 0.10,0.03 0.07,0.03

14.1 , 1 . 8 8.6 , 0 . 9 5.15±0.57 3.13 ~'-0.44 1.74,0.27 1.24~0.20 0.45i0.10 0.40±0.11 0.24±0.08

Total cross section (#b) 0.03,0.02 3.02--0.19 4.99--0.30

0.55,0.15 31.26±1.42 48.61,2.02

0.33±0.20 15.99,1.74 25.07,2.45

0.36±0.17 8.73±1.19 14.20±1.74

0.2,0.1 45.0,5.4 71.5,8.6

0.3-- 0.1 79.9, 9.6 135.8,16.4

1.3± 0.4 224 ±27 351 ~ 4 2

The a p p r o a c h B e c k h a m prefers is to derive a square well o p t i c a l p o t e n t i a l which r e p r o d u c e s (more-or-less) the free n e u t r o n - p r o t o n scattering differential cross section. H e calculates the 90 ° b r e m s s t r a h l u n g p r o d u c t i o n at three energies (20, 50 a n d 80 M e V for 100 M e V p r o t o n s incident) with various a s s u m p t i o n s a b o u t the nucleon m o m e n t u m d i s t r i b u t i o n inside the b e r y l l i u m nucleus. H e then selects the m o m e n t u m d i s t r i b u t i o n which gives the best fit to C o h e n ' s d a t a for Be. U s i n g this nucleon m o m e n t u m d i s t r i b u t i o n , he then calculates the a n g u l a r d i s t r i b u t i o n o f these p h o t o n s . W e can m a k e a c o m p a r i s o n with our d a t a at 140 M e V b y use o f the p r o p o r t i o n a l i t y rule o u t l i n e d earlier in subsect. 4.1. W e find t h a t the s p e c t r u m at 90 ° f r o m Be is q u a n t i t a t i v e l y correct. B e c k h a m ' s calculated points ( f r o m his m o m e n t u m d i s t r i b u t i o n 8 a n d square well n u m b e r 2) r e n o r m a l i z e d by the p r o p o r t i o n a l i t y rule are i n d i c a t e d

546

J. A. E D G I N G T O N A N D B. ROSE

in fig. 12. His calculations are in better a g r e e m e n t with our absolute scale than with C o h e n ' s results, b u t owing to the large error on C o h e n ' s absolute scale perhaps t o o m u c h should not be read into this fact. It appears to us t h a t B e c k h a m ' s conclusion that C o h e n ' s 100 M e V d a t a for AI an d Be show a m a r k e d l y different spectral shape and therefore require a different nuclear m o m e n t u m distribution is based u p o n a misreading f r o m one o f C o h e n ' s graphs. U n f o r t u n a t e l y C o h e n ' s data are only presented in graphical f o r m which makes c o m p a r i s o n s unnecessarily difficult. N o w m a k i n g a reasonable i n t e r p o l a t i o n between the p h o t o n energies o f 20. 50 TABLE 9 The quantity Eo in MeV evaluated in the lab system at various production angles and also (last column) for the total energy spectrum Element

lab production angle (deg) 30

D Be C N O Al Cu Pb

42

54

66

78

90

Total 102

114

126 21.5£5

23,3

24--3

25,4

26,4

26±7 23,3 20,4 21,2

21,4 21,3 19,3 32:!_6 23-k4

21,5 20-.'-2 1 5 , 3 21±6 19,2 22,3 24,8

18"6

17,3

18,2

22 _--_2.5

20~7

17,3 17,2 16~2 18,3

23.5--5 20.5,2 18.5,2.5 19 --1.5

The variation of Eo with angle and element is discussed in the text. The separate angular points for deuterium are not quoted owing to their large errors. TABLE 10 Ratios of differential cross sections to those at 126% for various elements Element

01a b

54 D

C O A1 Cu Pb Mean (excluding deuterium)

(deg) 90

2.1 ±0.6 a) 2.5±0.7 t~) 4.5,1.4 e) 4.1--0.5 3.7--'_0.5 3.9,0.5 4.0,0.5 3.4--0.5

0.9,0.3 0.9±0.3 1.1±0.5 1.95_0.2 1.9,0.2 1.9±0.2 1.8,0.2 1.8£-0.3

3.8,0.2

1.9,0.1

~) Assuming p-nucleon kinematics. b) Assuming p-deuteron kinematics. e) Lab system.

126

NUCLEAR BREMSSTRAHLUNG

547

and 80 MeV (equivalent, for 140 MeV incident protons, to energies of 28, 70 and 112 MeV, respectively) we may derive an angular distribution for the production of photons of energies greater than 28 MeV (Beckham's figs. 22-24, 26-28). We now apply a correction factor of 0.87 to convert Beckham's values to those to be expected from carbon; this correction factor is derived from the total cross sections listed in table 11. The result is plotted in fig. 11 and the general qualitative agreement is apparent, i.e. strong peaking in the forward hemisphere and the correct magnitude. We have also calculated the angular distribution on the assumptions that the bremstrahlung is produced by free p-n collisions within the nucleus, that the neutrons TABLE 11 T o t a l cross sections for b r e m s s t r a h l u n g p r o d u c t i o n with p h o t o n energies greater t h a n 30 M e V a n d 40 M e V Cross section (#b)

Cross section per n e u t r o n Qzb)

Target E r (MeV)

H D

Be C N O A1 Cu Ag W Pb

143 136

138 137 131 136 135 131 (143) (143) 139

> 30 M e V

> 40 M e V

< 0.10a)

< 0.02 a) 4.0___ 0.3 b) 4.34- 0.3 e) 5.14- 0.5 a) 20 , 2 23 , 3 23 , 3 26 , 3 45 , 5 80 , 1 0

36, 4 36~ 4 72~ 9 136±16

351,42

224

4-27

> 30 M e V

Wilson's results for cross section p e r > 40 M e V n e u t r o n E~ ~ 20 MeV e)

5.1±0.6 3.94-0.5

4.04-0.3 4.34-0.3 5.1,0.5 4.0,0.4 3.8,0.5 3.8,0.5 3.34-0.4 3.24-0.4 2.3--0.3

2.8,0.3

1.84-0.2

6.04-0.7 6.04-0.7

6.7 6.0

5.0 4.2 2.5 2.0

E- r is the energy at the centre o f t h e target. Errors are c o u n t i n g errors plus extrapolation errors c o m b i n e d quadratically (see text).

a) A t the 95 ~ confidence level. b) A s s u m i n g p - d kinematics. e) A s s u m i n g p - n kinematics. d) L a b system. e) N o r m a l i z e d to o u r result for carbon, > 30 MeV. All d e u t e r i u m values s h o w n have been reduced by 0.5 /~b to allow for the calculated radiative c a p t u r e cross section (see text).

are stationary, that the bremsstrahlung are produced isotropically in the p-n centreof-mass system and that they have a c.m. spectrum characterised by Eo -- 13 MeV. These naive assumptions produce quite a reasonable fit to the data, as is seen in fig. 11. The softening of the spectrum (see subsect. 3.4) as the target mass increases is in agreement with the general proposal by Beckham that, for the heavier targets, the protons will scatter inside the nucleus with a consequent reduction of their energy before radiating, and that therefore the photon spectrum produced from heavier

548

J.

A. E D G I N G T O N

AND

B.

ROSE

nuclei will be characteristic of a lower incident proton energy than in the case of light nuclei. While this prediction is confirmed it is clearly not a very strong effect. The simple model of quasi-free p-n collisions, outlined above, also predicts through kinematic effects alone a hardening of the spectrum in the forward direction, and in fig. 10(i) we show the expected variation of Eo with angle. Again the qualitative teatures of the data are well reproduced. IOO

S~

X

I0

u~

0

Q

F Z

o

~

Jb

. . . .

60

40

PHOTON

BO ENERGY

iO0

120

I~ M e V )

Fig. 12. C o m p a r i s o n o f observed energy spectrum for Be at 9 0 with previous results and theoretical prediction. © - this experiment, 140 M e V protons incident (the straight line is a fit to the results, using E0 -- 21 M e V ) . • - Cohen's results, 140 M e V protons incident. × - Cohen's results at 100 M e V adjusted to 140 M e V by m e a n s o f the proportionality rule (see text). • - B e c k h a m ' s calculated points at 100 MeV, similarly adjusted to 140 M e V . 4.3. P R O T O N - D E U T E R O N

DISCUSSION

The only experimental data we have for comparison are some preliminary work reported from Rochester 24), where at a mean proton energy of 148 MeV and a photon threshold of 25 MeV, a total cross section of ~ 26/~b was obtained. A rough extrapolation of our results to the lower photon threshold suggest a value of ~ 11 /xb. This apparent disagreement of a factor of two is as yet unexplained though part of it may lie in the definition of a "threshold". However, it should be noted that our cross sections for Be at 90 ° lab were higher than Cohen's by about a factor of two.

NUCLEAR

549

BREMSSTRAHLUNG

W e m a y n o w discuss the relation between p - d results and that from the free p - n interaction. It has already been remarked in subsect. 3.3 that the spectra f r o m deuterium showed a m a r k e d lack o f anything approximating to a radiative capture peak corresponding to the reaction p(n, 7)d. However, the laboratory angular distribution, the number o f photons per neutron in the target and the spectra are very similar to those from the lightest nuclei studied.

200

Pb

z 0 i-.u LL~

0 U .J

I00

Cu

S I-

0 ~ 0

r 10

I 20

(.A - ~ ) I A ~/3

Fig. 13. Total cross sections for bremsstrahlung production with E~ > 30 MeV as a function of A and Z. The line is drawn to guide the eye. Results not listed in table 11 have been derived by appropriate extrapolation from 40 MeV. B e c k h a m showed that for beryllium, the inhibition due to the exclusion principle was such that p h o t o n radiation at 90 ° (lab) at 20 and 50 M e V would be only about half that to be expected f r o m a free neutron (excluding radiative capture). Our results on total or differential cross sections from various nuclei s h o w that, with the assumption o f a p - n origin for bremsstrahlung, the experimental inhibition factor varies very slowly for the light nuclei from deuterium to oxygen. Accordingly the

J, A. E D G I N G T O N A N D

550

B. ROSE

observed radiation from deuterium must be a lower limit to that to be expected from the free neutron (again excluding radiative capture). If we assume that the inhibition factor calculated by Beckham for beryllium applies to all energies and angles, then the radiation from the free neutron should be twice that from beryllium. We thus arrive at tentative figures of ~ 14 /~b and ~ 8 /~b for the total cross sections for the production of photons of c.m. energy greater than 30 MeV and 40 MeV, respectively, for free p-n collisions. More certainly, these cross sections exceed 8 gb and 4 gb, respectively (the p-d values). The bremsstrahlung spectrum for the free p-n interaction has been calculated by Cutkosky 5) at 90 and 400 MeV, and by integrating his curves and interpolating to 140 MeV we derive cross sections of ~ 17 Fb and :~ 11 pb for photons of energies

0.4

"~ z

{)lab = 900

ALUMINIUM /

~-

T

/

O. 3

PER

i

W

~

0.2.

t~ k) d

©.1

--

o

Z W or"

;

w Lt_ U_

U,

! O

IO

20

40 PHOTON

60 ENERGY

80

(MeV)

Fig. 14. Our experimental results on the energy spectra for various elements, compared with Beckham's theoretical predictions multiplied by a factor o f 3.5.

> 30 MeV and > 40 MeV in the centre of mass, exclusive of the capture peak of 11 /~b which would be present in free p-n scattering. This is in good agreement with our own tentative figures of ~ 14 #b and ~ 8/~b. 4.4. P R O T O N - P R O T O N

DISCUSSION

We may compare our data at 90 ° with a preliminary value at ~ 200 MeV obtained at Rochester 24). The measured differential cross section for the production of photons of energy > 35 MeV (lab) was 3 8 + 7 nb • s r - ' , to be compared with our figure o f - 3 + 1 3 n b . sr -1. However, Ueda 26) makes two field theoretical calculations of bremsstrahlung production in the p-p system at 200 and 160 MeV, giving c.m. spectra at lab angles

NUCLEAR BREMSSTRAHLUNG

551

of 45 °, 90 ° and 135 °. F r o m these spectra one m a y make a reasonable graphical extrapolation to derive spectra at 140 MeV. Taking his calculation which gave the lower cross sections (that using a phenomenological f o r m factor) we derive values o f the differential cross section for production o f p h o t o n s o f energy > 40 MeV, which are plotted on fig. 8. The cross sections are clearly m u c h greater than our observed values, and it is important to note, are a b o u t equal to the background rates we observed. The corresponding total cross section is ~ 0.3 /~b to be c o m p a r e d with our value o f -0.06+_0.05 #b. For a threshold o f 30 MeV, the calculated total cross section is ~ 0.5/~b to be c o m p a r e d with our value of -0.01_+0.06 pb. These calculated values, assuming our extrapolation procedure to be valid, are therefore at least four times our measured upper limit (95 ~ confidence level). At 90 ° lab U e d a obtains a value o f 70 nb • sr-a at 200 MeV, a factor of two above the value measured at Rochester. We m a y compare the two experimental values by using our extrapolation o f U e d a ' s calculations on a relative basis only. These suggest that the cross section at 140 MeV for p h o t o n s > 35 M e V should only be one third o f that at 200 MeV, i.e. 12-t-2 n b " sr -1 which does not disagree with our measured value of - 3 _ + 1 3 n b • sr- 1 These calculations of U e d a lie much nearer the experimental values than do calculations o f Sobel 2o) and o f Sobel and Cromer 25). The latter calculations are on more specific p - p bremsstrahlung processes, in which both protons are observed, and are at least an order of magnitude higher than the experimental results 22-24) at 50, 160 and 200 MeV. We m a y c o m p a r e our results with Sobel's estimate 2 o). Using the Yale potential 21), he calculates the quantity d3~/df21df2~dE~, where E 1 is the energy of a p r o t o n scattered into an element o f solid angle dr21 and d(27 an element o f solid angle in the p h o t o n direction, which is restricted in his calculation to being perpendicular to the scattering plane of the p r o t o n (and therefore at 90 ° in the lab system). His calculation is carried out for an incident p r o t o n energy o f 142 MeV and a p h o t o n energy ot 27.5 MeV. We can convert this to a partial differential cross section over photon energy instead of proton energy by multiplying by dE1/dE ~ where the latter term is evaluated at a p h o t o n energy of 27.5 MeV. Integrating Sobel's numerical results over Q~ we find a value o f ~ 3 n b • s r - t • M e V - ~ as the contribution to the p h o t o n spectrum at 90 ° from those protons which are scattered in a plane at right angles to the direction in which the p h o t o n s are detected. This is clearly a lower limit and is to be compared with our observed value o f 0.1_+1.0 n b . sr -1 • MeV - t at an energy o f 34 MeV (lab). If we assume that this cross section is independent o f the plane o f scattering, then the calculated value rises to ~ 20 n b • s r - 1 - M e V - 1 , which is at least ten times the observed value and therefore markedly worse than Ueda's estimate. We cannot usefully c o m p a r e our result with the calculation of Dullemond and de Swart 6) owing to the narrow energy range which they considered near the peak o f the bremsstrahlung spectra and to our p o o r energy resolution.

552

J.A. EDGINGTON AND B. ROSE

Finally, we should call attention to the very small ratio between the total cross sections for photons > 49 MeV for the p-p and p-n systems viz. ( - 0 . 0 1 + 0 . 0 6 ) / 14 ~ -(0.001_+0.094). This was an early prediction of Ashkin and Marshak 1) which is confirmed experimentally for the first time. The Rochester group have recently 24) obtained a similar result. The authors are grateful for assistance from Mr. E. Wood and the synchrocyclotron staff at AERE, and to Dr. Frank, Dr. Wormald, Mr. J. Barclay and others on the Liverpool synchrocyclotron for assistance and advice during the calibration run on that machine. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 121 131 14) 15) 16) 171 181 191 20) 21) 22) 23) 24) 25) 26)

J. Ashkin and R. E. Marshak, Phys. Rev. 76 (19491 58 M. Krook, Proc. Phys. Soc. 62A (1949) 19 Pomeranchuk and Shmushkevich, Doklady 64 (19491 499 A. Simon, Phys. Rev. 79 (19501 573 R. E. Cutkosky, Phys. Rev. 103 (19561 505 C. Dutlemond and J. J. de Swart, Physica 26 (19601 664 R. Wilson, Phys. Rev. 85 (19521 563 D. Cohen, B. J. Moyer, H. C. Shaw and C. N. Waddell, Phys. Rev. 130 (19631 1505; D. Cohen, UCRL-3230 (19551 D. P. Jones, P. G. Murphy, P. L. O'Neill and J. R. Wormald, Proc. Phys. Soc. 77 (1961) 77 J. A. Edgington, thesis, Cambridge University (19651 unpublished A. Kantz and R. Hofstadter, Nucleonics 12, No. 3 (19541 36 B. Rossi, High energy particles (Prentice-Hall, New York, 19521 p. 83 ibid., pp. 27, 50 R. D. Birkhoff, Handbuch der Physik, Bd. 34 (Springer-Verlag, Berlin) P. H. Bowen et aL, Nuclear Physics 41 (1963) 177 and associated papers P. Bowen et aL, Nuclear Physics 22 (1961) 640 A. N. Gorbunov and A. T. Varfolomeev, Phys. Lett. 5 (19631 149; V. N. Fetisov, A. N. Gorbunov and A. T. Varfolomeev, Nuclear Physics 71 (19651 305 J. M. Cassels and J. D. Lawson, Proc. Phys. Soc. 67 (19541 125 W. C. Beckham, UCRL-7001, Livermore (19621 M. 1. Sobel, Phys. Rev. 138 (1965) B1517 K. E. Lassila et al., Phys. Rev. 126 (1962) 881 B. Gottschalk, W. J. Schlaer and K. H. Wang, Phys. Lett. 16 (1965) 294 R. E. Warner, Phys. Lett. 18 (1965) 289 K. W. Rothe, P. F. M. Koehler and E. H. Thorndike, contribution to the Williamsburg Conf. on intermediate energy physics (1966) M. I. Sobel and A. H. Cromer, Phys. Rev. 132 (19631 2698 Y. Ueda, Indiana University preprint (19651