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The (n, p), (n, d) and (n, α) reactions induced by 14.6 MeV neutrons in CsI(Tl) scintillation crystals
~ [
NuclearPhysics 4 2 Not
(1963) 27----46; ~ )
North-Holland Publishing Co., Amsterdam
to be reproduced by photoprint or microfilm without written permission from the publisher
T H E (n,p), (n, d) AND (n, a) REACTIONS INDUCED BY 14.6 MeV NEUTRONS I N CsI(TI) S C I N T I L L A T I O N C R Y S T A L S W. R. D I X O N
National Research Council, Ottawa, Canada Received 1 October 1962
Abstract: The (n, p), (n, d) and (n, a) reactions induced by 14.6 MeV neutrons in C s I ( T I ) scintillation crystals have been observed. Pulse shape discrimination has been used to distinguish the various particles, permitting an energy spectrum for each to be obtained. The proton and alpha particle spectra have been analysed from the point of view of the statistical theory of nuclear reactions, hut there are left over substantial components which must be attributed to direct interactions. The direct component for protons is estimated to be at least 45 %, and for alpha particles to be at least 38 ~o- Absolute cross sections have been obtained by the method of "tagging" the neutron beam by its associated particles; the averages for Cs and I are found to be a(n, p) 8+ I rob, o(n, d) = 1.2-t-0.2 mb and a(n, a) = 1.8±0.2 rob.
1. Introduction The study o f (n, p), (n, d) and (n, ~) reactions in medium and heavy nuclei is made difficult by the low cross sections and the impossibility o f getting charged particles out o f thick targets. F o r these reasons m o s t studies have been confined to measurements o f the cross section by activation methods, and there have been only a few attempts to measure energy and angular distributions o f the emitted particles. In the present experiment (n, p), (n, d) and (n, ~) reactions induced by 14.6 MeV neutrons in a CsI(TI) scintillation crystal have been observed, the crystal serving as both target and detector. Pulse shape discrimination has been used to identify the particle type and energy distributions for protons, deuterons and alpha particles have been measured. Absolute (n, p) and (n, ~) cross sections have been measured by "tagging" the neutron beam, that is by taking coincidences with the alpha particles associated with the production o f the neutrons in the d-t reaction. Although it is impossible to separate the contributions o f ssCs 133 and s3 I127 to the observed reactions, it is important to note that the two nucleides in question are close together in Z and A values, and that each contains an odd n u m b e r o f protons and an even n u m b e r o f neutrons. The Q values for the various reactions have been obtained f r o m the mass tables o f KiSnig, M a t t a u c h and Wapstra 1) and are listed in table 1. The values for the two nucleides are remarkably close together. Thus there is considerable d priori evidence for supposing that 55Cs t 33 and s 3I127 should behave similarly. 27
28
W.R.
DIXON
Experiments with CsI similar in principle to that described here have been reported by B o r m a n n et al. 2-4) and by Marcazzan et al.5). O f these, our experiment is the first in which the techniques o f pulse shape discrimination and beam-tagging have been combined to give the absolute cross sections for protons and alpha particles in single measurements. It is also the first o f these in which deuterons have been distinguished from protons. TABLE 1
Q values in MeV of various reactions in Cs x3~ and 1137 Reaction
Cstaa
I tu
(n, p) (n, np) (n, d) (n, c~) (n, n~) (n, 2n)
+0.36 .... 6.42 -4.20 +4.16 -2.32 -9.02
+0.10 - 6.25 -4.03 +4.22 -2.23 -9.15
2. Experimental Arrangement 2.1. GENERAL Neutrons o f energy 14.64-0.1 MeV were obtained from a Texas Nuclear Model 150-1H neutron generator in which deuterons are accelerated to energies up to 150 keV and allowed to strike a tritium target. A block diagram o f the electronic apparatus is shown in fig. 1. The diagram is divided into three section.~, o f which those labelled A and B were used for the cross section measurements, while those labelled A and C were used for the spectral measurements. This division was made merely for convenience, there being no reason in principle why both types o f measurements could not be made simultaneously. The c o m m o n section A includes amplifiers to handle both an integrated (or E-) pulse and a current pulse from the CsI(TI) crystal. The latter was analysed for decay time z, and a dot for each pair o f E- and z-pulses was then plotted on an oscilloscope screen. Protons and alpha-particles lay on two different loci on the screen. A mask was used to eliminate the undesired dots, so that one kind o f particle only could give rise to signals in a photomultiplier viewing the screen. The signals could be either counted in a scaler, or used to select certain E-pulses for pulse-height analysis. When the spectrum was being measured all pulses from the E-amplifier were intensified on the oscilloscope screen, while in the cross section measurement, only those in coincidence with the associated-particle detector were intensified. 2.2. THE CsI(TI) CRYSTAL The CsI(TI) crystal, obtained from Harshaw Chemical Co., had a diameter o f 2.0 cm and a thickness o f 1.0 cm. It was mounted inside a tantalum cup, and optically coupled to the face o f a D u Mont-6467 photomultiplier with a thin smear o f silicone grease. It was essential to avoid thick aluminium reflectors, and o f course, hydroge-
I
SCALER
SCALER
2 T = 3/.LS
/L. 1
]
I .......
C
] I STRETCHER
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E-
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READ TRIGGER OUT
LATE ANTICOINCIDENCE
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I STRETC"ERI
SHAPE ANALYZER
¼
l
WIDEBAND AMPLIFIERS
~ P.OTOMUL,.PL.ER
7OSCILLOSCOPE ~'
JPLDTTING
DELAY 3/J.S /
INTENSIFIER
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o7
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I INTEGRAL DISCRIMINATORI -
A
Csl(Tb) CURRENT PULSE
.
.
.
.
.
.
.
I
r
.
.
.
.
I
1
7 ~,C.ORTER~ I
.
._1
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Fig. I. Block diagram of the electronic apparatus used in conjunction with the CsI(TI) crystal. Sections A and C were used for spectrum measurements, A and B for absolute cross sections.
B
I
COINCIDENCE L JI
SINGLE CHANNEL
I 'MPL'F'ER J
ASSOCIATED--PARTICLE DETECTOR
C~I(T~) INTEGRATED PULSE
t~ ~D
O
> Z
30
w.R. DIXON
nous material, in order to reduce the external contribution of charged particles. The inside of the tantalum cup was aluminized by evaporation to a thickness of only about 0.1 mg/cm2; a hole at the top, which was used to allow charged particles to enter for energy calibration purposes, was covered with aluminium foil of thickness 0.32 mg/cm 2. During the neutron irradiation it was also covered with a tantalum disc. An energy calibration curve for protons was obtained by bombarding an Li6F target t with 130 keV deuterons. The reaction Li6(d, p)Li 7 produces protons of 4.29 and 3.88 MeV at an angle of 135°; when account is taken of the energy loss in the aluminium foil over the crystal, the energies are reduced to 4.27 and 3.86 MeV, respectively. In addition to these two proton peaks, there is also a proton peak from the interaction of bombarding deuterons on deuterium already occluded in the ,:,:get. At 135 ° the energy of these protons reaching the crystal is 2.72 MeV. The relative intensity of the latter peak is very small with a fresh target, but grows to be the predominant peak after a few hours bombardment. These peaks are shown'in fig. 2. Judging by the work ofQuinton et al. 4) and of Mead and Cohen 7) the response for protons is proportional to the energy. We have, therefore, made a least-squares fit for the best straight line through the three points and the origin. This line is shown in fig. 3. 1
w
I
:
I
I
I
I
I
~.0
I
I
DEUTERONS
-
PROTONS
Z
4.0
~:
3.0
~ .../
2.0
2
4
6
8
I0 ENERGY
12
14
16
18
20
22
IMev)
Fig. 3. The response of the CsI(TI) crystal to protons, deuterons and alpha-particles. The circles are experimental points. The line for protons has been obtained from a least-squares fit. The curves for alpha-particles and deuterons are from Mead and Cohen ~), normalized at an alpha-particle energy of 10.4 MeV.
For alpha particles the response is linear above about 8 MeV, but nowhere is it proportional to the energy. A point on the curve at 10.4 MeV is available from the Li6(d, ct)~t reaction at 135 °, and additional points were obtained at lower energies with a polonium alpha source. These were not sufficient, however, to establish the response curve in the energy region of interest (10-20 MeV), so that the curve of Mead and Cohen 7) was used, normalized at the value of 10.4 MeV. It is shown in fig. 3. Mead and Cohen 7) have also measured the response to deuterons (but not protons) * The LiSF target was supplied by the Atomic Energy Research Establishment, Harwell, England.
(n, p), (n, d) AND (n, ~t) REACTIONS
31
and found it to be proportional to the energy. Their response curve for deuterons is shown in fig. 3 and is seen to lie only slightly below our response curve for protons. Within the accuracy of the measurements the response to protons and deuterons is the same. The ordinate in fig. 3 is the ratio of peak channel observed to the peak channel for the Zn 65 photo peak, the latter being observed with the coarse gain of the amplifier increased by a factor of four. The Zn 6s source was used only as a monitor on the gain during the subsequent runs, so that the exact value of this factor is of no importance. The stability is, of course, important; the ratios in fig. 3 remained constant to within + 1% during the period in which runs were taken (one month). 2.3. P U L S E
SHAPE
DISCRIMINATION
Fig. 4 shows the spectrum of pulses produced by the CsI(Tl) crystal irradiated by 14 MeV neutrons. Most of the pulses are due to electrons and gamma-rays. The hump I00000
I
i
1
I
I
_\
I0000
\
\ i
,
ooo 1-
-~ r
p
b
i,i
tOO
o 1o
l0
{
I 40
I 80
I 120
CHANNEL
I 160
I 200
! 240
NUMBER
Fig. 4. Pulse-height distribution for CsI(TI) i~adiated with 14.6 MeV neurons. around around achieve Storey,
channel 130 is due to protons, and evidence of alpha particles is to be seen channel 200. The technique of pulse shape discrimination can be used to an excellent separation of these particles in CsI(T1). Following the work of Jack and Ward s) there have been a number of methods devised to achieve
32
w.R. DIXON
this separation; we have used the method of Biggerstaff et al. 9) in conjunction with a plotting oscilloscope. The circuit of Biggerstaff et aL 9) essentially measures the decay time of the current pulse from the photomultiplier. A time-to-amplitude converter produces a saw tooth output pulse whose amplitude is a measure of the scintillator decay time. For input pulses of amplitudes greater than a certain minimum value, the output is independent of the input amplitude, and depends only on the decay time of the scintillator. We call this output pulse the z-pulse. A plotting oscilloscope has been used to display the pulse-shape effect. The E-pulses were stretched to about 12/~sec and applied to the horizontal deflecting system, while the z-pulses were similarly stretched and applied to the vertical system. A pulse taken from an integral discriminator in the E-amplifier was used to generate an intensifying pulse after a delay of about 5 #sec. This delay was necessary to give the shape analyser enough time to complete its analysis. The result was a dot on the screen for each pulse, plotted according to its E- and z-values. A photograph of the dot pattern for charged particles emitted from a Li6F target bombarded with deuterons is shown in fig. 2, together with spectra of both the E- and z-pulses obtained with the kicksorter. Fig. 5 shows the dot pattern obtained from irradiating the CsI(TI) crystal with 14 MeV neutrons; the separation into gamma rays, protons and alpha particles is clearly visible. The physical equipment used for the display and recording of the dot pattern consisted of a Tektronix 585 oscilloscope (which proved to have sufficient stability), a P-15 cathode-ray tube with a decay time of 1.7/asec and a Tektronix C-12 camera with a Polaroid Land back. Over a limited energy range it is possible to use a single-channel analyser on the output of the shape analyser in order to select particles of the desired type. Fig. 5 however, shows that the z value for protons depends on the energy over the range 2-14 MeV, so that a more elaborate selection system was necessary. The method used is already well established in the literature: a mask was placed over the oscilloscope screen with a slit cut in it, so that the locus of dots due to one kind of particle only could be seen. A photomultiplier (Du Mont K1732) was placed in front of the screen and its output pulses were then used for selection purposes. The arrangement adopted was to focus the dots on a ground glass screen at the position normally occupied by the film in the Polaroid Land back. The ground glass screen then acted as a secondary source for the photomultiplier. A crude lens system was introduced to focus the light more effectively onto the rather small photomultiplier. Visual monitoring of the dot pattern was possible by virtue of the beam splitting mirror in the Tektronix C-12 camera without having to remove the photomultiplier assembly. When the counting rate was particularly low, photographic monitoring was necessary; this was easily achieved by sliding the photomultiplier assembly out of position and inserting in its place the Polaroid Land back.
ENERGY SPECTRUM Li s (d,p)
Lil(d.a)
d (d,p)t
J
o.
u
m
,tV,'tO
|
|
I
!
Fig. 2. Nuclear events from b o m b a r d i n g a LiSF target with deuterons, observed with a CsI(TI) crystal. The p h o t o g r a p h shows each event plotted as a dot on the oscilloscope screen, with energy as abscissa and shape as ordinate. The pulse-height distributions were obtained with the kicksorter, with the pulse-height scales matched to the photograph.
0¢
Fig. 5. Dot photograph for CsI(TI) irradiated with 14.6 MeV neutrons. The groups o f dots from top to b o t t o m are due to g a m m a rays, protons, deuterons and alpha particles.
W.
R.
DIXON
Facing p. 32
34
w.R.
DIXON
then is 2~NAk, which is independent of the type of particle being observed. A suitable choice of parameters is 2~ = 3/~sec, N^ = 10a per sec and k = 10, so that the chance rate is only 3 % of the true rate. With ~(n, p) ~ 10 - 2 6 c m 2 and v = 2 x 1022 atoms/ cm 2, the coincidence rate for protons is 12 counts per minute. r
I"
i
i
i
i
I
I 2 000
I0 000
8 000
o 6000
4 000 SINGLE CHANNEL
2 000
20
40
60 CHANNEL
BO
I00
120
140
NUMBER
Fig. 6. Pulse-height distribution in the associated-particle detector. The peaks shown are f r o m the d(d, p)t and d(t, n):t reactions.
The problem of getting k down to 10 or less is one of defining the tagged beam, and this is facilitated by reducing the diameter of the bombarded area on the tritium target, so that penumbra effects at the edges of the tagged beam are not predominant. We have used a collimator on the deuteron beam with a hole of diameter 0.32 cm. The associated particle beam was collimated to a diameter of 1.27 cm at a distance 12.2 cm. The CsI(Tl) crystal was located at a distance of about 5 cm from the target. In this analysis it is essential that one be able to use pulse shape discrimination on all coincident counts, true or chance. Thus one cannot simply feed intensifying pulses derived from the associated-particle detector into the plotting oscilloscope, because in a chance coincidence the intensification can take place during the rise or fall of the stretched pulses, and the dot on the screen is not located correctly. An external coincidence mixer is therefore required, and this is introduced most conveniently prior to the pulse-shape discrimination because of the long and variable time required for the shape analysis. The resolving time of the coincidence mixer was taken as large as
(n, p), (n, d) A N D
35
(n, a) R E A C T I O N S
2z = 3 ps in order to accommodate jitter in the times of arrival of the two pulses. The chance rate was measured by inserting extra delay into one of the inputs of the coincidence mixer. 3. Experimental Results 3.1. PROTON AND DEUTERON ENERGY SPECTRA The experimental spectrum of protons and deuterons, representing a total of about 60,000 counts, is shown in fig. 7. The main features of the spectrum are the peak in the region 8-11 MeV and a marked change in slope at about 11.7 MeV, the latter feature presumably signifying a high-energy direct component. Detailed attempts to analyse the spectrum into statistical and direct components, however, failed to give satisfactory results until the contribution of deuterons from the (n, d) reaction was dealt with. I
;
1
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-,
2 000
/ 1 500
0 o, ~--
•
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ol,.,pl 500
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1
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l
"-'-.,,i .....
i
8
I0
12
14
ENERGY
{MeV)
q
Fig. 7. Full curve: experimental distribution of protons and deuterons from reactions in Csl. Dashed curves: a possible decomposition into four components as described in the text. The m a x i m u m deuteron energy is 10.5+0.1 MeV (see table 1), and it is evident from fig. 7 that there is a bump at just this energy. Examination of the dot photographs showed that there was indeed a deuteron group which could be just resolved from the proton line. Fig. 5 has been chosen to show this feature clearly; not all photographs show as good a separation. While electronic separation seemed difficult, it was possible, by counting dots in several such photographs, to determine a rough deuteron energy spectrum. The spectrum obtained from an analysis of 364 dots is shown in fig. 8. It shows a prominent ground-state transition at an energy of 10.5 MeV on the proton energy scale and also transitions tO excited states. In the previous experiments of Bormann et aL 2-4) and of Marcazzan et al. 5) no separation of the deuteron contribution was achieved.
36
w.R. DIXON
In order to make a subtraction of the deuteron spectrum (fig. 8) from the combined spectrum of protons and deuterons (fig. 7), it was necessary to normalize one to the other. This was done by counting the alpha-particle dots on the same photographs as the deuteron dots and then using the measured absolute cross sections for the alphaparticle and proton reactions. (A direct comparison of the numbers of deuterons and protons in the photographs is made difficult by the smallness of this ratio: if the flux is too high, individual proton dots lie on top of one another, while if the flux is too low, the deuteron pattern cannot be recognized.) The result is that the (n, d) reaction contributes (11__1)~o of the total area of the experimental spectrum in fig. 7. A normalized deuteron spectrum is also shown in fig. 7. I
I
I Cs'l
3o° ~° 40
(n.~)
~
°:jm "~~20 ,0l 2
Z I
I
3 4 5 HORIZONTALDISPLACEMENT (cm)
~
6
Fig. 8. Experimentaldistributionof deuterondots, from the (n, d) reactionin Csl. When the deuteron contribution is subtracted, one is left with a proton spectrum consisting of contributions from statistical and direct interactions. The former includes a contribution from the (n, np) reaction. A conventional analysis has been made by plotting log N(E)/Eac versus E, where N(E) is the number of protons of energy E, and ac is the cross section for the bombardment of the residual, excited nucleus by protons of energy E. Values of a¢ were taken from Shapiro 11) for r o = 1.3 and r o = 1.5 fm. The plots for the two values are very similar; that for ro = 1.5 fm is shown in fig. 9. The low energy portion of the curve can be broken up into two straight-line sections with nuclear temperatures of T = 0.3 and T = 0.9 MeV. Following Allan 12, is), these can be attributed to the (n, np) and (n, p) reactions, respectively; the temperatures are in accord with Allan's results. The high energy residue is attributed to direct interactions. The decomposition of the initial spectrum is shown by the dashed curves in fig. 7. The curve marked (n, P)stat w a s obtained from the straight line portion of fig. 9 with T = 0.87 MeV, and the curves marked (n, P)alr and (n, np) were obtained by subtraction. This analysis of the spectrum attributes 11 ~ of the total counts to the (n, d) reaction, 45 ~ to the direct (n, p) reaction, 29 ~o to the statistical (n, p) reaction (with T = 0.87 MeV) and 1 5 ~ to the (n, np) reaction.
(n, p), (n, d) AND (n, at) REACTIONS
37
Several remarks concerning this analysis should be made. In the first place there is an experimental low-energy cutoff on the spectrum, which introduces some uncertainty in the (n, np) fraction and spectrum. More importantly, however, the decomposition into statistical and direct components, on the basis of fig. 9, is by no means unique. Indeed if one were prepared to be a little hazy about the region between 5 and 7 MeV, one could attribute nearly all of the high energy protons to a statistical process characterized by a temperature of about 1.45 MeV. Bormann et al. 2) have broken up their curve into two sections only, with no direct component at all. Our data have better statistics, and we do not believe that such an interpretation is possible. It should be pointed out that these results of Bormann 2) also differ from the present in that he found more low-energy protons, and a higher (n, p) cross section. I
I
I
I
I
I
I
I
I
I
I
I
I
I"
I
(n,pl to" Csl
I 0 II
lOa
-- T=0 31MIIV 0\ ~oQ
T- 0807~0000 10
i0 /
I
4
I
I
6
I
I
I
I
8 I0 E (MeV)
12
14
Fig. 9. Analysisof the proton spectrumaccordingto the statisticaltheoryof nuclearreactions.Values of trc were taken from Shapiro :'). The question arises whether our interpretation is affected materially by the choice of parameters and forms which enter into the statistical analysis. Although there is some effect in detail, the basic decomposition of the proton spectrum into three components, of roughly the magnitudes given, is not affected. Changing ro from 1.5 to 1.3 fm reduces the apparent temperature only slightly. If one plots log N(E)/Eac against (Era=x-E) ~ rather than against E, (in accordance with the Fermi gas leveldensity formula rather than the constant temperature formula), the break-up into three components is still demanded. Finally, one can surmise that the effect of using optical model inverse cross sections, instead of those of Shapiro 11), would be to
38
W.R.
DIXON
increase the experimental nuclear temperature slightly, and to enhance the statistical component at the expense of the direct, but not to eliminate any of the three components. The foregoing remarks were predicated on the assumption that any part of the spectrum which could be reasonably attributed to statistical processes should be. There is, of course, the possibility that nearly all of the higher energy protons are of a direct origin. From this point of view, one should regard the figure of 45 % assigned to the direct (n, p) component as a lower limit. 3.2. ALPHA PARTICLE E N E R G Y S P E C T R U M
The alpha-particle energy spectrum, representing a total of about 7000 counts, is shown in fig. 10. The main features of the spectrum are two peaks, one at about 15 MeV and the other at about 18.3 MeV. The lower of these peaks is attributed to I
1
I
I
1
1
!
I
I
1
800 Cs/ Ira=)
700
g
600 500
~,,
{ "./
400
?~.,,.... ~'°.o',,
300 z
o
200 it I00
I
I
2
4
, 6
/ 8
I0 ENERGY
, 12
14
iJ ] 16
"~,
18
c
20
(MeV)
Fig. 10. Full curve: experimental distribution of alpha particles from reactions in Csl. The decomposition into statistical and direct components has been accomplished with the aid of fig. 11.
an evaporation process, and the upper to a direct process. Bormann and Langkau 3) have also found two peaks (at energies of about 12 and 16 MeV), while Marcazzan et al. S) do not show two distinct peaks. The separation into statistical and direct components has been achieved by a procedure similar to that used for the proton spectrum. Fig. 11 shows a plot of log N(E)/Etr¢ versus E, where for ac we have used optical model values from Huizenga and lgo t3). The curve can be broken up into three sections, a low-energy straight line with T = 0.7 MeV, an intermediate-energy straight line with T = 1.15 MeV and a high-energy residue. By extrapolating the section with T = 1.15 MeV both ways, and subtracting, the decomposition into statistical and direct components shown in fig. 10 is obtained. This analysis attributes 60 ~o o f the alpha counts above 10 MeV to
39
(n, p), (n, d) A N D (n, ct) REACTIONS
an (n, :t) statistical process, 2 ~ to (n, n~t) and 38 ~o to a direct (n, ct) reaction. The counts below 10 MeV may be due partly to (n, net) and partly to alpha particles ejected from the surrounding material. There is a cutoff on the mask corresponding to about 7.2 MeV. The lack of alpha particles of still lower energies is evident from fig. 5. Some of the remarks made concerning the proton analysis apply equally to the alpha-particle analysis. For example, if we use the black-nucleus cross sections of Blatt and Weisskopf 14) with R = (1.5A*+ 1.21) fm, the nuclear temperature is about 1.07 MeV instead of 1.15 MeV. This reduces the statistical component to about 57 ~o and increases the direct component to about 41 ~o. The spectral shapes in the two cases are very similar. It is also possible that nearly all of the alpha particles should be attributed to direct processes, so that the figure of 38 ~o should be regarded as a lower limit for the direct fraction. 1
I
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I
1
Cli
in,=)
O
I0 s
-\oN~OT• O.'t4
MeV
104
/~(£)
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103 o '~o
102
TIll5 M|V ~
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0
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I I 14 16 E (MeV)
[ 18
I 20
Fig. 1I. Analysis of the alpha-particle spectrum according to the statistical theory of nuclear reactions. Values of tre were taken from Huizenga and lgo ,3). 3.3. ABSOLUTE CROSS SECTIONS The cross sections found in the present work by taking coincidences with the associated particles are as follows: o(n, p ) + a ( n , n p ) + a ( n , d) = ll.0_+ l.l mb
(E > 2.5 MeV),
a(n, ct)+a(n, net) = 1.9+0.2 mb
(E > 7.2 MeV).
From the analyses of the spectra given above we can obtain values for the cross sections as follows: a ( n , p ) = 8___1 mb, tr(n, d ) =
1.2+0.2 mb,
a(n, c t ) = 1.8+0.2 mb.
40
w.R.
DIXON
These values represent averages over Cs and I. For the (n, p) measurements a proton coincidence rate of about 10 per minute was used, and the chance rate was about 0.6 c/min. For the (n, ~) measurements the alpha particle coincidence rate was about 1.5 per minute, and the chance rate observed was one count in 60 minutes. During the (n, p) measurements, checks were made as follows: the window width on the associated alpha particle peak was narrowed and the CsI(T1) crystalwas moved closer to the tritrium target. As expected, neither action had an observable effect on the measured cross section. The cross sections given above include an 8 ~o correction for absorption of the tagged neutron beam in the cooling water and brass behind the tritium target. The narrow-beam attenuation of the tagged neutron beam amounts to 10~o, but this has been reduced slightly to allow for scattered neutrons which can still give rise to coincidences. It should be noted that there is no compensation arising from neutrons which start out in directions outside the tagged beam and are subsequently scattered in, since in these cases the associated alpha particle is not detected. There is an uncertainty in the cross sections of perhaps 2-3 ~ arising from uncertainty in this correction. No correction has been made for the attenuation of the tagged neutron beam in the CsI(TI) crystal itself, since this is largely compensated by the increased path length available to the neutrons scattered inside the crystal. TABLE 2
Cross sections in C s l for (A) tr(n, p ) + o ( n , np)+~r(n, d), (B) o(n, at) Method
N e u t r o n energy (MoV)
Ref.
(A)
Coincidences with s i m u l t a n e o u s discrimination
14.6
Present work
11.0+ 1.1
Coincidences w i t h o u t discrimination, followed by separation o f p and ~,
14.1
t)
Liei(Eu) m o n i t o r
14. I
s)
I.I -2:0.15
P r o t o n recoil m o n i t o r
14
5)
0.810.2
20
(B)
1.8-t-0.2
+3
Cross sections are given in millibarns per a t o m a n d are a n average between I it' a n d Cs 13s.
The results of Bormann et aL 2,3) and of Marcazzan et al. s), together with the present results, are summarized in table 2. While these results do not agree within the assigned errors, the differences are not overwhelming. The differences may be due in part to differences in the incident neutron energy. Another possibility is an error in the calibration of the neutron monitors in the other experiments; the method of tagging the neutron beam is in principle much more reliable for measurements of absolute cross sections than using other monitors. There is also the possibility of substantial contributions of charged particles from material surrounding the Csl(TI)
(n, p), (n, d) AND (n, a) REACTIONS
41
crystal. Low-Z material surrounding the crystal has high cross sections for both (n, p) and (n, ct) reactions, and so it should be replaced by high-Z material as far as possible. The problem with alpha particles is less serious than with protons because alpha particles from CsI are of considerably higher energies than those from the low-Z materials with high cross sections. Thus if there were an appreciable number of external alpha particles, their presence would be betrayed and confusion would be unlikely. TABLE 3
Cross sections (mb) for It~7(n,p), 1127(n,=) and Csm(n, at) Method
Neutron energy (MeV) Ref.
Activation Activation
14.5 14 -4-0.5
~5) :6)
Activation
14.1
Emulsions
14
:8)
Activation Irradiation o f NaI
14.5 14.05
~7) 40)
Theoretical Systematics
14.5 14
t~) 20)
2)
It27(n, p) 11.7+ 25
1127(n,=)
i.8
Csm(n, u) 1.9t0.2 1.04-0.3
+ 15
< 5/4~z m b / s r at 120 ° > 2 3 0 4 - 140
18 q-3 1.44-0.2
17 16
Table 3 summarizes other evidence on relevant cross sections in I t27 and Cs laB. The first three entries are activation measurements, of which those of Coleman et aL ts) are probably the most reliable. A direct comparison of these values with table 2 is not possible without taking into account the (n, np) and (n, d) cross sections, and allowing for both 1127 and Cs 133. If it is supposed that I t27 and Cs 133 have nearly equal cross sections, there seems to be good agreement between our present results and those of Coleman et al., particularly for a(n, 0t). The next entry in table 3 is a measurement by Allan is) at 120°; if the emission of protons were isotropic the total cross section would be less than 5 rob. The fifth entry is an old measurement by Paul and Clarke 17) which seems to be much too high for both It27(n, p ) a n d I127(n, ct). The sixth entry is a new measurement of I127(n, ct) by Bizzeti eta/. 4°) from the irradiation of NaI, which just agrees with our present result for CsI within the assigned errors. The last two entries in table 3 are a theoretical estimate for I127(n, p) by Brown and Muirhead 19) (17 mb) and a prediction on the basis of systematic trends by Gardner 20) (16 mb). The calculation of Brown and Muirhead is of considerable interest in that 16 mb is ascribed to direct (n, p) reactions and only 1 mb to statistical (n, p) processes. 4. Discussion
It was first shown by Paul and Clarke 17) that direct reactions play an important role in the emission of charged particles from intermediate and heavy nuclei. The
42
w.R. DIXON
values of (n, p) and (n, ~) cross sections measured for such nuclei were much higher than one expected on the basis of the statistical theory of nuclear reactions. Briefly, the reason for invoking direct reactions was that directly emitted particles tend to have higher energies, and hence are able to penetrate the Coulomb barrier. More recently, activation measurements by Coleman et al. 15) and by Strohal et al. 4i) have led to the same conclusion. A number of experiments have been performed to measure the energy and angular distributions of charged particles from (n, p) and (n, ~) reactions in light nuclei, and substantial direct components have been found. Similar experiments in heavy nuclei are much more difficult to perform, owing to the low yields, and there has been little direct experimental evidence available. It is therefore of interest to examine the results of the present experiment with a view to elucidating, if possible, reaction mechanisms in heavier nuclei. We propose to discuss the (n, d), (n, p) and (n, a) reactions in turn. Our only comment on the (n, d) reaction is that the deuteron spectrum shows a prominent ground-state transition. This is characteristic of a pick-up reaction rather than of an evaporation process. The secondary hump in the deuteron spectrum is somewhat similar to the hump found by Colli et al. 21) and by Peck 22) for Rht °3(n, d). The usual evidence cited for direct (n, p) reactions is the asymmetry about 90 ° in the angular distribution of the emitted protons, together with a high-energy residue left over when a statistical analysis is made of the experimental energy spectrum (e.g. Allan 12), March and Morton 23), Brown et al. 24), Colli et al. 25, z6), Hassler and Peck 27), Glover and Purser 2s), Glover and Weigold 29), Jack and Ward 30)). The fractions of protons ascribed to direct interactions generally lie in the range 10-40 ~o for Z < 30. For heavier nuclei there are not many measurements. Eubank, Peck and Zatzick 31 have made a survey of cross sections in the forward direction for elements near Z = 50, while Allan is) has made a survey of cross sections at 120°. In many cases the yield was too low to stand out from the background, but 51Sb was found to give an unusually high yield: Eubank et al. found 4 0 + 2 mb/sr at 0 °, while Allan found only about 1 mb/sr at 120 °. Such a large effect almost certainly indicates direct interactions. In the present experiment in Csl it was not possible to measure angular distributions. The evidence for direct (n, p) reactions is rather of two types: the high-energy residue left over in a statistical analysis of the proton energy distribution, and the magnitude of the cross section, which can be accounted for only by a direct interaction theory such as that of Brown and Muirhead 19). The result of Allan is) at 120 ° (see table 3) taken together with the total cross section suggests anisotropy but not necessarily asymmetry about 90 °, and hence cannot be adduced as evidence in favour of direct reactions. Theories applicable to direct (n, p) reactions have been of the volume type (Hayakawa. Kawai and Kikuchi 32), Brown and Muirhead tg)) and of the surface type
(n, p), (a, d) AND (n, ~) REACTIONS
43
(Austern, Butler and McManus 33), Elton and Gomes 3,)). There is no firm evidence in the present experiment to choose between these two possibilities. One could perhaps argue that since the (n, d) pickup reaction is essentially a surface effect, one should expect an (n, p) knockout reaction in the surface to be of the same order of magnitude. The fact that the direct (n, p) cross section is observed to be at least four times as large might then be adduced as evidence in favour of a volume theory. The argument is far from conclusive. Insofar as the spectral shape is concerned, there is no basis for choosing between surface and volume effects. Since it has been stated in the literature t2) that the observed shape of the direct spectrum (fig. 7) favours a surface rather than a volume theory, it is perhaps worthwhile pointing out explicitly how this shape arises in the volume theory. In that theory in its simplest form one imagines the incident neutron interacting with a Fermi sea of neutrons and protons. For the maximum proton energy, there must have been a complete energy transfer; this can take place only at the Fermi surface, since at any proton energy below the surface, there would be no place for the spent neutron to go. For smaller and smaller energy transfers, protons from greater and greater depths can participate, and still leave the neutron above the surface. Thus the peak in the spectrum comes about through the interplay of two factors: the Pauli principle making more and more protons available for interaction, and the Coulomb barrier inhibiting their emission. While there is no firm evidence in favour of the volume theory of Brown and Muirhead t9), and while that theory is almost certainly oversimplified, it has nevertheless enjoyed considerable success in predicting cross sections t s) and in predicting direct interaction fractions 27). It is therefore of interest to examine the calculation of the direct proton spectrum in more detail. The complicated expression given by Brown and Muirhead can be expanded as follows:
N(E) oc b l ( e m x - E) + b2(Em,x - E) 2 + b3(Em,x- E) 3 + . . . . if we disregard the Coulomb barrier. The coefficients b~ depend on the incident energy and the Fermi energy, but not critically. For 14.6 MeV neutrons, a potential well of 40 MeV, and a Fermi energy of 33.6 MeV, wefind b2/bl ~, - 0 . 0 1 and b3/b 1 l0 -4. Thus the predicted proton spectrum would be essentially linear in the residual energy, over a wide range of energy, if there were no barrier effect. With this variation in mind, it can be understood why the statistical component should peak some 3 MeV lower than the direct spectrum. In the statistical theory the shape of the proton spectrum is also determined by the interplay between two factors, the availability of states in the residual nucleus and the Coulomb barrier. The availability of states, however, goes up exponentially with the residual energy, instead of linearly, and this can produce a shift of the observed amount. It can also be understood that a direct spectrum can be approximately fitted by statistical formula, provided the tempearature parameter is made high enough (e.g. Bormann et al. 2)). The evidence for direct (n, ct) reactions in Csl is perhaps even stronger than the evidence for direct (n, p) reactions. The present experiment shows a clear separation
44
w.R.
DIXON
of the alpha-particle energy spectrum into two components, only one of which can be accounted for by a statistical analysis. The high-energy component is almost certainly due to direct ejection of alpha particles. It is not, however, possible to choose between knockout and pickup processes. The former would imply the pre-existence of alphaparticle clusters in the nuclear surface, a notion which has received strong advocacy from Wilkinson 3s). It might also be noted that Wildermuth and Carovillano 36) have argued that under certain conditions alpha clusters might have relatively long lifetimes in the interiors o f nuclei. Bormann and Langkau 4) have published a set of (n, ct) spectra from CsI at various neutron energies, and have noted that the fraction of counts in the high-energy peak decreases with increasing neutron energy. This behaviour would not be expected if the low-energy component were due solely to a statistical process. They have suggested that the high-energy peak is due to a pickup process, while the low-energy component is due both to direct knockout and evaporation of alpha particles. There is very little evidence on angular distributions for (n, a) reactions in heavy nuclei. Facchini et aL 37) have made a preliminary investigation on forward to backward asymmetry in the TalSl(n, ct) and Au197(n, ct) reactions, and report a ratio of about five to one. Ribe and Davis 3a) have observed a strong forward peak for 40Zr(n, ct), but it is not clear from their results if the angular distribution is actually asymmetric about 90 °. High-energy alpha-particle tracks from heavy constituents in nuclear emulsions are observed to be strongly forward (Jarvis 39)). We have not emphasized the statistical reactions in this discussion, because with the large admixture of direct effects, it is not possible to pinpoint the parameters or even to select the appropriate form of a statistical calculation. There is, however, one aspect of the statistical processes which should be pointed out. The (n, np) cross section is found to be considerably larger, relative to the (n, p) cross section, than the (n, net) relative to the (n, ~t) cross section. Stated in another way, the emission of alpha particles relative to protons is considerably more difficult after a neutron has already been emitted. That either the (n, np) or (n, n~) reaction is significant is a consequence of the fact that if the residual nucleus following the (n, n') reaction has an excitation less than 9 MeV, it is energetically impossible to emit a second neutron (see table 1). The author wishes to acknowledge valuable discussions of the present experiment with Mr. J. H. Aitken and Dr. R. S. Storey of this laboratory and the technical assistance of Mr. J. D. Stinson and Mr. J. P. Legault in some phases of the work. References
1) L. A. KOnig, J. H. E. Mattauch and A. H. Wapstra, Nuclear Physics 31 (1962) 18 2) M. Bormann, H. Jeremie, G. Andersson-LindstrOm, H. Neuert and H. Pollehn, Z. Naturforsch. 15a (1960) 200 3) M. Borrnann and R. Langkau, Z. Naturforsch. 16a (1961) 444
(n, p), (n, d) AND (n, a)
REACTIONS
45
4) M. Bormann and R. Langkau, in Proc. Rutherford Jubilee Int. Conf., Manchester, 1961, ed. by J. B. Birks (Academic Press, New York, 1961) p. 501 5) G. M. Marcazzan, E. Menichella Saetta and F. Tonolini, Nuovo Cim. 20 (1961) 903 6) A. R. Quinton, C. E. Anderson and W. J. Knox, Phys. Rev. 115 (1959) 886 7) J. B. Mead and B. L. Cohen, Phys. Rev. 125 (1962) 947 8) R. S. Storey, W. Jack and A. Ward, Proc. Phys. Soc. 72 (1958) 1 9) J. A. Biggerstaff, R. L. Becker and M.T McEIlistrem, Nucl. Instr. 10 (1961) 327 10) W. R. Dixon and J. H. Aitken, Nuclear Physics 24 (1961) 456 11) M. M. Shapiro, Phys. Rev. 90 (1953) 171 12) D. L. Allan, Nuclear Physics 10 (1959) 348 13) J. R. Huizenga and G. Igo, Nuclear Physics 29 (1962) 462 14) J. M. Blatt and V. F. Weisskopf, Theoretical nuclear physics (John Wiley & Sons, New York, 1952) p. 353 15) R. F. Coleman, B. E. Hawker, L. P. O'Connor and J. L. Perkin, Proc. Phys. Soc. 73 (1959) 215 16) H. G. Blosser, C. D. Goodman and T. H. Handley, Phys. Rev. I10 (1958) 531 17) E. B. Paul and R. L. Clarke, Can. J. Phys. 31 (1953) 267 18) D. L. Allan, Nuclear Physics 24 (1961) 274 19) G. Brown and H. Muirhead, Phil. Mag. 2 (1957) 473 20) D. G. Gardner, Nuclear Physics 29 (1962) 373 21) L. Colli, F. Cvelbar, S. Micheletti and M. Pignanelli, Nuovo Cim. 14 (1959) 1120 22) R. A. Peck, Phys. Rev. 123 (1961) 1738 23) P. V. March and W. T. Morton, Phil. Mag. 3 (1958) 143; 3 (1958) 577 24) G. Brown, G. C. Morrison, H. Muirhead and W. T. Morton, Phil. Mag. 2 (1957) 785 25) L. Colli, U. Facchini, I. lori, M. G. Marcazzan and A. M. Sona, Nuovo Cim. 13 (1959) 730 26) L. Colli, F. Cvelbar, S. Micheletti and M. Pignanelli, Nuovo Cim. 14 (1959) 81 27) F. L. Hassler and R. A. Peck, Phys. Rev. 125 (1962) 1011 28) R. N. Glover and K. H. Purser, Nuclear Physics 24 (1961) 431 29) R. N. Glover and E. Weigold, Nuclear Physics 24 (1961) 630 30) W. Jack and A. Ward, Proc. Phys. Soc. 75 (1960) 833 31) H. P. Eubank, R. A. Peck and M. R. Zatzick, Nuclear Physics 10 (1959) 418 32) S. Hayakawa, M. Kawai and K. Kikuchi, Prog. Theor. Phys. 13 (1955) 415 33) N. Austern, S. T. Butler and H. McManus, Phys. Rev. 92 (1953) 350 34) L. R. B. Elton and L. C. Gomes, Phys. Rev. 105 (1957) 1027 35) D. H. Wilkinson, in Proc. Int. Conf. on Nuclear Structure, Kingston, 1960, ed. by D. A. Bromley and E. W. Vogt (University of Toronto Press, Toronto, 1960), pp. 29-33, in Proc. Rutherford Jubilee Int. Conf., Manchester, 1961, ed. by J. B. Birks (Academic Press, New York, 1961) pp. 339-356 36) K. Wildermuth and R. L. Carovillano, Nuclear Physics 28 (1961) 636 37) U. Facchini, M. G. Marcazzan, F. Merzari and F. Tonolini, Phys. Lett. 1 (1962) 6 38) F. L. Ribe and R. W. Davis, Phys. Rev. 99 (1955) 331 39) C. J. D. Jarvis, private communication (1962) 40) P. G. Bizzeti, A. M. Bizzeti-Sona and M. Bocciolini, Nuclear Physics 36 (1962) 38 41) P. Strohal, N. Cindro and B. Eman, Nuclear Physics 30 (1962) 49
NuclearPhysics 4 2 Not
(1963) 27----46; ~ )
North-Holland Publishing Co., Amsterdam
to be reproduced by photoprint or microfilm without written permission from the publisher
T H E (n,p), (n, d) AND (n, a) REACTIONS INDUCED BY 14.6 MeV NEUTRONS I N CsI(TI) S C I N T I L L A T I O N C R Y S T A L S W. R. D I X O N
National Research Council, Ottawa, Canada Received 1 October 1962
Abstract: The (n, p), (n, d) and (n, a) reactions induced by 14.6 MeV neutrons in C s I ( T I ) scintillation crystals have been observed. Pulse shape discrimination has been used to distinguish the various particles, permitting an energy spectrum for each to be obtained. The proton and alpha particle spectra have been analysed from the point of view of the statistical theory of nuclear reactions, hut there are left over substantial components which must be attributed to direct interactions. The direct component for protons is estimated to be at least 45 %, and for alpha particles to be at least 38 ~o- Absolute cross sections have been obtained by the method of "tagging" the neutron beam by its associated particles; the averages for Cs and I are found to be a(n, p) 8+ I rob, o(n, d) = 1.2-t-0.2 mb and a(n, a) = 1.8±0.2 rob.
1. Introduction The study o f (n, p), (n, d) and (n, ~) reactions in medium and heavy nuclei is made difficult by the low cross sections and the impossibility o f getting charged particles out o f thick targets. F o r these reasons m o s t studies have been confined to measurements o f the cross section by activation methods, and there have been only a few attempts to measure energy and angular distributions o f the emitted particles. In the present experiment (n, p), (n, d) and (n, ~) reactions induced by 14.6 MeV neutrons in a CsI(TI) scintillation crystal have been observed, the crystal serving as both target and detector. Pulse shape discrimination has been used to identify the particle type and energy distributions for protons, deuterons and alpha particles have been measured. Absolute (n, p) and (n, ~) cross sections have been measured by "tagging" the neutron beam, that is by taking coincidences with the alpha particles associated with the production o f the neutrons in the d-t reaction. Although it is impossible to separate the contributions o f ssCs 133 and s3 I127 to the observed reactions, it is important to note that the two nucleides in question are close together in Z and A values, and that each contains an odd n u m b e r o f protons and an even n u m b e r o f neutrons. The Q values for the various reactions have been obtained f r o m the mass tables o f KiSnig, M a t t a u c h and Wapstra 1) and are listed in table 1. The values for the two nucleides are remarkably close together. Thus there is considerable d priori evidence for supposing that 55Cs t 33 and s 3I127 should behave similarly. 27
28
W.R.
DIXON
Experiments with CsI similar in principle to that described here have been reported by B o r m a n n et al. 2-4) and by Marcazzan et al.5). O f these, our experiment is the first in which the techniques o f pulse shape discrimination and beam-tagging have been combined to give the absolute cross sections for protons and alpha particles in single measurements. It is also the first o f these in which deuterons have been distinguished from protons. TABLE 1
Q values in MeV of various reactions in Cs x3~ and 1137 Reaction
Cstaa
I tu
(n, p) (n, np) (n, d) (n, c~) (n, n~) (n, 2n)
+0.36 .... 6.42 -4.20 +4.16 -2.32 -9.02
+0.10 - 6.25 -4.03 +4.22 -2.23 -9.15
2. Experimental Arrangement 2.1. GENERAL Neutrons o f energy 14.64-0.1 MeV were obtained from a Texas Nuclear Model 150-1H neutron generator in which deuterons are accelerated to energies up to 150 keV and allowed to strike a tritium target. A block diagram o f the electronic apparatus is shown in fig. 1. The diagram is divided into three section.~, o f which those labelled A and B were used for the cross section measurements, while those labelled A and C were used for the spectral measurements. This division was made merely for convenience, there being no reason in principle why both types o f measurements could not be made simultaneously. The c o m m o n section A includes amplifiers to handle both an integrated (or E-) pulse and a current pulse from the CsI(TI) crystal. The latter was analysed for decay time z, and a dot for each pair o f E- and z-pulses was then plotted on an oscilloscope screen. Protons and alpha-particles lay on two different loci on the screen. A mask was used to eliminate the undesired dots, so that one kind o f particle only could give rise to signals in a photomultiplier viewing the screen. The signals could be either counted in a scaler, or used to select certain E-pulses for pulse-height analysis. When the spectrum was being measured all pulses from the E-amplifier were intensified on the oscilloscope screen, while in the cross section measurement, only those in coincidence with the associated-particle detector were intensified. 2.2. THE CsI(TI) CRYSTAL The CsI(TI) crystal, obtained from Harshaw Chemical Co., had a diameter o f 2.0 cm and a thickness o f 1.0 cm. It was mounted inside a tantalum cup, and optically coupled to the face o f a D u Mont-6467 photomultiplier with a thin smear o f silicone grease. It was essential to avoid thick aluminium reflectors, and o f course, hydroge-
I
SCALER
SCALER
2 T = 3/.LS
/L. 1
]
I .......
C
] I STRETCHER
I AMPLIFIER
E-
I ]
GATE
.
.
I
II
i
.
I ''~LIP'ER I .
.
.
.
.
.
.
.
.
.
.
I .
I
CLAMP
.
I
I~
.JuNIVIBRATOR |
.
7I
.
I
J
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
READ TRIGGER OUT
LATE ANTICOINCIDENCE
.
I STRETC"ERI
SHAPE ANALYZER
¼
l
WIDEBAND AMPLIFIERS
~ P.OTOMUL,.PL.ER
7OSCILLOSCOPE ~'
JPLDTTING
DELAY 3/J.S /
INTENSIFIER
DELAY~ s
o7
-,.,"7~
DELAY/
I INTEGRAL DISCRIMINATORI -
A
Csl(Tb) CURRENT PULSE
.
.
.
.
.
.
.
I
r
.
.
.
.
I
1
7 ~,C.ORTER~ I
.
._1
.
Fig. I. Block diagram of the electronic apparatus used in conjunction with the CsI(TI) crystal. Sections A and C were used for spectrum measurements, A and B for absolute cross sections.
B
I
COINCIDENCE L JI
SINGLE CHANNEL
I 'MPL'F'ER J
ASSOCIATED--PARTICLE DETECTOR
C~I(T~) INTEGRATED PULSE
t~ ~D
O
> Z
30
w.R. DIXON
nous material, in order to reduce the external contribution of charged particles. The inside of the tantalum cup was aluminized by evaporation to a thickness of only about 0.1 mg/cm2; a hole at the top, which was used to allow charged particles to enter for energy calibration purposes, was covered with aluminium foil of thickness 0.32 mg/cm 2. During the neutron irradiation it was also covered with a tantalum disc. An energy calibration curve for protons was obtained by bombarding an Li6F target t with 130 keV deuterons. The reaction Li6(d, p)Li 7 produces protons of 4.29 and 3.88 MeV at an angle of 135°; when account is taken of the energy loss in the aluminium foil over the crystal, the energies are reduced to 4.27 and 3.86 MeV, respectively. In addition to these two proton peaks, there is also a proton peak from the interaction of bombarding deuterons on deuterium already occluded in the ,:,:get. At 135 ° the energy of these protons reaching the crystal is 2.72 MeV. The relative intensity of the latter peak is very small with a fresh target, but grows to be the predominant peak after a few hours bombardment. These peaks are shown'in fig. 2. Judging by the work ofQuinton et al. 4) and of Mead and Cohen 7) the response for protons is proportional to the energy. We have, therefore, made a least-squares fit for the best straight line through the three points and the origin. This line is shown in fig. 3. 1
w
I
:
I
I
I
I
I
~.0
I
I
DEUTERONS
-
PROTONS
Z
4.0
~:
3.0
~ .../
2.0
2
4
6
8
I0 ENERGY
12
14
16
18
20
22
IMev)
Fig. 3. The response of the CsI(TI) crystal to protons, deuterons and alpha-particles. The circles are experimental points. The line for protons has been obtained from a least-squares fit. The curves for alpha-particles and deuterons are from Mead and Cohen ~), normalized at an alpha-particle energy of 10.4 MeV.
For alpha particles the response is linear above about 8 MeV, but nowhere is it proportional to the energy. A point on the curve at 10.4 MeV is available from the Li6(d, ct)~t reaction at 135 °, and additional points were obtained at lower energies with a polonium alpha source. These were not sufficient, however, to establish the response curve in the energy region of interest (10-20 MeV), so that the curve of Mead and Cohen 7) was used, normalized at the value of 10.4 MeV. It is shown in fig. 3. Mead and Cohen 7) have also measured the response to deuterons (but not protons) * The LiSF target was supplied by the Atomic Energy Research Establishment, Harwell, England.
(n, p), (n, d) AND (n, ~t) REACTIONS
31
and found it to be proportional to the energy. Their response curve for deuterons is shown in fig. 3 and is seen to lie only slightly below our response curve for protons. Within the accuracy of the measurements the response to protons and deuterons is the same. The ordinate in fig. 3 is the ratio of peak channel observed to the peak channel for the Zn 65 photo peak, the latter being observed with the coarse gain of the amplifier increased by a factor of four. The Zn 6s source was used only as a monitor on the gain during the subsequent runs, so that the exact value of this factor is of no importance. The stability is, of course, important; the ratios in fig. 3 remained constant to within + 1% during the period in which runs were taken (one month). 2.3. P U L S E
SHAPE
DISCRIMINATION
Fig. 4 shows the spectrum of pulses produced by the CsI(Tl) crystal irradiated by 14 MeV neutrons. Most of the pulses are due to electrons and gamma-rays. The hump I00000
I
i
1
I
I
_\
I0000
\
\ i
,
ooo 1-
-~ r
p
b
i,i
tOO
o 1o
l0
{
I 40
I 80
I 120
CHANNEL
I 160
I 200
! 240
NUMBER
Fig. 4. Pulse-height distribution for CsI(TI) i~adiated with 14.6 MeV neurons. around around achieve Storey,
channel 130 is due to protons, and evidence of alpha particles is to be seen channel 200. The technique of pulse shape discrimination can be used to an excellent separation of these particles in CsI(T1). Following the work of Jack and Ward s) there have been a number of methods devised to achieve
32
w.R. DIXON
this separation; we have used the method of Biggerstaff et al. 9) in conjunction with a plotting oscilloscope. The circuit of Biggerstaff et aL 9) essentially measures the decay time of the current pulse from the photomultiplier. A time-to-amplitude converter produces a saw tooth output pulse whose amplitude is a measure of the scintillator decay time. For input pulses of amplitudes greater than a certain minimum value, the output is independent of the input amplitude, and depends only on the decay time of the scintillator. We call this output pulse the z-pulse. A plotting oscilloscope has been used to display the pulse-shape effect. The E-pulses were stretched to about 12/~sec and applied to the horizontal deflecting system, while the z-pulses were similarly stretched and applied to the vertical system. A pulse taken from an integral discriminator in the E-amplifier was used to generate an intensifying pulse after a delay of about 5 #sec. This delay was necessary to give the shape analyser enough time to complete its analysis. The result was a dot on the screen for each pulse, plotted according to its E- and z-values. A photograph of the dot pattern for charged particles emitted from a Li6F target bombarded with deuterons is shown in fig. 2, together with spectra of both the E- and z-pulses obtained with the kicksorter. Fig. 5 shows the dot pattern obtained from irradiating the CsI(TI) crystal with 14 MeV neutrons; the separation into gamma rays, protons and alpha particles is clearly visible. The physical equipment used for the display and recording of the dot pattern consisted of a Tektronix 585 oscilloscope (which proved to have sufficient stability), a P-15 cathode-ray tube with a decay time of 1.7/asec and a Tektronix C-12 camera with a Polaroid Land back. Over a limited energy range it is possible to use a single-channel analyser on the output of the shape analyser in order to select particles of the desired type. Fig. 5 however, shows that the z value for protons depends on the energy over the range 2-14 MeV, so that a more elaborate selection system was necessary. The method used is already well established in the literature: a mask was placed over the oscilloscope screen with a slit cut in it, so that the locus of dots due to one kind of particle only could be seen. A photomultiplier (Du Mont K1732) was placed in front of the screen and its output pulses were then used for selection purposes. The arrangement adopted was to focus the dots on a ground glass screen at the position normally occupied by the film in the Polaroid Land back. The ground glass screen then acted as a secondary source for the photomultiplier. A crude lens system was introduced to focus the light more effectively onto the rather small photomultiplier. Visual monitoring of the dot pattern was possible by virtue of the beam splitting mirror in the Tektronix C-12 camera without having to remove the photomultiplier assembly. When the counting rate was particularly low, photographic monitoring was necessary; this was easily achieved by sliding the photomultiplier assembly out of position and inserting in its place the Polaroid Land back.
ENERGY SPECTRUM Li s (d,p)
Lil(d.a)
d (d,p)t
J
o.
u
m
,tV,'tO
|
|
I
!
Fig. 2. Nuclear events from b o m b a r d i n g a LiSF target with deuterons, observed with a CsI(TI) crystal. The p h o t o g r a p h shows each event plotted as a dot on the oscilloscope screen, with energy as abscissa and shape as ordinate. The pulse-height distributions were obtained with the kicksorter, with the pulse-height scales matched to the photograph.
0¢
Fig. 5. Dot photograph for CsI(TI) irradiated with 14.6 MeV neutrons. The groups o f dots from top to b o t t o m are due to g a m m a rays, protons, deuterons and alpha particles.
W.
R.
DIXON
Facing p. 32
34
w.R.
DIXON
then is 2~NAk, which is independent of the type of particle being observed. A suitable choice of parameters is 2~ = 3/~sec, N^ = 10a per sec and k = 10, so that the chance rate is only 3 % of the true rate. With ~(n, p) ~ 10 - 2 6 c m 2 and v = 2 x 1022 atoms/ cm 2, the coincidence rate for protons is 12 counts per minute. r
I"
i
i
i
i
I
I 2 000
I0 000
8 000
o 6000
4 000 SINGLE CHANNEL
2 000
20
40
60 CHANNEL
BO
I00
120
140
NUMBER
Fig. 6. Pulse-height distribution in the associated-particle detector. The peaks shown are f r o m the d(d, p)t and d(t, n):t reactions.
The problem of getting k down to 10 or less is one of defining the tagged beam, and this is facilitated by reducing the diameter of the bombarded area on the tritium target, so that penumbra effects at the edges of the tagged beam are not predominant. We have used a collimator on the deuteron beam with a hole of diameter 0.32 cm. The associated particle beam was collimated to a diameter of 1.27 cm at a distance 12.2 cm. The CsI(Tl) crystal was located at a distance of about 5 cm from the target. In this analysis it is essential that one be able to use pulse shape discrimination on all coincident counts, true or chance. Thus one cannot simply feed intensifying pulses derived from the associated-particle detector into the plotting oscilloscope, because in a chance coincidence the intensification can take place during the rise or fall of the stretched pulses, and the dot on the screen is not located correctly. An external coincidence mixer is therefore required, and this is introduced most conveniently prior to the pulse-shape discrimination because of the long and variable time required for the shape analysis. The resolving time of the coincidence mixer was taken as large as
(n, p), (n, d) A N D
35
(n, a) R E A C T I O N S
2z = 3 ps in order to accommodate jitter in the times of arrival of the two pulses. The chance rate was measured by inserting extra delay into one of the inputs of the coincidence mixer. 3. Experimental Results 3.1. PROTON AND DEUTERON ENERGY SPECTRA The experimental spectrum of protons and deuterons, representing a total of about 60,000 counts, is shown in fig. 7. The main features of the spectrum are the peak in the region 8-11 MeV and a marked change in slope at about 11.7 MeV, the latter feature presumably signifying a high-energy direct component. Detailed attempts to analyse the spectrum into statistical and direct components, however, failed to give satisfactory results until the contribution of deuterons from the (n, d) reaction was dealt with. I
;
1
l
-,
2 000
/ 1 500
0 o, ~--
•
®
.
z
ol,.,pl 500
".
i
I
o \ 0
!<,.°>,,,".,\ ~0
;
...
,
, ",,i
%
, '. ;
"..i': .." 4
,~ "'~'''".
/ V
.-"i 2
o2
OO O°
/ 0
,ooo
I
7%° o
(,.pl
e~ 0 u
1
6
O^ ,
.,
"b
i
l
"-'-.,,i .....
i
8
I0
12
14
ENERGY
{MeV)
q
Fig. 7. Full curve: experimental distribution of protons and deuterons from reactions in Csl. Dashed curves: a possible decomposition into four components as described in the text. The m a x i m u m deuteron energy is 10.5+0.1 MeV (see table 1), and it is evident from fig. 7 that there is a bump at just this energy. Examination of the dot photographs showed that there was indeed a deuteron group which could be just resolved from the proton line. Fig. 5 has been chosen to show this feature clearly; not all photographs show as good a separation. While electronic separation seemed difficult, it was possible, by counting dots in several such photographs, to determine a rough deuteron energy spectrum. The spectrum obtained from an analysis of 364 dots is shown in fig. 8. It shows a prominent ground-state transition at an energy of 10.5 MeV on the proton energy scale and also transitions tO excited states. In the previous experiments of Bormann et aL 2-4) and of Marcazzan et al. 5) no separation of the deuteron contribution was achieved.
36
w.R. DIXON
In order to make a subtraction of the deuteron spectrum (fig. 8) from the combined spectrum of protons and deuterons (fig. 7), it was necessary to normalize one to the other. This was done by counting the alpha-particle dots on the same photographs as the deuteron dots and then using the measured absolute cross sections for the alphaparticle and proton reactions. (A direct comparison of the numbers of deuterons and protons in the photographs is made difficult by the smallness of this ratio: if the flux is too high, individual proton dots lie on top of one another, while if the flux is too low, the deuteron pattern cannot be recognized.) The result is that the (n, d) reaction contributes (11__1)~o of the total area of the experimental spectrum in fig. 7. A normalized deuteron spectrum is also shown in fig. 7. I
I
I Cs'l
3o° ~° 40
(n.~)
~
°:jm "~~20 ,0l 2
Z I
I
3 4 5 HORIZONTALDISPLACEMENT (cm)
~
6
Fig. 8. Experimentaldistributionof deuterondots, from the (n, d) reactionin Csl. When the deuteron contribution is subtracted, one is left with a proton spectrum consisting of contributions from statistical and direct interactions. The former includes a contribution from the (n, np) reaction. A conventional analysis has been made by plotting log N(E)/Eac versus E, where N(E) is the number of protons of energy E, and ac is the cross section for the bombardment of the residual, excited nucleus by protons of energy E. Values of a¢ were taken from Shapiro 11) for r o = 1.3 and r o = 1.5 fm. The plots for the two values are very similar; that for ro = 1.5 fm is shown in fig. 9. The low energy portion of the curve can be broken up into two straight-line sections with nuclear temperatures of T = 0.3 and T = 0.9 MeV. Following Allan 12, is), these can be attributed to the (n, np) and (n, p) reactions, respectively; the temperatures are in accord with Allan's results. The high energy residue is attributed to direct interactions. The decomposition of the initial spectrum is shown by the dashed curves in fig. 7. The curve marked (n, P)stat w a s obtained from the straight line portion of fig. 9 with T = 0.87 MeV, and the curves marked (n, P)alr and (n, np) were obtained by subtraction. This analysis of the spectrum attributes 11 ~ of the total counts to the (n, d) reaction, 45 ~ to the direct (n, p) reaction, 29 ~o to the statistical (n, p) reaction (with T = 0.87 MeV) and 1 5 ~ to the (n, np) reaction.
(n, p), (n, d) AND (n, at) REACTIONS
37
Several remarks concerning this analysis should be made. In the first place there is an experimental low-energy cutoff on the spectrum, which introduces some uncertainty in the (n, np) fraction and spectrum. More importantly, however, the decomposition into statistical and direct components, on the basis of fig. 9, is by no means unique. Indeed if one were prepared to be a little hazy about the region between 5 and 7 MeV, one could attribute nearly all of the high energy protons to a statistical process characterized by a temperature of about 1.45 MeV. Bormann et al. 2) have broken up their curve into two sections only, with no direct component at all. Our data have better statistics, and we do not believe that such an interpretation is possible. It should be pointed out that these results of Bormann 2) also differ from the present in that he found more low-energy protons, and a higher (n, p) cross section. I
I
I
I
I
I
I
I
I
I
I
I
I
I"
I
(n,pl to" Csl
I 0 II
lOa
-- T=0 31MIIV 0\ ~oQ
T- 0807~0000 10
i0 /
I
4
I
I
6
I
I
I
I
8 I0 E (MeV)
12
14
Fig. 9. Analysisof the proton spectrumaccordingto the statisticaltheoryof nuclearreactions.Values of trc were taken from Shapiro :'). The question arises whether our interpretation is affected materially by the choice of parameters and forms which enter into the statistical analysis. Although there is some effect in detail, the basic decomposition of the proton spectrum into three components, of roughly the magnitudes given, is not affected. Changing ro from 1.5 to 1.3 fm reduces the apparent temperature only slightly. If one plots log N(E)/Eac against (Era=x-E) ~ rather than against E, (in accordance with the Fermi gas leveldensity formula rather than the constant temperature formula), the break-up into three components is still demanded. Finally, one can surmise that the effect of using optical model inverse cross sections, instead of those of Shapiro 11), would be to
38
W.R.
DIXON
increase the experimental nuclear temperature slightly, and to enhance the statistical component at the expense of the direct, but not to eliminate any of the three components. The foregoing remarks were predicated on the assumption that any part of the spectrum which could be reasonably attributed to statistical processes should be. There is, of course, the possibility that nearly all of the higher energy protons are of a direct origin. From this point of view, one should regard the figure of 45 % assigned to the direct (n, p) component as a lower limit. 3.2. ALPHA PARTICLE E N E R G Y S P E C T R U M
The alpha-particle energy spectrum, representing a total of about 7000 counts, is shown in fig. 10. The main features of the spectrum are two peaks, one at about 15 MeV and the other at about 18.3 MeV. The lower of these peaks is attributed to I
1
I
I
1
1
!
I
I
1
800 Cs/ Ira=)
700
g
600 500
~,,
{ "./
400
?~.,,.... ~'°.o',,
300 z
o
200 it I00
I
I
2
4
, 6
/ 8
I0 ENERGY
, 12
14
iJ ] 16
"~,
18
c
20
(MeV)
Fig. 10. Full curve: experimental distribution of alpha particles from reactions in Csl. The decomposition into statistical and direct components has been accomplished with the aid of fig. 11.
an evaporation process, and the upper to a direct process. Bormann and Langkau 3) have also found two peaks (at energies of about 12 and 16 MeV), while Marcazzan et al. S) do not show two distinct peaks. The separation into statistical and direct components has been achieved by a procedure similar to that used for the proton spectrum. Fig. 11 shows a plot of log N(E)/Etr¢ versus E, where for ac we have used optical model values from Huizenga and lgo t3). The curve can be broken up into three sections, a low-energy straight line with T = 0.7 MeV, an intermediate-energy straight line with T = 1.15 MeV and a high-energy residue. By extrapolating the section with T = 1.15 MeV both ways, and subtracting, the decomposition into statistical and direct components shown in fig. 10 is obtained. This analysis attributes 60 ~o o f the alpha counts above 10 MeV to
39
(n, p), (n, d) A N D (n, ct) REACTIONS
an (n, :t) statistical process, 2 ~ to (n, n~t) and 38 ~o to a direct (n, ct) reaction. The counts below 10 MeV may be due partly to (n, net) and partly to alpha particles ejected from the surrounding material. There is a cutoff on the mask corresponding to about 7.2 MeV. The lack of alpha particles of still lower energies is evident from fig. 5. Some of the remarks made concerning the proton analysis apply equally to the alpha-particle analysis. For example, if we use the black-nucleus cross sections of Blatt and Weisskopf 14) with R = (1.5A*+ 1.21) fm, the nuclear temperature is about 1.07 MeV instead of 1.15 MeV. This reduces the statistical component to about 57 ~o and increases the direct component to about 41 ~o. The spectral shapes in the two cases are very similar. It is also possible that nearly all of the alpha particles should be attributed to direct processes, so that the figure of 38 ~o should be regarded as a lower limit for the direct fraction. 1
I
I
I
I
1
Cli
in,=)
O
I0 s
-\oN~OT• O.'t4
MeV
104
/~(£)
£o"c
103 o '~o
102
TIll5 M|V ~
~
0
I0
I I0
I 12
I I 14 16 E (MeV)
[ 18
I 20
Fig. 1I. Analysis of the alpha-particle spectrum according to the statistical theory of nuclear reactions. Values of tre were taken from Huizenga and lgo ,3). 3.3. ABSOLUTE CROSS SECTIONS The cross sections found in the present work by taking coincidences with the associated particles are as follows: o(n, p ) + a ( n , n p ) + a ( n , d) = ll.0_+ l.l mb
(E > 2.5 MeV),
a(n, ct)+a(n, net) = 1.9+0.2 mb
(E > 7.2 MeV).
From the analyses of the spectra given above we can obtain values for the cross sections as follows: a ( n , p ) = 8___1 mb, tr(n, d ) =
1.2+0.2 mb,
a(n, c t ) = 1.8+0.2 mb.
40
w.R.
DIXON
These values represent averages over Cs and I. For the (n, p) measurements a proton coincidence rate of about 10 per minute was used, and the chance rate was about 0.6 c/min. For the (n, ~) measurements the alpha particle coincidence rate was about 1.5 per minute, and the chance rate observed was one count in 60 minutes. During the (n, p) measurements, checks were made as follows: the window width on the associated alpha particle peak was narrowed and the CsI(T1) crystalwas moved closer to the tritrium target. As expected, neither action had an observable effect on the measured cross section. The cross sections given above include an 8 ~o correction for absorption of the tagged neutron beam in the cooling water and brass behind the tritium target. The narrow-beam attenuation of the tagged neutron beam amounts to 10~o, but this has been reduced slightly to allow for scattered neutrons which can still give rise to coincidences. It should be noted that there is no compensation arising from neutrons which start out in directions outside the tagged beam and are subsequently scattered in, since in these cases the associated alpha particle is not detected. There is an uncertainty in the cross sections of perhaps 2-3 ~ arising from uncertainty in this correction. No correction has been made for the attenuation of the tagged neutron beam in the CsI(TI) crystal itself, since this is largely compensated by the increased path length available to the neutrons scattered inside the crystal. TABLE 2
Cross sections in C s l for (A) tr(n, p ) + o ( n , np)+~r(n, d), (B) o(n, at) Method
N e u t r o n energy (MoV)
Ref.
(A)
Coincidences with s i m u l t a n e o u s discrimination
14.6
Present work
11.0+ 1.1
Coincidences w i t h o u t discrimination, followed by separation o f p and ~,
14.1
t)
Liei(Eu) m o n i t o r
14. I
s)
I.I -2:0.15
P r o t o n recoil m o n i t o r
14
5)
0.810.2
20
(B)
1.8-t-0.2
+3
Cross sections are given in millibarns per a t o m a n d are a n average between I it' a n d Cs 13s.
The results of Bormann et aL 2,3) and of Marcazzan et al. s), together with the present results, are summarized in table 2. While these results do not agree within the assigned errors, the differences are not overwhelming. The differences may be due in part to differences in the incident neutron energy. Another possibility is an error in the calibration of the neutron monitors in the other experiments; the method of tagging the neutron beam is in principle much more reliable for measurements of absolute cross sections than using other monitors. There is also the possibility of substantial contributions of charged particles from material surrounding the Csl(TI)
(n, p), (n, d) AND (n, a) REACTIONS
41
crystal. Low-Z material surrounding the crystal has high cross sections for both (n, p) and (n, ct) reactions, and so it should be replaced by high-Z material as far as possible. The problem with alpha particles is less serious than with protons because alpha particles from CsI are of considerably higher energies than those from the low-Z materials with high cross sections. Thus if there were an appreciable number of external alpha particles, their presence would be betrayed and confusion would be unlikely. TABLE 3
Cross sections (mb) for It~7(n,p), 1127(n,=) and Csm(n, at) Method
Neutron energy (MeV) Ref.
Activation Activation
14.5 14 -4-0.5
~5) :6)
Activation
14.1
Emulsions
14
:8)
Activation Irradiation o f NaI
14.5 14.05
~7) 40)
Theoretical Systematics
14.5 14
t~) 20)
2)
It27(n, p) 11.7+ 25
1127(n,=)
i.8
Csm(n, u) 1.9t0.2 1.04-0.3
+ 15
< 5/4~z m b / s r at 120 ° > 2 3 0 4 - 140
18 q-3 1.44-0.2
17 16
Table 3 summarizes other evidence on relevant cross sections in I t27 and Cs laB. The first three entries are activation measurements, of which those of Coleman et aL ts) are probably the most reliable. A direct comparison of these values with table 2 is not possible without taking into account the (n, np) and (n, d) cross sections, and allowing for both 1127 and Cs 133. If it is supposed that I t27 and Cs 133 have nearly equal cross sections, there seems to be good agreement between our present results and those of Coleman et al., particularly for a(n, 0t). The next entry in table 3 is a measurement by Allan is) at 120°; if the emission of protons were isotropic the total cross section would be less than 5 rob. The fifth entry is an old measurement by Paul and Clarke 17) which seems to be much too high for both It27(n, p ) a n d I127(n, ct). The sixth entry is a new measurement of I127(n, ct) by Bizzeti eta/. 4°) from the irradiation of NaI, which just agrees with our present result for CsI within the assigned errors. The last two entries in table 3 are a theoretical estimate for I127(n, p) by Brown and Muirhead 19) (17 mb) and a prediction on the basis of systematic trends by Gardner 20) (16 mb). The calculation of Brown and Muirhead is of considerable interest in that 16 mb is ascribed to direct (n, p) reactions and only 1 mb to statistical (n, p) processes. 4. Discussion
It was first shown by Paul and Clarke 17) that direct reactions play an important role in the emission of charged particles from intermediate and heavy nuclei. The
42
w.R. DIXON
values of (n, p) and (n, ~) cross sections measured for such nuclei were much higher than one expected on the basis of the statistical theory of nuclear reactions. Briefly, the reason for invoking direct reactions was that directly emitted particles tend to have higher energies, and hence are able to penetrate the Coulomb barrier. More recently, activation measurements by Coleman et al. 15) and by Strohal et al. 4i) have led to the same conclusion. A number of experiments have been performed to measure the energy and angular distributions of charged particles from (n, p) and (n, ~) reactions in light nuclei, and substantial direct components have been found. Similar experiments in heavy nuclei are much more difficult to perform, owing to the low yields, and there has been little direct experimental evidence available. It is therefore of interest to examine the results of the present experiment with a view to elucidating, if possible, reaction mechanisms in heavier nuclei. We propose to discuss the (n, d), (n, p) and (n, a) reactions in turn. Our only comment on the (n, d) reaction is that the deuteron spectrum shows a prominent ground-state transition. This is characteristic of a pick-up reaction rather than of an evaporation process. The secondary hump in the deuteron spectrum is somewhat similar to the hump found by Colli et al. 21) and by Peck 22) for Rht °3(n, d). The usual evidence cited for direct (n, p) reactions is the asymmetry about 90 ° in the angular distribution of the emitted protons, together with a high-energy residue left over when a statistical analysis is made of the experimental energy spectrum (e.g. Allan 12), March and Morton 23), Brown et al. 24), Colli et al. 25, z6), Hassler and Peck 27), Glover and Purser 2s), Glover and Weigold 29), Jack and Ward 30)). The fractions of protons ascribed to direct interactions generally lie in the range 10-40 ~o for Z < 30. For heavier nuclei there are not many measurements. Eubank, Peck and Zatzick 31 have made a survey of cross sections in the forward direction for elements near Z = 50, while Allan is) has made a survey of cross sections at 120°. In many cases the yield was too low to stand out from the background, but 51Sb was found to give an unusually high yield: Eubank et al. found 4 0 + 2 mb/sr at 0 °, while Allan found only about 1 mb/sr at 120 °. Such a large effect almost certainly indicates direct interactions. In the present experiment in Csl it was not possible to measure angular distributions. The evidence for direct (n, p) reactions is rather of two types: the high-energy residue left over in a statistical analysis of the proton energy distribution, and the magnitude of the cross section, which can be accounted for only by a direct interaction theory such as that of Brown and Muirhead 19). The result of Allan is) at 120 ° (see table 3) taken together with the total cross section suggests anisotropy but not necessarily asymmetry about 90 °, and hence cannot be adduced as evidence in favour of direct reactions. Theories applicable to direct (n, p) reactions have been of the volume type (Hayakawa. Kawai and Kikuchi 32), Brown and Muirhead tg)) and of the surface type
(n, p), (a, d) AND (n, ~) REACTIONS
43
(Austern, Butler and McManus 33), Elton and Gomes 3,)). There is no firm evidence in the present experiment to choose between these two possibilities. One could perhaps argue that since the (n, d) pickup reaction is essentially a surface effect, one should expect an (n, p) knockout reaction in the surface to be of the same order of magnitude. The fact that the direct (n, p) cross section is observed to be at least four times as large might then be adduced as evidence in favour of a volume theory. The argument is far from conclusive. Insofar as the spectral shape is concerned, there is no basis for choosing between surface and volume effects. Since it has been stated in the literature t2) that the observed shape of the direct spectrum (fig. 7) favours a surface rather than a volume theory, it is perhaps worthwhile pointing out explicitly how this shape arises in the volume theory. In that theory in its simplest form one imagines the incident neutron interacting with a Fermi sea of neutrons and protons. For the maximum proton energy, there must have been a complete energy transfer; this can take place only at the Fermi surface, since at any proton energy below the surface, there would be no place for the spent neutron to go. For smaller and smaller energy transfers, protons from greater and greater depths can participate, and still leave the neutron above the surface. Thus the peak in the spectrum comes about through the interplay of two factors: the Pauli principle making more and more protons available for interaction, and the Coulomb barrier inhibiting their emission. While there is no firm evidence in favour of the volume theory of Brown and Muirhead t9), and while that theory is almost certainly oversimplified, it has nevertheless enjoyed considerable success in predicting cross sections t s) and in predicting direct interaction fractions 27). It is therefore of interest to examine the calculation of the direct proton spectrum in more detail. The complicated expression given by Brown and Muirhead can be expanded as follows:
N(E) oc b l ( e m x - E) + b2(Em,x - E) 2 + b3(Em,x- E) 3 + . . . . if we disregard the Coulomb barrier. The coefficients b~ depend on the incident energy and the Fermi energy, but not critically. For 14.6 MeV neutrons, a potential well of 40 MeV, and a Fermi energy of 33.6 MeV, wefind b2/bl ~, - 0 . 0 1 and b3/b 1 l0 -4. Thus the predicted proton spectrum would be essentially linear in the residual energy, over a wide range of energy, if there were no barrier effect. With this variation in mind, it can be understood why the statistical component should peak some 3 MeV lower than the direct spectrum. In the statistical theory the shape of the proton spectrum is also determined by the interplay between two factors, the availability of states in the residual nucleus and the Coulomb barrier. The availability of states, however, goes up exponentially with the residual energy, instead of linearly, and this can produce a shift of the observed amount. It can also be understood that a direct spectrum can be approximately fitted by statistical formula, provided the tempearature parameter is made high enough (e.g. Bormann et al. 2)). The evidence for direct (n, ct) reactions in Csl is perhaps even stronger than the evidence for direct (n, p) reactions. The present experiment shows a clear separation
44
w.R.
DIXON
of the alpha-particle energy spectrum into two components, only one of which can be accounted for by a statistical analysis. The high-energy component is almost certainly due to direct ejection of alpha particles. It is not, however, possible to choose between knockout and pickup processes. The former would imply the pre-existence of alphaparticle clusters in the nuclear surface, a notion which has received strong advocacy from Wilkinson 3s). It might also be noted that Wildermuth and Carovillano 36) have argued that under certain conditions alpha clusters might have relatively long lifetimes in the interiors o f nuclei. Bormann and Langkau 4) have published a set of (n, ct) spectra from CsI at various neutron energies, and have noted that the fraction of counts in the high-energy peak decreases with increasing neutron energy. This behaviour would not be expected if the low-energy component were due solely to a statistical process. They have suggested that the high-energy peak is due to a pickup process, while the low-energy component is due both to direct knockout and evaporation of alpha particles. There is very little evidence on angular distributions for (n, a) reactions in heavy nuclei. Facchini et aL 37) have made a preliminary investigation on forward to backward asymmetry in the TalSl(n, ct) and Au197(n, ct) reactions, and report a ratio of about five to one. Ribe and Davis 3a) have observed a strong forward peak for 40Zr(n, ct), but it is not clear from their results if the angular distribution is actually asymmetric about 90 °. High-energy alpha-particle tracks from heavy constituents in nuclear emulsions are observed to be strongly forward (Jarvis 39)). We have not emphasized the statistical reactions in this discussion, because with the large admixture of direct effects, it is not possible to pinpoint the parameters or even to select the appropriate form of a statistical calculation. There is, however, one aspect of the statistical processes which should be pointed out. The (n, np) cross section is found to be considerably larger, relative to the (n, p) cross section, than the (n, net) relative to the (n, ~t) cross section. Stated in another way, the emission of alpha particles relative to protons is considerably more difficult after a neutron has already been emitted. That either the (n, np) or (n, n~) reaction is significant is a consequence of the fact that if the residual nucleus following the (n, n') reaction has an excitation less than 9 MeV, it is energetically impossible to emit a second neutron (see table 1). The author wishes to acknowledge valuable discussions of the present experiment with Mr. J. H. Aitken and Dr. R. S. Storey of this laboratory and the technical assistance of Mr. J. D. Stinson and Mr. J. P. Legault in some phases of the work. References
1) L. A. KOnig, J. H. E. Mattauch and A. H. Wapstra, Nuclear Physics 31 (1962) 18 2) M. Bormann, H. Jeremie, G. Andersson-LindstrOm, H. Neuert and H. Pollehn, Z. Naturforsch. 15a (1960) 200 3) M. Borrnann and R. Langkau, Z. Naturforsch. 16a (1961) 444
(n, p), (n, d) AND (n, a)
REACTIONS
45
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