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Large scintillation detector for photoneutron reactions
N U C L E A R I N S T R U M E N T S A N D M E T H O D S 59
(I968) 2 2 9 - 2 3 6 ; © N O R T H - H O L L A N D
PUBLISHING
CO.
LARGE S C I N T I L L A T I O N D E T E C T O R F O R P H O T O N E U T R O N REACTIONS* B. C. COOK and~C. C. J O N E S t
Institute for Atomic Research and Department of Physics, lowa State University, Ames, Iowa 50010, U.S.A. Received 16 October 1967 A 40" liquid scintillation detector was constructed for use in photonuclear work. Integrated cross sections for reactions in which one or two neutrons are emitted were measured up to 50 MeV for fluorine. The efficiency of the detector was about 6070.
1. Introduction Many photonuclear cross sections have been studied by the direct detection of photoneutrons. Ferguson et al. 1) Bramblett et al. 2) and Gerstenberg and Fuller 3) have used BF a detectors for this purpose. This method of neutron detection has the advantage of low sensitivity to gamma rays but efticiencies in excess of 40% have not been obtained. Thus, total neutron production without regard to neutron multiplicity are usually measured. The statistical theory or other experimental data for multiple neutron processes must be used for the interpretation of such data. Absolute photonuclear cross sections are still uncertain to _ 40% 3). One possible difficulty is the neutron energy dependence of detectors of this type. Large scintillation detectors 4,s) with high neutron detection efficiencies have been constructed and used with success in other applications. Use of such detectors in photonuclear research should permit more efficient separation of (~,2n) from (%n). Also the neutron energy dependence of such detectors will be essentially fiat. The construction and successful use of a 1000 liter liquid scintillation detector for the measurement of 19 F photoneutron cross sections is reported here.
2. Apparatus 2.1. THE DETECTOR AND ELECTRONICS The detector (fig. 1) is a cylindrical tank 40" dia. and 43" long modeled after similar units by Diven et al.4). It was constructed from aluminum plates. The inside is painted with TiO 2 base paint (Plasite no. 7100-B, Wisconsin Protective Coating Corp.). The phototubes were EMI type 9583-B, standard 11 stage 5" photomultiplier tube. Each tube viewed the scintillator through a plexiglass window so that individual tubes could be removed without draining the tank. The * Work was performed at the Ames Laboratory of the U.S. Atomic Energy Commission. A portion of this work was submitted by C. C. Jones as a thesis for a Ph.D. (Iowa State University, 1967, unpublished). t Present address: Physics Department, Union College, Schenectady, New York, U.S.A.
scintillator used (Arapahoe type H-F) had the empirical formula C1oH14 so that many protons were available for neutron thermalization. Signals were coupled out of the phototubes with emitter followers using type 2N2906 transistors. This transistor was selected for its good frequency and emitter-base breakdown specifications. The load resistor for each tube was set at about 1000 12. The 28 tubes were divided into two interlacing banks of 14 tubes so that adjacent tubes were never members of the same bank. The two banks were run in a coincidence arrangement (fig. 2) to cut down phototube noise. The signals at the input to the coincidence circuit were clipped to 30 nsec duration, so that the total coincidence resolving time was about 60 nsec. This is long enough so that the efficiency for detection of neutrons is not reduced and short enough to reduce tube noise. The upper and lower level discriminators were set to count the 2.225 MeV gamma ray resulting from the capture of neutrons by protons. An electron synchrotron produces short pulses of bremsstrahlung radiation which are collimated to a full angle of about 0.015 tad. This beam is directed down the center of a 3" beam tube through the center of the detector (fig. 3). The beam passes through the sample at the center of the detector and proceeds to an ionization type of beam monitor. Neutrons are produced in the sample during the beam pulse. They are thermalized by the protons in the scintillator in about 1 #sec. A counter is gated on 2 #sec after the beam pulse and remains on for 600 #sec. The scintillator was not loaded with gadolinium in this experiment so that the gating problems would not be so severe. The number of counts recorded by the counter after each beam burst is used to compile a table of the probability per beam pulse for the observation of k counts, where 0 < k < 9. This is the data. The beam intensity is adjusted so that the average number of counts per beam pulse is about one. 2.2. BACKGROUND, SHIELDING The main disadvantage of this type of detector is the
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LARGE SCINTILLATION DETECTOR FOR PHOTONEUTRON REACTIONS
to the edge of the tank, the number of counts under the sum peak was reduced. The unresolved doublet at about 1.25 MeV moved to lower channels due to increased escape of the Compton scattered gammas. The poor energy resolution (about 25% for the 2.2 MeV gamma ray) results partly from statistics of the electrons at the photocathodes and partly from nonuniformity of light collection over the volume of the scintillator. The number of photons per MeV incident on the photocathodes is very roughly 200 so that the number of photoelectrons produced per MeV (for a gamma ray) is about 20. These numbers are only order of magnitude estimates.
high efficiency for detection of background. In order to reduce this, massive iron and concrete shielding was placed around the tank. An additional 4" of lead placed around the detector reduced the background substantially. Under the experimental conditions used, in which the discriminators are set to observe the 2.225 MeV gamma ray, the background without the accelerator beam was about 0.5 counts per 600#see gating cycle, or about 1000 per sec. 2.3. RESOLVINGTIME The resolving time of the apparatus was about 0.3 #see. This was due primarily to the response time of the photomultipliers used. Since the half life of the neutrons in the detector was about 170/~sec, no dead time corrections had to be made. The most fundamental limitation to the resolving time would be the time taken for a photon to cross the tank (about 10 nsec). 2.4. GAMMA-RAYENERGYRESOLUTION Spectra of gamma-ray sources placed at the center of the detector had a peak which could be interpreted as a total absorption sum peak with a Compton tail. Since the materials in the scintillator are all low atomic numbers (carbon and hydrogen), all the interactions of the gamma rays are by means of the Compton effect. However, due to the large size of the detector, it is very likely that the scattered gamma ray will not escape but will scatter again. Sources at the center of the tank produced sum peaks so that the 6°Co source produced a peak at 2.5 MeV (fig. 4). When the source was moved
2.5. EFFICIENCYDETERMINATION The efficiency of the tank was measured as 55%. This was determined using an Am-Be neutron source of strength of about 104 neutrons/sec. The reaction involved is 9Be+4He ~ 12C+ in. About 60% of the neutrons are produced with a 4.5 MeV gamma ray from an excited state of 12C 6). To measure the efficiency, the neutron source is taped to a 2" NaI crystal (fig. 5) at the center of the beam tube. Pulses in the NaI system corresponding to the 4.5 MeV gamma ray were used to start the 600 psec gating cycle. The number of counts per gate cycle, after subtraction of the background counts per gate cycle, is a direct measurement of the efficiency. The background rate is determined by starting the gate sequence with a pulser.
]
BORAX 3 0 II
CONCRETE 7 AND IRON
BORAX
BEAM MONITOR
CERAMIC DONUT II
LIQUIDSCINTILLATOR[-] ~240 GALLONS II TARGET_~' TUNGSTEN] COLLIMATOR~
'1 ]
231
BORAX
Fig. 3. Experimental arrangement.
~"
LEAD
8"
IORN
232
13. C. C O O K A N D C. C. JONES
threshold for the (y,3n) reaction is above 45 MeV in fluorine, this assumption was good in this experiment. The method described below can be extended to include reactions of higher multiplicity. The first problem is to find the (y,n) and (y,2n) rates. Let R 1 and R 2 be the average number of reactions per beam pulse for reactions in which one and two neutrons are produced, respectively. The probability per beam pulse that m reactions of type (?,kn) where k is 1 or 2 can be written
I
Co 60, CENTER
P ( m , k ) = R• exp ( - Rk) / m !.
Let r k be the probability per beam pulse for the release of k neutrons in the sample, when all possible combinations of (?,n) and (?,2n) reactions are considered. r o = P(0,1)P(0,2),
Co 60,
r I = P(1,1)P(0,2),
EDGE
r2 = P(2,1)P(0,2) + P(0,1)P(1,2),
Fig. 4. Spectrum of 6°Co.
r3 = P(a,1)P(O,2)+P(1,1)P(1,2),
r4 = P(4,1)P(0,2)-F P(2,1)P(1,2) + P(0,1)P(2,2).
The efficiency measurement will be improved in the future with the use of a fission source and detector.
Note that the left and right sides of the above equations add up to unity. The rk could be computed directly from the data if the efficiency were 100%. To take account of the efficiency, let Yk be the probability per beam pulse for detection of k neutrons, and let e be the efficiency. Then
3. Data analysis The data consist of the probability per beam pulse for observation of k neutrons. The (7,n) and (7,2n) reaction rates are to be extracted from these data. I f the reaction rates are known for a set ofbremsstrahlung tip energies, a photonuclear yield curve can be constructed. The cross section is then extracted using the known photon spectrum. It is assumed that no processes in which three or more neutrons are emitted participate. Since the
Yo = ro + (1 - e)r I + (1 -- e)2r2 + (1 -- e) 3r 3 + .... Y1 =
+ 2e(l - e)r 2 + 3e(1 - e)2r3 + ....
erl
Y2 = }73
e2r
-I- 3e2(1 -- e)r a + .... earn + ....
=
40" NEUTRON DETECTOR
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Am-Be NEUTRON SOURCE
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COUNTS GATE CYCLES
L A R G E S C I N T I L L A T I O N D E T E C T O R FOR P H O T O N E U T R O N
I
Note that the sums of the left and right sides again add to unity. The two sets of equations can be written in general form as 3O
m,n
Y, = ~ ek(1 -- e) j -k [j ! / {(j _ k)!k! }] r i. Q:
L
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t
2O%
Yo = 1 - R 1 - R 2 ,
I10 = {1 + R i O - e ) + R 2 ( 1 - e ) 2 } e x p ( - R i - R 2 ) ,
These are the low intensity equations used by Ashby 5) and by Bramblett et al.2). If approximations are not made about R~, R2 and e, then a least-squares solution is clearly indicated. Let the functional relationships between the data Yk and the reaction rates R~ and R2 be represented byfk. Then ;~2 is computed according to the following expression.
Z 2 = ~ {(Yk--fk)/AYk} 2, k
where A Yk is the error in Yr. The sum was cut off so that statistics of numbers less than 100 would not have to be considered. The least-squares fitting procedure also gave the error in R~ and R2, s o that an error analysis could be carried out. The results of this analysis for the error in the (~,2n) yield are shown in fig. 6. This shows why high efficiency detectors are necessary. It also shows that the accelerator intensity should be adjusted so that the observed counts per beam pulse is about 0.3. The method of Goryachev 7) seems to be in agreement with the above analysis for beam intensities producing about 2 counts per beam pulse. That is, data submitted to both the least-squares fitting method and to Goryachev's method give the same results. However, he does not present a best operating intensity nor does he state the approximations of his analysis. 4. Results
4.1. YIELDS The yield function is defined as the number of reactions produced per MeV of incident beam energy per target nucleus as a function of the bremsstrahlung tip
I
I
j
I
B
I
W
60 '/=
5 4
BO % _
( )", 2 n ) l ( )',n )= 0 . 0 5 REP. RATE- 60/see
II1 = {Rle + 2REe(1--e)} e x p ( - R1 - RE), Yz = ( R z e Z ) e x p ( - R 1 - RE).
I
30 %
YI = R1, In the limit as R1 and RE are small but the efficiency is not equal to one, the equations reduce to the following:
I
20
In the limit as the efficiency approaches unity, R 1 and R2, approach zero, we get
I12 = R 2 .
I
ERROR IN (Y, 2n)vs. BEAM INTENSITY FOR VARIOUS EFFICIENCIES
r k = ~ R"~R~ exp { - ( R 1 +R2)}/(m!n!) but m +2n = k, j>-k
233
REACTIONS
_
2 HOUR RUNS
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0.2
0.4
0.6
0.8
1.0
1.2
TOTAL NUMBER OF COUNTS/BEAM Fig. 6. Error analysis results.
energy. The incident beam energy is measured using a thick-walled ionization chamber. The number of reactions is computed according to the analysis given above. Yield functions for reactions in which one or two neutrons were produced were measured for bremsstrahlung tip energies from 10 to 50 MeV in 5 MeV steps. The values for chi-squared were reasonable over the entire energy range. There was no indication of the presence of any (~,,3n) even at the highest energy. The yields at 50 MeV for reactions in which one and two neutrons are produced are 1.7 and 0.25 x 10 -28 reaction. cm2/MeV • atom, respectively. 4.2. CHECKS A number of checks were made to ensure that the results were not biased. Some of these considerations are discussed below. 4.2.1. Evidence for neutrons There are three indications that neutrons actually were observed. First, the pulse height spectrum produced shows a peak at about 2.2 MeV (fig. 7). This is the proper energy for the gamma ray produced when thermal neutrons capture in protons producing deuterons. Secondly, the half-life of the neutrons in the scintillator can be computed from the proton density and cross section for capture of a neutron by a proton. The computed value is about 187 psec; the observed
234
B. C. COOK AND C. C. JONES I
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PHOTONEUTRONSFROM TEFLON
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I 20
40
60
80 I00 CHANNEL Fig. 7. Photoneutron pulse height spectrum.
value is 163/tsec (fig. 8). The observed value might be expected to be smaller since neutrons can migrate out of the detector before capture. Thirdly, the thresholds for the (y,n) and (7,2n) reactions are at approximately the right energies. 4.2.2. Oxygen runs A water sample was bombarded at the center of the tank at 50 MeV. The results were of interest for both the (?,n) and (7,2n). The (r,n) yield was in very good agreement with values by Cook s) and Gerstenberg and Fuller3). The yield measured was higher than both, being 12% above the former and 6% above the latter. The (7,2n) yield for oxygen was barely observable. This showed that the large (7,2n) result in fluorine was not a property of the apparatus or of the method of analysis.
4.3. EXTRACTION OF THE INTEGRATED CROSS SECTIONS The yield for a reaction at a particular energy is
140
defined as the number of reactions per unit monitor response. The yield is related to the cross section according to
f
or(E) = {N/F(E)}
E
{(I)(E,k)/k}t~(k)dk, th
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---
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t~100
=; --'~'~! -- ~ -
4.2.3. Corrections Corrections for dead time, pulse pile up, and beam intensity fluctuations were estimated. The results indicated that these corrections would be equal to or less than the statistical errors so that the corrections were not applied. Experimental efforts to enlarge these errors failed to produce any observable result. Thus the dead time was doubled by changing the electronics, but no change was seen in the resulting values for the reaction rates.
120
.MACHINE
-
z~
GENERATED
--
~
3
BACKGROUND, NATURAL BACKGROUND, SUBTRACTED. "p~AWNIFTE0 S;OWBSAME HALF
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~
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DECAY OF MACHINE ~ [ I 0 - - GENERATED NEUTRONS _ IN 40" DETECTOR 0
I I00
I 200
I 300
I 400
~
~
500
t
~
600
TIME, UNITS /~ SECOND Fig. 8. Capture of photoneutrons in the detector.
700
LARGE SCINTILLATION
DETECTOR
where N is the number of nuclei/cm 2, F(E) is the monitor response, (,~/k)dk is the number of photons incident on the sample with energies between k and k+dk, and a(k) is the photonuclear cross section at energy k. The monitor response is =
i
i
i
i
i
! 200
o~D t-" o
o
I0
20
i
= ~ Nqgj. j=l
The elements of the matrix N u can be computed so that N - ~ can be computed. Then
30
40
50
ENERGY, MeV
Fig. 9. Integrated cross sections for fluorine.
and the integrated cross section is given by i O'int(Ei) =
where ~b has now absorbed factors such as N, F(E) and • /k. We make an approximation to q~ so that it can be taken out of the integral.
~ O'j. j=l
Due to the errors, the trj tend to oscillate at high energies. These oscillations can be smoothed out. The presented integrated cross sections are actually computed according to the method of Penfold and Leissl°). 4.4. ERRORS Systematic and random errors are summarized in table 1. These values are rough estimates for typical data points. Each data point resulted from about 6 h using a 60 accelerator beam pulses per sec. Improvements in apparatus, to be discussed, below, can improve the first two factors. The rest are not readily improved. 5. Discussion
J O'j = ~ N f i I Y / i=1
5.1. CROSS SECTION FOR 19F
TABLE 1
Errors*.
Counting statistics Efficiency determination Dose system Apparatus fluctuations Sample absorptions Pulse overlap Beam fluctuations Over-all errors
x = P A N D 2 p A N D d ANDa etc
~(e,,k)tr(k)dk,
~.,
Source of error
IO0 _
Ikj
j = l • kj-dk
1. 2. 3. 4. 5. 6. 7. 8.
i
300
235
REACTIONS
R(E)
where R(E) is the response of the monitor per unit of incident energy, and the integral is the total beam energy. Values for R(E) were taken from Pruitt and D o m e n 9) since the monitor used was designed accord= ing to the specifications of the NBS standard chamber. Values for the total beam energy are taken from Penfold and Leiss1°). Values for (~(E,k)/k are taken from SchiE 1I). Since the yield is not known continuously but rather at a discrete set of energies, the yield equation can be written as
Y(E,) =
FOR PHOTONEUTRON
Error (y,n) (%) 2 3 4 0.9 1 small small 6
Error (y,2n) (%) 5 6 4 0.9 1 4 2 10
The cross section for reactions in which one or two neutrons are emitted integrated over energy to 50 MeV is 221 _ 2 0 M e V . m b (fig. 9). This is well below the classical dipole sum of Levinger and Bethel2):
f tr(E)dE = 60(NZ/A)
MeV- mb.
In order to compare to the sum rule, cross sections for the production of protons would have to be taken into account. Cross sections as a functions of energy are not displayed since the energy bins used were too broad to give meaningful results. 5.2. DISCUSSION
* It should also be noted that there may be some correlations in these errors.
The large liquid scintillation detector will continue to be a useful tool for photonuclear research. It has proved
236
B. C. C O O K A N D C. C. J O N E S
practical as it now exists and will be even better as improvements are made. These include loading the scintillator with gadolinium and better measurements of efficiency. Gadolinium loading will increase the effectiveness of the apparatus in several ways: 1. The efficiency will be increased so that statistical errors will be reduced; 2. The background will be reduced due to the faster capture of neutrons. Thus, the present 600/~sec gate period will be reduced to 40 #sec or less. This reduces the natural background from a present value of 0.5 per beam pulse to 0.03 or less per beam pulse. Less background subtraction will decrease the statistical error of the experiment; 3. Since the background will be reduced, the beam intensity will be reduced to get closer to the minimum error; 4. More than 2.225 MeV will be released for each neutron which captures so that the discriminators may be run at higher values. This will also decrease the background. The efficiency can be more effectively determined if a spontaneous fission source is used. A fission detector would have a much higher efficiency than the 2" NaI crystal does for the 4.5 MeV gamma ray. Also, several neutrons are released per fission, compared to only one neutron per 4.5 MeV gamma ray for the Am-Be neutron source. Thus the efficiency of the detector could be easily monitored throughout the experiment. With these improvements, the experiment could be run about four times faster than it was run for this
work. It is questionable as to whether this apparatus will be useful for monochromatic gamma-ray work such as Bramblett et al.2). This is due to the low intensities available. If the monochromatic beams can be increased so that 0.3 neutrons per beam pulse are obtained, then this is the ideal apparatus for that type of experiment. Accurate integrated cross sections are necessary to compare with model-independent theoretical calculations12). At present, the experimental values vaiy widely3). This type of detector, in which the efficiency is very nearly independent of the neutron energy, is expected to help this situation.
References 1) G. A. Ferguson, J. Halpern, R. Nathans and P. F. Yergin, Phys. Rev. 95 (1954) 776. 2) R. L. Bramblett, J. T. Caldwell, B. L. Berman, R. R. Harvey and C. S. Fultz, Phys. Rev. 143 (1966) 790. a) H. M. Gerstenberg and E. G. Fuller, NBS Technical Report 416 (1967). 4) B. C. Diven, H. C. Martin, R. F. Taschek and J. Terrell, Phys. Rev. 101 (1956) 1012. 5) V. J. Ashby, H. C. Catron, L. L. Newkirk and C. J. Taylor, Phys. Rev. 111 (1958) 616. 6) F. Ajzenberg and T. Lauritsen, Rev. Mod. Phys. 27 (1955) 112. 7) B. I. Goryachev, Sov. J. Atomic Energy 12 (1962) 258. s) B. C. Cook, J. E. E. Baglin, J. N. Bradford and J. E. Griffin, Phys. Rev. 143 (1966) 724. 9) j. S. Pruitt and S. R. Domen, NBS Technical Report 6218 (1958). x0) A. S. Penfold and J. E. Leiss, unpublished report (University of Illinois, 1958). 11) L. I. Schiff, Phys. Rev. 83 (1951) 252. 12) j. S. Levinger and H. A. Bethe, Phys. Rev. 78 (1950) 115.
(I968) 2 2 9 - 2 3 6 ; © N O R T H - H O L L A N D
PUBLISHING
CO.
LARGE S C I N T I L L A T I O N D E T E C T O R F O R P H O T O N E U T R O N REACTIONS* B. C. COOK and~C. C. J O N E S t
Institute for Atomic Research and Department of Physics, lowa State University, Ames, Iowa 50010, U.S.A. Received 16 October 1967 A 40" liquid scintillation detector was constructed for use in photonuclear work. Integrated cross sections for reactions in which one or two neutrons are emitted were measured up to 50 MeV for fluorine. The efficiency of the detector was about 6070.
1. Introduction Many photonuclear cross sections have been studied by the direct detection of photoneutrons. Ferguson et al. 1) Bramblett et al. 2) and Gerstenberg and Fuller 3) have used BF a detectors for this purpose. This method of neutron detection has the advantage of low sensitivity to gamma rays but efticiencies in excess of 40% have not been obtained. Thus, total neutron production without regard to neutron multiplicity are usually measured. The statistical theory or other experimental data for multiple neutron processes must be used for the interpretation of such data. Absolute photonuclear cross sections are still uncertain to _ 40% 3). One possible difficulty is the neutron energy dependence of detectors of this type. Large scintillation detectors 4,s) with high neutron detection efficiencies have been constructed and used with success in other applications. Use of such detectors in photonuclear research should permit more efficient separation of (~,2n) from (%n). Also the neutron energy dependence of such detectors will be essentially fiat. The construction and successful use of a 1000 liter liquid scintillation detector for the measurement of 19 F photoneutron cross sections is reported here.
2. Apparatus 2.1. THE DETECTOR AND ELECTRONICS The detector (fig. 1) is a cylindrical tank 40" dia. and 43" long modeled after similar units by Diven et al.4). It was constructed from aluminum plates. The inside is painted with TiO 2 base paint (Plasite no. 7100-B, Wisconsin Protective Coating Corp.). The phototubes were EMI type 9583-B, standard 11 stage 5" photomultiplier tube. Each tube viewed the scintillator through a plexiglass window so that individual tubes could be removed without draining the tank. The * Work was performed at the Ames Laboratory of the U.S. Atomic Energy Commission. A portion of this work was submitted by C. C. Jones as a thesis for a Ph.D. (Iowa State University, 1967, unpublished). t Present address: Physics Department, Union College, Schenectady, New York, U.S.A.
scintillator used (Arapahoe type H-F) had the empirical formula C1oH14 so that many protons were available for neutron thermalization. Signals were coupled out of the phototubes with emitter followers using type 2N2906 transistors. This transistor was selected for its good frequency and emitter-base breakdown specifications. The load resistor for each tube was set at about 1000 12. The 28 tubes were divided into two interlacing banks of 14 tubes so that adjacent tubes were never members of the same bank. The two banks were run in a coincidence arrangement (fig. 2) to cut down phototube noise. The signals at the input to the coincidence circuit were clipped to 30 nsec duration, so that the total coincidence resolving time was about 60 nsec. This is long enough so that the efficiency for detection of neutrons is not reduced and short enough to reduce tube noise. The upper and lower level discriminators were set to count the 2.225 MeV gamma ray resulting from the capture of neutrons by protons. An electron synchrotron produces short pulses of bremsstrahlung radiation which are collimated to a full angle of about 0.015 tad. This beam is directed down the center of a 3" beam tube through the center of the detector (fig. 3). The beam passes through the sample at the center of the detector and proceeds to an ionization type of beam monitor. Neutrons are produced in the sample during the beam pulse. They are thermalized by the protons in the scintillator in about 1 #sec. A counter is gated on 2 #sec after the beam pulse and remains on for 600 #sec. The scintillator was not loaded with gadolinium in this experiment so that the gating problems would not be so severe. The number of counts recorded by the counter after each beam burst is used to compile a table of the probability per beam pulse for the observation of k counts, where 0 < k < 9. This is the data. The beam intensity is adjusted so that the average number of counts per beam pulse is about one. 2.2. BACKGROUND, SHIELDING The main disadvantage of this type of detector is the
229
230
B. C. C O O K
AND
C. C. $ O N E $
Fig. l, The 40 * tank.
ODD
TEC~
~ .
.
.
.
I_Z.J-I~-II'1 .
3 I00 n $
~byy~b ELECTRONICSCONFmURATION I IM'xl A: AMPLIFIER T:TRIGGER C: COINCIDENCE GG: GATE GENERATOR LG:L.INEAR GATE
I I l
I I
~
OISE
"
I I..-.
UoL.D
~4dbt~~
~250n$
2/~= 600V$ KNOCK-OUT PLUSE
" Fig. 2. Electronics block diagram.
ANT~! ~
'
LRESE~"
JLLL_~I~I ANALYZE R I
INTERRUPT DT0 910 COMPUTER
LARGE SCINTILLATION DETECTOR FOR PHOTONEUTRON REACTIONS
to the edge of the tank, the number of counts under the sum peak was reduced. The unresolved doublet at about 1.25 MeV moved to lower channels due to increased escape of the Compton scattered gammas. The poor energy resolution (about 25% for the 2.2 MeV gamma ray) results partly from statistics of the electrons at the photocathodes and partly from nonuniformity of light collection over the volume of the scintillator. The number of photons per MeV incident on the photocathodes is very roughly 200 so that the number of photoelectrons produced per MeV (for a gamma ray) is about 20. These numbers are only order of magnitude estimates.
high efficiency for detection of background. In order to reduce this, massive iron and concrete shielding was placed around the tank. An additional 4" of lead placed around the detector reduced the background substantially. Under the experimental conditions used, in which the discriminators are set to observe the 2.225 MeV gamma ray, the background without the accelerator beam was about 0.5 counts per 600#see gating cycle, or about 1000 per sec. 2.3. RESOLVINGTIME The resolving time of the apparatus was about 0.3 #see. This was due primarily to the response time of the photomultipliers used. Since the half life of the neutrons in the detector was about 170/~sec, no dead time corrections had to be made. The most fundamental limitation to the resolving time would be the time taken for a photon to cross the tank (about 10 nsec). 2.4. GAMMA-RAYENERGYRESOLUTION Spectra of gamma-ray sources placed at the center of the detector had a peak which could be interpreted as a total absorption sum peak with a Compton tail. Since the materials in the scintillator are all low atomic numbers (carbon and hydrogen), all the interactions of the gamma rays are by means of the Compton effect. However, due to the large size of the detector, it is very likely that the scattered gamma ray will not escape but will scatter again. Sources at the center of the tank produced sum peaks so that the 6°Co source produced a peak at 2.5 MeV (fig. 4). When the source was moved
2.5. EFFICIENCYDETERMINATION The efficiency of the tank was measured as 55%. This was determined using an Am-Be neutron source of strength of about 104 neutrons/sec. The reaction involved is 9Be+4He ~ 12C+ in. About 60% of the neutrons are produced with a 4.5 MeV gamma ray from an excited state of 12C 6). To measure the efficiency, the neutron source is taped to a 2" NaI crystal (fig. 5) at the center of the beam tube. Pulses in the NaI system corresponding to the 4.5 MeV gamma ray were used to start the 600 psec gating cycle. The number of counts per gate cycle, after subtraction of the background counts per gate cycle, is a direct measurement of the efficiency. The background rate is determined by starting the gate sequence with a pulser.
]
BORAX 3 0 II
CONCRETE 7 AND IRON
BORAX
BEAM MONITOR
CERAMIC DONUT II
LIQUIDSCINTILLATOR[-] ~240 GALLONS II TARGET_~' TUNGSTEN] COLLIMATOR~
'1 ]
231
BORAX
Fig. 3. Experimental arrangement.
~"
LEAD
8"
IORN
232
13. C. C O O K A N D C. C. JONES
threshold for the (y,3n) reaction is above 45 MeV in fluorine, this assumption was good in this experiment. The method described below can be extended to include reactions of higher multiplicity. The first problem is to find the (y,n) and (y,2n) rates. Let R 1 and R 2 be the average number of reactions per beam pulse for reactions in which one and two neutrons are produced, respectively. The probability per beam pulse that m reactions of type (?,kn) where k is 1 or 2 can be written
I
Co 60, CENTER
P ( m , k ) = R• exp ( - Rk) / m !.
Let r k be the probability per beam pulse for the release of k neutrons in the sample, when all possible combinations of (?,n) and (?,2n) reactions are considered. r o = P(0,1)P(0,2),
Co 60,
r I = P(1,1)P(0,2),
EDGE
r2 = P(2,1)P(0,2) + P(0,1)P(1,2),
Fig. 4. Spectrum of 6°Co.
r3 = P(a,1)P(O,2)+P(1,1)P(1,2),
r4 = P(4,1)P(0,2)-F P(2,1)P(1,2) + P(0,1)P(2,2).
The efficiency measurement will be improved in the future with the use of a fission source and detector.
Note that the left and right sides of the above equations add up to unity. The rk could be computed directly from the data if the efficiency were 100%. To take account of the efficiency, let Yk be the probability per beam pulse for detection of k neutrons, and let e be the efficiency. Then
3. Data analysis The data consist of the probability per beam pulse for observation of k neutrons. The (7,n) and (7,2n) reaction rates are to be extracted from these data. I f the reaction rates are known for a set ofbremsstrahlung tip energies, a photonuclear yield curve can be constructed. The cross section is then extracted using the known photon spectrum. It is assumed that no processes in which three or more neutrons are emitted participate. Since the
Yo = ro + (1 - e)r I + (1 -- e)2r2 + (1 -- e) 3r 3 + .... Y1 =
+ 2e(l - e)r 2 + 3e(1 - e)2r3 + ....
erl
Y2 = }73
e2r
-I- 3e2(1 -- e)r a + .... earn + ....
=
40" NEUTRON DETECTOR
~
Am-Be NEUTRON SOURCE
IO~sEC
t
EFFICIENCY MEAS PHD: PULSE HEIGHT DISCRIMINATOR Cl COINCIDENCE GG: GATE GENERATOR
&t
4 ~
~COUNTER
3.5ra$
Fig. 5. Arrangement for efficiency measurement.
J
COUNTS GATE CYCLES
L A R G E S C I N T I L L A T I O N D E T E C T O R FOR P H O T O N E U T R O N
I
Note that the sums of the left and right sides again add to unity. The two sets of equations can be written in general form as 3O
m,n
Y, = ~ ek(1 -- e) j -k [j ! / {(j _ k)!k! }] r i. Q:
L
I0%
t
2O%
Yo = 1 - R 1 - R 2 ,
I10 = {1 + R i O - e ) + R 2 ( 1 - e ) 2 } e x p ( - R i - R 2 ) ,
These are the low intensity equations used by Ashby 5) and by Bramblett et al.2). If approximations are not made about R~, R2 and e, then a least-squares solution is clearly indicated. Let the functional relationships between the data Yk and the reaction rates R~ and R2 be represented byfk. Then ;~2 is computed according to the following expression.
Z 2 = ~ {(Yk--fk)/AYk} 2, k
where A Yk is the error in Yr. The sum was cut off so that statistics of numbers less than 100 would not have to be considered. The least-squares fitting procedure also gave the error in R~ and R2, s o that an error analysis could be carried out. The results of this analysis for the error in the (~,2n) yield are shown in fig. 6. This shows why high efficiency detectors are necessary. It also shows that the accelerator intensity should be adjusted so that the observed counts per beam pulse is about 0.3. The method of Goryachev 7) seems to be in agreement with the above analysis for beam intensities producing about 2 counts per beam pulse. That is, data submitted to both the least-squares fitting method and to Goryachev's method give the same results. However, he does not present a best operating intensity nor does he state the approximations of his analysis. 4. Results
4.1. YIELDS The yield function is defined as the number of reactions produced per MeV of incident beam energy per target nucleus as a function of the bremsstrahlung tip
I
I
j
I
B
I
W
60 '/=
5 4
BO % _
( )", 2 n ) l ( )',n )= 0 . 0 5 REP. RATE- 60/see
II1 = {Rle + 2REe(1--e)} e x p ( - R1 - RE), Yz = ( R z e Z ) e x p ( - R 1 - RE).
I
30 %
YI = R1, In the limit as R1 and RE are small but the efficiency is not equal to one, the equations reduce to the following:
I
20
In the limit as the efficiency approaches unity, R 1 and R2, approach zero, we get
I12 = R 2 .
I
ERROR IN (Y, 2n)vs. BEAM INTENSITY FOR VARIOUS EFFICIENCIES
r k = ~ R"~R~ exp { - ( R 1 +R2)}/(m!n!) but m +2n = k, j>-k
233
REACTIONS
_
2 HOUR RUNS
I
I
I
I
I
I
0.2
0.4
0.6
0.8
1.0
1.2
TOTAL NUMBER OF COUNTS/BEAM Fig. 6. Error analysis results.
energy. The incident beam energy is measured using a thick-walled ionization chamber. The number of reactions is computed according to the analysis given above. Yield functions for reactions in which one or two neutrons were produced were measured for bremsstrahlung tip energies from 10 to 50 MeV in 5 MeV steps. The values for chi-squared were reasonable over the entire energy range. There was no indication of the presence of any (~,,3n) even at the highest energy. The yields at 50 MeV for reactions in which one and two neutrons are produced are 1.7 and 0.25 x 10 -28 reaction. cm2/MeV • atom, respectively. 4.2. CHECKS A number of checks were made to ensure that the results were not biased. Some of these considerations are discussed below. 4.2.1. Evidence for neutrons There are three indications that neutrons actually were observed. First, the pulse height spectrum produced shows a peak at about 2.2 MeV (fig. 7). This is the proper energy for the gamma ray produced when thermal neutrons capture in protons producing deuterons. Secondly, the half-life of the neutrons in the scintillator can be computed from the proton density and cross section for capture of a neutron by a proton. The computed value is about 187 psec; the observed
234
B. C. COOK AND C. C. JONES I
I
PHOTONEUTRONSFROM TEFLON
'
'
"
'
'
B
SAMPLE IN
(/) I-Z
o O
t
--
/
--
I
_
/
/
\
NATURAL
I 20
40
60
80 I00 CHANNEL Fig. 7. Photoneutron pulse height spectrum.
value is 163/tsec (fig. 8). The observed value might be expected to be smaller since neutrons can migrate out of the detector before capture. Thirdly, the thresholds for the (y,n) and (7,2n) reactions are at approximately the right energies. 4.2.2. Oxygen runs A water sample was bombarded at the center of the tank at 50 MeV. The results were of interest for both the (?,n) and (7,2n). The (r,n) yield was in very good agreement with values by Cook s) and Gerstenberg and Fuller3). The yield measured was higher than both, being 12% above the former and 6% above the latter. The (7,2n) yield for oxygen was barely observable. This showed that the large (7,2n) result in fluorine was not a property of the apparatus or of the method of analysis.
4.3. EXTRACTION OF THE INTEGRATED CROSS SECTIONS The yield for a reaction at a particular energy is
140
defined as the number of reactions per unit monitor response. The yield is related to the cross section according to
f
or(E) = {N/F(E)}
E
{(I)(E,k)/k}t~(k)dk, th
I00¢ COUNTS FROM TEFLON~ .,..~ SAMPLE,BACKGROUND - ~'~,,, SUBTRACTED,HALF LIFE-_ _= ~ 163/~ sec
---
I.g
t~100
=; --'~'~! -- ~ -
4.2.3. Corrections Corrections for dead time, pulse pile up, and beam intensity fluctuations were estimated. The results indicated that these corrections would be equal to or less than the statistical errors so that the corrections were not applied. Experimental efforts to enlarge these errors failed to produce any observable result. Thus the dead time was doubled by changing the electronics, but no change was seen in the resulting values for the reaction rates.
120
.MACHINE
-
z~
GENERATED
--
~
3
BACKGROUND, NATURAL BACKGROUND, SUBTRACTED. "p~AWNIFTE0 S;OWBSAME HALF
L)
~
--
--.
DECAY OF MACHINE ~ [ I 0 - - GENERATED NEUTRONS _ IN 40" DETECTOR 0
I I00
I 200
I 300
I 400
~
~
500
t
~
600
TIME, UNITS /~ SECOND Fig. 8. Capture of photoneutrons in the detector.
700
LARGE SCINTILLATION
DETECTOR
where N is the number of nuclei/cm 2, F(E) is the monitor response, (,~/k)dk is the number of photons incident on the sample with energies between k and k+dk, and a(k) is the photonuclear cross section at energy k. The monitor response is =
i
i
i
i
i
! 200
o~D t-" o
o
I0
20
i
= ~ Nqgj. j=l
The elements of the matrix N u can be computed so that N - ~ can be computed. Then
30
40
50
ENERGY, MeV
Fig. 9. Integrated cross sections for fluorine.
and the integrated cross section is given by i O'int(Ei) =
where ~b has now absorbed factors such as N, F(E) and • /k. We make an approximation to q~ so that it can be taken out of the integral.
~ O'j. j=l
Due to the errors, the trj tend to oscillate at high energies. These oscillations can be smoothed out. The presented integrated cross sections are actually computed according to the method of Penfold and Leissl°). 4.4. ERRORS Systematic and random errors are summarized in table 1. These values are rough estimates for typical data points. Each data point resulted from about 6 h using a 60 accelerator beam pulses per sec. Improvements in apparatus, to be discussed, below, can improve the first two factors. The rest are not readily improved. 5. Discussion
J O'j = ~ N f i I Y / i=1
5.1. CROSS SECTION FOR 19F
TABLE 1
Errors*.
Counting statistics Efficiency determination Dose system Apparatus fluctuations Sample absorptions Pulse overlap Beam fluctuations Over-all errors
x = P A N D 2 p A N D d ANDa etc
~(e,,k)tr(k)dk,
~.,
Source of error
IO0 _
Ikj
j = l • kj-dk
1. 2. 3. 4. 5. 6. 7. 8.
i
300
235
REACTIONS
R(E)
where R(E) is the response of the monitor per unit of incident energy, and the integral is the total beam energy. Values for R(E) were taken from Pruitt and D o m e n 9) since the monitor used was designed accord= ing to the specifications of the NBS standard chamber. Values for the total beam energy are taken from Penfold and Leiss1°). Values for (~(E,k)/k are taken from SchiE 1I). Since the yield is not known continuously but rather at a discrete set of energies, the yield equation can be written as
Y(E,) =
FOR PHOTONEUTRON
Error (y,n) (%) 2 3 4 0.9 1 small small 6
Error (y,2n) (%) 5 6 4 0.9 1 4 2 10
The cross section for reactions in which one or two neutrons are emitted integrated over energy to 50 MeV is 221 _ 2 0 M e V . m b (fig. 9). This is well below the classical dipole sum of Levinger and Bethel2):
f tr(E)dE = 60(NZ/A)
MeV- mb.
In order to compare to the sum rule, cross sections for the production of protons would have to be taken into account. Cross sections as a functions of energy are not displayed since the energy bins used were too broad to give meaningful results. 5.2. DISCUSSION
* It should also be noted that there may be some correlations in these errors.
The large liquid scintillation detector will continue to be a useful tool for photonuclear research. It has proved
236
B. C. C O O K A N D C. C. J O N E S
practical as it now exists and will be even better as improvements are made. These include loading the scintillator with gadolinium and better measurements of efficiency. Gadolinium loading will increase the effectiveness of the apparatus in several ways: 1. The efficiency will be increased so that statistical errors will be reduced; 2. The background will be reduced due to the faster capture of neutrons. Thus, the present 600/~sec gate period will be reduced to 40 #sec or less. This reduces the natural background from a present value of 0.5 per beam pulse to 0.03 or less per beam pulse. Less background subtraction will decrease the statistical error of the experiment; 3. Since the background will be reduced, the beam intensity will be reduced to get closer to the minimum error; 4. More than 2.225 MeV will be released for each neutron which captures so that the discriminators may be run at higher values. This will also decrease the background. The efficiency can be more effectively determined if a spontaneous fission source is used. A fission detector would have a much higher efficiency than the 2" NaI crystal does for the 4.5 MeV gamma ray. Also, several neutrons are released per fission, compared to only one neutron per 4.5 MeV gamma ray for the Am-Be neutron source. Thus the efficiency of the detector could be easily monitored throughout the experiment. With these improvements, the experiment could be run about four times faster than it was run for this
work. It is questionable as to whether this apparatus will be useful for monochromatic gamma-ray work such as Bramblett et al.2). This is due to the low intensities available. If the monochromatic beams can be increased so that 0.3 neutrons per beam pulse are obtained, then this is the ideal apparatus for that type of experiment. Accurate integrated cross sections are necessary to compare with model-independent theoretical calculations12). At present, the experimental values vaiy widely3). This type of detector, in which the efficiency is very nearly independent of the neutron energy, is expected to help this situation.
References 1) G. A. Ferguson, J. Halpern, R. Nathans and P. F. Yergin, Phys. Rev. 95 (1954) 776. 2) R. L. Bramblett, J. T. Caldwell, B. L. Berman, R. R. Harvey and C. S. Fultz, Phys. Rev. 143 (1966) 790. a) H. M. Gerstenberg and E. G. Fuller, NBS Technical Report 416 (1967). 4) B. C. Diven, H. C. Martin, R. F. Taschek and J. Terrell, Phys. Rev. 101 (1956) 1012. 5) V. J. Ashby, H. C. Catron, L. L. Newkirk and C. J. Taylor, Phys. Rev. 111 (1958) 616. 6) F. Ajzenberg and T. Lauritsen, Rev. Mod. Phys. 27 (1955) 112. 7) B. I. Goryachev, Sov. J. Atomic Energy 12 (1962) 258. s) B. C. Cook, J. E. E. Baglin, J. N. Bradford and J. E. Griffin, Phys. Rev. 143 (1966) 724. 9) j. S. Pruitt and S. R. Domen, NBS Technical Report 6218 (1958). x0) A. S. Penfold and J. E. Leiss, unpublished report (University of Illinois, 1958). 11) L. I. Schiff, Phys. Rev. 83 (1951) 252. 12) j. S. Levinger and H. A. Bethe, Phys. Rev. 78 (1950) 115.