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The emission spectra of NaD2O, InBe, LaBe and NaBe photoneutron sources
Journalof NuclearEncrg~.Vol.27, pp. 857to 873. PcrgmonPress1973. Printedin NorthernIreland
THE EMISSION SPECTRA OF Na-D,O, In-Be, La-Be AND Na-Be PHOTONEUTRON SOURCES K. MUECK and F. BENSCH Atominstitut der dsterreichischen Hochschulen, Vienna, Austria. (Received 23 July 1973)
Abstract-The energy distribution of the photoneutrons of Na-D,O, In-Be, La-Be and Na-Be source systems were measured by means of a proton-recoil proportional counting tube. Spherical lead-shields of various thicknesses (ranging from 1.5 to 13 cm) were used to reduce the intense gamma field accompanying the neutron spectra to be measured. The spectra of spherical heterogeneous source arrangements for three different Be-target thicknesses (0.5, 1.1 and 2.0 cm) were measured and compared with the theoretical distribution as obtained by Monte-Carlo calculations. The
change in spectrum shape due to the lead shields was also calculated by a Monte-Carlo routine. Good agreement between theoretical predictions and experimental results shows values for the peak of the neutron distribution of 264.1 f 0.5 keV for the Na-D,O system, 397.3 f 0.8 keV for the In-Be system, 761.7 f 0.7 keV for the La-Be system, and 966.9 rt 0.5 keV for the Na-Be source system. With the La-Be system a second neutron group of much lower intensity (6.5 per cent of the main group) could be found with a peak energy of 1097.5 f 1.0 keV in good agreement to recent gamma-spectroscopic measurements. INTRODUCTION
the existence of stronger neutron sources, radioactive neutron sources are of some importance in neutron physics chiefly due to their compactness and portability. Furthermore, they have small geometrical dimensions and their source strength-once determined-can be calculated by means of the half-life of the radioactive material. The additional advantage of (y, n)-neutron sources lies in the fact that, in contrast to (tl, n)-sources or fission sources, they emit neutrons of a narrow energy range. Therefore, they may conveniently be used in numerous experiments for measuring neutron cross-sections, the stopping power and diffusion characteristics of various materials, and the importance function in reactors and subcritical assemblies, particularly of fast type. Many experiments using photoneutron sources have been mentioned (e.g., POZE, 1956; BELANOVA, 1966; RYVES, 1971), most of which presented either one of two main obstacles in the interpretation of the data obtained: The difficulty of determining the source strength of a particular photoneutron emitter and the lack of knowledge of the neutron spectrum of a particular source arrangement. The first of these two obstacles has been successfully investigated recently (BENSCH, 1969). With regard to the second problem, successful attempts have been recently made to estimate the spectra by theoretical methods (Monte-Carlo calculations) (BENSCH, 1969; LALOVIC, 1970; RYVES, 1971). However, no experimental proof has been published so far, with the exception of the Sb-Be source where no good agreement between experiment and theory on the energy of the gamma quanta could be established (LALOVIC, 1970). DESPITE
An experimental test of the theoretical predictions is paramount considering the uncertainty in some of the parameters required for the theoretical calculations. In particular, the energy of the neutron-releasing gamma quanta was inadequately known and caused considerable discrepancy between the values established by various authors (see Table 1). 857
858
K.
MUECK
and F. BENSCH
TABLE. I.-PREVIOUS EXPERIMENTAL RESULTS IN COMPARISON WITH THE CALCULATED RESULTS FOR THE PEAK ENERGY OF THE NEUTRON DISTRIBUTION
En WV)
Source
En (keV)
measured calculated act. to equ. (1) up to now
Half-life
(M%)
2PNa-D,0
15.0hr
2.153
264
220
WATTENFIERG (1946)
llGIn-Be
54.1 min
2.112
391
300
HUGHES~~~ EGGLER (1947)
IdoLa-Be
40.23hr
2.522
162
620
WATTENBERG
system
(1946) aaNa-Be
15.0hr
2.153
961
830
WATTENBERG
(1946) Photoneutron sources usually consist of a gamma emitter surrounded by a beryllium or heavy water target. The gamma quanta hitting the target will release neutrons, the energy E,, (in MeV) of which may be calculated by the well-known formula : A-l
En = --yj-
(Ey- Et) f E, cosy
JW - l)(E, -
Et)
931.A
where E, is the primary energy of the gamma quantum, Et the threshold energy of the (y, n)-reaction considered, A the mass number of the target material and y the angle between the direction of the gamma quanta and neutron emission. By using different gamma emitters with only one gamma level above threshold energy, a set of nearly monoenergetic neutron sources in the fast energy region from 20 keV to 1 MeV (BENSCH,1969) is obtained. Up to now the values for the energies of the maximum of the neutron distribution have differed considerably from the experimental results. These values are listed in Table 1. If the most recent data on the energy of the gamma quanta (KARLSSON, 1967; BAER, 1968; ENDT, 1967; RABENSTEIN,1970) are used in the calculations of the neutron energies, the values differ somewhat from those used so far by most experimenters working with photoneutron sources. Despite the use of these data, no good agreement between the theoretically calculated energy of the neutron “line” and the experimental results reported so far (WATTENBERG,1946; HUGHES, 1947) could be obtained (see Table 1). One of the main purposes of this work, therefore, was to investigate closely the neutron energies of the photoneutron sources listed in Table 1 and to compare these values with the theoretical predictions obtained from the most recent values for the gamma energies. From equation (1) it is obvious that the neutrons emitted from the (y, n)-target are not exactly monoenergetic, but have a certain energy spread caused by the energy dependence on the angle between the direction of neutron emission and the direction of the gamma quanta. In addition to this deviation from a monoenergetic spectrum inherent in a (y, n)-reaction, photoneutron sources of usual dimensions show an even greater divergence due to the unavoidably finite dimensions of the source. It is not possible to design source arrangements sufficiently small for an acceptable
The emission spectra of Na-D,O,
In-Be, La-Be and Na-Be photoneutron
sources
859
neutron yield. The usual source systems have diameters from 1 to 10 cm, which is of the same order of magnitude as the mean free path for neutrons in beryllium, D,O and most of the gamma-emitting materials. Therefore, the moderation of neutrons on their passage through the (y, n)-target is not negligible. This fact and the energy loss of the gamma quanta due to scattering before neutron production induce a broadening of the neutron spectrum with the source arrangements used in practice. This moderation and broadening of the peak of the neutron spectrum results in a decrease in the mean neutron energy with increasing source dimensions. The change in the spectrum shape influences the corrections which account for deviations from the desired monoenergetic emission. Therefore, most experiments involving photoneutron sources require more detailed knowledge of the neutron emission spectra. So far only two experimental approaches to determine the spectra of the neutron sources discussed in this paper have been reported: HUGHES (1947) investigated the spectrum of an In-Be source with proton recoils in a hydrogen-filled cloud chamber. The main drawbacks were the poor statistical accuracy of the method applied and the insufficient energy calibration, which resulted in a lower peak value of the neutron distribution than theoretically predicted. OEHLER (1964) measured the spectrum of a Na-Be source with a hydrogen-filled ionization chamber, but the energy resolution of their spectrometer was rather low (17 per cent). Moreover, no energy calibration independent of the neutron spectrum to be measured was used; in fact the peak energy of the neutron distribution as calculated from the gamma energy using equation (1) was taken to calibrate the energy scale. Therefore, experimental determination of the neutron energies was not possible. In addition to a careful checking of the neutron energy of the four photoneutron sources investigated against the theoretical values, great emphasis was placed on the determination of the spectra of various source-arrangements and particularly the dependence on the thickness of the beryllium or D,O-target. The results of these measurements were carefully cross checked against the spectra obtained by theoretical calculations (Monte-Carlo techniques) for the same source geometries (BENSCH,1969). EXPERIMENTAL METHOD A proton-recoil type proportional counter spectrometer was chosen to measure the emission spectra. A detailed discussion of this method is given by BENNETT (1967). Particular reasons for the choice of this type of neutron spectrometer in our case are found in the following requirements: For radiation protection reasons, the activity of the gamma emitter should not exceed several Ci. Then the neutron source strength is of the order of magnitude of 105-107s-1 (e.g. Na-Be source strength per unit activity; Q/A w 5 x lo6 s-l Ci-I). Therefore, a high sensitivity of the spectrometer in the energy range 100 keV - 1 MeV is required. Because of the high-energetic gamma background of great intensity (photon-to-neutron ratio M 104-106), it is essential that the spectrometer has a low sensitivity to gamma rays or at least provides a good separation between proton-recoil and gamma-induced pulses. The proportional counter is of the conventional type, as sucessfully used for spectrum measurements of fast reactors and subcritical assemblies (BENNETT,1968).
K. MIJECKand F. BENSCH
860
The outer electrode has a cylindrical form, the overall length being 25.75 cm; the ends of the cylinder are defined by guard-tubes giving an active volume of 185 cm length and 5.33 cm dia. The counter is filled with ultrapure methane and a small admixture of 0.5 per cent 3He. For neutron sources with high mean neutron energy, such as La-Be and Na-Be sources, a gas pressure of 2 atm. was used to keep the wall-effects in the counter low. For measurements of In-Be and Na-D,O sources this pressure was reduced to 1.4 atm to obtain better discrimination against the gamma background. The gas multiplication factor chosen was 35.
Channel number
FIG. I.-Response
of the proportional counter spectrometer to monoenergetic protons of the 8He(n, p)SH-reaction.
The counter was calibrated with 764 keV protons from the 3He (n,~) 3H reaction. Irradiation of the small admixture of 3He to the counting gas with thermal neutrons gives rise to protons of that energy, the pulse height distribution of which is used as one calibrating point. The whole energy scale can be calibrated since the energy per production of an ion pair in methane is constant over a wide energy range, at least in the range of interest here. Extrapolation of the straight line ionization versus energy to small energies shows a cut-off at a positive energy value. The energy cut-off model of BENNETT (1967) and POWELL (1970), which implies a cut-off at 4 keV, was used as this model seems to show the most satisfactory agreement with recent measurements. Besides, measurements in combination with the experiments reported in this article demonstrated a greater probability of the validity of this model than of the 30 keV-cut-off model. The 764 keV protons from the 3He (n, p) 3H reaction were used to test the counter resolution and response-function to protons of that energy. Figure 1 shows the counter response to protons of the 3He reaction upon irradiation with thermal neutrons. The response-function obtained in this way was used to check the calculated response-function at 764 keV. Because of radiation hazard problems and, in particular, pulse pile-up in the spectrometer, the activity of the gamma emitters had to be kept within tolerable values (up to 4 Ci). Since the (y, n)-cross-section in Be or 2H is small (- 1 x lo-31 m2)
The emission spectra of Na-D,O,
In-Be, La-Be and Na-Be photoneutron
sources
861
and only a part of the gamma quanta emitted have energies above the (y, n)-threshold (only 35 per cent in the case of La), long periods of measurement were necessary to obtain proton-recoil spectra of sufficient statistical accuracy. In the optimum case of a Na-Be source with a high relative intensity (1.0) of the neutron-producing gamma radiation and a high activity shortly after irradiation of the nuclide, this period amounted to 5 hr, in the worst case of a La-Be source after some half-lives of the gamma emitter as much as 48 hr were necessary to obtain a statistical accuracy of better than 1 per cent error per channel. These long measuring periods require a high stability of spectrometer and analyzer system with time. Together with tests using a mercury precision pulser, the 764 keV protons of the 3He reaction were again used to test carefully the stability of the system with time. The spectrometer was irradiated with thermal neutrons for a period of a week and the proton distribution in the spectrometer was measured at intervals of half an hour to two hours. The gamma-to-neutron ratio is at best (Na-Be source, thickest Be-target) about 0.8 x 104, at worst (La-Be source, O-5cm thick Be-target) about 106. In order to avoid pulse pile-up from this intense gamma ray field and still to obtain satisfactory proton-recoil pulse rates, the gamma background was reduced by a lead shield between the photoneutron source and the spectrometer. As the neutron sources are spherical, the lead shield was also spherical with the neutron source in the centre. Thus, the spherical symmetry remained undisturbed and a reduction of the neutron count-rate due to elastic scattering of neutrons in the lead shield could be avoided, since the same amount of neutrons (neglecting absorption) scattered out of the primary direction will reach the spectrometer after being scattered somewhere in the lead shield. Three different thicknesses of the lead shield were applied with the measurements, the radius of the outer sphere varying from 4 to 14 cm. Thereby it was possible to compare three different spectra with the theoretical calculations and obtain a reliable extrapolation to a lead thickness of 0 cm. The lead shield influences not only the intensity, but also the energy of the gamma quanta. With increasing lead thickness the energy loss of the gamma quanta will also increase, resulting in a registration of the gamma-induced pulses in channels of the pulse height analyzer corresponding to lower energies. This yields a wider energy range of the neutron spectrum undisturbed by the gamma-induced pulses. With low-energy neutron sources as In-Be and Na-D,O, neutron spectra well separated from the gammainduced pulses could be obtained with the thickest lead shield. THE
SOURCE-SPECTROMETER
ARRANGEMENT
The measurements of the source spectra were obtained in a geometrical set-up as shown in Fig. 2. The photoneutron source was surrounded with a lead shield as described above. The neutron incidence on the spectrometer was approximately perpendicular to the counter axis. Advantages of this arrangement include: A higher counting rate of neutron-induced pulses can be obtained since in this set-up it is possible to use a shorter mean distance between source and spectrometer; the calculation and correction of the wall effect distortion is less complex (see below) if the number of distorted pulses is low compared to the total number of recorded pulses; the measured neutron spectrum is only weakly dependent on the direction of neutron
K.
862 Neutron
source
MIJJEK and
F.
BENSCH
Shodow cone (used only for background measurements)
Neutron
spectrometer
Active volume (14 75cm long, 5.33cm dia 1
(4.0.6OMOcm
I I
II
radius) paraffin layer i (14cmthick) Imm cadmium absorber
I I
3 0.0 cm------c(
FIG. 2.-Source-detector
arrangement.
incidence if the neutrons enter the counting volume perpendicular rather than parallel to the axis. Compared to the moderation by the various target materials at the counter ends, the moderation of the neutrons entering the counter volume through the comparatively thin counter walls is very small and simply estimated. In order to avoid distortion of the measured spectra due to backscattering of neutrons from the laboratory walls and the floor, spectrum measurements are usually performed in “free geometry” with the largest possible distance between the sourcespectrometer set-up and any scattering material. But even then it is impossible to obtain spectra completely free from distortion and some correction has to be applied. Another approach was chosen in our case: Because of the intense gamma background no spectrum measurements below about O-2 MeV were possible. Therefore, neutrons with energies lower than this energy limit will not give rise to any distortion of the spectrum range under consideration. In order to slow down backscattering neutrons to energies below this value those targets closest to the source-spectrometer set-up (especially the floor below the set-up) are covered with a paraffin layer of 7 cm thickness. Neutrons scattered in the paraffin layer will lose a sufficient part of energy if care is taken that the scattering angle is less than 50” which may be easily achieved by a proper geometrical set-up and minimum distance to the nearest target (MUECK, 1972). Measurements of the background spectrum were carried out by the use of a “shadow-cone” between source and spectrometer as illustrated in Fig. 2. This shadow-cone consisted of a 14 cm thick paraffin block and a 1 mm cadmium foil on the spectrometer side. These measurements showed that no neutrons could be recorded in addition to the small amount (about 2 per cent) passing the shadowcone without scattering or with a small energy loss as a result of scattering in the shadow-cone. Consequently, no attempts for a correction of background scattered neutrons were made.
The emission spectra of Na-D,O, In-Be, La-Be and Na-Be photoneutron sources THEORETICAL
DETERMINATION OF THE NEUTRON SPECTRA
863
EMISSION
In a recent paper (BENSCH,1969) a Monte-Carlo routine was presented by means of which the neutron spectra of various photoneutron source systems can be investigated. Results for certain common types of source systems were presented as well, but no experimental verification was attempted at that time. For comparison purposes the experimental results presented here were obtained with the same source systems as in this earlier paper. Since it was necessary to reduce the intense gamma back-ground by surrounding the neutron source with a lead shield, a moderation of the photoneutron spectra was to be expected. Although this moderation is rather small due to the small energy loss of elastic scattering and the comparatively high mean free path of 3-10 cm in the interesting energy range, a careful calculation of the change of the intensity distribution of the emitted neutrons had to be undertaken. For this purpose a MonteCarlo code was developed to take into account the various particular factors influencing the neutron spectrum : the angular distribution of the emitted neutrons, the anisotropic elastic scattering, the inelastic scattering, and the inhomogeneity of the neutron target (lead shield with the neutron source at centre). The calculated neutron spectra for the various source systems (BENSCH, 1969) experimentally investigated in this paper were used as input parameter to the code. Since approximately 7 per cent of the neutrons emitted by the photoneutron source into the lead “target” would be backscattered into the neutron source before leaving the lead target, the code was adapted to take into account this backscattering with the relevant parameters in beryllium or D,O, respectively, the various gamma emitter materials. By means of more sophisticated Monte-Carlo routines (e.g. statistical weights of the neutrons, etc.) an appreciable reduction of the amount of time required to calculate one spectrum could be achieved. Using an IBM 360/24, spectra with a sufficient accuracy of better than 1 per cent were obtained in 4-15 min according to the thickness of the lead shield. The results of these calculations are shown in Figs. 3 and 4 for the Na-Be source with two different outer radii of the Be-sphere. Instead of the representation of the results by step-functions, as common with Monte-Carlo routines, a representation was chosen in which the discrete energy intervals were connected by a fourthorder polynomial fit. In this way the spectra alteration with increasing thickness of the lead shield is seen more clearly. The spectra are normalized to equal source strength. As can be seen, the “moderation” of the spectra results in a shift of the maximum of the distribution to lower energies, an increase in the FWHM and an increase in the low-energy part of the spectrum. All of these alterations were quantitatively well confirmed by the experimental results (see below). In order to compare the calculated spectra with the experimental results, the finite resolution of the spectrometer had to be taken into account. For this purpose a numerical smoothing method similar to that described by BENJAMIN(1968) was applied, by which any theoretical resolution could be superposed to the theoretical spectra. The parameters of the smoothing programme were adjusted to give the same resolution for the theoretical spectrum as for the measured spectrum. In Figs. 8-17 only the superposed neutron spectra are shown. 3
864
K. MUECK and F.
03
BENSCH
Na - Be source I.0 cm radius
of
0.1 .-6 + z? .e b A!? -e, 6 ti 2 = v .-E 0 g
o-4
0.3
No -Be source 25 cm radius of
2
Neutron
energy,
keV
FIGS. 3-4.-Alteration of the neutron spectrum of a Na-Be source of 1-Ocm and 2.5 cm Be-target radius due to varying thickness of the lead shield (calculated by MonteCarlo routines).
UNFOLDING
OF THE
RECOIL
SPECTRA
Neglecting some effects causing distortion of the spectra like the finite resolution of the spectrometer, finite size effects etc., the energy distribution of the proton recoils P(E) is given by the well-known formula: P(E) = NT
sE
m @(En) Q)(E,) $
n
(2)
where N is the number of hydrogen atoms in the active volume, T the time of measurement, o(E,) the scattering cross section, E, the neutron energy, and cp(E,) the neutron flux density per unit energy. Taking into account the construction properties of proportional counters, the proton-recoil spectrum obtained with conventional counter designs deviates from this theoretical distribution. The use of such a distorted recoil spectrum will lead by means of (2) to an incorrect neutron distribution. Therefore, efforts have to be made to correct the proton distribution measured to obtain a distortion-free distribution. Such efforts demand a careful determination of the response of the spectrometer system to protons of various energies. Several approaches to this
The emission spectra of Na-DaO, In-Be, La-Be and Na-Be photoneutron
sources
865
problem have already been proposed, using either Monte-Carlo techniques (BENJAMIN, 1964), experimental methods (BENNETT, 1968) and analytical calculations of the path length probability functions of protons in certain geometrical counter types (SNIDOW, 1967). For the measurements presented here the analytical approach was used. The reasons were: The analytical method is by far the fastest approach to a useful solution; such a solution may be obtained for certain commonly used counter geometries (spherical and cylindrical) of arbitrary dimensions; the parameters on which the response of the counter depends as the type of gas, the gas pressure, and the counter dimensions, may be easily adapted to give a solution for any arbitrary spectrometer. The quality of the solutions obtained by the analytical method are comparable to any other method (see below) especially for higher energies (above 200-500 keV according to the particular counter). The geometry of the photoneutron sources is rather simple. The calculation of these spectra depends only weakly-in contrast to fast reactor spectra-on the accurate knowledge of various cross section values and a multitude of geometrical parameters. Therefore, theoretically obtained spectra of photoneutron sources seem to be more reliable than reactor spectra and may advantageously be used for an experimental test of the analytical methods of SNIDOW (1967). Applying these calculations a computer code was developed by which the response-matrix of the counter spectrometer was calculated in less than 2 min (using an IBM 360/44). The response-matrices calculated by the code were tested in three independent ways : (1) the response of the counter to the 764 keV protons of the 3He (n,p) 3H-reaction was measured and compared with the response function as calculated by the code for that energy (see Fig. 1). For this purpose, the admixture of 3He was increased to 3 per cent while the overall gas pressure remained at the same value. In order to avoid disturbance by high energetic gamma rays always present at a reactor thermal column, neutrons from a Pu-Be source (Q = 5.64 x lo6 s-l) moderated by a graphite block of 1.5 m dia. were used with these measurements. Good agreement was established for the calculated as well as for the measured response-functions. (2) The experimentally determined response-matrix for a counter as used by BENNETT(1968) was compared to the response-matrix as calculated by the code for a counter of same dimensions and gas pressure. Good agreement was found in the high energy region, while the correspondence in the low energy region was not so good, probably due to field distortions at the counter ends. (3) The proton-recoil distribution was calculated from the Monte-Carlocalculated theoretical neutron distribution by means of equation (2) and by multiplication with the calculated response-matrix. This distribution was compared with the proton distribution obtained experimentally. If the Monte-Carlo-calculated neutron distributions are correct, then this test is very sensitive to errors in the response-matrix elements. No deviations larger than the statistical error could be observed. The proton-recoil spectra measured were corrected by a code similar to that used by BENNETT(1968). Thereby the solution is calculated by iteration. The effect of an accurate wall effect correction may be seen in Fig. 5 in which the neutron spectra derived from the proton-recoil distribution measured, both uncorrected and corrected are shown.
K. MUECK and F. BENSCH
866
Channel
FIG. L-Effects
number
of a proper wall effect correction on the derived neutron spectrum of a photoneutron source
0 measured, wall effect distorted proton-recoil
distribution
0 wall effect corrected,
distribution
“infinite” proton-recoil
??neutron spectrum derived from the wall effect distorted proton spectrum
??neutron spectrum derived from the corrected proton spectrum + neutron spectrum corrected by formula (3) for least square fit distortion
When the measured proton distribution has been corrected for wall effect distortions, the neutron distribution is obtained by inversion of (2). This gives the well-known relation according to which the neutron spectrum is obtained by differentiation of the proton spectrum. As in most cases, numerical differentiation of a non-analytical function poses serious difficulties. According to BENNETT (1967), the best approach to obtain the derivative of first order appeared to be by a straight line least square fitted through a certain number of spectrum points. This number depends on the statistical error of the spectrum values and on the amount of resolution loss one is willing to tolerate. An odd number of values (2~ + 1)-in our unfolding procedures the maximum encountered 7 values-is applied for the least square fit. Then the slope of the straight line renders the solution for the derived curve in the centre point. The drawbacks of such a procedure are obvious. Since the length of the square fit line is not infinitely small, distortions compared with the analytical derivative will be the result. No distortions will occur on that part of the proton distribution which shows a straight line. It is obvious that distortions will increase with increasing curvature of the neutron spectrum derived. Apart from that, the amount of distortion also depends on the number of points used for the least square fit, and may be kept small if this number is kept reasonably small-say 3-7. In spite of these drawbacks, this procedure is still advantageous compared to other methods which either incorporate a greater loss in resolution of the spectra or put up with an inevitable loss of a well-smoothed neutron spectrum. Consequently the linear least square fit method was used and a formula was obtained by which the distortion described above was successfully corrected. Such a formula as tested
The emission spectra of Na-D,O,
In-Be, La-Be and Na-Be photoneutron
sources
867
by means of various theoretical distributions is given by: &JN’f) N(r)
where
=
N(f)
_
O-167 ms -
(3)
dE2
Net) is the undistorted neutron distribution as obtained by analytical derivation, N(f) is the distorted neutron distribution as obtained by least square fit, m is the number of points used for the least square fit line on each side of the centre point (least square fit through 2m + 1 points). 1
IO
FIG. 6.-Distortion
30
20
Channel
40
number
of Gaussian distributions of varying FWHM’s tiation by least square fitting
due to differen-
-
undistorted Gaussian distribution “Gaussian distribution” derived by least square fit through eleven values (m = 5) for each value of the distribution 0 o 0 “distribution” obtained by correcting the distorted distribution by means of formula (3).
The corrections obtained by formula (3) are demonstrated in Fig. 6 for the physically likely case of a Gaussian distribution. For Gaussian distributions with great FWHM (low curvature) the corrections applied reproduce the theoretical curve well. Gaussian distributions with small FWHMs (high curvature)-not too common with the usual spectrometer resolutions-and a great number of points used for the least square fit are not so well reproduced. The latter is not necessarily a great disadvantage since undesired oscillations as given e.g. by statistical errors, are damped. The effect of this correction on a typical neutron spectrum may be seen in Fig. 5. Distortions of the spectrum in the “peak” and other parts with a high curvature are well corrected. Nevertheless, oscillations due to statistical distributions are smoothed satisfactorily. THE
NEUTRON
SPECTRA
DERIVED FROM GEOMETRIES
THE
VARIOUS
SOURCE
Although the measurements and calculations were performed for all different combinations of source geometry and lead shield thickness, only the most typical
868
K. MUECKand F. BENSCH
spectra are given in Figs. 8-17. Only the spectra of the smallest Na-Be source are shown with various lead shield thicknesses (Figs. 8-10) since the results of these figures may be taken as proof of the accuracy of the applied Monte-Carlo method in calculating the spectrum change due to the lead shield. Both the shift to lower energies (“moderation”) and the “flattening” of the measured spectrum agree well with the calculated spectrum change. In the low energy part of the spectrum, particularly of the Na-Be and La-Be sources, there are structures which cannot only be due to statistical fluctuations. The main cause (for these structures) may be found in the elastic scattering of neutrons I I o /Proton recoil pulses and oo r -induced pulses
ClJ
IO3P : : e (0 2 0’ IO’U
Intense
group at 762 keV
00 /
o 0 0
0
0 \“oo
Weak neutron group at 1097 keV
neutnxl group at 1097 kd, is omitted I IO
I 20
Channel
FIG. 7.-Measured
I
I
neutron
Proton recoi I ‘0 spectrum corrected o fory-induced pulses ’
IO’
I
I
-
0 o 0
\ ‘, ( 30
\
I 40
50
number
proton-recoil spectrum of the 1.6 cm radius La-Be source (14.0 cm lead shield radius).
in the Be-target. As these targets are comparatively thin, the scattering probability for a neutron between origin and leaving the target is rather low. The probability of secondary scattering within this target is still much lower than that. Therefore, a sharp separation between neutrons scattered only once and those scattered twice, should appear in the spectrum. The maximum energy loss when scattered in beryllium is 348 keV for Na-Be neutrons of energy 967 keV, and 274 keV for the La-Be neutrons with energy 762 keV, respectively. This gives a lower energy limit of 619 keV and 488 keV, respectively, for neutrons which were scattered once. These energy limits may be clearly seen in the experimentally and theoretically determined distributions of Figs. 8-14. The radioactive decay of 140La includes more than only one gamma ray emitted with an energy above the threshold of the (y, n)-reaction in 9Be. The intensity of these lines is low, compared to the overall gamma emission. Only about 3.5 per cent of the most densely populated gamma transition are emitted with the 2.5 MeV-line. Only 0.07 per cent are emitted with a second, much weaker 2.9 MeV-line. Despite the low intensity of the second line, the neutron group produced by this y-line could be definitely traced by our measurements of the La-Be spectrum. Figure 7 shows the proton-recoil spectrum of one of the La-Be sources, in that respect similar to
The emission spectra of Na-D,O, In-Be, La-Be and Na-Be photoneutron sources
869
the other source arrangements. The threshold of the I.097 MeV-neutron group produced by the 2.9 MeV y-line is clearly demonstrated thereby. Also with the derived neutron spectra (Figs. 13 and 14) the second neutron group becomes apparent. Efforts had been made to determine the relative intensities of the neutron groups. Very similar results were obtained for all different source geometries and lead shield, and a mean value of 0.0655 f 0*0030 resulted from the different measurements. Using the values for the relative intensities of the y-lines as reported by KARLSSON (1967) and BAER(1968), and the relative values for the (y, n)-cross section as given by JAKOBSON(1961), the relative neutron intensities should only result in 0,044 & 0.011 which might be due to either erroneous cross section values or incorrect values of the gamma intensities. Further measurements will be carried out to clarify this point. The agreement between the theoretically calculated and measured neutron spectra for the Na-Be source was extremely good. But no such agreement was originally found for the In-Be source spectra. The theoretical calculations deviated by about 23 keV in the energy axis from the experimental results. The well founded reason for this deviation was the use of an energy value for the y-quanta of the neutron producing line as given by the Nuclear Data Sheets (1964). Since the original Monte-Carlo calculations of the spectra had been carried out 4yr ago (BENSCH, 1969), only the data as given there could be used. The curve thereby obtained is shown by the solid line in Figs. 15 and 16. According to recent measurements (RABENSTEIN,1970), the energy of the neutron producing gamma line has been modified to a value of 2.1121 f 0*0004 MeV and the re-evaluation by use of the same Monte-Carlo method yielded a spectrum shown by the dotted line in Figs. 15 and 16. The excellent correspondence between this theoretical curve and the measured spectrum is obvious. The results of the calculated spectrum of the In-Be source previously published (BENSCH, 1969) should therefore be corrected by a shift in the energy axis of +23*2 keV. Because of the low energy of the neutron group of the Na-D,O source, a measurement of the low energy part of the spectrum was not possible. However, an estimation of the maximum neutron energy of the source and a determination of the energy of the maximum of the neutron distribution was carried out as can be seen from the results given in Fig. 17. The data may be seen in Table 2. RESULTS
AND
DISCUSSIONS
From the theoretically derived neutron spectra the peak of the neutron distribution was determined by least square fitting a Gaussian distribution through a certain number of the statistically distributed values (approximately 15 values) in the vicinity of the distribution maximum. The data obtained thereby are given in Table 2. The mean energy of the neutron distribution was calculated from both the measured and the calculated spectra. Since the agreement was sufficient, only the data obtained from the theoretical calculations are given in Table 2. Despite the fact that measurements were performed with lead shield of varying, but non-zero thickness, the data are given for the extrapolated case of lead shield thickness 0 as this is the most interesting case as far as applications are considered. Because of the unsymmetrical distribution of the photoneutron spectra a minor shift of the peak energy to lower energies (7 keV with the In-Be source and 15 keV
x
‘0
N
-62
0.2 -
0.4-
06-
02
0.4
06
.
.
Neutron
.
??
?? Y
r3= 4,Ocm
r,=i.Ocm
No -.Be
energy,
Lowest energy of source neutrons after single elastic scattering on Be -nuclei
FIG. I-12.-Neutron
MeV
i
-0
Neutron
r3= 14-O cm
Na-Be r,=?5cm
spectra of the Na-Be source with varying source
06
energy,
MeV
P a
The emission spectra of Na-D,O, In-Be, La-Be and Na-Be photoneutron sources
871
TABLE
P.--PEAK
ENERGY
AND
MEAN
ENERGY
OF
THE
VARIOUS
SOURCE
DIMENSIONS
264.1 f 0.5
247 f 5
381 f 7
741 & 13 1070 & 24
946 f 1.5
with lead shield (14 cm radius)
753 f 3* 759 f 3t 392 & 3 256 =t 2
962 f 5 760 + 3* 766 f 3t 397 f 3 260 i 2
971 & 18 765 f 15 1099 * 30 399 5 10 264 f 8
959 f 5
1.0
1.6
radius of the Be target 2.5
if the
246 f 2
371 f 3
745 f 3* 751 f 37
954 i 5
Mean neutron energy (no lead shield) (keV)
no lead shield
Determined from the experimental distribution
(keV)
* These values were obtained by only considering the main neutron group at 762 keV (neglecting the high energy neutron group); second neutron group is taken into account, an energy shift of 6 keV has to be applied. These values are indicated in the table by t.
246.8 f 2
2752.9 f 0.2
aaNa-D,O
397.3 f 0.8
379.7 * 2
761.7 f- 0.7 1097.5 f 1.0
738.1 + 2 1069.5 f 3
2522.0 f 0.3 2899.8 & 0.5
2112.1 & 0.4
966.9 -f 0.5
942.2 + 2
no lead shield
2152.9 + 0.2
Yn-Be
Photoneutron source
with lead shield (14 cm radius)
Energy of the neutron-producing y-rays (keV)
Calculated from the energy of the y-rays
Peak energy of the neutron distribution
values for the mean neutron energies and the peak energy determined with no lead shield are corrected for the peak shift due to the finite counter resolution (extrapolated to counter resolution 0 per cent). The values determined with the lead shield are not corrected for this peak shift and therefore agree with the experimental curves given in Figs. S-17.
All
i
: p. ?t w B
!!
5
P
The emission spectra of Na-D,O,
In-Be, La-Be and Na-Be photoneutron
sources
873
with the Na-Be source) occurs due to the finite spectrometer resolution. The size of this shift was calculated by using the same code as described above (BENJAMIN, 1968), and was considered either with the theoretically calculated or with the experimentally obtained distributions when comparing both of them. In Table 2 with the values for the 14 cm radius lead shield, the theoretical values were corrected accordingly, while with the extrapolated values (thickness 0) and with the values for the mean energy, the experimental values were corrected corresponding to the shift mentioned. Thus, these latter values may be used directly as reference for further experiments. Acknowledgements-The authors would like to express their special gratitude to Dr. R. Gold and Dr. E. F. Bennett for their kindness in making available the counter tube used in the experiments and for valuable advice during the progress of this work. The authors are also indebted to Dr. H. Jasicek for generous help and discussion. REFERENCES BAER A. W., REIDY J. J. and WIEDENBECK M. L. (1968)Nucl. Phys.A113,33.
BELANOVA T. S., VAN’KOVA. A., MIKHAILUSF. F. and STA~JX~KII Y. Y. (1966) J. nucl. Energy 20,411. BENJAMINP. W., KEMSHALLC. D. and BRICK~TOCKA. (1968) Rep. AWRE O-9/68. BENJAMINP. W., KEMSHALLC. D. and REDFEARNJ. (1964) Rep. AWRE 2/64. BENNEIT E. F. (1967) Nucl. Sci. Enging 27, 16. BENNEITE. F., GOLD R. and OLSONI. K. (1968) Rep. ANL-7394. BENSCHF. and V~SELYF. (1969) J. nucl. Energy 23,531; (1970) J. nucl. Energy 24,57. ENDT P. M. and VAN D. LEUN C. (1967) Nucl. Phys. A105,l. HUGHESD. and ECXLER C. (1947) Phys. Reu. 72,902. JAKOBSONM. J. (1961) Phys. Rev. 123,229. KARLSSONS. E., SVAHN B., PEX~RSSON H., MALM~TENG. and DEAI~ENBERG E. Y. (1967), Nucl. Phys. AlOO, 113. LAL~VIC M. and WERLEH. (1970), J. nucl. Energy 24,123. MUECK K. (1972) Dissertation, Atominstitut, Vienna. OEHLERH., KOEHLERH. and POSE H. (1964) Kernenergie 7,325. ORNL-Nuclear Data Sheets (1964). Academic Press, New York. POWELLJ. E. and ROGERSJ. W. (1970)Nucl. Instrum. Meth. 87,29. POZE K. R. and GLAZKOVN. P. (1956) Sov. Phys. JETP 3,745. RAFJENSTEIN D. (1970) 2. Phys. 240,244. R~vrs T. B. and ROBERTSON J. G. (1971) J. nucl. Energy 25, 557. SNIDOWN. L. and WARRENH. D. (1967) Nucl. Znstrum. Meth. 51, 109. WA~TENBERGA. (1946) Phys. Rev. 71,497.
THE EMISSION SPECTRA OF Na-D,O, In-Be, La-Be AND Na-Be PHOTONEUTRON SOURCES K. MUECK and F. BENSCH Atominstitut der dsterreichischen Hochschulen, Vienna, Austria. (Received 23 July 1973)
Abstract-The energy distribution of the photoneutrons of Na-D,O, In-Be, La-Be and Na-Be source systems were measured by means of a proton-recoil proportional counting tube. Spherical lead-shields of various thicknesses (ranging from 1.5 to 13 cm) were used to reduce the intense gamma field accompanying the neutron spectra to be measured. The spectra of spherical heterogeneous source arrangements for three different Be-target thicknesses (0.5, 1.1 and 2.0 cm) were measured and compared with the theoretical distribution as obtained by Monte-Carlo calculations. The
change in spectrum shape due to the lead shields was also calculated by a Monte-Carlo routine. Good agreement between theoretical predictions and experimental results shows values for the peak of the neutron distribution of 264.1 f 0.5 keV for the Na-D,O system, 397.3 f 0.8 keV for the In-Be system, 761.7 f 0.7 keV for the La-Be system, and 966.9 rt 0.5 keV for the Na-Be source system. With the La-Be system a second neutron group of much lower intensity (6.5 per cent of the main group) could be found with a peak energy of 1097.5 f 1.0 keV in good agreement to recent gamma-spectroscopic measurements. INTRODUCTION
the existence of stronger neutron sources, radioactive neutron sources are of some importance in neutron physics chiefly due to their compactness and portability. Furthermore, they have small geometrical dimensions and their source strength-once determined-can be calculated by means of the half-life of the radioactive material. The additional advantage of (y, n)-neutron sources lies in the fact that, in contrast to (tl, n)-sources or fission sources, they emit neutrons of a narrow energy range. Therefore, they may conveniently be used in numerous experiments for measuring neutron cross-sections, the stopping power and diffusion characteristics of various materials, and the importance function in reactors and subcritical assemblies, particularly of fast type. Many experiments using photoneutron sources have been mentioned (e.g., POZE, 1956; BELANOVA, 1966; RYVES, 1971), most of which presented either one of two main obstacles in the interpretation of the data obtained: The difficulty of determining the source strength of a particular photoneutron emitter and the lack of knowledge of the neutron spectrum of a particular source arrangement. The first of these two obstacles has been successfully investigated recently (BENSCH, 1969). With regard to the second problem, successful attempts have been recently made to estimate the spectra by theoretical methods (Monte-Carlo calculations) (BENSCH, 1969; LALOVIC, 1970; RYVES, 1971). However, no experimental proof has been published so far, with the exception of the Sb-Be source where no good agreement between experiment and theory on the energy of the gamma quanta could be established (LALOVIC, 1970). DESPITE
An experimental test of the theoretical predictions is paramount considering the uncertainty in some of the parameters required for the theoretical calculations. In particular, the energy of the neutron-releasing gamma quanta was inadequately known and caused considerable discrepancy between the values established by various authors (see Table 1). 857
858
K.
MUECK
and F. BENSCH
TABLE. I.-PREVIOUS EXPERIMENTAL RESULTS IN COMPARISON WITH THE CALCULATED RESULTS FOR THE PEAK ENERGY OF THE NEUTRON DISTRIBUTION
En WV)
Source
En (keV)
measured calculated act. to equ. (1) up to now
Half-life
(M%)
2PNa-D,0
15.0hr
2.153
264
220
WATTENFIERG (1946)
llGIn-Be
54.1 min
2.112
391
300
HUGHES~~~ EGGLER (1947)
IdoLa-Be
40.23hr
2.522
162
620
WATTENBERG
system
(1946) aaNa-Be
15.0hr
2.153
961
830
WATTENBERG
(1946) Photoneutron sources usually consist of a gamma emitter surrounded by a beryllium or heavy water target. The gamma quanta hitting the target will release neutrons, the energy E,, (in MeV) of which may be calculated by the well-known formula : A-l
En = --yj-
(Ey- Et) f E, cosy
JW - l)(E, -
Et)
931.A
where E, is the primary energy of the gamma quantum, Et the threshold energy of the (y, n)-reaction considered, A the mass number of the target material and y the angle between the direction of the gamma quanta and neutron emission. By using different gamma emitters with only one gamma level above threshold energy, a set of nearly monoenergetic neutron sources in the fast energy region from 20 keV to 1 MeV (BENSCH,1969) is obtained. Up to now the values for the energies of the maximum of the neutron distribution have differed considerably from the experimental results. These values are listed in Table 1. If the most recent data on the energy of the gamma quanta (KARLSSON, 1967; BAER, 1968; ENDT, 1967; RABENSTEIN,1970) are used in the calculations of the neutron energies, the values differ somewhat from those used so far by most experimenters working with photoneutron sources. Despite the use of these data, no good agreement between the theoretically calculated energy of the neutron “line” and the experimental results reported so far (WATTENBERG,1946; HUGHES, 1947) could be obtained (see Table 1). One of the main purposes of this work, therefore, was to investigate closely the neutron energies of the photoneutron sources listed in Table 1 and to compare these values with the theoretical predictions obtained from the most recent values for the gamma energies. From equation (1) it is obvious that the neutrons emitted from the (y, n)-target are not exactly monoenergetic, but have a certain energy spread caused by the energy dependence on the angle between the direction of neutron emission and the direction of the gamma quanta. In addition to this deviation from a monoenergetic spectrum inherent in a (y, n)-reaction, photoneutron sources of usual dimensions show an even greater divergence due to the unavoidably finite dimensions of the source. It is not possible to design source arrangements sufficiently small for an acceptable
The emission spectra of Na-D,O,
In-Be, La-Be and Na-Be photoneutron
sources
859
neutron yield. The usual source systems have diameters from 1 to 10 cm, which is of the same order of magnitude as the mean free path for neutrons in beryllium, D,O and most of the gamma-emitting materials. Therefore, the moderation of neutrons on their passage through the (y, n)-target is not negligible. This fact and the energy loss of the gamma quanta due to scattering before neutron production induce a broadening of the neutron spectrum with the source arrangements used in practice. This moderation and broadening of the peak of the neutron spectrum results in a decrease in the mean neutron energy with increasing source dimensions. The change in the spectrum shape influences the corrections which account for deviations from the desired monoenergetic emission. Therefore, most experiments involving photoneutron sources require more detailed knowledge of the neutron emission spectra. So far only two experimental approaches to determine the spectra of the neutron sources discussed in this paper have been reported: HUGHES (1947) investigated the spectrum of an In-Be source with proton recoils in a hydrogen-filled cloud chamber. The main drawbacks were the poor statistical accuracy of the method applied and the insufficient energy calibration, which resulted in a lower peak value of the neutron distribution than theoretically predicted. OEHLER (1964) measured the spectrum of a Na-Be source with a hydrogen-filled ionization chamber, but the energy resolution of their spectrometer was rather low (17 per cent). Moreover, no energy calibration independent of the neutron spectrum to be measured was used; in fact the peak energy of the neutron distribution as calculated from the gamma energy using equation (1) was taken to calibrate the energy scale. Therefore, experimental determination of the neutron energies was not possible. In addition to a careful checking of the neutron energy of the four photoneutron sources investigated against the theoretical values, great emphasis was placed on the determination of the spectra of various source-arrangements and particularly the dependence on the thickness of the beryllium or D,O-target. The results of these measurements were carefully cross checked against the spectra obtained by theoretical calculations (Monte-Carlo techniques) for the same source geometries (BENSCH,1969). EXPERIMENTAL METHOD A proton-recoil type proportional counter spectrometer was chosen to measure the emission spectra. A detailed discussion of this method is given by BENNETT (1967). Particular reasons for the choice of this type of neutron spectrometer in our case are found in the following requirements: For radiation protection reasons, the activity of the gamma emitter should not exceed several Ci. Then the neutron source strength is of the order of magnitude of 105-107s-1 (e.g. Na-Be source strength per unit activity; Q/A w 5 x lo6 s-l Ci-I). Therefore, a high sensitivity of the spectrometer in the energy range 100 keV - 1 MeV is required. Because of the high-energetic gamma background of great intensity (photon-to-neutron ratio M 104-106), it is essential that the spectrometer has a low sensitivity to gamma rays or at least provides a good separation between proton-recoil and gamma-induced pulses. The proportional counter is of the conventional type, as sucessfully used for spectrum measurements of fast reactors and subcritical assemblies (BENNETT,1968).
K. MIJECKand F. BENSCH
860
The outer electrode has a cylindrical form, the overall length being 25.75 cm; the ends of the cylinder are defined by guard-tubes giving an active volume of 185 cm length and 5.33 cm dia. The counter is filled with ultrapure methane and a small admixture of 0.5 per cent 3He. For neutron sources with high mean neutron energy, such as La-Be and Na-Be sources, a gas pressure of 2 atm. was used to keep the wall-effects in the counter low. For measurements of In-Be and Na-D,O sources this pressure was reduced to 1.4 atm to obtain better discrimination against the gamma background. The gas multiplication factor chosen was 35.
Channel number
FIG. I.-Response
of the proportional counter spectrometer to monoenergetic protons of the 8He(n, p)SH-reaction.
The counter was calibrated with 764 keV protons from the 3He (n,~) 3H reaction. Irradiation of the small admixture of 3He to the counting gas with thermal neutrons gives rise to protons of that energy, the pulse height distribution of which is used as one calibrating point. The whole energy scale can be calibrated since the energy per production of an ion pair in methane is constant over a wide energy range, at least in the range of interest here. Extrapolation of the straight line ionization versus energy to small energies shows a cut-off at a positive energy value. The energy cut-off model of BENNETT (1967) and POWELL (1970), which implies a cut-off at 4 keV, was used as this model seems to show the most satisfactory agreement with recent measurements. Besides, measurements in combination with the experiments reported in this article demonstrated a greater probability of the validity of this model than of the 30 keV-cut-off model. The 764 keV protons from the 3He (n, p) 3H reaction were used to test the counter resolution and response-function to protons of that energy. Figure 1 shows the counter response to protons of the 3He reaction upon irradiation with thermal neutrons. The response-function obtained in this way was used to check the calculated response-function at 764 keV. Because of radiation hazard problems and, in particular, pulse pile-up in the spectrometer, the activity of the gamma emitters had to be kept within tolerable values (up to 4 Ci). Since the (y, n)-cross-section in Be or 2H is small (- 1 x lo-31 m2)
The emission spectra of Na-D,O,
In-Be, La-Be and Na-Be photoneutron
sources
861
and only a part of the gamma quanta emitted have energies above the (y, n)-threshold (only 35 per cent in the case of La), long periods of measurement were necessary to obtain proton-recoil spectra of sufficient statistical accuracy. In the optimum case of a Na-Be source with a high relative intensity (1.0) of the neutron-producing gamma radiation and a high activity shortly after irradiation of the nuclide, this period amounted to 5 hr, in the worst case of a La-Be source after some half-lives of the gamma emitter as much as 48 hr were necessary to obtain a statistical accuracy of better than 1 per cent error per channel. These long measuring periods require a high stability of spectrometer and analyzer system with time. Together with tests using a mercury precision pulser, the 764 keV protons of the 3He reaction were again used to test carefully the stability of the system with time. The spectrometer was irradiated with thermal neutrons for a period of a week and the proton distribution in the spectrometer was measured at intervals of half an hour to two hours. The gamma-to-neutron ratio is at best (Na-Be source, thickest Be-target) about 0.8 x 104, at worst (La-Be source, O-5cm thick Be-target) about 106. In order to avoid pulse pile-up from this intense gamma ray field and still to obtain satisfactory proton-recoil pulse rates, the gamma background was reduced by a lead shield between the photoneutron source and the spectrometer. As the neutron sources are spherical, the lead shield was also spherical with the neutron source in the centre. Thus, the spherical symmetry remained undisturbed and a reduction of the neutron count-rate due to elastic scattering of neutrons in the lead shield could be avoided, since the same amount of neutrons (neglecting absorption) scattered out of the primary direction will reach the spectrometer after being scattered somewhere in the lead shield. Three different thicknesses of the lead shield were applied with the measurements, the radius of the outer sphere varying from 4 to 14 cm. Thereby it was possible to compare three different spectra with the theoretical calculations and obtain a reliable extrapolation to a lead thickness of 0 cm. The lead shield influences not only the intensity, but also the energy of the gamma quanta. With increasing lead thickness the energy loss of the gamma quanta will also increase, resulting in a registration of the gamma-induced pulses in channels of the pulse height analyzer corresponding to lower energies. This yields a wider energy range of the neutron spectrum undisturbed by the gamma-induced pulses. With low-energy neutron sources as In-Be and Na-D,O, neutron spectra well separated from the gammainduced pulses could be obtained with the thickest lead shield. THE
SOURCE-SPECTROMETER
ARRANGEMENT
The measurements of the source spectra were obtained in a geometrical set-up as shown in Fig. 2. The photoneutron source was surrounded with a lead shield as described above. The neutron incidence on the spectrometer was approximately perpendicular to the counter axis. Advantages of this arrangement include: A higher counting rate of neutron-induced pulses can be obtained since in this set-up it is possible to use a shorter mean distance between source and spectrometer; the calculation and correction of the wall effect distortion is less complex (see below) if the number of distorted pulses is low compared to the total number of recorded pulses; the measured neutron spectrum is only weakly dependent on the direction of neutron
K.
862 Neutron
source
MIJJEK and
F.
BENSCH
Shodow cone (used only for background measurements)
Neutron
spectrometer
Active volume (14 75cm long, 5.33cm dia 1
(4.0.6OMOcm
I I
II
radius) paraffin layer i (14cmthick) Imm cadmium absorber
I I
3 0.0 cm------c(
FIG. 2.-Source-detector
arrangement.
incidence if the neutrons enter the counting volume perpendicular rather than parallel to the axis. Compared to the moderation by the various target materials at the counter ends, the moderation of the neutrons entering the counter volume through the comparatively thin counter walls is very small and simply estimated. In order to avoid distortion of the measured spectra due to backscattering of neutrons from the laboratory walls and the floor, spectrum measurements are usually performed in “free geometry” with the largest possible distance between the sourcespectrometer set-up and any scattering material. But even then it is impossible to obtain spectra completely free from distortion and some correction has to be applied. Another approach was chosen in our case: Because of the intense gamma background no spectrum measurements below about O-2 MeV were possible. Therefore, neutrons with energies lower than this energy limit will not give rise to any distortion of the spectrum range under consideration. In order to slow down backscattering neutrons to energies below this value those targets closest to the source-spectrometer set-up (especially the floor below the set-up) are covered with a paraffin layer of 7 cm thickness. Neutrons scattered in the paraffin layer will lose a sufficient part of energy if care is taken that the scattering angle is less than 50” which may be easily achieved by a proper geometrical set-up and minimum distance to the nearest target (MUECK, 1972). Measurements of the background spectrum were carried out by the use of a “shadow-cone” between source and spectrometer as illustrated in Fig. 2. This shadow-cone consisted of a 14 cm thick paraffin block and a 1 mm cadmium foil on the spectrometer side. These measurements showed that no neutrons could be recorded in addition to the small amount (about 2 per cent) passing the shadowcone without scattering or with a small energy loss as a result of scattering in the shadow-cone. Consequently, no attempts for a correction of background scattered neutrons were made.
The emission spectra of Na-D,O, In-Be, La-Be and Na-Be photoneutron sources THEORETICAL
DETERMINATION OF THE NEUTRON SPECTRA
863
EMISSION
In a recent paper (BENSCH,1969) a Monte-Carlo routine was presented by means of which the neutron spectra of various photoneutron source systems can be investigated. Results for certain common types of source systems were presented as well, but no experimental verification was attempted at that time. For comparison purposes the experimental results presented here were obtained with the same source systems as in this earlier paper. Since it was necessary to reduce the intense gamma back-ground by surrounding the neutron source with a lead shield, a moderation of the photoneutron spectra was to be expected. Although this moderation is rather small due to the small energy loss of elastic scattering and the comparatively high mean free path of 3-10 cm in the interesting energy range, a careful calculation of the change of the intensity distribution of the emitted neutrons had to be undertaken. For this purpose a MonteCarlo code was developed to take into account the various particular factors influencing the neutron spectrum : the angular distribution of the emitted neutrons, the anisotropic elastic scattering, the inelastic scattering, and the inhomogeneity of the neutron target (lead shield with the neutron source at centre). The calculated neutron spectra for the various source systems (BENSCH, 1969) experimentally investigated in this paper were used as input parameter to the code. Since approximately 7 per cent of the neutrons emitted by the photoneutron source into the lead “target” would be backscattered into the neutron source before leaving the lead target, the code was adapted to take into account this backscattering with the relevant parameters in beryllium or D,O, respectively, the various gamma emitter materials. By means of more sophisticated Monte-Carlo routines (e.g. statistical weights of the neutrons, etc.) an appreciable reduction of the amount of time required to calculate one spectrum could be achieved. Using an IBM 360/24, spectra with a sufficient accuracy of better than 1 per cent were obtained in 4-15 min according to the thickness of the lead shield. The results of these calculations are shown in Figs. 3 and 4 for the Na-Be source with two different outer radii of the Be-sphere. Instead of the representation of the results by step-functions, as common with Monte-Carlo routines, a representation was chosen in which the discrete energy intervals were connected by a fourthorder polynomial fit. In this way the spectra alteration with increasing thickness of the lead shield is seen more clearly. The spectra are normalized to equal source strength. As can be seen, the “moderation” of the spectra results in a shift of the maximum of the distribution to lower energies, an increase in the FWHM and an increase in the low-energy part of the spectrum. All of these alterations were quantitatively well confirmed by the experimental results (see below). In order to compare the calculated spectra with the experimental results, the finite resolution of the spectrometer had to be taken into account. For this purpose a numerical smoothing method similar to that described by BENJAMIN(1968) was applied, by which any theoretical resolution could be superposed to the theoretical spectra. The parameters of the smoothing programme were adjusted to give the same resolution for the theoretical spectrum as for the measured spectrum. In Figs. 8-17 only the superposed neutron spectra are shown. 3
864
K. MUECK and F.
03
BENSCH
Na - Be source I.0 cm radius
of
0.1 .-6 + z? .e b A!? -e, 6 ti 2 = v .-E 0 g
o-4
0.3
No -Be source 25 cm radius of
2
Neutron
energy,
keV
FIGS. 3-4.-Alteration of the neutron spectrum of a Na-Be source of 1-Ocm and 2.5 cm Be-target radius due to varying thickness of the lead shield (calculated by MonteCarlo routines).
UNFOLDING
OF THE
RECOIL
SPECTRA
Neglecting some effects causing distortion of the spectra like the finite resolution of the spectrometer, finite size effects etc., the energy distribution of the proton recoils P(E) is given by the well-known formula: P(E) = NT
sE
m @(En) Q)(E,) $
n
(2)
where N is the number of hydrogen atoms in the active volume, T the time of measurement, o(E,) the scattering cross section, E, the neutron energy, and cp(E,) the neutron flux density per unit energy. Taking into account the construction properties of proportional counters, the proton-recoil spectrum obtained with conventional counter designs deviates from this theoretical distribution. The use of such a distorted recoil spectrum will lead by means of (2) to an incorrect neutron distribution. Therefore, efforts have to be made to correct the proton distribution measured to obtain a distortion-free distribution. Such efforts demand a careful determination of the response of the spectrometer system to protons of various energies. Several approaches to this
The emission spectra of Na-DaO, In-Be, La-Be and Na-Be photoneutron
sources
865
problem have already been proposed, using either Monte-Carlo techniques (BENJAMIN, 1964), experimental methods (BENNETT, 1968) and analytical calculations of the path length probability functions of protons in certain geometrical counter types (SNIDOW, 1967). For the measurements presented here the analytical approach was used. The reasons were: The analytical method is by far the fastest approach to a useful solution; such a solution may be obtained for certain commonly used counter geometries (spherical and cylindrical) of arbitrary dimensions; the parameters on which the response of the counter depends as the type of gas, the gas pressure, and the counter dimensions, may be easily adapted to give a solution for any arbitrary spectrometer. The quality of the solutions obtained by the analytical method are comparable to any other method (see below) especially for higher energies (above 200-500 keV according to the particular counter). The geometry of the photoneutron sources is rather simple. The calculation of these spectra depends only weakly-in contrast to fast reactor spectra-on the accurate knowledge of various cross section values and a multitude of geometrical parameters. Therefore, theoretically obtained spectra of photoneutron sources seem to be more reliable than reactor spectra and may advantageously be used for an experimental test of the analytical methods of SNIDOW (1967). Applying these calculations a computer code was developed by which the response-matrix of the counter spectrometer was calculated in less than 2 min (using an IBM 360/44). The response-matrices calculated by the code were tested in three independent ways : (1) the response of the counter to the 764 keV protons of the 3He (n,p) 3H-reaction was measured and compared with the response function as calculated by the code for that energy (see Fig. 1). For this purpose, the admixture of 3He was increased to 3 per cent while the overall gas pressure remained at the same value. In order to avoid disturbance by high energetic gamma rays always present at a reactor thermal column, neutrons from a Pu-Be source (Q = 5.64 x lo6 s-l) moderated by a graphite block of 1.5 m dia. were used with these measurements. Good agreement was established for the calculated as well as for the measured response-functions. (2) The experimentally determined response-matrix for a counter as used by BENNETT(1968) was compared to the response-matrix as calculated by the code for a counter of same dimensions and gas pressure. Good agreement was found in the high energy region, while the correspondence in the low energy region was not so good, probably due to field distortions at the counter ends. (3) The proton-recoil distribution was calculated from the Monte-Carlocalculated theoretical neutron distribution by means of equation (2) and by multiplication with the calculated response-matrix. This distribution was compared with the proton distribution obtained experimentally. If the Monte-Carlo-calculated neutron distributions are correct, then this test is very sensitive to errors in the response-matrix elements. No deviations larger than the statistical error could be observed. The proton-recoil spectra measured were corrected by a code similar to that used by BENNETT(1968). Thereby the solution is calculated by iteration. The effect of an accurate wall effect correction may be seen in Fig. 5 in which the neutron spectra derived from the proton-recoil distribution measured, both uncorrected and corrected are shown.
K. MUECK and F. BENSCH
866
Channel
FIG. L-Effects
number
of a proper wall effect correction on the derived neutron spectrum of a photoneutron source
0 measured, wall effect distorted proton-recoil
distribution
0 wall effect corrected,
distribution
“infinite” proton-recoil
??neutron spectrum derived from the wall effect distorted proton spectrum
??neutron spectrum derived from the corrected proton spectrum + neutron spectrum corrected by formula (3) for least square fit distortion
When the measured proton distribution has been corrected for wall effect distortions, the neutron distribution is obtained by inversion of (2). This gives the well-known relation according to which the neutron spectrum is obtained by differentiation of the proton spectrum. As in most cases, numerical differentiation of a non-analytical function poses serious difficulties. According to BENNETT (1967), the best approach to obtain the derivative of first order appeared to be by a straight line least square fitted through a certain number of spectrum points. This number depends on the statistical error of the spectrum values and on the amount of resolution loss one is willing to tolerate. An odd number of values (2~ + 1)-in our unfolding procedures the maximum encountered 7 values-is applied for the least square fit. Then the slope of the straight line renders the solution for the derived curve in the centre point. The drawbacks of such a procedure are obvious. Since the length of the square fit line is not infinitely small, distortions compared with the analytical derivative will be the result. No distortions will occur on that part of the proton distribution which shows a straight line. It is obvious that distortions will increase with increasing curvature of the neutron spectrum derived. Apart from that, the amount of distortion also depends on the number of points used for the least square fit, and may be kept small if this number is kept reasonably small-say 3-7. In spite of these drawbacks, this procedure is still advantageous compared to other methods which either incorporate a greater loss in resolution of the spectra or put up with an inevitable loss of a well-smoothed neutron spectrum. Consequently the linear least square fit method was used and a formula was obtained by which the distortion described above was successfully corrected. Such a formula as tested
The emission spectra of Na-D,O,
In-Be, La-Be and Na-Be photoneutron
sources
867
by means of various theoretical distributions is given by: &JN’f) N(r)
where
=
N(f)
_
O-167 ms -
(3)
dE2
Net) is the undistorted neutron distribution as obtained by analytical derivation, N(f) is the distorted neutron distribution as obtained by least square fit, m is the number of points used for the least square fit line on each side of the centre point (least square fit through 2m + 1 points). 1
IO
FIG. 6.-Distortion
30
20
Channel
40
number
of Gaussian distributions of varying FWHM’s tiation by least square fitting
due to differen-
-
undistorted Gaussian distribution “Gaussian distribution” derived by least square fit through eleven values (m = 5) for each value of the distribution 0 o 0 “distribution” obtained by correcting the distorted distribution by means of formula (3).
The corrections obtained by formula (3) are demonstrated in Fig. 6 for the physically likely case of a Gaussian distribution. For Gaussian distributions with great FWHM (low curvature) the corrections applied reproduce the theoretical curve well. Gaussian distributions with small FWHMs (high curvature)-not too common with the usual spectrometer resolutions-and a great number of points used for the least square fit are not so well reproduced. The latter is not necessarily a great disadvantage since undesired oscillations as given e.g. by statistical errors, are damped. The effect of this correction on a typical neutron spectrum may be seen in Fig. 5. Distortions of the spectrum in the “peak” and other parts with a high curvature are well corrected. Nevertheless, oscillations due to statistical distributions are smoothed satisfactorily. THE
NEUTRON
SPECTRA
DERIVED FROM GEOMETRIES
THE
VARIOUS
SOURCE
Although the measurements and calculations were performed for all different combinations of source geometry and lead shield thickness, only the most typical
868
K. MUECKand F. BENSCH
spectra are given in Figs. 8-17. Only the spectra of the smallest Na-Be source are shown with various lead shield thicknesses (Figs. 8-10) since the results of these figures may be taken as proof of the accuracy of the applied Monte-Carlo method in calculating the spectrum change due to the lead shield. Both the shift to lower energies (“moderation”) and the “flattening” of the measured spectrum agree well with the calculated spectrum change. In the low energy part of the spectrum, particularly of the Na-Be and La-Be sources, there are structures which cannot only be due to statistical fluctuations. The main cause (for these structures) may be found in the elastic scattering of neutrons I I o /Proton recoil pulses and oo r -induced pulses
ClJ
IO3P : : e (0 2 0’ IO’U
Intense
group at 762 keV
00 /
o 0 0
0
0 \“oo
Weak neutron group at 1097 keV
neutnxl group at 1097 kd, is omitted I IO
I 20
Channel
FIG. 7.-Measured
I
I
neutron
Proton recoi I ‘0 spectrum corrected o fory-induced pulses ’
IO’
I
I
-
0 o 0
\ ‘, ( 30
\
I 40
50
number
proton-recoil spectrum of the 1.6 cm radius La-Be source (14.0 cm lead shield radius).
in the Be-target. As these targets are comparatively thin, the scattering probability for a neutron between origin and leaving the target is rather low. The probability of secondary scattering within this target is still much lower than that. Therefore, a sharp separation between neutrons scattered only once and those scattered twice, should appear in the spectrum. The maximum energy loss when scattered in beryllium is 348 keV for Na-Be neutrons of energy 967 keV, and 274 keV for the La-Be neutrons with energy 762 keV, respectively. This gives a lower energy limit of 619 keV and 488 keV, respectively, for neutrons which were scattered once. These energy limits may be clearly seen in the experimentally and theoretically determined distributions of Figs. 8-14. The radioactive decay of 140La includes more than only one gamma ray emitted with an energy above the threshold of the (y, n)-reaction in 9Be. The intensity of these lines is low, compared to the overall gamma emission. Only about 3.5 per cent of the most densely populated gamma transition are emitted with the 2.5 MeV-line. Only 0.07 per cent are emitted with a second, much weaker 2.9 MeV-line. Despite the low intensity of the second line, the neutron group produced by this y-line could be definitely traced by our measurements of the La-Be spectrum. Figure 7 shows the proton-recoil spectrum of one of the La-Be sources, in that respect similar to
The emission spectra of Na-D,O, In-Be, La-Be and Na-Be photoneutron sources
869
the other source arrangements. The threshold of the I.097 MeV-neutron group produced by the 2.9 MeV y-line is clearly demonstrated thereby. Also with the derived neutron spectra (Figs. 13 and 14) the second neutron group becomes apparent. Efforts had been made to determine the relative intensities of the neutron groups. Very similar results were obtained for all different source geometries and lead shield, and a mean value of 0.0655 f 0*0030 resulted from the different measurements. Using the values for the relative intensities of the y-lines as reported by KARLSSON (1967) and BAER(1968), and the relative values for the (y, n)-cross section as given by JAKOBSON(1961), the relative neutron intensities should only result in 0,044 & 0.011 which might be due to either erroneous cross section values or incorrect values of the gamma intensities. Further measurements will be carried out to clarify this point. The agreement between the theoretically calculated and measured neutron spectra for the Na-Be source was extremely good. But no such agreement was originally found for the In-Be source spectra. The theoretical calculations deviated by about 23 keV in the energy axis from the experimental results. The well founded reason for this deviation was the use of an energy value for the y-quanta of the neutron producing line as given by the Nuclear Data Sheets (1964). Since the original Monte-Carlo calculations of the spectra had been carried out 4yr ago (BENSCH, 1969), only the data as given there could be used. The curve thereby obtained is shown by the solid line in Figs. 15 and 16. According to recent measurements (RABENSTEIN,1970), the energy of the neutron producing gamma line has been modified to a value of 2.1121 f 0*0004 MeV and the re-evaluation by use of the same Monte-Carlo method yielded a spectrum shown by the dotted line in Figs. 15 and 16. The excellent correspondence between this theoretical curve and the measured spectrum is obvious. The results of the calculated spectrum of the In-Be source previously published (BENSCH, 1969) should therefore be corrected by a shift in the energy axis of +23*2 keV. Because of the low energy of the neutron group of the Na-D,O source, a measurement of the low energy part of the spectrum was not possible. However, an estimation of the maximum neutron energy of the source and a determination of the energy of the maximum of the neutron distribution was carried out as can be seen from the results given in Fig. 17. The data may be seen in Table 2. RESULTS
AND
DISCUSSIONS
From the theoretically derived neutron spectra the peak of the neutron distribution was determined by least square fitting a Gaussian distribution through a certain number of the statistically distributed values (approximately 15 values) in the vicinity of the distribution maximum. The data obtained thereby are given in Table 2. The mean energy of the neutron distribution was calculated from both the measured and the calculated spectra. Since the agreement was sufficient, only the data obtained from the theoretical calculations are given in Table 2. Despite the fact that measurements were performed with lead shield of varying, but non-zero thickness, the data are given for the extrapolated case of lead shield thickness 0 as this is the most interesting case as far as applications are considered. Because of the unsymmetrical distribution of the photoneutron spectra a minor shift of the peak energy to lower energies (7 keV with the In-Be source and 15 keV
x
‘0
N
-62
0.2 -
0.4-
06-
02
0.4
06
.
.
Neutron
.
??
?? Y
r3= 4,Ocm
r,=i.Ocm
No -.Be
energy,
Lowest energy of source neutrons after single elastic scattering on Be -nuclei
FIG. I-12.-Neutron
MeV
i
-0
Neutron
r3= 14-O cm
Na-Be r,=?5cm
spectra of the Na-Be source with varying source
06
energy,
MeV
P a
The emission spectra of Na-D,O, In-Be, La-Be and Na-Be photoneutron sources
871
TABLE
P.--PEAK
ENERGY
AND
MEAN
ENERGY
OF
THE
VARIOUS
SOURCE
DIMENSIONS
264.1 f 0.5
247 f 5
381 f 7
741 & 13 1070 & 24
946 f 1.5
with lead shield (14 cm radius)
753 f 3* 759 f 3t 392 & 3 256 =t 2
962 f 5 760 + 3* 766 f 3t 397 f 3 260 i 2
971 & 18 765 f 15 1099 * 30 399 5 10 264 f 8
959 f 5
1.0
1.6
radius of the Be target 2.5
if the
246 f 2
371 f 3
745 f 3* 751 f 37
954 i 5
Mean neutron energy (no lead shield) (keV)
no lead shield
Determined from the experimental distribution
(keV)
* These values were obtained by only considering the main neutron group at 762 keV (neglecting the high energy neutron group); second neutron group is taken into account, an energy shift of 6 keV has to be applied. These values are indicated in the table by t.
246.8 f 2
2752.9 f 0.2
aaNa-D,O
397.3 f 0.8
379.7 * 2
761.7 f- 0.7 1097.5 f 1.0
738.1 + 2 1069.5 f 3
2522.0 f 0.3 2899.8 & 0.5
2112.1 & 0.4
966.9 -f 0.5
942.2 + 2
no lead shield
2152.9 + 0.2
Yn-Be
Photoneutron source
with lead shield (14 cm radius)
Energy of the neutron-producing y-rays (keV)
Calculated from the energy of the y-rays
Peak energy of the neutron distribution
values for the mean neutron energies and the peak energy determined with no lead shield are corrected for the peak shift due to the finite counter resolution (extrapolated to counter resolution 0 per cent). The values determined with the lead shield are not corrected for this peak shift and therefore agree with the experimental curves given in Figs. S-17.
All
i
: p. ?t w B
!!
5
P
The emission spectra of Na-D,O,
In-Be, La-Be and Na-Be photoneutron
sources
873
with the Na-Be source) occurs due to the finite spectrometer resolution. The size of this shift was calculated by using the same code as described above (BENJAMIN, 1968), and was considered either with the theoretically calculated or with the experimentally obtained distributions when comparing both of them. In Table 2 with the values for the 14 cm radius lead shield, the theoretical values were corrected accordingly, while with the extrapolated values (thickness 0) and with the values for the mean energy, the experimental values were corrected corresponding to the shift mentioned. Thus, these latter values may be used directly as reference for further experiments. Acknowledgements-The authors would like to express their special gratitude to Dr. R. Gold and Dr. E. F. Bennett for their kindness in making available the counter tube used in the experiments and for valuable advice during the progress of this work. The authors are also indebted to Dr. H. Jasicek for generous help and discussion. REFERENCES BAER A. W., REIDY J. J. and WIEDENBECK M. L. (1968)Nucl. Phys.A113,33.
BELANOVA T. S., VAN’KOVA. A., MIKHAILUSF. F. and STA~JX~KII Y. Y. (1966) J. nucl. Energy 20,411. BENJAMINP. W., KEMSHALLC. D. and BRICK~TOCKA. (1968) Rep. AWRE O-9/68. BENJAMINP. W., KEMSHALLC. D. and REDFEARNJ. (1964) Rep. AWRE 2/64. BENNEIT E. F. (1967) Nucl. Sci. Enging 27, 16. BENNEITE. F., GOLD R. and OLSONI. K. (1968) Rep. ANL-7394. BENSCHF. and V~SELYF. (1969) J. nucl. Energy 23,531; (1970) J. nucl. Energy 24,57. ENDT P. M. and VAN D. LEUN C. (1967) Nucl. Phys. A105,l. HUGHESD. and ECXLER C. (1947) Phys. Reu. 72,902. JAKOBSONM. J. (1961) Phys. Rev. 123,229. KARLSSONS. E., SVAHN B., PEX~RSSON H., MALM~TENG. and DEAI~ENBERG E. Y. (1967), Nucl. Phys. AlOO, 113. LAL~VIC M. and WERLEH. (1970), J. nucl. Energy 24,123. MUECK K. (1972) Dissertation, Atominstitut, Vienna. OEHLERH., KOEHLERH. and POSE H. (1964) Kernenergie 7,325. ORNL-Nuclear Data Sheets (1964). Academic Press, New York. POWELLJ. E. and ROGERSJ. W. (1970)Nucl. Instrum. Meth. 87,29. POZE K. R. and GLAZKOVN. P. (1956) Sov. Phys. JETP 3,745. RAFJENSTEIN D. (1970) 2. Phys. 240,244. R~vrs T. B. and ROBERTSON J. G. (1971) J. nucl. Energy 25, 557. SNIDOWN. L. and WARRENH. D. (1967) Nucl. Znstrum. Meth. 51, 109. WA~TENBERGA. (1946) Phys. Rev. 71,497.