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Some effects of the self-absorption of neutrons in neutron-detecting foils
J. Nuckm Enalg.
1956. Vol. 2; pp. 286 to 290.
I’m
PmiLtd..
Ladon
SOME EFFECTS OF THE SELF-ABSORPTION OF NEUTRONS IN NEUTRON-DETECTING FOILS # M. W. THOMPSON Atomic Energy Research Establishment, Harwell, Didcot, Rerks (Received 24 March 1955; in revisedform 14 September 1955) Abstract-The distortion of neutron flux by detecting foils is discussed and a method described by which it has been measured. The results, which are compared with theory, show how the mean distorted flux changes with foil-thickness for indium foils in different graphite-pile spectra. From these results the effect of a change in irradiation spectrum on the intercalibration of foils is calculated. The interaction of two indium foils in the same graphite system has been studied experimentally.
INTRODUC%ON
has been extensively used for the measurement of both relative and absolute neutron flux. Detectors of this type inevitably distort the flux which they are measuring, and this can effect their use in certain cases. The expression for the number of activated nuclei in a detector foil is:
NEUTRON-INDUCED radioactivity
Na M . A . p . f . (1 - e-“r) . eeU .+ where : mean distorted flux in the volume of the foil,
43
a = average absorption cross-section for the neutron irradiation
spectrum,
IV= Avogadro’s number, M = atomic weight, A = area of foil, ,u = area1 density of foil, il.= decay constant, of activated nuclei; T =
irradiation time,
t = time from end of irradiation.
The actual /?,r counting-rate measured on a particular counting system will depend on the sensitivity of the counter and on the self-absorption of @-and y-rays. The problem of absolute /?-ray counting has been dealt with elsewhere (e.g., BURT, 1949; THOMPSON, 1955), and will not be discussed further. The purpose of the experiments described below was to ascertain the effect of varying foil-thickness on 4 in different irradiation spectra. 2. THE
THEORY
OF NEUTRON
SELF-ABSORPTION
IN FOILS
Consider a detecting foil embedded in a large volume of moderator in which thermal neutrons diffuse. We define the flux-distortion factor B/4 as the ratio of the 286
287
Self-absorptionin neutrondetecting foils
mean distorted flux to the mean original ffur~in the volume of the foil. For foils of ’ finite thickness this is less than unity because of two effects:(i) The introduction of “negative sources ” into the moderator which reduces the local flux. This effect will depend on the probability of absorption for one crossing of the foil, and also on the relation of scattering mean free path in the moderator and lateral foil dimensions (H&BAN pi al., 1942). (ii) The shielding of the inside of the foil by the outer layers. This will depend on the absorption cross-section and the foil dimensions.
/J fad
thickness
Mgfcm’
Fra. 1.-The variation of #+ with foil thickness.
We shall refer to the first of these effects as flux perturbation, the second as flux depression, and the collective effect as ffux distortion. SKYBE (1943) and BOTHB (1943) have separately produced formulae dealing with the problem for thermal neutrons, and TIITLE (1951) has modified BOTHE’Sformula. SKYRME’Sformula deals with both flux perturbation and depression, whilst BOTHE’Sformula deals only with the former. A comparison of these formulae for an indium foil in graphite is shown in Table 1 and Fig; I. TABLEl.-FLUX
DISlDRTION
FOR DISC-SHAPED
INDITJM
FOILS OF
1 CM
RADIUS
(au for In taken as 190band / Foil thickness,mg/cmS
-r
W
GRAPHITE
-
20
30
50
100
0.995
0.993
@989
0,979
0.963
0.950
0.990
0.985
0.975
0.951
0.902
0.853
0.941
0.918
0.875
0,781
0.622
0.487
288
M. W. THOMPWN
Suppose now that the neutrons in the moderator have a pile spectrum of energies. In this case we have also to consider the effect on the fast neutrons which will be slowing down in the moderator.. In the case of a “l/zi” absorber the chief effect will be a thermal flux perturbation and depression, the fast neutrons being little affected. For a “resonance” absorber the effects are greatly modified. Consider first the neutrons in the resonance band of energies. These will suffer a large flux depression due to their short mean free path in the detector. The perturbation cannot occur in the same way as for thermal neutrons, since a fast neutron cannot diffuse back to the same point and maintain the same energy. However, if we consider a point close to one side of the foil, we observe that very few resonance neutrons will arrive after passing through the foil, although the flux from the open side will not be altered (THOMPSON,1955). This must lead to a perturbation of about one-half. The neutrons in the thermal-energy group will undergo perturbation and depression as described above. 3. THE EXPERIMENTAL DETERMINATION OF FLUX DISTORTION FACTORS FOR INDIUM FOILS IN A THERMAL SPECTRUM AND TWO PILE SPECTRA A stack of identical indium foils (1 in. x 2 in., and each 31 mg/cm2 thick) was irradiated in the same flux for the same time as a similar single foil. The foils were counted separately, in rotation, on G.M.4. Geiger counters, and the ratio of activity of each stacked foil relative to that of the single foil determined. Since /I and y absorption effects are the same for each foil, the activity ratio for any foil gives the ratio of 4 in the foil to 4 in the single foil. The mean ratio for the stack gives the ratio of &r$ for a foil of the same thickness as the stack to $/$ for the single foil. This mean ratio is then determined for stacks of various thickness. By extrapolating back to the point of zero thickness, and normalizing all values to this point, a curve of B/$ versus thickness is obtained. It was found that the thinnest foil that could be conveniently handled was 30 mg/cm2 thick. This was not thin enough for an extrapolation to zero thickness to be attempted. Sets of three identical foils, backed on graphite slabs, were therefore used. Each set had about one-half the thickness of the previous set, the thickest being about 16 mg/cm2 thick. Two of each set were irradiated face to face, forming a stack of two, the other one irradiated separately. In this way the minimum thickness was decreased from 31 mg/cm2 to 0.39 mg/cm2. The experiment was performed in a thermal flux and in two different pile spectra which had cadmium ratios, measured with indium foils, of 1.9 and 2.9. A correction was made for slight differences in the thickness of foils in a set. The results are shown graphically in Fig. 1. A comparison of the results in a thermal flux with the theoretical formulae shows them to agree well with SKYRME’S formula, but not with BOTHE’Sformula. This is to be expected, since the flux depression is much greater than the perturbation owing to the high absorption cross-section of indium and the long scattering mean free path in graphite. The results in a pile spectrum show the flux distortion to increase rapidly as,.cadmium ratio decreases. Measurements by FITCH and DRUMMOND (1954) using mdium foils in light water, agree well with BOTHE’Sformula after a correction for flux depression has been applied. KLEMAand RITCHIE(1952) have made measurements with indium and gold in graphite
Self-absorption
in neutron-detecting
289
foils
and also obtain good agreement with BOTHE’Sformula, but it is not clear whether or not a flux depression correction was applied in this case. Both the above pairs of experimenters used methods different from the one described here, and these involved extrapolating from larger foil thicknesses. 4. THE EFFECT OF A CHANGE OF SPECTRUM ON FOIL INTERCALIBRATION Suppose two foils of slightly different thickness are intercalibrated in one spectrum and then irradiated in another. It can be shown (THOMPSON,1955) that there will be does not change. In Fig. 2
no
F
50 fi FIG. 2.-The
foil
150 200 loo thickness Mg/cm’
250
variation of foil calibration with cadmium ratio
R.
this quantity is plotted as a function of foil thickness, using values from Fig. 1. In Table 2 the percentage change in calibration factor for two foils differing in thickness by 5 per cent due to a change in cadmium ratio from 1.9 to co is shown for several foil thicknesses. TABLE 2.
It is clear that a thicker foil is less prone to intercalibration changes in going from one spectrum to another.
5. THE
INTERACTION
OF
DETECTORS
When two detectors are irradiated in the same system there may be interaction between them. This will depend on how large is the region of perturbed flux that each produces. If these regions overlap, then the foils interact. The size of this region will depend on the foil size and material, on the scattering mean free path in the moderator, and on whether or not the unperturbed flux is isotropic.
290
M. W. Triosrmo~: Self-absorption in neut.rondet&ing foils
An experiment has been done in which two identical foils were irradiated in an originally isotropic flux at various distances apart with their planes parallel and their centres in line. Each foil consisted of 31 mg/cms of indium on a disc of graphite 1 in. in diameter. They were irradiated in a graphite-pile spectrum of cadmium ratio 25 After irradiation they were counted relative to a monitor foil which had been irradiated for the same length of time. The relative counting-rate of one foil was observed for various separations. In an isotropic flux no interaction was observed until the foils were 2.5 cm apart, which is approximately the scattering mean free path in graphite. The experiment was repeated in the same spectrum, but with an anisotropic flux equivalent to 6 per cent change in flux per centimetre along the line of centres. The relative counting rate of the foil in the lowest flux was measured as the other was brought closer. In this case interaction was observed at distances up to 25 cm apart. Acknowledgements-The author wishes to thank Miss CUIUIS, Mrs. DAVEY,Mrs. FIRK, Miss NEWTON,and Messrs, CALDER and SHORTERfor their help in irradiation and counting foils; Mr. J. G. ROBINSfor making the foils, and Dr. C. G. CAMPBELL and Mr. P. W. MUMMERY for helpful discussions. REFERENCqS R~TIIEW. (1943) Concerning the methodology of neutron probes. Z. P/y. 120,437, U.S. Translation-A.E.C./Tr-1691. BURTB. P. (1949) Absolute beta counting. Nucleonics, 5,2,28. Frrcu S. H. and DRUMMOND J. E. (1954) Neutron detector perturbations. U.S. Report, L.R.L.-95. HALBANH., FJZNNING F. W., and KOWARSKI L. (1942) The sensitivity of Dysprosium detectors as affected by their finite area and thickness, British Report, B.R.-194. KLEMAE. D. and Rrrcrue R. H. (1952) Thermal neutron flux measurements in graphite using gold and indium foils. Pl?ys. Rev. 87, 167. SKVRME T. H. R. (circa 1943) The reduction in neutron density caused by.an absorbing disc. The absorption of neutrons by a thin circular disc of radius comparable with the mean free path. British Report, M.S.-91, and appendix. Trrr~~ C. W. Slow neutron detection by foils 8, 6, 5, 1951 Nucleonics
( 9,1,60,1951 THOMPSON M. W. (.1955) Some effects of the self absorption of beta rays and neutrons in neutrondetecting foils. British Report, A.E.R.E.-R/PR-1549.
1956. Vol. 2; pp. 286 to 290.
I’m
PmiLtd..
Ladon
SOME EFFECTS OF THE SELF-ABSORPTION OF NEUTRONS IN NEUTRON-DETECTING FOILS # M. W. THOMPSON Atomic Energy Research Establishment, Harwell, Didcot, Rerks (Received 24 March 1955; in revisedform 14 September 1955) Abstract-The distortion of neutron flux by detecting foils is discussed and a method described by which it has been measured. The results, which are compared with theory, show how the mean distorted flux changes with foil-thickness for indium foils in different graphite-pile spectra. From these results the effect of a change in irradiation spectrum on the intercalibration of foils is calculated. The interaction of two indium foils in the same graphite system has been studied experimentally.
INTRODUC%ON
has been extensively used for the measurement of both relative and absolute neutron flux. Detectors of this type inevitably distort the flux which they are measuring, and this can effect their use in certain cases. The expression for the number of activated nuclei in a detector foil is:
NEUTRON-INDUCED radioactivity
Na M . A . p . f . (1 - e-“r) . eeU .+ where : mean distorted flux in the volume of the foil,
43
a = average absorption cross-section for the neutron irradiation
spectrum,
IV= Avogadro’s number, M = atomic weight, A = area of foil, ,u = area1 density of foil, il.= decay constant, of activated nuclei; T =
irradiation time,
t = time from end of irradiation.
The actual /?,r counting-rate measured on a particular counting system will depend on the sensitivity of the counter and on the self-absorption of @-and y-rays. The problem of absolute /?-ray counting has been dealt with elsewhere (e.g., BURT, 1949; THOMPSON, 1955), and will not be discussed further. The purpose of the experiments described below was to ascertain the effect of varying foil-thickness on 4 in different irradiation spectra. 2. THE
THEORY
OF NEUTRON
SELF-ABSORPTION
IN FOILS
Consider a detecting foil embedded in a large volume of moderator in which thermal neutrons diffuse. We define the flux-distortion factor B/4 as the ratio of the 286
287
Self-absorptionin neutrondetecting foils
mean distorted flux to the mean original ffur~in the volume of the foil. For foils of ’ finite thickness this is less than unity because of two effects:(i) The introduction of “negative sources ” into the moderator which reduces the local flux. This effect will depend on the probability of absorption for one crossing of the foil, and also on the relation of scattering mean free path in the moderator and lateral foil dimensions (H&BAN pi al., 1942). (ii) The shielding of the inside of the foil by the outer layers. This will depend on the absorption cross-section and the foil dimensions.
/J fad
thickness
Mgfcm’
Fra. 1.-The variation of #+ with foil thickness.
We shall refer to the first of these effects as flux perturbation, the second as flux depression, and the collective effect as ffux distortion. SKYBE (1943) and BOTHB (1943) have separately produced formulae dealing with the problem for thermal neutrons, and TIITLE (1951) has modified BOTHE’Sformula. SKYRME’Sformula deals with both flux perturbation and depression, whilst BOTHE’Sformula deals only with the former. A comparison of these formulae for an indium foil in graphite is shown in Table 1 and Fig; I. TABLEl.-FLUX
DISlDRTION
FOR DISC-SHAPED
INDITJM
FOILS OF
1 CM
RADIUS
(au for In taken as 190band / Foil thickness,mg/cmS
-r
W
GRAPHITE
-
20
30
50
100
0.995
0.993
@989
0,979
0.963
0.950
0.990
0.985
0.975
0.951
0.902
0.853
0.941
0.918
0.875
0,781
0.622
0.487
288
M. W. THOMPWN
Suppose now that the neutrons in the moderator have a pile spectrum of energies. In this case we have also to consider the effect on the fast neutrons which will be slowing down in the moderator.. In the case of a “l/zi” absorber the chief effect will be a thermal flux perturbation and depression, the fast neutrons being little affected. For a “resonance” absorber the effects are greatly modified. Consider first the neutrons in the resonance band of energies. These will suffer a large flux depression due to their short mean free path in the detector. The perturbation cannot occur in the same way as for thermal neutrons, since a fast neutron cannot diffuse back to the same point and maintain the same energy. However, if we consider a point close to one side of the foil, we observe that very few resonance neutrons will arrive after passing through the foil, although the flux from the open side will not be altered (THOMPSON,1955). This must lead to a perturbation of about one-half. The neutrons in the thermal-energy group will undergo perturbation and depression as described above. 3. THE EXPERIMENTAL DETERMINATION OF FLUX DISTORTION FACTORS FOR INDIUM FOILS IN A THERMAL SPECTRUM AND TWO PILE SPECTRA A stack of identical indium foils (1 in. x 2 in., and each 31 mg/cm2 thick) was irradiated in the same flux for the same time as a similar single foil. The foils were counted separately, in rotation, on G.M.4. Geiger counters, and the ratio of activity of each stacked foil relative to that of the single foil determined. Since /I and y absorption effects are the same for each foil, the activity ratio for any foil gives the ratio of 4 in the foil to 4 in the single foil. The mean ratio for the stack gives the ratio of &r$ for a foil of the same thickness as the stack to $/$ for the single foil. This mean ratio is then determined for stacks of various thickness. By extrapolating back to the point of zero thickness, and normalizing all values to this point, a curve of B/$ versus thickness is obtained. It was found that the thinnest foil that could be conveniently handled was 30 mg/cm2 thick. This was not thin enough for an extrapolation to zero thickness to be attempted. Sets of three identical foils, backed on graphite slabs, were therefore used. Each set had about one-half the thickness of the previous set, the thickest being about 16 mg/cm2 thick. Two of each set were irradiated face to face, forming a stack of two, the other one irradiated separately. In this way the minimum thickness was decreased from 31 mg/cm2 to 0.39 mg/cm2. The experiment was performed in a thermal flux and in two different pile spectra which had cadmium ratios, measured with indium foils, of 1.9 and 2.9. A correction was made for slight differences in the thickness of foils in a set. The results are shown graphically in Fig. 1. A comparison of the results in a thermal flux with the theoretical formulae shows them to agree well with SKYRME’S formula, but not with BOTHE’Sformula. This is to be expected, since the flux depression is much greater than the perturbation owing to the high absorption cross-section of indium and the long scattering mean free path in graphite. The results in a pile spectrum show the flux distortion to increase rapidly as,.cadmium ratio decreases. Measurements by FITCH and DRUMMOND (1954) using mdium foils in light water, agree well with BOTHE’Sformula after a correction for flux depression has been applied. KLEMAand RITCHIE(1952) have made measurements with indium and gold in graphite
Self-absorption
in neutron-detecting
289
foils
and also obtain good agreement with BOTHE’Sformula, but it is not clear whether or not a flux depression correction was applied in this case. Both the above pairs of experimenters used methods different from the one described here, and these involved extrapolating from larger foil thicknesses. 4. THE EFFECT OF A CHANGE OF SPECTRUM ON FOIL INTERCALIBRATION Suppose two foils of slightly different thickness are intercalibrated in one spectrum and then irradiated in another. It can be shown (THOMPSON,1955) that there will be does not change. In Fig. 2
no
F
50 fi FIG. 2.-The
foil
150 200 loo thickness Mg/cm’
250
variation of foil calibration with cadmium ratio
R.
this quantity is plotted as a function of foil thickness, using values from Fig. 1. In Table 2 the percentage change in calibration factor for two foils differing in thickness by 5 per cent due to a change in cadmium ratio from 1.9 to co is shown for several foil thicknesses. TABLE 2.
It is clear that a thicker foil is less prone to intercalibration changes in going from one spectrum to another.
5. THE
INTERACTION
OF
DETECTORS
When two detectors are irradiated in the same system there may be interaction between them. This will depend on how large is the region of perturbed flux that each produces. If these regions overlap, then the foils interact. The size of this region will depend on the foil size and material, on the scattering mean free path in the moderator, and on whether or not the unperturbed flux is isotropic.
290
M. W. Triosrmo~: Self-absorption in neut.rondet&ing foils
An experiment has been done in which two identical foils were irradiated in an originally isotropic flux at various distances apart with their planes parallel and their centres in line. Each foil consisted of 31 mg/cms of indium on a disc of graphite 1 in. in diameter. They were irradiated in a graphite-pile spectrum of cadmium ratio 25 After irradiation they were counted relative to a monitor foil which had been irradiated for the same length of time. The relative counting-rate of one foil was observed for various separations. In an isotropic flux no interaction was observed until the foils were 2.5 cm apart, which is approximately the scattering mean free path in graphite. The experiment was repeated in the same spectrum, but with an anisotropic flux equivalent to 6 per cent change in flux per centimetre along the line of centres. The relative counting rate of the foil in the lowest flux was measured as the other was brought closer. In this case interaction was observed at distances up to 25 cm apart. Acknowledgements-The author wishes to thank Miss CUIUIS, Mrs. DAVEY,Mrs. FIRK, Miss NEWTON,and Messrs, CALDER and SHORTERfor their help in irradiation and counting foils; Mr. J. G. ROBINSfor making the foils, and Dr. C. G. CAMPBELL and Mr. P. W. MUMMERY for helpful discussions. REFERENCqS R~TIIEW. (1943) Concerning the methodology of neutron probes. Z. P/y. 120,437, U.S. Translation-A.E.C./Tr-1691. BURTB. P. (1949) Absolute beta counting. Nucleonics, 5,2,28. Frrcu S. H. and DRUMMOND J. E. (1954) Neutron detector perturbations. U.S. Report, L.R.L.-95. HALBANH., FJZNNING F. W., and KOWARSKI L. (1942) The sensitivity of Dysprosium detectors as affected by their finite area and thickness, British Report, B.R.-194. KLEMAE. D. and Rrrcrue R. H. (1952) Thermal neutron flux measurements in graphite using gold and indium foils. Pl?ys. Rev. 87, 167. SKVRME T. H. R. (circa 1943) The reduction in neutron density caused by.an absorbing disc. The absorption of neutrons by a thin circular disc of radius comparable with the mean free path. British Report, M.S.-91, and appendix. Trrr~~ C. W. Slow neutron detection by foils 8, 6, 5, 1951 Nucleonics
( 9,1,60,1951 THOMPSON M. W. (.1955) Some effects of the self absorption of beta rays and neutrons in neutrondetecting foils. British Report, A.E.R.E.-R/PR-1549.