Measurement of number albedo of backscattered photons

N U C L E A R I N S T R U M E N T S AND METHODS

159 ( 1 9 7 9 )

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N O R T H - H O L L A N D PUBLISHING CO.

MEASUREMENT OF NUMBER ALBEDO OF BACKSCATTERED PHOTONS* M. BISWAS ~, A. K. SINHA + and S. C. ROY

Nuclear Physics Laboratory, Bose Institute, Calcutta-700009, India Received 7 June 1978 and in revised form 18 September 1978 A uniform response photon counter has been used to measure the differential number albedo of backscattered photons. The application of this counter eliminated the use of tedious efficiency corrections needed when conventional counting systems are used. The differential albedo has been measured for five elements (paraffin, aluminium, concrete, iron and lead) and for three different primary photon energies (145 keV, 279 keV, 840 keV) in angular steps of 10°. The total albedo has been calculated from the measured differential albedo by numerical integration. The measured values have been compared with the available results.

1. Introduction Extensive experimental investigations 1-~°) on the backscattering of gamma rays have been made for more than a decade. But the systematic investigations of the phenomenon covering a wide range of energies and elements are few. In fact, most of the measurements of number and energy albedo of backscattered photons have been made for gamma rays obtained from ~37Cs (0.662 MeV) and 6°Co (1.25 MeV). The backscattered gamma rays have a continuous energy distribution and in most of the measurements excepting that of Sinha et al. 9) it is necessary to apply corrections due to the variation of the detecting efficiency with photon energy. For continuous distributions these corrections are tedious and cannot be known with 100% certainty. To obviate this difficulty a detector whose efficiency is independent of photon energy will be useful in this situation. Ghose ~) developed an ingenious method to make the sensitivity of the scintillation counter uniform over a wide energy range. The measurement of number albedo for gamma rays obtained from radioactive I37Cs and 6°Co by Sinha l°) and its comparison with available results proves conclusively that such a detecting system is a useful tool in situations where one is interested only in the number of photons irrespective of their energies. However the sensitivity of the detecting system used by Sinha is uniform for photon energies above 200-t500keV and cannot be * Work performed under the sponsorship of a research grant obtained from Dept. of Science and Technology, Governmerit of India. * Guest worker from New Alipore College, Calcutta-700053, India. + Present address: Dept. of Physics, Regional Engineering College, Silchar (Assam) 788010, India.

used in low energy measurements. 1~ the modified instrument used by us the sensitivity is practically constant for any energies up to 1500 keV. In section 2 a brief description of the development of the detecting system will be given. Using this instrument we have measured the differential number albedo of backscattered photons for five different elements (paraffin, aluminium, concrete, iron and lead) and three different primary photon energies (145 keV, 279 keV and 840 keV) at an angular step of 10°. The details of the method of measurement will be presented in section 3. A comparison of the present result with the existing theoretical and experimental results will be presented in section 4.

2. Uniform sensitivity photon counter It has been shown by Ghose ~) that the energy independence of a photon counter can be achieved by placing a filter of suitable thickness before the scintillation detector. The filter acts as a diverging agent and prevents part of the incident photons from entering the detector and the principle of uniformity of response is thus preferably the same as that used in optics in the construction of an achromatic lens. For paraxially incident gamma rays the efficiency of a filter-crystal combination can be represented by the equation: = ( 1 - e -~") e -b~,

(1)

where a and b are the thickness of the crystal and filter respectively~ (0 and p represent the total and non-coherent, absorption coefficient of the filter and crystal respectively. If a numerical weight factor.l; which corresponds to the fraction of the time the filter is present before the scintillator, be intro-

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M. BISWAS et al.

duced then the efficiency of such a detecting system can be represented by = ( 1 - - e -"u) { ( l - f ) = e o {(1

+fe

--f) +fF},

(2)

where eo = l - e

0.1 0

-"u

and

0.2

F = e -be.

For a specific photon energy, scintillator and filter eq. (2) is linear with respect to ,/'. If for a particular set of values of a and b all straight lines obtained plotting against f for different photon energies intersect at a particular point between f = 0 and 1 then we can say that the efficiency of the detecting system is constant for that particular value of f The plot of e against f for a 2"×2"NaI(Tl) crystal and with aluminium filter of thickness 35 g/cm 2 for different photon energies is shown in fig. 1. From the graph the optimum value of f obtained is 0.8. The efficiency e calculated for photon energies up to 2.0 MeV for this particular set of scintillator and filter is presented in fig. 2.

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Fig. 2. Variation of calculated efficiency with energy of the photon.

3. Experimental method The gamma ray sources 54Mn, 2°3Hg and ~4~Ce used in the present investigation are of a few /tCi strength. The largest dimension of the source used was that of 3 mm in diameter. Scatterers used in the experiment are paraffin, iron, aluminium, concrete and lead. The sizes and thicknesses .of the scatterers were chosen so as to ensure full emergence of the backscattered radiation. The uniform sensitivity photon counter consisting of an aluminium filter of 35 g/cm 2 combined with a 2":4 2" NaI(TI) crystal was used in the present measurement. The conventional electronic circuitry comprising a pulse amplifier, single channel analyser and decade scaler was used. The stability and linearity of the system were tested periodically and found to be excellent. Scatterers are placed vertically on a goniometer with a point isotropic source at the centre of the scatterer face and on the axis of the goniometer. The distance between the centre of the scatterer face and the scintillation head is 1 m. Scatterer slabs are placed at different angular positions by rotating the goniometer and the angle between the normal to the scatterer surface and the detector axis measures the angle 0. Backscattered photons are measured from 0° to 90° at an angular step of 10°. To eliminate forward-scattered radiation at

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I Foam B~I Fig. 3. Schematic diagram of the experimental arrangement.

NUMBER

ALBEDO

OF

ALUMiNIUM

the 90° position the goniometer is set at an angle o.s close to 90°. A schematic diagram of the experimental arrangement is shown in fig. 3. The differential number albedo Nd(O,x) for the 0.4 angle 0 and scatterer thickness x is expressed by the fraction of the emergent photons at the angle 0 per steradian for one primary photon incident on ~ e3 the scatterer. The number of backscattered pho- -*_ tons is obtained from the difference between the < integral counts with and without the scatterer. A ~_ 0.2 typical differential number albedo vs scatterer thickness plot is shown in fig. 4. The differential 04 albedo values at saturation thickness for different kLUMINIUM

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ALUMINIUM 279 KeV

60

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F i g . 5. V a r i a t i o n o f t o t a l n u m b e r a l b e d o w i t h s c a t t e r e r t h i c k ness for aluminium with different photon energies.

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elements and photon energies are presented in table 1. The total number albedo values for each scatterer obtained by integrating corresponding differential values over angular coordinates have been measured for three different bias settings and then extrapolated to zero bias. A graph showing the typical variation of total number albedo with thickness of aluminium scatterer for different photon energies has been presented in fig. 5. The uniform sensitive counter has been designed on the assumption of paraxially incident rays which can be realised by placing a point source at large distances. Errors may creep in due to the non-uniformity of detector response arising from the finite size of the source and large dimension of the scatterer acting as a secondary source. The change in detector efficiency due to these factors has been calculated and found to be less than 1%. The error which may arise due to scattering from the floor of the room, base of the goniometer etc. has been minimised by placing the entire arrangement over a foam plastic bed. Therefore the major contribution in the uncertainty of the measurement comes from the normal statistical error. The differential albedo except for lead has been measured within an error of + 10% and the total albedo w i t h i n - + 1%. The observed statistics is poor in the case of lead due to its large absorbing property.

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M. B I S W A S et al.

TABLE 1 Differential n u m b e r albedo for different scatterers and g a m m a ray energies. ~ d ( O , x ) × l O 3 sr ]. Scatterer

Paraffin

Aluminium

Concrete

Iron

Lead

Energy of the source (MeV)

0°

10°

20 °

angle

0.145 0.279 0.840 0.145 0.279 0.840 0.145 0.279 0.840 0.145 0.279 0.840 0.145 0.279 0.840

106.8 67.3 86.5 69.2 51.1 95.0 104.1 45.3 91.0 23.5 32.0 57.0 19.0 15.2 14.1

113.7 67.3 78.9 65.2 50.0 90.2 96.7 46.5 92.5 21.6 28.5 63.8 16.2 16.8 12.9

103.7 68.3 69.4 64.6 51.2 97.4 89.8 46.2 88.4 21.8 29.1 60.6 22.9 13.7 11.0

30 °

40 °

50 °

60 °

70 °

80 °

90 °

88.4 71.3 69.9 46.5 50.2 78.5 75.3 44.6 81.2 19.4 29.6 62.0 20.0 13.1 11.9

91.7 67.0 75.0 42.6 55.4 79.3 67.7 48.0 85.6 20.9 30.0 62.5 13.2 8.6 11.6

91.2 70.4 74.0 37.6 55.0 67.9 56.6 39.2 72.9 16.2 26.5 58.4 9.9 7.0 8.6

75.0 70.0 74.9 33.1 40.0 70.1 54.5 36.2 73.3 12.9 27.7 49.9 7.5 6.0 9.9

68.4 58.3 69.3 22.9 42.9 61.4 48.4 34.8 65.7 8.9 17.6 48.8 7.9 7.5 8.6

62.6 47.6 59.8 16.7 29.0 38.4 34.0 21.0 40.6 7.7 13.3 34.6 6.9 2.3 5.4

58.3 23.4 53.7 8.9 23.5 29.0 19.4 14.6 22.5 5.2 12.5 27.8 -0.9 2.0 6.8

4. Results and discussion

It has been found that the differential number albedo values lbr the scatterers under investigation indicated the anisotropic distribution of photons as a function of the emerging angle (emerging angle 0 = 180°-angle of scattering). Fig. 6 typically shows the monotonic decrease in the intensity of the scattered radiation with increase of 0 for all substances; for substances with large Z, a steeper slope of this function as 0 approaches 90 ° is observed. It is evident from the experimental results that the contribution to backscattered radiation by low energy photons is higher than that from high energy photons. This may be attributed to less penetration and higher rate of multiple interaction inside the scattering medium by low energy photons. This is in conformity with the results obtained by Pozdneyev6). The backscattering of gamma rays is influenced by the energy of the primary photon. The present experimental values along with the values obtained for 662 keV and 1250 keV photons by Sinha t°) in this laboratory in an identical experimental arrangement are presented in fig. 7 typically for paraffin and iron. The theoretical values obtained by Berger and Raso ~2) using a Monte Carlo technique have also been shown by a dotted line. The agreement is found to be satisfactory.

Comparison of our total albedo values presented in table 2 with the available experimental and theoretical values shows that the albedo values obtained in the present investigation are in good agreement with the theoretical Monte Carlo values ~2) and the experimental values obtained by

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ANGLE IN DEGREES Fig. 6. A n g u l a r distribution of backscattered intensity for different elements.

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Ener&y m MeV Fig. 7. C o m p a r i s o n of the observed energy d e p e n d e n c e of total albedo with theoretical values.

TABLE 2 Total n u m b e r albedo for different scatterers and g a m m a ray energies. N a m e of the scatterer

Paraffin

Aluminium

Concr ete

Iron

Lead

a For water. b For 0.765 MeV.

Ph oton energy fMeV)

Present investigation

0.145 0.279 0.840 0.145 0.279 0.840 0.145 0.279 0.840 0.145 0.279 0.840 0.145 0.279 0.840

0.5400_+0.007 0.4730 + 0.009 0.4450_+ 0.009 0.2175_+0.007 0.3100_+0.005 0.4500_+0.009 0.3700_+0.007 0.2800 _+0.007 0.4700_+ 0.009 0.1270±0.005 0.2250_+ 0.005 0.3700+0.009 0.0715 _+0.008 0.0720_+ 0.011 0.0710_+0.007

P oz dne ye v 6)

0.5884 0.5654 0.1845 0.3955 0.42 _+_0.03b 0.1179 0.1933 0.34 + 0 . 0 3 b 0.0644 0.0618 b

M o n t e Carlo 12) (interpolated values) 0.5571 a 0.5573 a 0.4804 a 0.1513 0.2880 0.3250 0.0266 0.0837

162

M. BISWAS et al.

Pozdneyev6). Due to lack of any experimental measurements for 840 keV it has not been possible to compare with experimental values of any other group. Our albedo values at 279 keV for all elements excepting lead are consistently lower than those observed by Pozdneyev 6) and Berger and Raso~2). This might be due to the presence of a systematic error in this particular measurement. Due to the lack of any other experimental measurement at low energy it is very difficult to assign a definite reason. The overall agreement of our experimental values with the theoretical and the existing experimental values clearly proves that the uniform spectral sensitivity photon counter used here is a successful tool in the measurement of backscattered intensity. The advantage of using this tool over the conventional detector is to avoid the evaluation of the response matrix of the detector and laborious efficiency corrections using computers. Moreover, this tool can be used for all experimental situations involving a continuous gamma energy spectrum where one is interested in getting the number of photons irrespective of their energies. The results of the present measurement along with the results obtained earlier in this la-

boratory will be utilised to study the systematics of backscattering of photons and to develop a semiempirical formula for number albedo. The authors are thankful to Dr. S. C. Bhattacharyya, Director, Bose Institute for his kind interest in this work. They are also grateful to Prof. A. M. Ghose, Head of the Department of Physics, Bose Institute, for many helpful discussions.

References 1) E. Hayward and J. H. Hubbell, Phys. Rev. 93 (1954) 955. 2) T. Hyodo, Nucl. Sci. Eng. 12 (1962) 178. 3) H. Fujita, K. Kobayashi and T. Hyodo, Nucl. Sci. Eng. 19 (1964) 437. 4) C. E. Clifford, Can, J. Phys. 42 (1964) 957. 5) D. B. Pozdneyev and S. A. Churin, J. Nucl. Energy 21 (1967) 313. 6) D. B. Pozdneyev, J. Nucl. Energy 21 (1967) 197.' 7) j. j. Steyn and D. G. Andrews, Nucl. Sci. Eng. 27 (1967) 318. 8) E. Elias, Y. Segal and A. Notea, J. Nucl. Energy 27 (1973) 351. 9) A. K. Sinha, A. Chatterjee and A. M. Ghose, J. Mysore Univ. 26B (1976) 271. 10) A. K. Sinha, Thesis (Calcutta University, 1976). 11) A. M. Ghose, Nucl. Instr. and Meth. 34 (1965) 45. 12) M. J. Berger and D. J. Raso, Rad. Res. 12 (1960) 20.