AE-309 UDC 53S.12S.5.161 539.125.5.523 Measurement of the Decay of Thermal Neutrons in Water Poisoned with the Non-1/v Neutron Absorber Cadmium L. G. Larsson and E. Möller AKTIEBOLAGET ATOMENERGI STOCKHOLM, SWEDEN 1967 AE-309 •MEASUREMENT OF THE DECAY OF THERMAL NEUTRONS IN WATER POISONED WITH THE NON-l/v NEUTRON ABSORBER CADMIUM L G Larsson ' and E Möller SUMMARY Measurements have been made of the decay constant of thermal neutrons in water poisoned with the non-1/v absorber cadmium. An experimental method has been used in which proper spatial integration of the neutron flux enables data, representative of the infinite medium to be accumulated without waiting for the establishment of a fundamental mode distribution. The change in effective cross section with concen- daeff tration of the dissolved cadmium, —rr=—. has been determined for in- dN finite medium at 20 C. Two- and three parameter fits of the decay- constant yield -(0. 32 ± 0. 09) • 1 O-1 7 barn cm3 and -(0. 47 ± 0. 1 0) • 1 0"1 7 3 barn cm , respectively. Earlier published measurements have resulted in two to five times larger values, whereas a published calculated value -17 3 for Nelkin's model is - 0. 33 • 10 barn cm . *) Now at Research Institute of Swedish National Defence. Printed and distributed in January 1968. LIST OF CONTENTS Page 1 . Introduction 2. Principles of the experiment 3. Results of the measurements 4. Discussion of the results 5. Conclusion Acknowledgements References Table I Table II Figures - 3 - 1 . INTRODUCTION Various methods may be used for integral studies of thermal neu­ tron scattering in moderators. Well known examples are the measure­ ments of stationary neutron spectra in moderators, pure or poisoned with different absorbers. The pulsed neutron experiment is another example. The decay constant for thermal neutrons in a moderator as­ sembly varies with the absorption and the leakage according to the equa­ tion X = X + D B2 - CB4 + . (1) a o 2 where X is the decay constant for absorption only, B is the geomet- rical buckling of the assembly, D is the diffusion constant and C is the diffusion cooling constant describing the effect of the preferential leak­ age of high energy neutrons from the system. D and C are integral parameters of the scattering law, and the comparison between experi­ mental and calculated values may serve as a check of the validity of the scattering model, on which the calculations are based. The perturbation of a Maxwellian neutron distribution, occurring when an absorber of the non-1/v type is distributed in a moderator is reflected in the decay constant. In the resonance region neutrons are absorbed at a higher rate than in other regions. The result is a smaller value of the effective cross section than calculated by averaging the cross section with a Maxwellian flux. The decay constant for a therma- lized neutron field in an infinite moderator is given by the expression, analogous to (1 ) da rr y X = X + v a ,, . N + v .!:. • N + . (2) a o o eff o dN v ' where N is the non-1/v absorber concentration in atoms per cm , v is the most probable velocity of thermal neutrons at a moderator tem­ perature of 20 C, 2200 m/s, CT ,, is the effective cross section of the absorber in a Maxwellian distribution of neutrons, and X is the decay ' o } constant for thermal neutrons in the unpoisoned moderator. This param- doeff eter —-j^j— is, like the diffusion cooling coefficient, related to the rate - 4 - daeff of energy exchange between the neutrons and the moderator (- v —-rrj— is also called the absorption cooling coefficient). In a pulsed neutron measurement with a moderator assembly of finite size and with non-l/v absorption present the decay constant will be given by combination of all the terms in Eqs. (1) and (2), but now the leakage parameters in Eq. (1 ) are functions of the concentration N and the absorption parameters in Eq. (Z) are functions of the geometri- 2 cal buckling B . Measurements to determine these parameters have been made by Santandrea [l ], Verdaguer [2,3], Meadows and Whalen [4] and Friedman [5, 6]. The values obtained have been given with poor accuracy and of the order of two to five times higher than those given by calculations, based on current models of neutron scattering in water. Calame [7] made an extensive numerical study of the effect and com­ pared his result with experimental results, which led to the conclusion that the experimental results are wrong. Beckurts [8] pointed out that the effect is of principal interest and that efforts ought to be made to resolve the discrepancy. Several factors may contribute to the difficulties in obtaining reliable results in the experiments. It is necessary to wait for a long time after the injection of the fast neutron pulse before the fundamental spatial mode has been established, otherwise Eq. (1) will not be valid. During the waiting time, a great loss of neutrons will occur, resulting in a poor statistical accuracy in the determination of the decay constant. The great number of parameters and specially the intricate coupling between the leakage and the absorption parameters in the combination of Eqs. (1 ) and (2) result in large errors when the parameters are evaluated all at a time from the measurement. Larsson, Möller and Purohit [9] showed how studies of neutron moderation in hydrogeneous media by the time dependent reaction rate method may be performed under conditions which, in the time region from injection to complete thermalization, yield results representative of the case of an infinite medium. This time interval can be expanded to an interval just after the thermalization period, when neutron leakage can still be considered negligible. Using the experimental method pre- _ d-^eff sented in [7 J for the measurement of ,...— , it would be possible to get results which may be analysed on the basis of Eq. (2) only, thus avoiding the above mentioned problems. - 5 - 2. PRINCIPLES OF THE EXPERIMENT The decay of neutrons in a moderator may be followed by the de­ tection and time analysis of gamma radiation from neutron capture in the moderator atoms and in dissolved absorbers. Under certain condi­ tions a gamma detector situated outside a moderator assembly of finite size can be used to record a reaction rate which is representative of the infinite medium. The following requirements should be fulfilled: 1 ) The neutron pulse shall be produced at the center of the moderator vessel and the source shall be isotropic. 2) The energy of the neutrons from the source shall be so low that the number of neutrons reaching the moderator boundary during the slowing down period, is negligible. 3) The sensitivity of the detector shall be such that the same weight is given to all radii in the spatial integration of the gamma radiation from the reaction rate which is performed by the detector. 4) The measure­ ments shall cover only a time period after the neutron pulse injection, during which the leakage is negligible. This means that one should not wait for the establishment of the fundamental mode but perform the decay constant measurement during a short period after the completion of the neutron thermalization. This short period of course, makes the method suitable for measuring decay constants of the order of the in­ verse of the time of measurement. Calculations performed in [9] showed that a detector for gamma radiation placed outside a finite moderator vessel will not immediately satisfy condition 3) above. The efficiency of an available detector could, however, in a chosen geometry be modified by means of a lead collima­ tor to become independent of radius within a few per cent. The suitable conditions were found by trial and error adjustments of the collimator and corresponding measurements of the efficiency for the 2. 6 MeV gam­ ma radiation from a RdTh source, which was rotated on a number of radii. The remaining radial efficiency dependence will in practice be further reduced since the spatial distribution of neutrons will make the contribution to the recorded reaction rate from large radii in the spatial integration relatively small. - 6 - The method of neutron flux measurement used by Pönitz and Wattecamps [l 0] is based on the same principle with the additional requirement that the leakage can be neglected during the whole life time of the neutrons in the system. In their geometry, which is simi­ lar to ours, the calculated detection efficiency for capture of neutrons in a manganese sulphate bath is constant within 0. 8 per cent in the energy region 1 0 keV - 1 MeV. This is also an indication that decay constant measurements may be performed under infinite medium con­ ditions . The experimental set-up is shown in Fig. 1 . The water container, which is approximately cylindrical with a diameter of 36 cm, height 32 cm and a volume of about 32 liters, is surrounded with a neutron shield of boron loaded plastic. Neutrons are produced at the center, where a pulsed beam of 3 MeV protons hits a thick beryllium target. The choice of this target and accelerator energy results in a very low number of neutrons in the outer region of the assembly, as can be seen in the measurements by Foster [1 1 ] of the spatial distribution of ther- malized neutrons from a 1 MeV neutron source in water. The gamma ray detector is a plastic scintillator with a diameter of 5 cm and a length of 20 cm, connected to a photomultiplier by means of a light pipe.