J. Nuclear Enqy I. 1957, Vol. 4. pp. 38 to 43. Pergsmon Press Ltd., London

THE CROSS-SECTION FOII: lj238 l?ISSION BY FISSION NEUTRONS*

R. B. LEACHMAN and H. W. SCHMITTt Los Alamos Scientific Laboratory, Los Alamos, New Mexico

(Received 18 May 1956)

AbstracGThe cross-section for U aa8 fission by neutrons from the thermal-neutron-induced fission of UeS6 has been measured to be (0.756 f O.~S)/V barn, where v is the average number of neutions emitted per U 886 fission. Used with the most recent value of v for IPa, v = 2.46 h 0.03, this gives 0.307 f 0.005 barn for the Uase fission cross-section.

INTRODUCTION -

ASIDE from its importance in neutron calculations of critical assemblies, an accurate determination of the cross-section for U 238 fission by fission neutrons provides a test of the combined accuracy of the measurements of the fission neutron spectrum’ and of the IP8 fission cross-section a(E,J as a function of neutron energy E,,. This test is provided by the relation

(0

where P(E,) is the fission neutron spect*m, here considered to be normalized to unity, and 5 is the cross-section for U23s fission by fission neutrons.

To obtain an accurate 5 measurement, a method was used requiring no neutron detection, but only fission detection and a knowledge of Y, the average number of neutrons from fission. Since Y for thermal-neutron-induced fission of U235 is known with high accuracy, 5 can be determined with an accuracy better than that of the current measurements of either a(E,) or P(E,).

METHOD

In the present measurement of 6, the neutrons from an observed number of U235 fissions induced an observed number of U23* fissions in a well-defined neutron geometry. Absolute determinations of the number of fissions in the U235 and U23s were usually made by fission pulse counting in ionization chambers. To fulfil the requirement of a well-defined geometry for the fission neutrons and yet to use a large fraction of these neutrons, a hemispherical geometry of U238 around the U2% source was used.

In Fig. 1 are shown some of the details of the double ionization chamber used for this purpose. Its mounting on the Los Alamos Homogeneous Reactor is shown by the cutaway drawing of Fig. 2. A thermal-neutron flux of ~3(10’) neutrons/cm2/sec from the reactor induced fission in the U235 disc seen at the centre of the hemispheres

* Work performed under the auspices of the U.S. Atomic Energy Commission. 7 Now at Oak Ridge National Laboratory, Oak Ridge, Tennessee.

38

The cross-section for UBs8 fission by fission neutrons 39

in Fig. 1. The neutrons from these U 235 fissions induced fissions in the U238 coating on an aluminium hemisphere.after passing through an inner cadmium hemisphere, which was provided to stop thermal neutrons from the reactor. To minimize fissions in the U238 hemisphere by pile neutrons which have leaked through the cadmium, uranium of 105 : 1 isotopic abundance of U23s was used.

With a point source of fission neutrons at the centre of the U238 hemisphere, the number Fs3s of fissions of N2s8 atoms of U238 anywhere on the hemisphere of radius R, is related to the number F235 of U2% fissions by the equation

F238 = ‘235 N238 ii

4~ Rh2 ' (2)

STEEL CYLINDRICAL CASE COPPER HEMISPHERICAL CASE

U*” COATING ON 6” ALUMINUM HEMISPHERE

MONITOR FOIL U235 DISC SOURCE

CADMIUM SHIELD

_LECTING HEMISPHERE

CONNECTION

PARALLEL PLATE IONIZATION CHAMB

U235 DISC I i

PLATINUM FOIL U”35 MONITOR COATING

l/32” DURAL

FIG. I.-Detail of the double ionization chamber.

For the case of a U2% disc source of radius R, at the centre of a uniform deposit of Uz3* on a hemisphere, the relation can be shown to be

F238 = (3)

With R, = 7/16 inch and R, = 3 inches, the radii used for these measurements, the errorin using (3) for the extremes of a total concentration of U238 at either the hemi- sphere pole or equator can be shown to be l-4 per cent. In practice, the error was seen always to be much less than this by visual inspection of the uniformities of the U23s deposits.

40 R. B. LEACHMAN and H. W. SCHMIDT

The U238 thicknesses were about 0.16 mg/cm2, for which a calculated 0.7 per cent of the fissions have both fragments stoppedin the U 23* and thus not observed. Corrections were made for these unobserved fissions. Uncertainties in the counting of U23* fissions (F2s8) of much less than one per cent uncertainty were obtained in runs of roughly two hours duration. However, the geometry and the available thermal- neutron flux required a U235 source much thicker than the U238. To avoid uncertain- ties in the number of unobserved U 235 fissions, fissions were not directly counted in the 0401- to 0408-inch thick discs of U2% metal used. Instead, F235 was usually determined from the number of fissions F, in a U235 monitor foil of known mass and

FIG. 2.-Cutaway view of the reactor and chamber showing the experimental arrangement.

of the same diameter as the source disc. As shown in Fig. 1, this foil was placed adjacent to the source disc, and exposed to the same flux of thermal neutrons. Given the U2% mass of the monitor foil and that of the source disc, together with the number of fissions I;, occurring in the monitor foil, the number of fissions occurring in the source disc could be determined. Corrections were incorporated for self- absorption of neutrons, in the disc source.

The numbers of fissions Fm and F238 for each run were determined by standard pulse counting techniques. Cylindrical extensions of the hemispherical ionization chamber not coated with U23s prevented edge losses of Ps fissions. The chamber was filled with argon. Scalars and pulse amplifiers of standard Los Alamos design were used. Corrections of less than one per cent were made for the 1-psec dead time

The cross-section for TP* fission by fission neutrons 41

of the scalars when thick monitor foils resulted in high fission rates. From the pulse counting, determinations of F, and Fss5 were possible to better than one per cent accuracy by the usual method of plateau curves (ROSSI and STAUB, 1949).

The neutron absorption factor which was applied to determine Fss5 from F, was determined from separate measurements in a double “back-to-back” ionization chamber with thin deposits of U235 on platinum sandwiching the disc being measured. Comparisons of the foil fissions for the two cases of the thermal-neutron beam incident on one monitor foil and then the other eliminated the need for knowledge of the foil masses in these measurements.

Thermal-neutron scattering in the l/32-inch dural plate between the U235 monitor and disc (see Fig. 1) resulted in a calculated flux O-8 per cent larger in the monitor than incident on the disc. This correction is included in the results.

A background of U 235 fissions was present due to gamma rays from both the reactor and neutron capture and also due to fast neutrons from the reactor. This background was measured in runs with the U 235 disc source removed. Since the attenuation of the thermal neutron flux by the disc might affect this background, background tests were made with aluminium-boron of the same thermal-neutron opacity replacing the disc. In the same manner, the background effect of the fission gamma rays from the disc was tested by replacing it with a gold disc. Both texts showed these effects to be less than one per cent of the background.

MASS DETERMINATIONS

The greatest difficulty in obtaining a 3 measurement of accuracy comparable to that of Y was fund in the mass determinations, i.e., the quantities N238 and F235, where F235 is obtained from N,, the number of U235 atoms in the monitor foil. The quantity N335 was easily determined by weighing. The O-OS- to 171- ,ug quantities used for various U235 monitor foils and the 50- to 65- mg quantities of U23s on the various hemispheres used were determined by several different methods.

The deposits of U238 were made by painting U23802(N03)2(6H20) in an alcohol solution and then oven heating to convert the nitrate to U323808. Since the hemispheres were of thin aluminium, the temperature required for complete conversion of the nitrate to oxide could not be used. Thus, hemisphere weights were used only as a rough indication of N238. However, accurate determinations were made by alpha counting and, at the end of the measurements, by calorimetric analyses of the U238 masses. In the alpha counting, the usual corrections for finite thickness of the source and scattering of alpha particles from the backing (CRAWFORD, 1949) were made. The N238 determinations by alpha counting* in general agreed within one per cent with the calorimetric analyses.

The smaller area of the monitor foil, and thus the smaller mass of U235, made determinations of N, with such accuracy more difficult. The heavier three of the six monitor foils consisted of 75 to 171 ,ug of U235 and, for each of these, N235 was determined by both weighing and calorimetry as discussed above. The 0.08 to

* For the alpha-particle measurements, the half-life of Uz3s samples deposited on platinum.

was determined by 2n counting of US38

used on the hemispheres; The Uzs8 deposits were of approximately the same thicknesses as those

was possible. These Uz3* since the backing was platinum, however, complete conversion to the oxide

masses could then be determined both by weight and by calorimetric analysis. The Uz3* half-life was determined to be 4.56 * 003(10’) years, in agreement with the results of FLEMNG et al. (1952), but in disagreement with the result of KIENBERGER (1949).

3A--(4 pp.)

42 R. B. LEACHMAN and H. W. Sm

I.2 rug of U% of the lighter three made possible comparison fission counting of each of these foils directly against well known standards of V5. These measurements were made in the thermal column of the Los Alamos Homogeneous Reactor in a “back-to-back” double ionization chamber of well calibrated characteristics.

As still another determination of F 235, quantitative analyses of the Moss fission products were made on three of the U 235 disc sources. Calibrations of this method have indicated an accuracy of better than five per cent.

In all, eight different combinations of monitor foils, source discs, and Uz3* hemi- spheres were used in the various determinations of (7. Since the greatest uncertainty in the measurements was the value of Fzs5, the internal consistency of the S results provided a means of identifying the gross error (considered here as an error greater than eight per cent) in differing Fsa6 determinations. For each 3 measurement, usually two or three different measurements discussed above were made of Fzs5. Even though great care was taken in all measurements, these tests showed a gross error in one of the three weight determinations, one of the three calorimetric deter- minations, and in one of the three MoQ9 analysis, but in none of the three comparison counting determinations. These failures are cited not as an indication of the reli- ability of each method, but to demonstrate the practical difficulties of determining to about one per cent the number of fissions in a thick source.

NEUTRON SCATTERING In the derivation of eq. (3), only unscattered neutrons from fissions in the disc

source are considered. However, fission neutrons scattered from the various hemi- spheres and from the reactor face induce an appreciable number of U238 fissions in addition. Detailed calculations of these corrections have been made by LEACHMAN and SCHMITT (1953).

Neutrons scattered from the hemispheres at angles near 7r/2 can undergo relatively long transits through the U238 and thus have a larger probability of inducing fission. Calculated corrections of O-5 per cent, 0.2 per cent, and I.9 per cent due to scattering from the copper case, aluminium collecting, and cadmium shield hemispheres, res- pectively, were included in the results. A measurement of the increase of the Uess fission rate with a doubling of the copper-case thickness confirms the first of these calculations. Seven of the eight measurements of 3 were with 0.022~inch aluminium hemispheres for the U238 and a calculated 2.3 per cent correction was made for neutron scattering from these. Since this was the largest correction in the measurement, an additional ci measurement was made with a O-038-inch hemisphere. This 3 measure- ment with its calculated 4-O per cent correction agreed with the other measurements and this qualitatively confirmed these scattering calculations.

Albedo calculations indicated that O-7 per cent of the Pas fissions were by fission neutrons scattered from the reactor face. This correction was included in the results. Similar considerations show the effect of floor scatterings and other scatterings to be negligible in comparison.

RESULTS In the measurements of 3, the largest uncertainty was in the determination of

F 235’ To take this into account in finding the mean value of 3, each of the measure- ments of I? was weighted by the one half power of the number of separate deter- minations of Fs35 made, whether directly by Mog9 analysis or indirectly by N,

The cross-section for U238 fission by fission neutrons 43

determinations. The mean value of ii thus obtained is d = (O-756 & 0*008)/~ barn, where the uncertainty is the standard deviation of the mean of the measurements and does not include uncertainties in the neutron scattering calculations, in the calculations of the unobserved U a38 fissions, or in the method of background measure- ment. These uncertainties, however, do not contribute appreciably to the overall uncertainty given above.

With the most recent value v = 2.46 f O-03 reported by HARVEY and HUGHES (1955), a value of ii = 0.307 f O-005 barn is obtained. This compares. favourably with the value 5 = 0.31 calculated from eq. (1) using the 8(&) measurements of HENKEL and JARVIS, which were reported by HARVEY and HUGHES (1955), and the P(E,) relation given by WATT (1952).

Acknowledgements-The authors wish to thank G. W. KNOBLOCH for assistance in the comparison fission counting, A. L. HENICKSMAN for calorimetric determinations, J. P. BALAGNA JR. for the Mogg analyses, D. H. SCHELL for assistance in the weight determinations, and J. G. POVELITES for preparing the uranium deposits.

REFERENCES

CRAWFORD J. A. (1949) The Transuranium Elements: Research Papers (McGraw-Hill Book Company, Inc., New York), Paper No. 16.55, National Nuclear Energy Series, Plutonium Project Record, Division IV, Volume 14B.

FLEMING, GHIORSO, and CUNNINGHAM (1952) The specific alpha-activities and half-lives of Uas4, Uzs6, and UBs8. Phys. Rev. 88, 642.

HUGH= D. J. and HARVEY J. A. (1955) Neutron cross sections, BNL-325, Superintendent of Docu- ments, U.S. Government Printing Office, Washington, D.C.

KIENBERGER C. A. (1949) The uranium-234 content of national uranium and the specific alpha- activities of the isotopes. Phys. Rev. 76, 1561.

LEACHMAN R. B. and SCHMITT H. W. (1953) Average fission cross section of Uaaa for fission neutrons, LA-1624, Technical Information Service, P.O. Box 1001, Oak Ridge, Tennessee.

ROSSI B. B. and STAUB H. H. (1949) Ionization Chambers and Counters, McGraw-Hill Book Com- pany, Inc., New York.

WATT B. E. (1952) Energy spectrum of neutrons from thermal fission of U235. Phys. Rev. 87,1037.