Abstract
Calculated critical masses of bare metal spheres for 28 actinide isotopes, using the SCALE/XSDRNPM one-dimensional, discrete-ordinates system, are presented. ENDF/B-VI, ENDF/B-VII, and JENDL-3.3 cross sections were used in the calculations. Results are given for isotopes of uranium, neptunium, plutonium, americium, curium, californium, and for one isotope of einsteinium. Calculated k�� values for these same nuclides are also given. We show that, for non-threshold or low-threshold fission nuclides, a good approximation for the nuclide k�� is the value of nubar at 1 MeV.
A plot of the critical mass versus k�� values is given for 19 nuclides with A-numbers between 232 and 250. The peaks in the critical mass curve (for seven nuclides) correspond to dips in the k�� curve. For the seven cases with the largest critical mass, six are even-even nuclides. Neptunium-237, with a critical mass of about 62.7 kg (ENDF/B-VI calculation), has an odd number of protons and an even number of neutrons. However, two cases with quite small critical masses, 232U and 236Pu, are also even-even. These two nuclides do not exhibit threshold fission behavior like most other even-even nuclides. The largest critical mass is 208.8 kg for 243Am and the smallest is 2.44 kg for 251Cf. The calculated k�� values vary from 1.5022 for 234U to 4.4767 for 251Cf.
A correlation between the calculated critical mass (kg) and the fission spectrum averaged value of is given for the elements U, Np, Pu, Am, Cm, and Cf. For each of the five elements, a fit to the data for that element is provided. In each case the fit employs a negative exponential of the form
mass = exp(A + B �~ ln( )
The values of A and B are element dependent and vary slightly for each of the five elements. The method described here is mainly applicable for non-threshold fission nuclides (15 of the 28 nuclides considered in this paper). There are three exceptions, 238Pu, 244Cm, and 250Cf, which all exhibit threshold fission behavior.