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As part of the standards effort of the American Nuclear Society to establish subcritical mass limits for actinide nuclides other than ^{233}U, ^{235}U, and ^{239}Pu, updated critical mass estimates are first being calculated for various actinide nuclides. This paper describes updated critical mass estimates for ^{238}Pu using several combinations of computer codes and nuclear data sets. A brief description of the analytical methods employed is followed by a presentation of the results.
ANSI/ANS8.151981, "Nuclear Criticality Control of Special Actinide Elements" is in the process of being revised. For the purpose of this standard, special actinides refer to neutronfissionable actinides other than the nuclides ^{233}U, ^{235}U, and ^{239}Pu. These actinide nuclides are typically created by neutroninduced transmutation during the irradiation of nuclear fuels. Several of these nuclides exist in sufficient quantities to be used in nuclear medicine, heat sources, neutron sources, and recycled nuclear fuels. Thus, subcritical limits must be established for the safe handling and use of these nuclides.
One of the nuclides of interest for the update of ANSI/ANS8.151981 is ^{238}Pu. The relatively sparse experimental data which exists on the measured reactivity coefficient of ^{238}Pu relative to ^{239}Pu has been generated by primarily by Stubbins, et. al. [1] and, to a lesser degree, by Byers, et. al. [2] The high heat output (0.557 watts/g) of ^{238}Pu makes experiments difficult to perform. Therefore, the majority of ^{238}Pu critical mass estimates are based on the analysis of hypothetical systems using various computer codes and nuclear data sets. Data from hypothetical studies by Clark [3] and Westfall [4] served as the basis for the ^{238}Pu subcritical limits originally developed for ANSI/ANS8.151981. Since then, improvements have been made to nuclear data sets, more data sets are available, and more computer codes are currently in use as well.
The primary purpose of the present paper is to describe an updated analysis of hypothetical ^{238}Pu critical systems for use in the revision of ANSI/ANS8.151981. However, a few other calculations of interest related to ^{238}Pu are included as well. The scope includes:
The international nuclear community also appears to be interested in the development of a standard dealing with special actinide nuclides. Therefore, the secondary purpose of this paper is to include a representative combination of available computer codes and nuclear data sets such that the results can be of use in the development of an international standard.
Critical core radii searches were performed with the following codes and nuclear data sets:
SCALE4.3; KENOVa with ENDF/BV, 238 group cross sections [5];
MCNP4b with ENDF/BV continuous cross sections [6];
MCNP4b with ENDF/BVI continuous cross sections [6] ;
MCNP4b with JENDL3.2 continuous cross sections [7];
MONK7B with UKNDL 8220 group cross sections [8,9];
MONK7B with JEF2.2 13193 group cross sections [8,10];
DANTSYS 3.0 with ENDF/BV 238 group cross sections [11].
For the monte carlo codes (KENOVa, MCNP4b, MONK7B), critical radii search results were considered acceptable if the calculated K_{eff} = 1.0 +/ one standard deviation (< 0.003 when using 100,000 neutron histories). The calculated critical radii and material densities were then used to obtain critical mass estimates. For the DANTSYS 3.0 discrete ordinates transport code, all critical radii searches used S_{16} quadrature, P_{3} scattering, and a convergence criterion of 0.001, or less.
Other data of interest are as follows: a 30 cm. thickness was used for all reflectors: ^{238}Pu metal density was adjusted relative to 19.84g/cm^{3} for plutonium containing 95 % ^{239}Pu and 5% ^{240}Pu; ^{238}Pu oxide density was adjusted similarly relative to 11.46 g/cm^{3}.
The computer code and data set combinations were validated against the experimental data of Stubbins, et. al. These experimental data show that the ratio of the reactivity worth of ^{238}Pu/^{239}Pu for bare metal was 0.99 +/ 0.09 (subcritical measurements) and 1.02 +/ 0.09 (critical measurements). A code and data set combination was considered acceptable if the ^{238}Pu/^{239}Pu calculated critical mass ratio for bare metal ranged between 0.9 (i.e., 0.99  0.09) to 1.11 (i.e., 1.02 + 0.09). Table 1 presents the calculated bare critical mass of ^{238}Pu, ^{239}Pu, and the ^{238}Pu/^{239}Pu critical mass ratio. All code and data set combinations met the validation criterion.
Table I. Code and Data Set Validation

^{238}Pu 
^{239}Pu 
^{238}Pu/^{239}Pu 
SCALE4.3; KENOVa; ENDF/BV, 238 gr. 
9.66 
10.06 
0.960 
MCNP4b; ENDF/BV cont. 
10.06 
9.78 
1.029 
MCNP4b; ENDF/BVI cont. 
10.07 
10.00 
1.007 
MCNP4b; JENDL3.2 cont. 
8.16 
8.09 
1.009 
MONK7B; UKNDL 8220 gr. 
10.31 
9.48 
1.088 
MONK7B; JEF2.2 13193 gr. 
9.04 
10.02 
0.902 
DANTSYS 3.0, ENDF/BV 238 gr. 
9.61 
10.10 
0.951 
Calculated critical masses for ^{238}Pu metal and dry oxide systems, bare and reflected in each case, are given in Table II and III, respectively. ^{238}Pu is dependent on fast neutrons for criticality. Of the three reflectors chosen for study, 304 stainless steel has the greatest reflector worth, reducing critical mass by 47  50% of the values for the unreflected metal system and by 50  57% of the critical values for the unreflected oxide system. Carbon steel has somewhat less reflector worth than 304 stainless steel. A water reflector has the least reflector worth and only reduces the critical mass by approximately 17  24% compared to the unreflected values for either the metal or oxide system. Table II also includes the earlier Clark [3] and Westfall [4] results for the purpose of comparison.
Table II. Calculated Critical Masses for ^{238}Pu Metal Systems

Bare 
Water 
304 Stainless Steel^{a }Reflected (kg) 
Carbon Steel^{b }Reflected (kg) 
SCALE4.3; KENOVa; ENDF/BV, 238 gr. 
9.66 
7.43 
4.93 
5.42 
MCNP4b; ENDF/BV cont. 
10.06 
7.84 
5.10 
5.44 
MCNP4b; ENDF/BVI cont. 
10.07 
8.10 
5.16 
5.56 
MCNP4b; JENDL3.2 cont. 
8.16 
6.66 
4.54 
4.80 
MONK7B; UKNDL 8220 gr. 
10.31 
8.11 
5.50 
5.87 
MONK7B; JEF2.2 13193 gr. 
9.04 
7.29 
4.72 
5.10 
DANTSYS 3.0; ENDF/BV 238 gr. 
9.61 
7.43 
4.78 
5.10 
Clark 
7.45 
 
 
 
Westfall 
7.1 
6.1 
4.2 
 
^{a}Type 304 stainless steel; density = 7.9 g/cm^{3}; number densities (atoms/barncm): C = 3.16914, Cr = 1.64712, Mn = 1.73213, Fe = 6.0362, Ni = 6.48343, Si = 1.6943 as contained in the SCALE/KENOVa data library.
^{b}Carbon steel; density = 7.82 g/cm^{3;} number densities (atoms/barncm): C = 3.9213, Fe = 8.34912 as contained in the SCALE/KENOVa data library.
Table III. Calculated Critical Masses for ^{238}Pu Oxide Systems
Code/Data Set 
Bare 
Water 
304
Stainless Steel 
Carbon
Steel 
SCALE4.3; KENOVa; ENDF/BV, 238 gr. 
25.42 
19.26 
11.14 
12.50 
MCNP4b; ENDF/BV cont. 
25.19 
20.61 
12.37 
13.02 
MCNP4b; ENDF/BVI cont. 
25.68 
20.92 
12.68 
13.37 
MCNP4b; JENDL3.2 cont. 
24.97 
20.35 
12.14 
13.20 
MONK7B; UKNDL 8220 gr. 
26.44 
20.70 
12.68 
13.61 
MONK7B; JEF2.2 13193 gr. 
23.93 
19.47 
10.89 
12.12 
DANTSYS 3.0; ENDF/BV 238 gr. 
25.16 
19.31 
10.81 
11.80 
Mixtures of ^{238}Pu and ^{239}Pu are of interest in preparing heat sources. Generally, such mixtures contain approximately two thirds ^{238}Pu and onethird ^{239}Pu. The processing of this type of material typically involves the handling of both dry oxide and oxide mixed with water, with the potential for water reflection in either case. However, depending on the isotopic mix, either the dry oxide reflected by water, or a wateroxide mixture reflected by water, may result in the limiting critical mass. For ease of operations, it is useful to determine the isotopic mix for which the Pu mass and limiting value for K_{eff} of the dry oxide reflected by water is the same as that for a wateroxide mixture reflected by water. Due to uncertainties in the ^{238}Pu cross sections, Clark [3] suggested during the original preparation of ANSI/ANS8.151981 a limiting value of K_{eff} = 0.9 as adequate to ensure subcriticality. Clark calculated that a total Pu mass of 8.15 kg , with an isotopic mix containing 67 wt. % ^{238}Pu/ 33 wt. % ^{239}Pu, would result in K_{eff }=_{ }0.9_{ }for both dry Pu oxide reflected by water and a waterPu oxide mixture reflected by water. Although updated nuclear data sets are available, uncertainties in the ^{238}Pu cross sections remain and no experimental data exists for such systems. Therefore, a limiting value of K_{eff }=_{ }0.9_{ }is maintained as a suitable subcritical value for this paper. Table IV gives the calculated total Pu mass and isotopic mix, for dry Pu oxide reflected by water or for a waterPu oxide mixture reflected by water, for a limiting value of K_{eff }=_{ }0.9 for three of the code/data set combinations.
Table IV. Total Pu Mass and Isotopic Mix, as Dry Pu Oxide Reflected by Water, or an Aqueous Mixture of Pu Oxide Reflected by Water, for K_{eff }=_{ }0.9
Code/Data Set 
Total
Pu Mass 
Isotopic
Mix 
SCALE4.3; KENOVa; ENDF/BV, 238 gr. 
9.56 
68.0/32.0 
MCNP4b; ENDF/BV cont. 
9.93 
67.0/33.0 
MCNP4b; ENDF/BVI cont. 
10.13 
67.0/33.0 
The thermal neutron fission cross section is higher than the fast neutron fission cross section for ^{238}Pu. However, the corresponding capture cross section is such that the probability of fission is much higher for fast neutrons. Therefore, it is of interest to determine the minimum H/^{238}Pu ratio for ^{238}Pu metalwater mixtures for which K_{inf} = 1.0. This ratio is useful for developing a subcritical concentration limit for ^{238}Pu. Clayton and Bierman [12] previously published a value for the minimum H/^{238}Pu ratio of 3.8 for K_{inf} = 1.0 for metalwater mixtures using cross section data from the late 1960's. Table V give the minimum H/^{238}Pu ratio, and equivalent ^{238}Pu concentration, for K_{inf} = 1.0 for each of the code and data set combinations used in this paper.
Table V. H/^{238}Pu Ratio and Equivalent ^{238}Pu Concentration for K_{inf} = 1.0
Code/Data Set 
H/^{238}Pu 
^{238}Pu
Concentration 
SCALE4.3; KENOVa; ENDF/BV, 238 gr. 
4.60 
4.45 
MCNP4b; ENDF/BV cont. 
4.18 
4.79 
MCNP4b; ENDF/BVI cont. 
4.18 
4.79 
MCNP4b; JENDL3.2 cont. 
4.30S 
4.68 
MONK7B; UKNDL 8220 gr. 
8.19 
2.77 
MONK7B; JEF2.2 13193 gr. 
4.29 
4.69 
DANTSYS 3.0; ENDF/BV 238 gr. 
4.55 
4.48 
The final parameter of interest related to ^{238}Pu which was calculated as part of this paper is K_{inf} of the metal. Srinavasan, et. al.[13] have previously published K_{inf }= 2.884 for ^{238}Pu metal. Table VI gives K_{inf }for five of the code and data set combinations used in this paper.
TABLE VI. K_{inf} for ^{238}Pu Metal
Code/Data Set 
K_{inf} 
SCALE4.3; KENOVa; ENDF/BV, 238 gr. 
2.770 
MCNP4b; ENDF/BV cont. 
2.765 
MCNP4b; ENDF/BVI cont. 
2.764 
MCNP4b; JENDL3.2 cont. 
2.881 
DANTSYS 3.0; ENDF/BV 238 gr. 
2.769 
In summary, this paper has examined several systems of interest related to ^{238}Pu. Critical masses were calculated for ^{238}Pu metal and oxide (bare, water reflected, 304 stainless steel reflected, and carbon steel reflected). The subcritical limit was calculated for isotopic mixtures of ^{238}Pu and ^{239}Pu oxide, dry or optimally moderated with water. The H/^{238}Pu ratio for which K_{inf} = 1.0 and K_{inf} for ^{238}Pu metal were also calculated. The analyses have demonstrated the: