# Difference in multiplication factor

Hello.
We are preparing two group neutron cross sections for VVER fuel assembly.
Then we compare k_inf computed by OpenMC and k_inf_xs calculated using the prepared by OpenMC two group neutron cross sections as follows:

R_inf = S12/Sa2
k_inf_xs = (nuSf1 + nuSf2*R_inf)/(S12+Sa1)

where the notations are clear.

Between two k_inf we have difference (delta_k_inf) about 0.1%
( delta_k_inf = 100*(k_inf_xs - k_inf)/k_inf_computed ).
The difference does not depends on statistics.
We can not understand why do we have such difference (0.1 %).
We expected to see a difference of about 0.01%

Below we demonstrate our results as the function of coolant density:

coolant density(g/cm3) k_inf_xs k_inf delta_k_inf
0.200 0.9416 0.9420 -0.046
0.224 0.9691 0.9702 -0.104
0.248 0.9927 0.9934 -0.072
0.272 1.0136 1.0144 -0.079
0.296 1.0318 1.0329 -0.111
0.320 1.0478 1.0489 -0.096
0.344 1.0620 1.0628 -0.070
0.368 1.0744 1.0754 -0.099
0.392 1.0853 1.0864 -0.099
0.416 1.0950 1.0961 -0.106
0.440 1.1030 1.1040 -0.088
0.464 1.1104 1.1113 -0.083
0.488 1.1166 1.1175 -0.079
0.512 1.1224 1.1233 -0.079
0.536 1.1269 1.1280 -0.092
0.560 1.1311 1.1323 -0.106
0.584 1.1346 1.1357 -0.095
0.608 1.1376 1.1390 -0.114
0.632 1.1401 1.1415 -0.119
0.656 1.1419 1.1430 -0.091
0.680 1.1434 1.1447 -0.110
0.704 1.1447 1.1457 -0.088
0.728 1.1453 1.1461 -0.071
0.752 1.1457 1.1472 -0.135
0.776 1.1460 1.1470 -0.083
0.800 1.1458 1.1472 -0.124
0.824 1.1455 1.1465 -0.081
0.848 1.1447 1.1458 -0.095
0.872 1.1438 1.1447 -0.075
0.896 1.1428 1.1436 -0.070
0.920 1.1416 1.1429 -0.114
0.944 1.1401 1.1410 -0.079
0.968 1.1386 1.1398 -0.098
0.992 1.1369 1.1382 -0.112

We will be grateful for any explanation of such differences.
Thank you in advance!