# Difference in multiplication factor **URL:** \ **Category:** Validation and Verification\ **Created:** [February 8, 2023, 11:37am UTC](https://openmc.discourse.group/t/difference-in-multiplication-factor/2701 "2023-02-08T11:37:42Z")\ **Posts on this page:** 2\ **Page:** 1
**Author:** ![Denis\_Solovyev](https://avatars.discourse-cdn.com/v4/letter/d/47e85d/32.png) [@Denis\_Solovyev](https://openmc.discourse.group/u/Denis_Solovyev)\ **Post date:** [February 8, 2023, 11:37am UTC](https://openmc.discourse.group/t/difference-in-multiplication-factor/2701/1 "2023-02-08T11:37:42Z")
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! ---
**Author:** ![Denis](https://avatars.discourse-cdn.com/v4/letter/d/5e9695/32.png) [@Denis](https://openmc.discourse.group/u/Denis)\ **Post date:** [May 9, 2025, 2:47pm UTC](https://openmc.discourse.group/t/difference-in-multiplication-factor/2701/2 "2025-05-09T14:47:40Z")
Hi Denis\_Solovyev, This is a good question. We face the same problem with the multigroup cross sections generated with OpenMC for the model with reflective boundary conditions. The Kinf calculated with the multigroup cross sections is different from the Kinf calculated by OpenMC (the difference can be up to 300 pcm). I thought initially that taking into account the upscattering cross section (scattering from thermal to fast group) could improve the situation, but it makes the results even worse. Assuming zero upscattering reduces the discrepancy up to 100 - 150 pcm. I also found that using ‘consistent nu-scatter matrix’ also improves the results a bit. I am not sure what the reason is for such results produced by OpenMC, although I haven’t spent a lot of time investigating this issue. I am planning to repeat the procedure with Dragon and/or Serpent codes and see what the discrepancies will be in Kinf with the cross sections generated by these codes.