Subcritical Multiplication and Spontaneous Fission in Uranium
Posted: Fri Nov 18, 2005 12:52 am
I have been working on some experiments whose principal relevance is to obtain measurable subcritical multiplication in uraniferous samples using a large He-3 detector and a small AmBe neutron source as a "driver". The concept is simple (neutron source is near a detector; induced fissions in a uranium sample placed near the source will increase the neutron population in the detector), but in practice this is a tricky measurement and I conclude from the preliminary data (following) that my method would take days of measuring time to get a statistically-significant "positive" for neutron multiplication. However, another interesting finding is that spontaneous fission neutrons from U-238 are easy to measure with the He-3 tube. I'll leave some suggestions for another post about how to improve the technique to better detect induced fission, since this post will be ungodly long for the sake of completeness.
The setup: See two images at bottom. A six-sided moderating reflector is composed of about 120 lb of Astorlite J-300 wax composite (has some vegetable oil mixed with paraffin). This stuff is much easier to cut into bricks than straight paraffin and that's why I used it, but on the downside it is softer and stickier. He-3 tube runs though center. The neutron source (~ 1 mCi AmBe) is rigidly held in graphite blocks at the right of tube. Other side of tube has an empty cavity for uranium samples. The uranium sample used comprised all of the following, in separate plastic bottles:
-26 g. DU metal plate
-4 g. DU metal plate
-20 g. DU3O8
(Total of 47 g uranium)
I could have used pieces of the large quantity of uranium ores on hand, some of which do have 85% non-depleted uranium by weight. I may yet try that, but I think there are large concentrations of neutron absorbers in most of this stuff (cadmium, cobalt, boron, rare earths). Having a few hundred ppm of these in the mix will totally trash a neutron experiment, whereas the loss of 3/4 of the U-235 in pure depleted U is comparably a minor reduction in fission neutron economy. One item that warrants explanation is the large quantity of wax: people might think they could get by with less, but we have to realize that the source and the sample will in reality add some moderating and reflecting capability. The goal of the large wax enclosure is to approach maximum possible reflectivity BEFORE anything else is added next to the tube, so that the reflection from those items is not going to be a significant contribution.
The method: Tube pulses were shaped and amplified (3 us, Ortec 571) and sent to Tracor-Northern MCS. An external timer (Tennelec 536) was used to drive the MCS dwell advance every 3 minutes. The neutron detector signal was aggressively windowed to discriminate against noise, gammas, and whatnot: the LLD was right below the 570 keV "step" in the absorbed-energy spectrum, and the ULD was right above the tail for the full energy peak. The order of the measurements is important because it helps add control to the experiment. In this order, the source and the uranium only need to be physically positioned in the apparatus once to get all the data. Neutron contributions are identified as those from the source (S), background (B), spontaneous fission of U-238 (SF), and induced fission mainly of U-235 (IF). The count results shown below are averages and standard deviations per three minute interval. Different numbers of samples were used for different experiments.
1. Empty sample chamber, source in (measure S + B). Result: 1057.2 +/- 2.3
2. Uranium in sample chamber, source in (measure IF + SF + S + B). Result: 1066.1 +/- 2.1
3. Uranium in sample chamber, source out (measure SF + B). Result: 19.6 +/- 0.24
4. Empty sample chamber, source out (measure B). Result: 13.80 +/- 0.31
5. 5 uCi Ra-226 ionotron strip against tube, source out (test gamma sensitivity G). Result: 13.87 +/- 0.17
The analysis and results: To isolate the IF component, the counts from Measurement 4 are first subtracted from Measurement 1 to isolate (S), taking care of course to propagate the uncertainties from the raw data through the subtraction; Measurement 3 is subtracted from Measurement 2 to isolate (IF + S); (IF + S) is compared to (SF) using MS Excel's t-test tool (with the null hypothesis being that <S> = <IF + S>) and the probability of a difference in these means due to chance alone is determined. It was noticed then that <SF + B> looked significantly larger than <B> and the t-test between the two was used to find the approximate probability of that difference being due to chance. (It turns out to be miniscule.) Lastly, we do the t-test between Measurement 5 and Measurement 4. The null hypothesis is accepted here, since there is a very large probability (>78%) that these measurements are not different from one another.
Subcricital multiplication:
S = 1043.4 +/- 2.3
IF + S = 1046.5 +/- 2.1
From Excel:
t Stat 0.994998
P(T<=t) one-tail 0.160149
P(T<=t) two-tail 0.320298
Spontaneous fission:
SF + B = 19.6 +/- 0.24
B = 13.80 +/- 0.31
From Excel:
t Stat 15.23779
P(T<=t) one-tail 6.73E-41
P(T<=t) two-tail 1.35E-40
Gamma rejection:
G = 13.87 +/- 0.17
B = 13.80 +/- 0.31
From Excel:
t Stat 0.27627
P(T<=t) one-tail 0.391292
P(T<=t) two-tail 0.782584
Conclusion: You'll notice that while <IF + S> is indeed larger than <S>, it is only by about 3 counts per interval. Maybe this is due to induced fission, and maybe it is just due to statistical chance. You can consider either the one-sided or two-sided probability of the measurements being not different, but either way they're rather large (16% or 32%). This is high enough that I can't say with much certainty that the difference is due to subcritical multiplication. The remedy to clear this up would be many more sample intervals. As it was, the combined measurement had 454 3-minute intervals, so it was already almost a day long. ON THE OTHER HAND, there is almost absolute certainty that <SF + B> and <B> are statistically different, giving a very strong case for spontaneous fission being measured to the tune of 2 extra counts per minute. Literature reports that U-238 gives about 0.011 n / g / s through SF, or about 30 n / minute for my sample, so the absolute detection efficiency is probably somewhere in the range of 1/15. That ain't bad for fast fission neuts. Lastly, the gamma rejection is very good. The radium source used is a much stronger beta/gamma source than the non-equilibrium uranium materials (even though the latter represents a higher total activity, ~25 uCi.). And yet there is a 78% likelihood that <G + B> is no different than <B>. If there ARE any extra counts physically associated with the radium source, my guess is that it is actual neutrons from O(a,n) in the air near it; Al(a,n) on the tube wall; or the like.
The setup: See two images at bottom. A six-sided moderating reflector is composed of about 120 lb of Astorlite J-300 wax composite (has some vegetable oil mixed with paraffin). This stuff is much easier to cut into bricks than straight paraffin and that's why I used it, but on the downside it is softer and stickier. He-3 tube runs though center. The neutron source (~ 1 mCi AmBe) is rigidly held in graphite blocks at the right of tube. Other side of tube has an empty cavity for uranium samples. The uranium sample used comprised all of the following, in separate plastic bottles:
-26 g. DU metal plate
-4 g. DU metal plate
-20 g. DU3O8
(Total of 47 g uranium)
I could have used pieces of the large quantity of uranium ores on hand, some of which do have 85% non-depleted uranium by weight. I may yet try that, but I think there are large concentrations of neutron absorbers in most of this stuff (cadmium, cobalt, boron, rare earths). Having a few hundred ppm of these in the mix will totally trash a neutron experiment, whereas the loss of 3/4 of the U-235 in pure depleted U is comparably a minor reduction in fission neutron economy. One item that warrants explanation is the large quantity of wax: people might think they could get by with less, but we have to realize that the source and the sample will in reality add some moderating and reflecting capability. The goal of the large wax enclosure is to approach maximum possible reflectivity BEFORE anything else is added next to the tube, so that the reflection from those items is not going to be a significant contribution.
The method: Tube pulses were shaped and amplified (3 us, Ortec 571) and sent to Tracor-Northern MCS. An external timer (Tennelec 536) was used to drive the MCS dwell advance every 3 minutes. The neutron detector signal was aggressively windowed to discriminate against noise, gammas, and whatnot: the LLD was right below the 570 keV "step" in the absorbed-energy spectrum, and the ULD was right above the tail for the full energy peak. The order of the measurements is important because it helps add control to the experiment. In this order, the source and the uranium only need to be physically positioned in the apparatus once to get all the data. Neutron contributions are identified as those from the source (S), background (B), spontaneous fission of U-238 (SF), and induced fission mainly of U-235 (IF). The count results shown below are averages and standard deviations per three minute interval. Different numbers of samples were used for different experiments.
1. Empty sample chamber, source in (measure S + B). Result: 1057.2 +/- 2.3
2. Uranium in sample chamber, source in (measure IF + SF + S + B). Result: 1066.1 +/- 2.1
3. Uranium in sample chamber, source out (measure SF + B). Result: 19.6 +/- 0.24
4. Empty sample chamber, source out (measure B). Result: 13.80 +/- 0.31
5. 5 uCi Ra-226 ionotron strip against tube, source out (test gamma sensitivity G). Result: 13.87 +/- 0.17
The analysis and results: To isolate the IF component, the counts from Measurement 4 are first subtracted from Measurement 1 to isolate (S), taking care of course to propagate the uncertainties from the raw data through the subtraction; Measurement 3 is subtracted from Measurement 2 to isolate (IF + S); (IF + S) is compared to (SF) using MS Excel's t-test tool (with the null hypothesis being that <S> = <IF + S>) and the probability of a difference in these means due to chance alone is determined. It was noticed then that <SF + B> looked significantly larger than <B> and the t-test between the two was used to find the approximate probability of that difference being due to chance. (It turns out to be miniscule.) Lastly, we do the t-test between Measurement 5 and Measurement 4. The null hypothesis is accepted here, since there is a very large probability (>78%) that these measurements are not different from one another.
Subcricital multiplication:
S = 1043.4 +/- 2.3
IF + S = 1046.5 +/- 2.1
From Excel:
t Stat 0.994998
P(T<=t) one-tail 0.160149
P(T<=t) two-tail 0.320298
Spontaneous fission:
SF + B = 19.6 +/- 0.24
B = 13.80 +/- 0.31
From Excel:
t Stat 15.23779
P(T<=t) one-tail 6.73E-41
P(T<=t) two-tail 1.35E-40
Gamma rejection:
G = 13.87 +/- 0.17
B = 13.80 +/- 0.31
From Excel:
t Stat 0.27627
P(T<=t) one-tail 0.391292
P(T<=t) two-tail 0.782584
Conclusion: You'll notice that while <IF + S> is indeed larger than <S>, it is only by about 3 counts per interval. Maybe this is due to induced fission, and maybe it is just due to statistical chance. You can consider either the one-sided or two-sided probability of the measurements being not different, but either way they're rather large (16% or 32%). This is high enough that I can't say with much certainty that the difference is due to subcritical multiplication. The remedy to clear this up would be many more sample intervals. As it was, the combined measurement had 454 3-minute intervals, so it was already almost a day long. ON THE OTHER HAND, there is almost absolute certainty that <SF + B> and <B> are statistically different, giving a very strong case for spontaneous fission being measured to the tune of 2 extra counts per minute. Literature reports that U-238 gives about 0.011 n / g / s through SF, or about 30 n / minute for my sample, so the absolute detection efficiency is probably somewhere in the range of 1/15. That ain't bad for fast fission neuts. Lastly, the gamma rejection is very good. The radium source used is a much stronger beta/gamma source than the non-equilibrium uranium materials (even though the latter represents a higher total activity, ~25 uCi.). And yet there is a 78% likelihood that <G + B> is no different than <B>. If there ARE any extra counts physically associated with the radium source, my guess is that it is actual neutrons from O(a,n) in the air near it; Al(a,n) on the tube wall; or the like.