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Sun Jan 27, 2019, 12:36 AM

An extraordinarily high neutron capture cross section has been discovered in a zirconium isotope.

Last edited Tue Jan 29, 2019, 09:38 PM - Edit history (1)

The paper I'll discuss in this post is this one: The surprisingly large neutron capture cross-section of 88Zr (Jennifer A. Shusterman, et al Nature 565, 328–330 (2019) ).

(It is nice to note that 4 of the 10 authors of this paper, including the lead author, are women scientists.)

The first step I personally took in my path from being a poorly educated anti-nuke to believing - as I do now - that for the foreseeable future nuclear fission energy is the only environmentally acceptable and only sustainable form of energy there is, was when I encountered a parameter called the "neutron capture cross section" in a table of nuclides in a book that is seldom necessary to own these days (but was critical in former times), the CRC Handbook of Chemistry and Physics. I was looking at these tables because it was around the time that Chernobyl blew up, and I was trying to familiarize myself with the half-lives of some of the fission products that were in the news around that time, thinking, as proved not to be true, that these isotopes would kill hundreds of thousands of people.

If I recall correctly, the existence of this parameter, which is generally described in a parameter called "barns," immediately suggested to me at the time that it should be possible to transmute radioactive materials I then thought of as "nuclear wastes" into non-radioactive materials. I was so stupid and so ignorant that I actually thought that people were ignoring this, despite the fact that the "neutron capture cross section" and related "cross sections" such as fission, scattering, [n, 2n] etc, etc are fundamental considerations that any competent nuclear engineer must understand completely.

(The "barn" was an originally whimsical term for the apparent "target" area that an atomic nucleus represents to a neutron setting out to run into it, and probably comes from the idiom "couldn't hit the side of a barn." It's units are area, and a barn is 10^(-24) square centimeters.)

The most famous, I think, of so called "nuclear wastes" is the element cesium, in particular, the Cs-137 isotope, which has a half-life of 30.08 years It occurred to me - and it turns out fairly naively, since at the time I was as much a moron as, say, the badly educated, arrogant, and ignorant anti-nuke Harvey Wasserman - that if Cs-137 captured a neutron, as the existence of the parameter implied it could do, it would be transformed into Cs-138, which had a half-life of 33.41 minutes, decaying rapidly into the stable isotope barium-138.

This raised the question one often hears from people who think they're pretty smart but actually know nothing at all, which is "Why don't 'they' just (do x, y, or z)" as in "why don't 'they' just desalinate the ocean" (often heard in droughts) or "why don't 'they' just go solar" or "why don't 'they' just run cars on hydrogen" and so on and on...

My form was, "Why don't 'they' just have cesium-137 capture a neutron and rapidly become non-radioactive barium-137."

Now, older and wiser, I realize I should have paused to consider who "they" might be, and in consideration of this, I have been studying the work that "they" - in this case nuclear engineers and nuclear scientists - have been doing, and trust me, they have considered all the points that ignoramuses staring at the Table of Nuclides might have considered that "they" should "just" consider doing.

(Speaking of "they," this reminds me of a cute exchange I had with a dumb anti-nuke over at Daily Kos, who like many people on the left who pretend to give a shit about climate change without understanding a damned basic practical thing about the practical aspects of actually addressing it as opposed to drooling over consumer junk like Tesla cars, who arrogantly told me with a patina of schadenfreude glee , after the Fukushima event, "'They' said this could never happen!" We may take this as evidence that anti-nukes, even those who write bathos inspiring newspaper articles about historic "Navajo" (Dine) uranium miners - without considering how many human beings die every day from air pollution - seldom open a science book or a scientific paper that "they" have written. By contrast with this dumb guy, who happens to be a journalist, I read scientific papers about nuclear energy all the time, and there are many thousands of papers written about all sorts of bad things that could happen, but only do so rarely. In fact, nuclear energy is the only form of energy that was investigated for worst cases before it was constructed. We may contrast this with dangerous coal, dangerous petroleum, and dangerous natural gas, especially with respect to the latter two with “fracking,” all of which have been built without consideration of possible consequences, and indeed continue to operate without consideration of their dire observed consequences, the worst of which is climate change.

Happily for both sides, I was banned (or liberated) from Daily Kos, as I like to say, for telling the truth, and this may come under the general rubric for those familiar with Christian mythology, of "Forgive them, for they know not what they do,” – not about me, since I’m hardly even close to being Jesus – but about the unbelievable stupidity of opposing nuclear energy. Ignorance kills . It kills people since nuclear energy saves lives. This is a fact Facts matter. There is no such thing as an "alternate fact." )

Anyway, it turns out that it is not really practical to transmute cesium-137 into barium-138 in a significant way that would be worthwhile, but it really doesn't matter because it is easy (and quite possibly critical) to find uses for this wonderful isotope, more uses than those few that currently exist. Although it will always be available in limited supply, regrettably, because of a physical limitation known as the “Bateman Secular Equilibrium,” this isotope can do some pretty wonderful things connected with cleaning things up, particularly some dangerous chemical things, should we ever be serious about doing so, not that there is any evidence that we will ever be so.

The range of values for known neutron capture cross sections for the thousands of known nuclides in the Table of Nuclides goes from zero (for Helium-4) to 2,600,000 (for Xenon-135). Until the paper cited at the outset, the second highest known neutron capture cross section was 250,000 barns (for Gadolinium-157.) All of these aforementioned isotopes play a role in nuclear technology, the helium and gadolinium in some reactors, the xenon-135 is all reactors. The first, helium, has been used as a combined coolant/moderator is gas cooled reactors, the second has been used either as a “burnable poison” in fuel or in control rods. The last, xenon-135, is a radioactive fission product, generally produced as a result of the decay of iodine-135, also a fission product. It’s neutron capture cross section is so high that it is necessary to follow its accumulation – to be aware of it – and add reactivity to the core to account for it. It was first discovered with the operation of the earliest nuclear reactors utilized during the Manhattan project, and it is a credit to the genius of the early reactor designers, notably Enrico Fermi, to quickly recognize and account for its effects.

All competent nuclear engineers know all about “xenon poisoning” – the effect wherein xenon-135 can cause a reactor to shut down. It can also cause a delay in the time it takes a reactor to restart after it shuts down. Xenon-135 is usually not formed directly in nuclear fission, but is actually a decay product of another radioactive isotope which forms in the reactor, Iodine-135. This isotope has a half-life of 6.57 hours. During normal reactor operations both I-135 and Xe-135 reach secular equilibrium, the point at which they are decaying as quickly as they are formed, I-135 largely by β- decay, and Xe-135 by a combination of neutron capture, where it is transformed into the stable (and valuable) isotope Xe-136, and by β- decay – it’s half-life is about 9.2 hours - where it is transformed into the radioactive (but short lived, (13 day half-life roughly) isotope Cs-136, Cesium-136) which itself decays into stable Ba-136.

When a reactor shuts down and fission (except for spontaneous fission) stops, iodine-135 is no longer being formed, and equilibrium is no longer established, while xenon-135 is no longer being consumed by neutron poisoning. As the iodine-135 decays from its steady state concentration, the amount of xenon-135 increases, until it also decays. Because of the neutron absorption of these higher concentrations of xenon-135, the reactor cannot be restarted for several hours, again, as all competent nuclear engineers know.

This graph shows the effect:

The caption:

2: Xe-135 concentration in the reactor and neutrons reactivity. (Source: Wikimedia Commons)

Apparently incompetent nuclear engineers also know about “xenon” poisoning, and did something very stupid, after disabling all of a reactor's safety systems in order to overcome it. To wit:

The Chernobyl accident occurred in one of four RBMK1000 reactors at the Chernobyl site 100 miles north of Kiev. The operators were preparing an experiment in which the energy of rotation of the turbine during shut down should produce emergency electrical power for the support of the diesel generators. Unexpectedly the experiment had to be interrupted for some time to comply with electricity supply which led to the buildup of the fission product Xe-135 (neutron poison). When the experiment could be continued the power level dropped to about 30 MW(th) because of operator error. This led to additional buildup of Xe-135 (neutron poison). As a consequence the operators had to withdraw the control rods manually to their upper limits after they had shut off the automatic control system. The RBMK1000 was known to have a positive coolant temperature coefficient. This gave rise to instabilities in power production, coolant flow and temperatures in the low power range.

Then the experiment began at the power level of 200 MW(th). Steam to the turbine was shut off. The diesel generators started and picked up loads. The primary coolant pumps also run down. However this led to increased steam formation as the coolant temperature was close to its boiling temperature. With its positive coolant temperature coefficient the RBMK1000 reactor now was on its way to power runaway. When the SCRAM button was pushed the control elements started to run down into the reactor core. However, due to a wrong design of the lower part of the control elements (graphite sections) the displacement of the water by graphite led to an increase of criticality. A steep power increase occurred, the core overheated causing the fuel rods to burst, leading to a large scale steam explosion and hydrogen formation...

The Severe Reactor Accidents of Three Mile Island, Chernobyl, and Fukushima

Interestingly, many people cite this event as "proof" that nuclear energy is unsafe, even though they don't announce that aircraft crashes prove that flying is unsafe, or that automotive crashes prove that cars are unsafe, or that natural gas explosions prove that dangerous natural gas is unsafe, or most interestingly, the deaths of more than 225 million people from air pollution since 1986 prove that dangerous fossil fuels are unsafe.

Selective attention I guess.

In the next 24 hours, more than 19,000 people will die from air pollution.

Global, regional, and national comparative risk assessment of 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks, 1990–2015: a systematic analysis for the Global Burden of Disease Study 2015 (Lancet 2016; 388: 1659–724)

We couldn't care less.

Anyway, let’s leave those implications aside, and go to the physics. A higher neutron capture cross section than gadolinium-157 has been discovered in a nucleon, Zr-88.

From the introductory text of the paper cited at the outset:

The neutron capture reaction cross-sections for the vast majority of radioactive nuclei are poorly known, despite the importance of this information to a range of topics in both fundamental and applied nuclear science. Essentially all the elements that are heavier than iron were created via successive neutron capture reactions and β decays (which convert neutrons to protons within the nucleus) in celestial environments, such as asymptotic giant branch stars13, core-collapse supernovae and neutron star mergers14. Understanding the origin of the elements in the cosmos is one of the most important overarching challenges in nuclear science and requires neutron capture cross-sections for radioactive nuclei produced along the nucleosynthesis pathways. Over the last century, nuclear reactors and weapons have exploited neutron-induced reactions to harness enormous amounts of energy, relying upon a detailed neutron inventory for predictable performance. In a nuclear reactor, nuclides with large neutron capture cross-sections act as poisons in the fuel and diminish performance, or can be introduced intentionally to control fuel reactivity. The United States’ Science-Based Stockpile Stewardship Program, which is used to maintain high confidence in the safety, security, reliability and effectiveness of the nuclear stockpile in the absence of nuclear testing15, relies in part on cross-sections for radioactive isotopes to interpret archival data from underground tests of nuclear devices. The transmutation of stable Y and Zr detector material used in underground tests produced radioactive isotopes, such as 88Zr (half-life t1/2 = 83.4 d), that served as important diagnostics sensitive to neutron and charged-particle fluences16...

88Zr is a neutron deficient nucleus, unlike the majority of fission products, which are generally neutron rich. However, neutron poor nuclei can be formed in high energy neutron fluxes by spallation reactions, for example, for the stable isotope 90Zr, 90Zr[n,3n]88Zr, which according to the paper, was known from underground nuclear weapons tests, in which 88Zr formed.

It should be pointed out however that in a nuclear explosion, a prompt critical event, the neutron flux is extremely high. By contrast, in a nuclear reactor, one would not expect 88Zr to form. However, were it to form, it apparently wouldn't survive very long, because, as the title indicates, the neutron capture cross section is huge. Just as the formation of 135Cs is suppressed by the enormously high capture cross section of 135Xe, which is normally rapidly depleted at a rate dwarfing its (short) half-life, so would any 88Zr formed be eliminated.

For the experiment, 88Zr was not made by neutron induced reactions, but rather in a cyclotron by proton bombardment:

In this work, the 88Zr(n,γ )89Zr cross-section was measured by producing and chemically separating multiple 88Zr samples, irradiating them in a high thermal-neutron flux of (6.7–8.7) × 1013 n cm−2 s−1 and determining the quantities of 88Zr and of the reaction product 89Zr using γ-ray spectroscopy. The 88Zr target material was produced via the 89Y(p,2n)88Zr reaction using a proton (p) beam from the University of Alabama at Birmingham Cyclotron Facility. 88Zr was chemically purified using anion-exchange chromatography and assayed before encapsulation as a salt residue in high-purity quartz tubes. The 37-kBq 88Zr samples and accompanying quartz-encapsulated natural-metal foils (Fe, Zr, Mo and Y), which served as flux monitors, were irradiated for 5 min–50 h in a primarily thermal-neutron flux in the graphite reflector of the University of Missouri Research Reactor (MURR). The neutron flux was determined with precision of 7%–11% from reactions in the monitor foils (Extended Data Table 1), which have well established cross-sections20, together with detailed MCNP5 (Monte Carlo N-Particle code, version 5) modelling of the neutron flux at the irradiation position to provide the neutron energy distribution (Extended Data Fig. 1).


Figure 1:

The caption:

The spectra, which were collected with HPGe detectors immediately upon receipt at LLNL, are normalized on the basis of the live time of the measurement, initial target atoms and neutron flux. No decay or detector efficiency corrections have been applied. The unlabelled peaks between 400 and 800 keV, aside from the 511-keV peak, are from 187W and 82Br (activation products of residual impurities in the sample). The 511-keV pair-annihilation peak is primarily due to the positron emission from the decay of 89Zr and follows a trend nearly identical to that of the 909-keV peak.

From the calculated flux in the Missouri University Research reactor, the neutron capture cross section was derived from the following curves:

The caption:

Measured 88Zr atoms (blue squares) and 89Zr atoms (red circles) present in the samples following irradiation, as well as 88Zr atoms lost (black triangles), are normalized by the initial number of 88Zr atoms in each sample. The blue solid, red solid and black dashed lines show the corresponding fitting curves. The Zr populations have been corrected for decay between the beginning of irradiation and the measurements performed after irradiation. The error bars (1σ uncertainties) represent the summed correlated and uncorrelated contributions.

A graphic of the determined neutron capture cross sections, with an inset for the known cross sections for "normal" nucleons.

The caption:

The main plot shows all the existing data on a linear scale, and the inset displays the same data on a logarithmic scale. The vertical lines indicate the neutron-shell closures, which occur for nuclei with 2, 8, 20, 28, 50, 82 and 126 neutrons. The three isotopes with cross-sections of more than 105 b are labelled along with the year of the measurement.

It is interesting to note that many of the highest neutron capture cross sections exist in nuclei having neutron numbers that correspond roughly to the lanthanide elements. Some of these, at least the lighter lanthanides, are prominent fission products. In fact in solid fueled nuclear reactors, the fuel stops functioning well before the fissionable nuclei in it are consumed. This is because of the accumulation of highly neutron absorbing isotopes of elements like samarium, and to a lesser extent, europium and even promethium (as well as some other elements). This suggests that in a sensible world where people give a rat's ass about climate change - which is clearly not the world in which we live - that elements of used nuclear fuel might displace the elements now utilized in control rods, to adjust reactivity in fuel cores, since, despite what you may have heard, nuclear energy is the only form of energy that is scalable enough, sustainable enough and safe enough to address climate change.

Another interesting point suggested by the information above is a comment on the "reality" of concepts like "area" in the case of atomic nuclei. Above I indicated that a "barn" was a unit of area that is 10^(-24) cm^2 (10^(-28) m^2). If one does some simple, but naive calculations this suggests that a mole of xenon-135, (roughly 135 grams) should have, as a consequence of its neutron capture cross section of 2,600,000 barns, a combined nuclear area of around 156 square meters. Of course this is not observed. Although most - certainly among chemists - scientists tend to think of quantum effects involving electrons, which are fermions best described by wave functions subject to the Pauli exclusion principle...

(This text, excepted immediately below from the original form of this post, is wrong, as was pointed out in comments below by a correspondent. Both neutrons and protons are Fermions, and the Paui Exclusion Principle applies. On reflection, this should have been obvious to me, given that transitions between nuclear isomers is usually "monochromatic. For example, the decay of radioactive Ba-137m to stable Ba-137, a feature of the decay series of Cs-137 - and accounting for the gamma output of this series - always releases radiation with an energy of 661.659 keV. This would not be the case for a Bose-Einstein system. I thank the correspondent for the correction from which I learned two things, the fact of the matter, and not to rely too much on memory. The correspondent also pointing out that Wigner won his Nobel for the nuclear shell model by which this system operates.)

neutrons and protons are bosons, and thus fill nuclei under a different kind of statistics, Bose-Einstein statistics, according to the Breit-Wigner distribution; for orbitals of neutrons and protons, the Pauli exclusion principle does not apply.

Nevertheless, like all quantum phenomena, a nucleus has a wave function and should not be thought of as strictly particulate in nature. In fact, the neutron capture cross section is best described in a "center of mass" frame and not a laboratory frame, and a neutron about to collide with a nucleus is in fact a system, as opposed to to "particles" colliding. This wave function is thus a function of the energy of a system: The apparent "size" at which a neutron "sees" a nucleus as having depends on the energy (the velocity) the neutron possesses with respect to the target nuclei. The 2,600,000 barn figure for Xe-135 is only true for "thermal" neutrons, generally taken to be neutrons with an average energy of 0.253 eV. Despite the units of area, a nucleus is neither a thing nor a wave, but both.

(Eugene Wigner, co-developer of the formula above for neutron capture resonances, and also a Nobel Laureate, co-wrote with Alvin Weinberg, the first nuclear engineering textbook, in 1956. I believe it's still in print. The technical basis of most of the world's operating reactors was based on technology known in the 1950s and 1960s.)

The ideas around neutron cross sections have been floating in my brain for several decades now, and I was intrigued by this interesting paper which showed up just recently in Nature. Papers on this topic always grab my attention when I see them.

I wish you a pleasant Sunday.

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Reply An extraordinarily high neutron capture cross section has been discovered in a zirconium isotope. (Original post)
NNadir Jan 2019 OP
caraher Jan 2019 #1
NNadir Jan 2019 #2
caraher Jan 2019 #3
NNadir Jan 2019 #4
NNadir Jan 2019 #5

Response to NNadir (Original post)

Mon Jan 28, 2019, 07:26 PM

1. One quick correction

Protons and neutrons, as spin-1/2 particles, certainly are not bosons, but are, like electrons, fermions. Pauli exclusion is a core principle of the nuclear shell model, for which J. Hans D. Jensen, Eugene Wigner, and Maria Goeppert-Mayer shared the 1963 Nobel Prize in Physics (marking the first time since Marie Curie and last time until this past year that a woman won a Nobel Prize in physics).

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Response to caraher (Reply #1)

Mon Jan 28, 2019, 09:06 PM

2. You're right and I'm wrong.

That's what happens when you get old, and rely too much on memory.

A quick google demonstrated my mistake.

Early in my career I had to perform an experiment involving the sorting of small beads into multiple containers under quasi-random conditions, which was a Bose-Einstein statistical problem, and my memory told me that the place from which this idea this came was from from protons and neutrons in atomic nuclei. Now I have to remember how I came to know about Bose Einstein statistics.

Sorry about that. I'm a chemist, not a physicist, if that's an excuse.

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Response to NNadir (Reply #2)

Mon Jan 28, 2019, 09:15 PM

3. Maybe something about photons rather than protons?

Photons are spin-1 bosons, so they definitely obey Bose-Einstein statistics.

It's also the case that some systems of fermions behave as bosons. One notable example of this is the formation of Cooper pairs in superconductors; a Cooper pair consists of two electrons interacting with phonons of a metal lattice.

Anyway, no need to provide for excuses... we all get misconceptions, and the nice thing about science is that ones like this are easily straightened out!

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Response to caraher (Reply #3)

Tue Jan 29, 2019, 06:54 AM

4. And another nice thing is when you make a mistake you learn something.

Thanks for the correction and the comments. I learned something.

I doubt it would have been photons that I was learning about all those years ago, though. I recall going to some early lectures on superconducting ceramics many years ago, that could have been it. In any case it was at least 25 years ago when I had that problem when I had to study the sorting of beads into containers, early in the days of combinatorial chemistry.

My son, an excellent undergraduate student in Materials Science Engineering likes to tell me, by the way, why my demonstrations when he was a kid were lousy. He also likes to correct me on the pronunciation of certain terms and names.

I love it.

Thanks again.

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Response to NNadir (Original post)

Tue Jan 29, 2019, 09:39 PM

5. Errata.

A note has been added to the original post pointing out the correction graciously offered in the comments.

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