B How much rubidium-88 is there in nature?

[snorkack]

Sorry, what is SF? I think F stand for fission but what is S? Those 87Rb don't need minutes or hours to become 88Rb if they are exposed to neutron rays?

Spontaneous.
Any single 87Rb that captures a neutron becomes 88Rb in yoctosecond timeframe.
However, if many more neutrons come along, they may turn more 87Rb into 88Rb - or 88Rb into 89Rb.

 

[pbuk]

So the moment an amount of 87Rb are exposed to neutron radiation they immediately become 88Rb which in turn become 88Sr after around 18 minutes? Those 87Rb don't need minutes or hours to become 88Rb if they are exposed to neutron rays?

Yeah, that's how it works: there is loads of Rubidium floating around in the atmosphere and the Sun is firing "neutron rays" of exactly the right energy precisely targeted at its nucleii, avoiding everything else along the way.

I am not sure what planet this might happen on, but this is nothing like what actually happens on Earth. The only ⁸⁸Rb here is that created in reactor laboratories. Note that it's half-life of around 18 minutes does NOT mean that it becomes ⁸⁸Sr after 18 minutes.

 

[Astronuc]

15O exists in nature as it is a product of gamma-bombardment of 16O. As it has a half-life of just over 2 minutes it is not practical to quantify its abundance, however because it is not nil we give it the qualitative value of "trace".

Certainly, ¹⁶O (γ,n) ¹⁵O is a possibility, but it requires a gamma of sufficient energy, which can happen with thunderstorms. The reaction requires a photon (gamma) of at least 5.183 MeV, the energy of the first excited state in ¹⁶O.
https://cea.hal.science/cea-04920214v1/document - see reference 14
[14] F. Ajzenberg-Selove, “Energy levels of light nuclei A = 13–15,” Nuclear Physics A, vol. 523, no. 1, pp. 1-196, 1991.

In the earth's atmosphere, as well as in particle accelerators, ¹⁵O is formed by several reactions:

¹⁴N (d,n) ¹⁵O

¹⁵N (p,n) ¹⁵O, ¹⁵N has low abundance in earth's atmosphere compared to ¹⁴N

¹⁶O (p,pn) ¹⁵O

Ref: https://link.springer.com/chapter/10.1007/978-94-011-2584-0_9

Production rates in Nature depend on the p and d fluxes (and energy spectra) from sun and the cosmos, as well as gamma flux and spectrum.

 

[Astronuc]

According to https://www.osti.gov/servlets/purl/1414348, it was stated 'Nevertheless, at high neutron densities, up to 54 % of the total 85Kr captures a neutron, generating 86Kr, eventually leading to an enrichment of 88Sr (Fig. 5).

Note the context of the paper - Strontium and barium isotopes in presolar silicon carbide grains . . .

The first sentence in the introduction, "Primitive meteorites and interplanetary dust particles contain small quantities of isotopically anomalous refractory dust grains that are older than our Solar System and commonly called40 “presolar grains” (Davis, 2011; Zinner, 2014)." So, the sun did not exist, and the earth formed after the sun.

The Sun and the planets formed together, 4.6 billion years ago, from a cloud of gas and dust called the solar nebula. A shock wave from a nearby supernova explosion probably initiated the collapse of the solar nebula.

https://www.amnh.org/exhibitions/permanent/the-universe/planets/formation-of-our-solar-system

The solar system as it is now, is a very different from pre-solar times; the solar system formed about 4.5-4.6 billion years ago. The heavy elements would have formed in conjunction with the supernova.

Look at the Wikipedia article...
https://en.wikipedia.org/wiki/Delayed_neutron
It just... jumps to "groups"? Without any attempt of explanation why these are "groups"! Or why 6 vs. 8.

The Wikipedia article is brief. The table cites
J. R. Lamarsh, Introduction to Nuclear Engineering, Addison-Wesley, 2nd Edition, 1983, page 76. (I have the 1977 edition), and G. R. Keepin, Physics of Nuclear Kinetics, Addison-Wesley, 1965.

In the context of nuclear reactor theory and practice (neutronic, or nuclear reactor physics), the number of groups is arbitrary. The various delayed-neutron precursors are grouped according to half-life/decay constant. The number of groups was established at a time when computational resources were limited; computers were limited in speed and precision (in the 1960s and 1970s, we did not have the microprocessors we've had since the 2000s, and now there are even move powerful computational systems). Computer memory was also quite limited. Six groups is sufficient for performing the computations to simulate how a reactor should perform, how one should approach criticality and how rapid the power will ascend with the removal of one or more control rods, or dilution of borated water in a PWR.

But about isotope lists, see:
https://en.wikipedia.org/wiki/Isotopes_of_krypton#List_of_isotopes
Kr isotopes 85, 86, 89 and 92 are marked as "fission products", but 87, 88, 90 and 91 are not.
Why, do you guess?
Are they provably absent in fission fragments to adequate precision?
Or did Wikipedia editors neglect to add the notes to these isotopes?
Or did people working on fission not bother to measure their yields and publicize their results?

Wikipedia articles are not necessarily comprehensive or accurate.
See - https://www.physicsforums.com/threads/how-much-rubidium-88-is-there-in-nature.1079228/post-7249625

If one checks the 'Chart of Nuclides', https://www.nndc.bnl.gov/nudat3/ , one will find the fission yield of ⁸⁸Rb and a host of others. ⁸⁸Rb is both a fission product and the daughter of another fission product, ⁸⁸Kr, which itself is both a fission product and daughter of a fission product ⁸⁸Sr and so on. The further a radionuclide is from the 'line/curve of stability' the lower the fission yield.
https://www.physicsforums.com/threads/how-much-rubidium-88-is-there-in-nature.1079228/post-7249567

In the chart of nuclides, the default is Half-life. Select a nuclide of interest, e.g., ⁸⁸Rb, one can select a tab 235U IFY (independent fission yield), and in the same row of tabs, to the right, one has an option to select the tab Fission Yields, which gives a menu of Independent (IFY) and Cumulative (cFY) fission yelds, the latter of which includes the production from decay of precursors.

For ⁸⁸Rb, 235U IFY = 2.23 E-4 (from thermal fission of ²³⁵U), 235U cFY = 3.57E-2. The in-reactor environment is more complex since fission may be induced by any neutron of energy between 0.001 eV to 10 MeV, and in various isotopes (radionucles) of U, Np. Pu, Am, Cm, . . .

There are a various nuclear production methods: neutron capture, decay, photonuclear and spallation reactors involved. These occur in different amounts according to 'local' conditions, e.g., nuclear reactor, particle accelerator target, earth's (or planetary) atmosphere (interactions with the solar wind and cosmic radiation), stars, and supernovae.

Some of the heavier transuranics were identified in early thermonulcear tests during the 1950s, otherwise they were developed from heavy ion collisions with lighter TU nuclides.

 

[snorkack]

If one checks the 'Chart of Nuclides', https://www.nndc.bnl.gov/nudat3/ , one will find the fission yield of ⁸⁸Rb and a host of others. ⁸⁸Rb is both a fission product and the daughter of another fission product, ⁸⁸Kr, which itself is both a fission product and daughter of a fission product ⁸⁸Sr and so on. The further a radionuclide is from the 'line/curve of stability' the lower the fission yield.
https://www.physicsforums.com/threads/how-much-rubidium-88-is-there-in-nature.1079228/post-7249567

How´s that possible?
Rb must form with Cs (because 92-37=55)
The only stable isotope of Rb is 85. The only stable isotope of Cs is 133. This totals 218.
The average neutron multiplicity of U-238 fission is 2,0 (coincidental average of varying individual integers), so this accounts of mass number 220. Obviously there are 18 extra neutrons, and the fission yield of neutron-rich unstable isotopes must be far larger than that of stable ones.
The chart of nuclides specifies that the biggest yield of the isotopes of Rb is that of ⁹³Rb, which incidentally is a delayed neutron source. The biggest yield of Cs isotopes is that of ¹⁴³Cs, also a delayed neutron source.

 

[Astronuc]

How´s that possible?
Rb must form with Cs (because 92-37=55)
The only stable isotope of Rb is 85. The only stable isotope of Cs is 133. This totals 218.

The answer is Nature. I'm not sure why one introduces the stable isotopes in a discussion about fission.

The Z's of the fission products must add to 92, of course, for fission of a U atom. The distribution of neutrons tends toward the heavier fission products.

Take ${^{88}_{37}}Rb$ and ${^{146}_{\ 55}}Cs$, one can ratio A/Z or (A-Z)/Z = N/Z, where N is the number of neutrons, Z is the atomic number or number of protons. Note: the sum of A's = 234, assuming 2 neutrons are related upon fission.

For ${^{88}_{37}}Rb$, one has 88/37 = 2.3784, or (88-37)/37 = 1.3784.
For ${^{146}_{\ 55}}Cs$, one has 146/55 = 2.6545, or (146-55)/55 = 1.6545.

In the case of ²³⁵U, the atomic mass (A's), must add to 234 or 233, depending on whether 2 or 3 neutrons are released from the excited ²³⁶U nucleus.

For example, ${^{235}_{\ 92}}U + n \rightarrow {^{236}_{\ 92}}U{^*} \rightarrow {^{88}_{37}}Rb + {^{146}_{\ 55}}Cs + 2n$

The reaction has a lower likelihood than the production of say, ${^{92}_{37}}Rb + {^{142}_{\ 55}}Cs + 2n$, or ${^{92}_{37}}Rb + {^{141}_{\ 55}}Cs + 3n$, or one's example,
${^{93}_{37}}Rb + {^{141}_{\ 55}}Cs + 2n$

${^{146}_{\ 55}}Cs$ may release a neutron as it beta decays.

The most probable outcome of fission of ²³⁵U is ${^{100}_{\ 40}}Zr + {^{134}_{\ 52}}Te$

Fission of ²³⁸U is different, since it requires a fast neutron, and it has 3 more neutrons than 235. Capture of a lower energy neutron more likely produces ²³⁹U, which then decays to ²³⁹Np by beta decay, which either decays to ²³⁹Pu, or if ²³⁹Np captures a neutron, it becomes ²⁴⁰Np, which decays to ²⁴⁰Pu. Likewise, ²³⁹Pu may capture a neutron and either fission or emit a gamma and become ²⁴⁰Pu.

Not discussed here is the presence of gammas. About 7 or 8 prompt gammas are released from fission. In addition, some fission products may absorb neutrons and promptly release a gamma (so-called radiative capture) with sufficient energy to initiate a photonuclear reaction (either photoneutron in any nuclide, or photo-fission in U, Np, Pu and heavier nuclides). The cross-sections for photonuclear reactions have lower bounding thresholds (least binding energy of a neutron in a given nucleus) and are dependent on photon energy. Then there is isomeric transition of excited nuclei, e.g., ^135mXe, where the 'm' indicates a metastable nuclide.

 

[snorkack]

The answer is Nature. I'm not sure why one introduces the stable isotopes in a discussion about fission.

Replying to you. Shortening your quote to show that you introduced the stable isotopes:

The further a radionuclide is from the 'line/curve of stability' the lower the fission yield.

In the case of ²³⁵U, the atomic mass (A's), must add to 234 or 233, depending on whether 2 or 3 neutrons are released from the excited ²³⁶U nucleus.

How broad is the distribution of count of neutron multiplicity? Is it only 2 or 3, never an average between fission events with 1 and events with 4?
This
https://cdn.lanl.gov/files/m-app-to-neutron-multiplicity-counting_9ea55.pdf
figure 1.2, page 10 gives multiplicity distribution for Pu-240 spontaneous fission, with 6,6% aneutronic.
https://cdn.lanl.gov/files/6-passive-neutron-multiplicity_3cae7.pdf
figure 6.2 page 2 contrasts it with fast fission of Pu-239

Fission of ²³⁸U is different, since it requires a fast neutron,

Or nothing. ²³⁸U is much more likely to undergo spontaneous fission.

and it has 3 more neutrons than 235. Capture of a lower energy neutron more likely produces ²³⁹U, which then decays to ²³⁹Np by beta decay, which either decays to ²³⁹Pu, or if ²³⁹Np captures a neutron, it becomes ²⁴⁰Np, which decays to ²⁴⁰Pu. Likewise, ²³⁹Pu may capture a neutron and either fission or emit a gamma and become ²⁴⁰Pu.

Not in nature.
Consider that even rich ores like pitchblende where few neutrons are lost in O, H or elsewhere and mostly all neutrons are captured by U have not been critical for last 1,8 Gyr. The enrichment of U has fallen over 4 times since then. I presume most natural fission, even in rich ores, is spontaneous because k is not just under 1 but well below half.
The partial halflife of U-238 to spontaneous fission is 8 Pyr
And the burnup of the ore does not accumulate over the existence of the ore... why?
Because when U-238 does absorb 1 neutron, the resulting Pu-239 has halflife 24 kyr... to α. Which drops the mass number to 235. To produce a nucleus of Pu-240 requires the Pu-239 nucleus to catch the second neutron, not within the Gyr that the ore lies in ground but within the 24 kyr before Pu-239 decays.
See how low the burnup of natural ores is, and why.
Neutron-rich isotopes of actinides, anything with mass number past 239, are extremely improbable to form on Earth even in trace amounts.
Neutron-rich isotopes of fission fragments, however, DO form naturally on Earth as products of spontaneous fission.

 

[Astronuc]

Shortening your quote to show that you introduced the stable isotopes:

Incorrect. I was referring to radionuclides, as in "The further a radionuclide is from the 'line/curve of stability' the lower the fission yield." This is evident when reviewing the 'chart of nuclides'. Not only is the fission yield lower, but the half-lives tend to be shorter, i.e., the radionuclides are less stable.

Taking a look at the Chart of Nuclides, and the independent fission yields (IFY) of ²³⁵U and ²³⁹Pu (for thermal neutrons) sit on or below the 'line/curve of stability', so they are inherently 'neutron-rich'. See attached image (green means very low probability, the orange/brown squares are below the 'line/curve of stability'.

How broad is the distribution of count of neutron multiplicity? Is it only 2 or 3, never an average between fission events with 1 and events with 4?

The free neutron yield per fission would be averaged over the multiplicity range, usually between 2 or 3 for practical purposes, i.e., in a nuclear reactor, and the multiplicity vector shifts with the incident neutron energy. I picked a simple example of 2 or 3 neutrons per fission. I also left out ternary fissions, in which a nucleus fission into three fission products, the lightest ones of concern being T and less oftern ⁴He, and even rarer quaternary fission.
https://en.wikipedia.org/wiki/Ternary_fission

238U is much more likely to undergo spontaneous fission.

More likely that what? Note the half-life of ²³⁸U, which means a very low decay rate, then SF occurs 5.44E-5% of the time, so not very often.

Consider that even rich ores like pitchblende where few neutrons are lost in O, H or elsewhere and mostly all neutrons are captured by U have not been critical for last 1,8 Gyr.

This is not necessarily correct. One does not find pure UO₂ or U₃O₈ in ores, but it is distributed with other metal oxides, e.g., oxides of Th, Pb, lanthanides, elements from the decay of Th, U, . . . , in addition to other minerals. Oklo was a unique event.
https://world-nuclear.org/informati...uranium-resources/geology-of-uranium-deposits

It is true that the 'enrichment', or proportion of ²³⁵U in 'natural' U has decreased (by decay, an d perhaps by one more criticality events (with attendant production of fission products)) over the last ~4.5 billion years, so events like Oklo 'natural reactor' are exceedingly rare, if not impossible.

And the burnup of the ore does not accumulate over the existence of the ore.

Please explain one's statement. Burnup, in the context of a nuclear reactor, is simply the energy produced per unit mass of fuel. One may quantify burnup in terms of fissions per initial metal atoms (FIMA, often given as a percent) or in terms of MWh/kgHM or GWd/tHM, where HM = heavy metal atoms, which is U in conventional LWR, or (Th, U, Pu)X, where X could be O₂, N, C, Zr, Mo, . . . . Some folks like to report burnup in terms of mass of metal oxide.

Because when U-238 does absorb 1 neutron, the resulting Pu-239 has halflife 24 kyr... to α. Which drops the mass number to 235. To produce a nucleus of Pu-240 requires the Pu-239 nucleus to catch the second neutron, not within the Gyr that the ore lies in ground but within the 24 kyr before Pu-239 decays.

Perhaps I should have prefaced the comments about ₂₃₈U and production of Pu isotopes with "In a nuclear reactor, . . . ", or in a supernova, or some configuration where there is an amount of ²³⁸U in a copious quantity of neutrons.

A situation like Oklo, or other 'natural reactor', the geochemistry complicates the systems, since the enviornmental conditions change, e.g., continents drift, and some land was underwater for a period, and different minerals have different solubilities depending on pH (acidity or alkalinity). It could have been a one time event, or successive events separated by some undetermined time span (millenia, or eons). When an even happens, it would be a transient event; some fission products will be lost, while others will remain nearby. Each geological system is unique regarding composition, homogeneity/heterogeneity, hydrology, . . . .

Neutron-rich isotopes of fission fragments, however, DO form naturally on Earth as products of spontaneous fission.

Certainly.

For general interest - https://indico.fnal.gov/event/16420/attachments/23235/28811/NVassh_FRIBGW170817_2018.pdf

 

[snorkack]

Incorrect. I was referring to radionuclides, as in "The further a radionuclide is from the 'line/curve of stability' the lower the fission yield." This is evident when reviewing the 'chart of nuclides'. Not only is the fission yield lower, but the half-lives tend to be shorter, i.e., the radionuclides are less stable.

Taking a look at the Chart of Nuclides, and the independent fission yields (IFY) of ²³⁵U and ²³⁹Pu (for thermal neutrons) sit on or below the 'line/curve of stability', so they are inherently 'neutron-rich'. See attached image (green means very low probability, the orange/brown squares are below the 'line/curve of stability'.

For ease of doing the review, let´s see the chart as link again:
https://www.nndc.bnl.gov/nudat3/
Let´s compare nuclides and take Rb for example. Independent fission yields (IFY) of ²³⁵U, and half-lives and modes

1. ⁸⁴Rb - 2.16*10^-12; 33 d; β^- and 96.1% β⁺ and ε
2. ⁸⁵Rb - 2.37*10^-5; stable
3. ⁸⁶Rb - 3.22*10^-8; 19 d; β^- and 0.0052% ε
4. ⁸⁷Rb - 2.50*10^-5; 4.97*10¹⁰ yr; β^-
5. ⁸⁸Rb - 2.23*10^-4; 18 min; β^-
6. ⁸⁹Rb- 2.04*10^-3; 15 min; β^-
7. ⁹⁰Rb- 7.06*10^-3; 2.6 min; β^-
8. ⁹¹Rb- 2.22*10^-2; 58 s; β^-
9. ⁹²Rb- 3.13*10^-2; 4.48 s; β^- and 0.011% β^-n
10. ⁹³Rb- 3.06*10^-2; 5.85 s; β^- and 1.46% β^-n
11. ⁹⁴Rb- 1.56*10^-2; 2.74 s; β^- and 10.3% β^-n
12. ⁹⁵Rb- 7.63*10^-3; 0.38 s; β^- and 8.75% β^-n
13. ⁹⁶Rb- 1.68*10^-3; 0.2 s; β^- and 13.8% β^-n
14. ⁹⁷Rb- 3.79*10^-4; 0.17 s; β^- and 25.5% β^-n
15. ⁹⁸Rb- 2.35*10^-5; 0.115 s; β^- and 14.3% β^-n
16. ⁹⁹Rb- 4.67*10^-7; 0.054 s; β^- and 19.8% β^-n
17. ¹⁰⁰Rb- 3.47*10^-4; 0.052 s; β^- and 6% β^-n
18. ¹⁰¹Rb- 1.57*10^-8; 0.032 s; β^- and 27% β^-n
19. ¹⁰²Rb- 1.47*10^-11; 0.037 s; β^- and 65% β^-n

I guess it´s typical (maybe of odd elements?) but I haven´t taken the time yet to write through the other elements. Note key features:

1. there is tendency for the stability of isotopes to fluctuate, Rb-86 has halflife 18 days but Rb-87 50 Gyr
2. there is a small but nonzero yield of stable isotope - and indeed of radioactive, neutron-poor isotopes
3. from the stable Rb-85 the stability decreases with increasing mass number, with fluctuations, but the yield increases, also with fluctuations, up to Rb-92 (halflife 4,5 s). Only after after Rb-93 do both yield and stability decrease as you say.

Please explain one's statement. Burnup, in the context of a nuclear reactor, is simply the energy produced per unit mass of fuel. One may quantify burnup in terms of fissions per initial metal atoms (FIMA, often given as a percent) or in terms of MWh/kgHM or GWd/tHM, where HM = heavy metal atoms, which is U in conventional LWR, or (Th, U, Pu)X, where X could be O₂, N, C, Zr, Mo, . . . .

My next passage you quoted.
FIMA would be an indicator of the probability that a nucleus has captured not just one but multiple neutrons.
But in an ore, where FIMA is accumulated over a period much longer than the halflife of the daughter (Pu-239), it is not actually relevant. What matters is the amount of fissions that takes place before the daughter decays in her turn.