Spontaneous fission, decay rates, and critical mass

Hi DWIII, thanks -- you beat me to it.

Nonukes quite correctly points out the errors in the preceding, namely, that the phenomenon of induced fission, which proceeds extremely rapidly on the successful absorption of a free neutron, is very different from spontaneous fission, which is an extremely rare phenomenon compared to the typical natural decay rate of a radioactive substance.

Agreed, but that is not all of the picture. The physical constraints that result in the relative stability seen today affect not just decay rates, and any changes that result in an increase in decay rates have effects on other aspects of the stability of atoms.

From How did the Aborigines get to Australia? where this was off-topic:

Message 63 NoNukes: The mechanism for increasing the decay rate has not been specified. At this point the mechanism is PFM (pure freaking magic). I think it is reasonable (but perhaps not inevitable) that the mechanism will increase spontaneous fission in the same way it increases U238 decay rates, exactly as you have proposed, and I have assumed that such a thing will happen.

We are in agreement then, that keeping things working according to the scientific principles, increasing the decay rate results in less stable atomic materials, and that any claim otherwise invokes PFM (otherwise known as god/s-did-it), which means you can make up your own fantasies.

(ibid) I think our disagreement results from your belief that enrichment enables criticality by increasing the number of spontaneously generated neutrons.

That is not what I have argued.

I have argued (and provided evidence) that the level of enrichment in the past in natural ores was sufficient to cause a natural reactor to form. Several did in Oklo.

I have argued that changing the stability of atoms to increase the decay rate would mean that more such natural reactor events should have occurred, even for a small change in decay rate to be achieved.

For the purpose of continuing this debate I will stipulate that claiming a strict 1 to 1 correlation\relationship between decay rates and critical mass is incorrect.

It is a little more complicated than that. It involves the physics of atomic stability to change the decay rate, and this has larger effects than just changing the decay rate.

Message 60 Zen Deist: http://nuclearweaponarchive.org/Library/Fission.html quote: The stability of an atomic nucleus is determined by its binding energy - the amount of energy required to disrupt it. Any time a neutron or proton is captured by an atomic nucleus, the nucleus rearranges its structure. If energy is released by the rearrangement, the binding energy decreases. If energy is absorbed, the binding energy increases. The isotopes important for the large scale release of energy through fission are uranium-235 (U-235), plutonium-239 (Pu-239), and uranium- 233 (U-233). The binding energy of these three isotopes is so low that when a neutron is captured, the energy released by rearrangement exceeds it. The nucleus is then no longer stable and must either shed the excess energy, or split into two pieces. Since fission occurs regardless of the neutron's kinetic energy (i.e. no extra energy from its motion is needed to disrupt the nucleus), this is called "slow fission". By contrast, when the abundant isotope uranium-238 captures a neutron it still has a binding energy deficit of 1 MeV after internal rearrangement. If it captures a neutron with a kinetic energy exceeding 1 MeV, then this energy plus the energy released by rearrangement can over come the binding energy and cause fission. Since a fast neutron with a large kinetic energy is required, this is called "fast fission". In nuclear reactions today some neutrons are lost from the chain reaction due to neutron capture without fission, due to the binding energy level of the various isotopes. Curiously, the binding energy also affects the decay rate, and increased decay rate means that the effective binding energy of the atom\isotope is reduced. With lower binding energy, neutron capture is more likely to exceed the (lower) binding energy limit for fission to occur, with the result that induced fission would occur more often: less critical mass is needed. In addition, the numbers of neutrons resulting from fission would also increase: quote: (ibid) The nuclei of these isotopes are just barely stable and the addition of a small amount of energy to one by an outside neutron will cause it to promptly split into two roughly equal pieces, ... and several new neutrons (an average of 2.52 for U-235, and 2.95 for Pu-239). Amusingly, neutrons exist in integer quantities, not fractions. There is variation in the number of neutrons produced from individual events. The number of neutrons produced is also related to the binding energy that controls decay rates. Faster decay = more neutrons produced by induced fission = less critical mass.

Because the atoms are less stable (to allow the increased decay rate) they are more susceptible to fission, and have a lower threshold to energy increases that result in induced fission.

It is just not logical (without invoking PFM) that any change that allows for atoms with less hold on decay particles (to increase the rate of decay) would not also have less hold on neutrons etc in the nucleus, and on holding themselves together. These are due to the same atomic bonding forces.

Thus lower energy neutrons would induce fission rather than just be absorbed (as often happens today), AND induced fission would release more neutrons than now (an "average of 2.52 for U-235, and 2.95 for Pu-239" today) ... neglecting for now that this could result in ²³⁸U and other elements being able to support a chain reaction, the inevitable result is that smaller critical mass would be the case.

You just can't invoke an increase in the rate of decay without getting a reduction in the stability of atoms across the board. Unless you want to invoke PFM.

Enjoy

Edited by Zen Deist, : wrding

Edited by Zen Deist, : more wrding

Hi NoNukes and DWIII (and anyone else reading)

No one disputes that the spontaneous fission rate would increase.

So it appears that we are all in agreement, as I said in Message 3:

quote:

---

We are in agreement then, that keeping things working according to the scientific principles, increasing the decay rate results in less stable atomic materials, and that any claim otherwise invokes PFM ...

---

Would you not also agree that this change in stability necessarily affects the behavior of other particles, nuclei, etc, operating under the same laws and forces that regulate decay rates? That this is why the occurrence of spontaneous fission would increase, not just decay events, yes?

There should be no special pleading for one set of particle\behavior compared to others operating by the same laws and forces.

Thus lower energy neutrons would induce fission rather than just be absorbed (as often happens today), AND induced fission would release more neutrons than now (an "average of 2.52 for U-235, and 2.95 for Pu-239" today) I note that this is the first time you have made this argument. Most (if not all) of your previous arguments haven't dealt with chain reactions. ...

You can consider this a more detailed explanation than before (or that I am "changing gears", etc., if you want). I sometimes get ahead of myself.

But essentially every low energy neutron (upwards of 96 per cent) captured by a U235 atom already produces an induced fission. There simply isn't much room for improvement in this area. In the six factor formula, this ratio is wrapped up into "eta" which is the neutron yield per captured neutron.

But even a 1% increase would cause more induced fission than now would it not? This would translate to less critical mass needed to achieve a sustained chain reaction would it not?

I am aware of no good reason why the products from fission would necessarily include more neutrons simply because the binding energy changes.

Are they not operating under the same laws and forces that hold the decay particles in the nucleus until decay occurs? Can I affect one without affecting the other(s)? Is there any good reason to think that they would NOT be affected? See next.

A typical split of a U235 atom yields two big roughly equal sized fragments, with some alpha particles and some neutrons and a bunch of energy in the form of gamma rays and kinetic energy of the fragments. ...

With increased decay rates and atomic stability it would seem highly likely that the numbers of alpha particles (bound by the same laws and forces as the ones involved in alpha decay events, after all) would increase in number in these events as well. Would not whatever binds one also bind the other to the same degree, whether effectively increasing the binding energy or decreasing it.

More alpha particles lost in fission would mean that the main members, the "two big roughly equal sized fragments" would be slightly smaller than the ones we see today.

Stable atoms generally have decreasing proportions of neutrons to protons as they get smaller ...

See link to periodic chart to compare atomic number (number of protons) to atomic mass (number of protons, neutrons, et.)
(from http://wikis.lawrence.edu/...iodic+Table+%28Ashley+Vokral%29)

... so this would mean the smaller "big roughly equal sized fragments" produced compared to the ones we see today would, on average contain fewer neutrons, thus indicating that the number of neutrons would also increase, yes?

Even with no other considerations it seems we should see an increase in the number of neutrons produced.

... I will accept the values you provide as average values for the produced neutrons. ...

It seems to me that the variation is likely due to the variation in energy of the neutrons that cause the induced fission and the variation in energy levels within the nuclei being struck. Higher energy combinations leading to the larger production of neutrons and lower energy combinations leading to the lesser production of neutrons.

If nothing else we have a balance between events resulting in 2 neutrons and events resulting in 3 neutrons (and possibly rarer events resulting in 1 or 4 neutrons). Likely there is a (skewed) probability distribution in the numbers of neutrons produced.

The reduced stability of the atoms necessary to achieve a reduction in decay rate would affect this proportion and logically result in more neutrons than we see today.

Would you not agree that a slight shift in the proportions of these events, that raised the average number, say by 1% (+0.03 neutrons on average), would cause more induced fission than now, yes? And this would translate to less critical mass needed to achieve a sustained chain reaction would it not?

... But who knows what the mix might be if we introduce supernatural meddling? More alphas? More neutrons? ...

Indeed, even (perhaps) resulting in all radioactive elements falling apart, or engaging in run-away fission reactions, especially when you get to the level of change required to turn 4.55 billion years into a YEC age (ie several orders of magnitude of change in the decay rates), yes?

... Slightly bigger fragments and fewer neutrons?

Not likely imhysao, as that would be a more stable, lower energy, condition.

... Fast neutrons, on the other hand have a lowered probability of being captured by a U235 nucleus. I'm curious to see what use you make of this information.

And logically they also would have more energy (same laws and forces). The whole energy spectrum should shift to a slightly higher level, which would be in keeping with compressing radioactive decay behavior into shorter time periods.

I also look at the energy required to cause fission in ²³⁸U:

http://nuclearweaponarchive.org/Library/Fission.html

quote:

---

By contrast, when the abundant isotope uranium-238 captures a neutron it still has a binding energy deficit of 1 MeV after internal rearrangement. If it captures a neutron with a kinetic energy exceeding 1 MeV, then this energy plus the energy released by rearrangement can over come the binding energy and cause fission. Since a fast neutron with a large kinetic energy is required, this is called "fast fission".

---

Thus we should see a point where the increased particle energy coupled with the increased instability of the nuclei would result in a chain reaction in ²³⁸U. It would not take much of a change to reach this point.

... I don't dispute that changing the nuclear binding energy might make other nuclei capable of sustaining a chain reaction, ...

At that point it would be ball-game over for any reduced decay rate hypothesis would it not?

Enjoy.

Hi NoNukes, thanks.

I appreciate the work you put into these posts.

I agree that such a change might have the effect you describe, but maybe not. When a U235 nucleus absorbs a neutron and forms U236, the U236 nucleus may either fission or emit a gamma ray. If we lowered the binding energy, why wouldn't the gamma ray emission probability be increased?

I don't think it would be the case of one or the other, but both would be affected. If the number of absorptions increases then both more fission and more gamma ray emission could occur, and quite possibly in the same ratio.

What we can say for sure is that an enormous increase in the decay rate ...

Curiously, when we are talking about changing the age of the earth from 4.55 billion years to 10,000 years we are talking about an enormous increase in the decay rate, yes?

... could correspond to only a tiny effect on criticality through this mechanism. ...

Or it could correspond to a significant effect. You need to show why you think there would only be a small effect, yes?

... Surely this effect cannot be used to demonstrate that no rapid decay occurred in the past because of the lack of more natural reactors.

We have evidence of several natural reactors in Oklo, so the question is not whether natural reactors could form, but the number of reactors that could form and the number that should form under reduced binding energy that would allow faster decay to occur. We may even be able to go further and see if we can parse out some evidence that should occur and not occur under rapid decay physics and then test to see if they are present anywhere. For instance, should the behavior at Oklo have been different under rapid decay?

Give me an argument for the above. Coincidentally, I had to tutor a high school student on nuclear reactions including fission this afternoon. It turns out that fission fairly rarely produces alpha particles directly. However, I think this is actually a side issue. With respect to sustaining a chain reaction, the important fission products are neutrons, and the production of those particular fission fragments that beta decay to produce neutron emitters.

If the binding energy holding alpha particles is reduced to allow more rapid decay, then it is also reduced for holding alpha particles within a nucleus, and they are more likely to be released under impact.

Consider a billiard table with magnetic balls: smack a group of balls with the cue ball and a number of different results can occur:

1. The cue ball is absorbed into the group of balls, which is otherwise virtually unaffected
   
2. The cue ball is absorbed into the group and one or more balls break away from the group
   
3. The cue ball is absorbed into the group, which then splits into to two smaller groups and one or more balls break away from the group
   
4. The cue ball is absorbed into the group, which then splits into to several smaller groups and several balls break away from the group
   
5. The cue ball is absorbed into the group, which then splits up into many smaller groups and individual balls
   
6. The cue ball shatters the group into individual balls.

Would you agree, for the sake of the argument, that these scenarios are roughly sorted by the initial energy of the cue ball? Would you not agree that 1 occurs with significantly less cue ball energy than number 6 but that 2 only needs a little bit more energy than 1?

If we take just 1 and 2 above, for example, we should be able to determine a threshold cue ball energy level below which 1 takes place and above which 2 takes place, for a constant input of magnetic force between the balls, yes?

Next we reduce the force of the magnets and repeat. With less binding energy I would expect there to be a shift towards the more energetic responses, wouldn't you?

The threshold between 1 and 2 would be shifted to occur with less cue ball energy than before, yes?

Similar threshold shifts should happen for all the other possibilities as well, yes?

Maybe. But perhaps fewer neutrons might be produced than we see today. My gut feeling is that there would be no significant effect, but I'm not professing to know the answer.

Can you see a scenario in the billiard analogy where this would be the case as you decrease the magnetic forces?

Compared with the other effects that are postulated to have resulted in the natural reactors at Oklo going critical, the theoretical maximum contribution to keff from increasing the probability that a captured thermal neutron will cause fission is quite small, making it impossible to say that we would have seen more such natural reactors if the creationists were right. Yes, if this were the only effect. And maybe the effect is even larger than you postulate. But you need to give me a reason to believe that the effect would occur, and be in the direction you say. I still maintain that I haven't yet seen an argument that a higher average number of neutrons would be produced from fission.

So maybe we need to take it step by step and review the K_eff equation and the individual factors.

(from http://en.wikipedia.org/wiki/Six_factor_formula)

k = η•f•p•ε•P_FNL•P_TNL

where

• η = the production factor (typical values* 1.65, 2.02)
  
• f = the thermal utilization factor (typical values 0.71, 0.799)
  
• p = the resonance escape probability (typical values 0.87, 0.80)
  
• ε = the fast fission factor (typical values 1.02, 1.04)
  
• P_FNL = the fast non-leakage probability (typical values 0.97, 0.865)
  
• P_TNL = the thermal non-leakage probability (typical values 0.99, 0,861)

* - first value from wiki table, second value from diagram below

Also shown diagrammatically (in a different order) by:

From http://nuclearpowertraining.tpub.com/...2/css/h1019v2_35.htm

I note from the formulas for each factor that several of them are inter-related, and four of the formulas are approximations.

In addition I note that the probability factors, f, p, P_FNL, and P_TNL, would have maximum values of 1.0

The values for the factors in the diagram multiplied together = 1.00.

The values for the factors in the wiki table multiplied together = 0.998.

The next question then is which of these factors are affected by reducing the binding energy of the nucleus.

We can start with η, the production factor

η = υ•σF_f/σF_a

where

• υ = the average number of neutrons produced per fission in the medium
  
• σF_f = the microscopic fission cross section
  
• σF_a = the microscopic absorption cross section

Interestingly, the wiki table here lists 2.43 for the average number of neutrons produced per fission in Uranium-235, where previously we had 2.52.

Enjoy

Edited by Zen Deist, : (deleted duplicate post)

Hi NoNukes,

I've been doing some reading for this and the other thread, and I've had some additional thoughts on the matter, which I'll add below.

We can start with η, the production factor η = υ•σFf/σFa where υ = the average number of neutrons produced per fission in the medium σFf = the microscopic fission cross section σFa = the microscopic absorption cross section If we start here, we aren't going to get very far. We currently disagree on how u is affected. I have been arguing that the effect on the cross section ratio must be small given that the ratio is already close to 1 and cannot exceed 1.

In other words, the only variable worth investigating in this equation is υ, the average number of neutrons produced per fission in the medium, and we disagree on whether or not it would be affected by the theoretical YEC mechanism that increases the decay constant of radioactive materials across the board (lets call this the "YEC factor" for brevity). I say more neutrons would be produced, you say you are not so sure there would be any difference. Fine.

I think we can agree though, that IF ν increased - and nothing else occurred - that THEN the scenario I have proposed for decreased critical mass and more frequent occurrence of natural reactors should result, yes? If it doubled it would have a significant effect, yes?

A simple yes or no at this time should suffice (caveat: it is my job to show that it could happen when we come back to this).

Curiously, when we are talking about changing the age of the earth from 4.55 billion years to 10,000 years we are talking about an enormous increase in the decay rate, yes? Yes, but we are discussing a parameter (fraction of neutrons absorbed by U235 that result in fission) that is already fairly close to 1, and which cannot increase above 1.

Is this is the f factor, the thermal utilization factor (the probability that a neutron that gets absorbed does so in the fuel material, with typical values 0.71, 0.799), that you are talking about?

Or is this the ε factor, the fast fission factor (total number of fission neutrons/total fission neutrons from thermal neutrons, with typical values 1.02, 1.04)?

Certainly we can give a preliminary go at each of the factors to determine which would be most useful to pursue and which we can eliminate as not significantly involved in the changes due to the YEC factor.

f = the thermal utilization factor (typical values 0.71, 0.799) = ΣF_a/Σ_a

Where ΣF_a and Σ_a are the macroscopic absorption cross sections in fuel and in total, respectively.

Now it should be evident that this would have a maximum value of 1 (ie everything is fuel), so a maximum effect would be on the order of ~20% increase in fission or reduction in critical mass. We can agree that this would not be significant, yes?

I don't see a reason to chase this down. Creating more alpha particles does not give us more neutrons. It might even result in fewer neutrons because alpha particles are such a stable and preferred arrangement. I've also argued that changing the fission product mix can produce results that lower criticality even if more neutrons are produced directly from fission. (See comments on Xe135 and neutron pre-cursors).

I'll use this as a segue to some additional thoughts.

What is produced is one of the issue here, certainly but first let's consider:

The YEC factor increases decay, so on one hand we have

• faster α decay, faster β decay
  
• faster spontaneous fission
  
• and in between these we can add cluster decay

And on the other hand we have induced fission, and

• induced fission affected by the YEC factor to increase fission
  
• induced fission unaffectedby the YEC factor
  
• induced fission affected by the YEC factor to decrease induced fission

Now one of the things we could do is compare the results for decay and induced fission within the materials at the Oklo reactors and other locations:

IF induced fission affected by the YEC factor increases fission, THEN there should be evidence of such fission in other locations.

IF induced fission is unaffected or negatively affected, THEN the decay of materials should be affected by decay disproportionately to the effects of induced fission.

Enjoy.

Edited by Zen Deist, : fishining

Edited by Zen Deist, : β decay link

Hi again NoNukes,

Absolutely. Increasing u has the potential for being a highly significant effect.

So that is A possibility to investigate further.

No. Here I was still talking about the cross section ratio in the equation for η.

And any variation there would be swamped by any variation in υ, thus we default to looking at variation in υ to modify η in any significant way by the YEC factor.

R and b are constant distances used to parametricize the potential felt by an alpha particle escaping the nucleus. I have no idea how to calculate R but it must be on the order of the size of the nucleus. Gamow gives a relation for b. I think the remaining variables in the equations are pretty straight forward. In the end, Gamow lumps all of the constants and gives a pretty simply relation between binding energy and the decay constant.

Wouldn't R be the nucleus\charge radius?

http://en.wikipedia.org/wiki/Charge_radius

quote:

---

The rms charge radius is a measure of the size of an atomic nucleus, particularly of a proton or a deuteron. It can be measured by the scattering of electrons by the nucleus and also inferred from the effects of finite nuclear size on electron energy levels as measured in atomic spectra.

---

The question then would be what the constants are, and which ones could be "tricked" by the YEC factor to create a shorter decay half-life.

I don't think we can make that assumption. The cross section ratio in the η formula is for a single material, U235 and is primarily a characteristic of U235 alone. In contrast, cross section ratio in the formula for f depends on the relative amounts of all absorbing materials in the reactor. In a commercial operating nuclear reactor a typical value might be .8, but in a natural mix of materials, f might be any value less than or equal to 1. This factor is one of the parameters through which lowered enrichment makes it impossible for a natural U235 reactor to form today.

Just in simple terms (1/0.8) = 1.25, or a 25% increase possible if ALL the material were included. This would not be a significant increase to the overall fission equation, correct?

However, it could be lower if there were smaller amounts of material available -- as there is today compared to the time the Oklo reactions occurred.

Or, for instance, if we assume that induced fission is unaffected by the YEC factor while the decay constant is changed to a much higher value, and then the fissile material would undergo this rapid decay and be removed from the reaction material, yes? And we should be able to compare the proportions of decay product to the fission product and see if there are anomalies, correct?

Further, the neutron absorption reaction is nothing like a decay reaction. I don't think Gamow's formula would help us predict how absorption rates would be affected by the change in energy. ...

So can we assume that the f factor would not be affected by the YEC factor?

... Similarly the factor p is also difficult to analyze.

Where p = the resonance escape probability (typical values 0.87, 0.80):

p ≈ e^{{Σ_(i=1→N)(N_i,I_r,A,i}/{(ζΣ_p)_mod}}

... looks like I'm going to need to learn how to write formulas ... especially when I_r,A,i is even more complicated ...

Given that the maximum value is 1 so there is little room for significant effect, and that this is an approximation, I would be happy to agree that this would not be likely to change in any way that would significantly affect the issue of run-away fission or decreased critical mass.

Moving on would take us to the ε factor, the fast fission factor (total number of fission neutrons/total fission neutrons from thermal neutrons, with typical values 1.02, 1.04)?

I would agree that this would change little, with some neutrons now having the additional energy to cause fission while others would become too energetic for thermal fission, and that any change here would be captured in the other factors. Certainly it would not go below 1.0, and, while there could be more fast neutron fissions with less stable nuclei, there is little reason to think that this would be significant to the overall picture, yes?

Next we can consider the fast non-leakage probability factor:

P_FNL ≈ e^{-B_g2•τ_th}

This is the probability that a fast neutron will not leak out of the system (with typical values 0.97, 0.865).

Once again we have a maximum value of 1.0 so any increase from the YEC factor would not be a significant effect on the issue of run-away fission or decreased critical mass.

Similar for the thermal non-leakage probability factor:

P_TNL = ≈ 1/{1+L_th²•B_g²}

This is the probability that a thermal neutron will not leak out of the system (with typical values 0.99, 0,861)

And once again we have a maximum value of 1.0 so any increase from the YEC factor would not be a significant effect on the issue of run-away fission or decreased critical mass.

In summary,

the possibilities for significant increase in induced fission come down to:

• a significant increase in υ
  
• no offsetting changes in the other factors (no effect from the YEC factor)
  while the possibilities for significant decrease in induced fission come down to:
  
• significant decreases in all the factors other than υ
  
• no offsetting increase in υ

OR

k = η•f•p•ε•P_FNL•P_TNL

k = (υ•σF_f/σF_a)•f•p•ε•P_FNL•P_TNL

k = υ•(σF_f/σF_a•f•p•ε•P_FNL•P_TNL)

or, for brevity, k = υ•F_c

Where F_c is all the other factors combined.

And for k = 1 (the boundary condition) υ = 1/F_c

And we get these conditions:

1. IF υ >> 1/F_c THEN significantly more fission should occur, the critical mass required should be smaller;
   
2. IF υ ≈ 1/F_c THEN no significant change in fission should occur, the critical mass required should be about the same as today;
   
3. IF υ << 1/F_c THEN significantly less fission should occur, the critical mass required should be larger

Now, I would argue that the existence of the Oklo reactors is sufficient evidence that option 3 did not occur, would you agree?

Enjoy.

Hi NoNukes, I'll reply to Message 21 as well.

Thanks to you I am making some headway in my thoughts, even if they aren't quite in the direction I originally proposed.

Message 22: Finally, let's take a crude look at a possibility that an increased in the speed of light might have an affect on alpha decay rates. The speed of light is inversely proportional to the square root permittivity of free space. So changing the speed of light could result from a change in permittivity. While the speed of light also depends on the permeability of free space, permeability does not affect the decay constant. I think we can ignore this latter possibility, since we are not trying to claim that halo data proves that the speed of light is constant. The problem for this hypothesis is that according to Gamow's work, both the decay energy and the decay constant are strongly dependent on the permittivity of free space. This means that changing the permittivity of free space should disturb halo production.

So we know that didn't happen, due to the uranium halos.

SN1987A also does a good job of showing constant speed of light. It also has absorption bars in the spectrum for various elements produced during the nova, some of which are radioactive, and they (⁵⁶Co in particular, half-life=77.27 days) appear to decay during the supernova to the same decay constant that we see here today.

This, of course, is a bit of a tangent issue, but I think we can eliminate any change to c, and concentrate on binding energy.

Finally I note that changing the decay rate without changing the decay energy does not seem to be a great way of resolving the issue of what happens to all of that heat when nuclides decay.

Yes, to reduce the heat that would be generated by increased decay there would have to be a reduction in particle energy (which also would have shown up in the uranium halos).

This too is a bit of a tangential issue here, and I think we can ignore this for now.

One could argue, perhaps, that the effect of shorter time would make the particles behave as if they had more energy, which would be mathematically similar to lowering the binding energy.

Message 21: Gamow models the potential acting on an alpha particle leaving the nucleus as a square potential well up to radius R and a coulombic (eletrostatic) potential outside of that distance. So R is related to the distance over which a nuclear attractive force holds a nucleon in place. I think it is likely that R is related to the radius of the nucleus or the number of nucleons in the nucleus in some complex way. I don't know if it is worth the effort to investigate it any further than that. Message 22: As previously discussed Gamow models the potential which the emitted particle as a combination of a square well potential and a coulombic field. A neutron, having no charge is not affected by coulombic forces. I doubt that it is appropriate to simply substitute zero into the equations for Zalpha, but doing so result in there being no binding energy dependency on the decay constant. Secondly, if the nucleus splits or becomes significantly smaller during decay then the characterization of the nucleon attractive force using R and Zd from the original nucleus would seem to be entirely inappropriate.

One thing we need to remember is that within the nucleus, protons and neutrons are not fixed particles, but are constantly change from one to the other by exchanging a β particle\electron\gluons, and this is why β decay results in an additional proton in the nucleus. The probability of neutron emission would then be a result of the probability of the particle being a neutron when the time comes to be emitted.

Another thing I have considered is that the υ factor - the production of neutrons during induce fission - is likely bound more by the resultant daughter nuclei and their stability, their need for neutrons: the neutrons are produced because they are extra, the daughter nuclei don't need them.

This would make it difficult to change this factor by the YEC factor affecting decay, yes? If it did, this would more likely be a result of a change across the board (all elements\isotopes) in the number of neutrons needed in the nucleus for stability. Not sure we need to go there.

So can we assume that the f factor would not be affected by the YEC factor? Message 21: I think that's a good first guess. At this point, if I were to propose a negative effect or an uncertain effect, I think I'd owe you an explanation. I think factor "p" is likely to be a different story. I'm still considering my position on "p". Message 22: Let's consider the application of Gamow's model to nuclear absorption. Neutrons experience essentially no barrier to entering a nucleus. We haven't discussed exactly how the modification of the binding energy is accomplished, but I would expect that all of the energy states of the nucleus are effected. Thus the probably absorption of fast neutrons and the resulting fissions, which includes absorption at resonance peaks based on the energy states of the nucleus is likely to be affected in some way. I have yet to figure out how to characterize this.

I think we should focus on the issue of the stability of the nuclei and how that can vary: this is what I see the YEC factor affecting in order to reduce the decay time. Then we can see how that might affect the different factors in the k equation.

Nucleic stability and particle decay are dependent on the binding energy, which is essentially the strong force.

http://en.wikipedia.org/wiki/Nuclear_force

quote:

---

The nuclear force (or nucleon-nucleon interaction or residual strong force) is the force between two or more nucleons. It is responsible for binding of protons and neutrons into atomic nuclei. The energy released causes the masses of nuclei to be less than the total mass of the protons and neutrons which form them. The force is powerfully attractive between nucleons at distances of about 1 femtometer (fm) between their centers, but rapidly decreases to insignificance at distances beyond about 2.5 fm. At very short distances less than 0.7 fm, it becomes repulsive, and is responsible for the physical size of nuclei, since the nucleons can come no closer than the force allows.

The nuclear force is now understood as a residual effect of the even more powerful strong force, or strong interaction, which is the attractive force that binds particles called quarks together, to form the nucleons themselves. This more powerful force is mediated by particles called gluons. Gluons hold quarks together with a force like that of electric charge, but of far greater power

---

The binding energy is the energy needed to overcome the strong force/s.

I come back to this, from Message 20, updated:

quote:

---

1. IF υ >> 1/F_c THEN significantly more fission should occur, the critical mass required should be smaller;
   
2. IF υ ≈ 1/F_c THEN no significant change in fission should occur, the critical mass required should be about the same as today;
   
3. IF υ << 1/F_c THEN significantly less fission should occur, the critical mass required should be larger

---

... for ²³⁵U fission.

This is also assuming that the products of fission would remain the same as today, even though the nuclei have less stability, and I don't necessarily agree that this is a valid assumption (and I believe you have said similar).

Discussing different possible daughter fission products from ²³⁵U fission, in my opinion anyway, would not be too productive at this time because (a) it is speculative and (b) it would have shown up in the Oklo reactions.

It seems we can have a pretty solid assumption\conclusion that the Oklo reactions were virtually identical to modern reactor reactions, in the way the fission occurred and in the products of fission, and in the time it took for the reactions to occur.

This takes me back to comparing decay at Oklo to fission at Oklo, Message 18:

quote:

---

Now one of the things we could do is compare the results for decay and induced fission within the materials at the Oklo reactors and other locations:

IF induced fission affected by the YEC factor increases fission, THEN there should be evidence of such fission in other locations.

IF induced fission is unaffected or negatively affected, THEN the decay of materials should be affected by decay disproportionately to the effects of induced fission.

---

The problem I have here is that there is no evidence that this disproportion did occur.

http://oklo.curtin.edu.au/when.cfm

quote:

---

The history of the Oklo fossil reactors spans almost the entire history of the earth. ‘Oklotime’ can be divided into four stages:

1. U mobilization phase: Commenced ~3500 million years ago.
   
2. U ore/reactor formation: Started ~2800 million years ago.
   
3. Reactor operation: Commenced 2000 million years ago (for about a million years).
   
4. Waste movement: The last 2000 million years.

Each reactor operated on an intermittent basis for a period ranging from a few years to hundreds of thousands of years. The total time period over which the reactors operated is thought to be about a million years.

---

If the YEC factor does not affect induced fission, but does shorten "2000 million years" (2 billion) into a short enough period to fit a YEC scenario, then how could so much product of fission have occurred without the reactor lasting "hundreds of thousands of years" to "a million years"?

The other issue I have is ²³⁸U fission.

We see that Oklo acted as a breeder reactor:

quote:

---

Initially the fission and resulting neutrons come from the fission of 235U. However, the presence of very high abundance of 238U absorbs some of the neutrons to become 239U. This in turn decays by beta decay to Neptunium 239 and the 239Pu. The Resulting 239Pu then fissions but there is another twist to the story. The natural reactors operated for so long that the 239Pu had sufficient time to decay by alpha decay to 235U. Thus the natural reactors were true ‘Breeder’ reactors, fissioning in some cases more 235U than originally existed in the reactors.

---

(Hence resulting in the enriched ore that brought this site to international scientific attention)

Here we have ²³⁸U fission.

As I understand it ²³⁵U fission is fissile and ²³⁸U fission is fissionable.

http://en.wikipedia.org/wiki/Fissile

quote:

---

"Fissile" is distinct from "fissionable." A nuclide capable of undergoing fission after capturing a neutron is referred to as "fissionable." A fissionable nuclide that can be induced to fission with low energy thermal neutrons is referred to as "fissile." Although the terms were formerly synonymous, fissionable materials include also those (such as uranium-238) that can be fissioned only with high-energy neutrons. As a result, fissile materials (such as uranium-235) are a subset of fissionable materials.

Uranium-235 fissions with low-energy thermal neutrons because the binding energy resulting from the absorption of a neutron is greater than the critical energy required for fission; therefore uranium-235 is a fissile material. By contrast, the binding energy released by uranium-238 absorbing a thermal neutron is less than the critical energy, so the neutron must possess additional energy for fission to be possible. Consequently, uranium-238 is a fissionable material but not a fissile material. [2]

---

Now we can agree that ²³⁵U fission is pretty much "maxed" out on several of the factors in the k formula -- due to it being fissile. But what about ²³⁸U?

The difference between ²³⁵U (fissile) and ²³⁸U (fissionable) is the bonding energy, the same bonding energy that affect decay rates.

quote:

---

(ibid) Under all definitions above, uranium-238 (U-238) is fissionable, but because it cannot sustain a neutron chain reaction, it is not fissile. Neutrons produced by fission of U-238 inevitably inelastically scatter to an energy below 1 MeV (i.e., a speed of about 14,000 km/s), the fission threshold to cause subsequent fission of U-238, so fission of U-238 does not sustain a nuclear chain reaction.

---

Would not a reduction in bonding energy (by the YEC factor to increase decay) also affect the boundary between fissile and fissionable isotopes?

Note that 1 MeV is less than most decay energies, so we are not talking about a large change here. Certainly it seems reasonable to think that a reduction in bonding energy that allow sufficient change in decay to make a significant impact on the measured age of the earth would be plenty of a shift to turn ²³⁸U into a fissile isotope.

If this did happen then there should have been a lot more natural reactors and there should be evidence of ²³⁸U fission in other locations where ²³⁵U fission was not a factor, yes?

Enjoy.

Hi NoNukes

I think this is a rather curious thing to say. I don't think there is a time for a nucleus to emit a neutron.

Just a conceptualization trying to tie your zero energy barrier for neutrons into the probability matrix.

I didn't address this argument. The problem see with the argument is that we need to know the crank that was actually turned so that we can model the change in each nuclide. Was the binding energy of each nuclei changed by a constant factor, decremented by a constant amount, is it possible was some other independent parameter was varied in a consistent way for each atom so that decay rates changed by constant ratios? I am not sure exactly where to start.

One way would be to start with several instances (not just Oklo) where radioactive dating confirms the scientific date by several different methods - they arrive at the same dates by different methods from different decay materials, some with multiple steps (parent daughter analysis).

Another way would be to calculate the change in binding energy to double the rate, and then see if that makes some fissionable isotopes (²³⁸U for instance) become fissile in average concentrations known today.

If you can't reduce the decay time for ²³⁸U significantly with binding energy without the material becoming fissile and subject to inductive fission from a stray neutron (in the way that ²³⁵U is today, except that ore exists with much higher concentrations of ²³⁸U than ²³⁵U, right?) ... then changing the binding energy is not the solution.

With c already ruled out that doesn't leave much wiggle room.

Enjoy.

Hi NoNukes,

My point is that once magic is invoked, any and all rules might be broken.

Then the available evidence unequivocally shows the earth to be billions of years old.

Changing c would be invoking magic, and changing the strong force would be invoking magic. The question is whether or not we can eliminate any "natural" change to c or the strong force in some distant past through the evidence available.

Let's do a bit of a review here.

The issue raised by foreveryoung was whether the decay rate could be increased. This would have to apply across the board for all systems that use radioisotopes for dating, and this includes virtually every radioactive molecule.

We looked quickly at the c constant, because

M₁ = M₂ + mp + e/c²

where
M₁ is the mass of the nucleus before decay
M₂ is the mass of the nucleus after decay
mp is the mass of the particle
e is the decay energy of particle mp
c is the speed of light constant

We noted also that there is a relationship between decay energy and half-life:

quote:

---

Are Uranium Halos the best evidence of (a) an old earth AND (b) constant physics? Message 7:

... Once an approximate size of the nucleus was obtained by Rutherford scattering, one could calculate the height of the Coulomb barrier at the radius of the nucleus. It was evident that this energy was several times higher than the observed alpha particle energies. There was also an incredible range of half lives for the alpha particle which could not be explained by anything in classical physics.

The resolution of this dilemma came with the realization that there was a finite probability that the alpha particle could penetrate the wall by quantum mechanical tunneling. Using tunneling, Gamow was able to calculate a dependence for the half-life as a function of alpha particle energy which was in agreement with experimental observations.

---

We have shown through reviewing the Gamow equations that the decay half-life is related inversely to the binding energy, and that a change in one effectively changes the other.

If we change c then e changes and the decay half-life changes.

Unfortunately, for foreveryoung anyway, uranium halos show that the decay energy did not change for the duration of the halo formation, which is hundreds of thousands of years. This alone effectively rules out any past change to c per the above equation.

Skipping over the whole issue of ²³⁵U for now, we can note that another possible path to increase decay is to reduce the stability of the molecules so that they decay faster but don't change the decay energy (a finely tuned adjustment eh?).

This is directly related to the strong force. If the strong force were reduced, the binding energy would be reduced, thus allowing shorter decay half-lives. With a little mathematical gymnastics we can likely calculate a relationship that would hold e (or e/c) constant while reducing the binding energy of the nucleus, would you not agree?

Thus we need to look into the effects of such a reduction in strong force and see if there is any evidence to show that this did not occur "naturally" in some distant past.

I put it to you that, for such a reduction in strong force to have a significant effect on the half-lives of radioactive decay, that this would also result in fissionable element\isotopes becoming fissile element\isotopes and that we would see mountains of evidence of this. For example, ²³⁸U would only need its binding energy reduced by ~1 MeV, a rather small amount. We know - from the current concentrations of ²³⁸U in some ores, that this did not happen.

We should also be able to calculate the approximate effect on half-life this 1 MeV change would have, and then show that this is not sufficiant to significantly alter the age of the earth enough for YEC needs.

That only leaves magic.

Enjoy.