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Author Topic:   Spontaneous fission, decay rates, and critical mass
NoNukes
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Posts: 9993
From: Central NC USA
Joined: 08-13-2010
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Message 16 of 29 (647496)
01-10-2012 12:29 AM
Reply to: Message 15 by RAZD
01-09-2012 1:57 PM


Re: Decay rates, change, and atomic stability
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.

If both increased in the same ration, there would be no effect on k. It would mean that the lifetime of a generation of neutrons is shorter, but that would not affect criticality.

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.

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

I think I just did. I'm pretty sure that I made the same argument in a previous post.

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.

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).

ZD writes:

NN writes:

... 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.

Didn't I argue exactly that point? My point is that the contribution, if any, from affecting the number of captured neutrons that cause fission is far less than the other sources of positive reactivity that we believe contributed to the forming of natural reactors, such that we cannot say that there should be more natural reactors than we currently find if the binding energy were lowered in the past.


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.

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.

Actually I cited 2.4+.


Under a government which imprisons any unjustly, the true place for a just man is also in prison. The proper place to-day, the only place which Massachusetts has provided for her freer and less desponding spirits, is in her prisons, to be put out and locked out of the State by her own act, as they have already put themselves out by their principles. Thoreau: Civil Disobedience (1846)

This message is a reply to:
 Message 15 by RAZD, posted 01-09-2012 1:57 PM RAZD has responded

Replies to this message:
 Message 17 by RAZD, posted 01-10-2012 7:06 PM NoNukes has acknowledged this reply
 Message 18 by RAZD, posted 01-10-2012 7:23 PM NoNukes has responded

    
RAZD
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Posts: 19079
From: the other end of the sidewalk
Joined: 03-14-2004
Member Rating: 2.6


Message 17 of 29 (647696)
01-10-2012 7:06 PM
Reply to: Message 16 by NoNukes
01-10-2012 12:29 AM


Re: Decay rates, change, and atomic stability

Edited by Zen Deist, : (deleted duplicate post)


we are limited in our ability to understand
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... to learn ... to think ... to live ... to laugh ...
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This message is a reply to:
 Message 16 by NoNukes, posted 01-10-2012 12:29 AM NoNukes has acknowledged this reply

  
RAZD
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Posts: 19079
From: the other end of the sidewalk
Joined: 03-14-2004
Member Rating: 2.6


Message 18 of 29 (647700)
01-10-2012 7:23 PM
Reply to: Message 16 by NoNukes
01-10-2012 12:29 AM


Re: Decay rates, change, and atomic stability
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) = ΣFaa

Where ΣFa and Σa 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

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


we are limited in our ability to understand
by our ability to understand
Rebel American Zen Deist
... to learn ... to think ... to live ... to laugh ...
to share.


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This message is a reply to:
 Message 16 by NoNukes, posted 01-10-2012 12:29 AM NoNukes has responded

Replies to this message:
 Message 19 by NoNukes, posted 01-11-2012 10:02 AM RAZD has responded

  
NoNukes
Member
Posts: 9993
From: Central NC USA
Joined: 08-13-2010
Member Rating: 2.3


Message 19 of 29 (647784)
01-11-2012 10:02 AM
Reply to: Message 18 by RAZD
01-10-2012 7:23 PM


Re: Decay rates, change, and atomic stability
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?

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

Zen Deist writes:

NN writes:

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?

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

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 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.

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. Similarly the factor p is also difficult to analyze.

I did take a look at Gamow's formulas, and I thought I would say something about the variables involved.

The Z values are the number of units of charge on a particle, and in the formula Zalpha = 2, and ZD is the number of protons in the decaying nucleus.

ε0, is the permittivity of free space, which is a constant.
http://en.wikipedia.org/wiki/Vacuum_permittivity. A dependency on the speed of light might be introduced via this constant.

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.


Under a government which imprisons any unjustly, the true place for a just man is also in prison. The proper place to-day, the only place which Massachusetts has provided for her freer and less desponding spirits, is in her prisons, to be put out and locked out of the State by her own act, as they have already put themselves out by their principles. Thoreau: Civil Disobedience (1846)

This message is a reply to:
 Message 18 by RAZD, posted 01-10-2012 7:23 PM RAZD has responded

Replies to this message:
 Message 20 by RAZD, posted 01-11-2012 3:45 PM NoNukes has responded

    
RAZD
Member
Posts: 19079
From: the other end of the sidewalk
Joined: 03-14-2004
Member Rating: 2.6


Message 20 of 29 (647851)
01-11-2012 3:45 PM
Reply to: Message 19 by NoNukes
01-11-2012 10:02 AM


Re: Decay rates, change, and atomic stability
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(i=1→N)(Ni,Ir,A,i}/{(ζΣp)mod}

... looks like I'm going to need to learn how to write formulas ... especially when Ir,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:

PFNL ≈ e-Bg2•τth

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:

PTNL = ≈ 1/{1+Lth2•Bg2}

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•PFNL•PTNL

k = (υ•σFf/σFa)•f•p•ε•PFNL•PTNL

k = υ•(σFf/σFa•f•p•ε•PFNL•PTNL)

or, for brevity, k = υ•Fc

Where Fc is all the other factors combined.

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

And we get these conditions:

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


we are limited in our ability to understand
by our ability to understand
Rebel American Zen Deist
... to learn ... to think ... to live ... to laugh ...
to share.


• • • Join the effort to solve medical problems, AIDS/HIV, Cancer and more with Team EvC! (click) • • •

This message is a reply to:
 Message 19 by NoNukes, posted 01-11-2012 10:02 AM NoNukes has responded

Replies to this message:
 Message 21 by NoNukes, posted 01-11-2012 4:34 PM RAZD has acknowledged this reply
 Message 22 by NoNukes, posted 01-12-2012 1:04 PM RAZD has responded

  
NoNukes
Member
Posts: 9993
From: Central NC USA
Joined: 08-13-2010
Member Rating: 2.3


(1)
Message 21 of 29 (647862)
01-11-2012 4:34 PM
Reply to: Message 20 by RAZD
01-11-2012 3:45 PM


Re: Decay rates, change, and atomic stability
Greetings Zen Deist,

Zen Deist writes:

So that is A possibility to investigate further.

Yes. It is likely to be the most important one.

Zen Deist writes:

Wouldn't R be the nucleus\charge radius?

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.

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?

IMO, that proposition is not correct. There is no reason to expect that the f cannot decrease to zero or that f is nominally 0.8 in a natural critical reactor. The value of f varies strongly and directly with the enrichment ratio and indirectly with the amount of reactivity poisons. The argument used to limit excursions of the cross section ratio in η does NOT apply to f.

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

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".

Some of the factors in the keff formula can be greater than one, although that possibility does not apply to the factors we've discussed so far absent some pretty funky mechanisms.

ABE
oops. the reproduction factor in a critical reactor is of course greater than 1.

Edited by NoNukes, : No reason given.

Edited by NoNukes, : No reason given.


Under a government which imprisons any unjustly, the true place for a just man is also in prison. The proper place to-day, the only place which Massachusetts has provided for her freer and less desponding spirits, is in her prisons, to be put out and locked out of the State by her own act, as they have already put themselves out by their principles. Thoreau: Civil Disobedience (1846)

This message is a reply to:
 Message 20 by RAZD, posted 01-11-2012 3:45 PM RAZD has acknowledged this reply

    
NoNukes
Member
Posts: 9993
From: Central NC USA
Joined: 08-13-2010
Member Rating: 2.3


(1)
Message 22 of 29 (647984)
01-12-2012 1:04 PM
Reply to: Message 20 by RAZD
01-11-2012 3:45 PM


More thoughts about Gamow's equations or "When nuclides decay"
I was doing some more thinking about Gamow's derivation, and I think that we cannot say that his result applies to situations where uncharged particles are emitted from a nucleus, or where the nucleus that does not remain largely intact.

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.

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.

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.

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.
One might also ask why someone who believes in a fine tuned universe would make such an argument.

Edited by NoNukes, : One two many "finally"s


Under a government which imprisons any unjustly, the true place for a just man is also in prison. The proper place to-day, the only place which Massachusetts has provided for her freer and less desponding spirits, is in her prisons, to be put out and locked out of the State by her own act, as they have already put themselves out by their principles. Thoreau: Civil Disobedience (1846)

This message is a reply to:
 Message 20 by RAZD, posted 01-11-2012 3:45 PM RAZD has responded

Replies to this message:
 Message 23 by RAZD, posted 01-12-2012 5:45 PM NoNukes has responded

    
RAZD
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Posts: 19079
From: the other end of the sidewalk
Joined: 03-14-2004
Member Rating: 2.6


Message 23 of 29 (648029)
01-12-2012 5:45 PM
Reply to: Message 22 by NoNukes
01-12-2012 1:04 PM


Re: More thoughts about Gamow's equations or "When nuclides decay"
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/Fc THEN significantly more fission should occur, the critical mass required should be smaller;
  2. IF υ ≈ 1/Fc THEN no significant change in fission should occur, the critical mass required should be about the same as today;
  3. IF υ << 1/Fc 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.


we are limited in our ability to understand
by our ability to understand
Rebel American Zen Deist
... to learn ... to think ... to live ... to laugh ...
to share.


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This message is a reply to:
 Message 22 by NoNukes, posted 01-12-2012 1:04 PM NoNukes has responded

Replies to this message:
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NoNukes
Member
Posts: 9993
From: Central NC USA
Joined: 08-13-2010
Member Rating: 2.3


Message 24 of 29 (648042)
01-12-2012 7:09 PM
Reply to: Message 23 by RAZD
01-12-2012 5:45 PM


Re: More thoughts about Gamow's equations or "When nuclides decay"
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.

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.

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.

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.

I'll ponder this some more, but I won't spend any more time on keff.

Edited by NoNukes, : No reason given.


Under a government which imprisons any unjustly, the true place for a just man is also in prison. The proper place to-day, the only place which Massachusetts has provided for her freer and less desponding spirits, is in her prisons, to be put out and locked out of the State by her own act, as they have already put themselves out by their principles. Thoreau: Civil Disobedience (1846)

This message is a reply to:
 Message 23 by RAZD, posted 01-12-2012 5:45 PM RAZD has responded

Replies to this message:
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RAZD
Member
Posts: 19079
From: the other end of the sidewalk
Joined: 03-14-2004
Member Rating: 2.6


Message 25 of 29 (648053)
01-12-2012 10:34 PM
Reply to: Message 24 by NoNukes
01-12-2012 7:09 PM


Re: More thoughts about Gamow's equations or "When nuclides decay"
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.


we are limited in our ability to understand
by our ability to understand
Rebel American Zen Deist
... to learn ... to think ... to live ... to laugh ...
to share.


• • • Join the effort to solve medical problems, AIDS/HIV, Cancer and more with Team EvC! (click) • • •

This message is a reply to:
 Message 24 by NoNukes, posted 01-12-2012 7:09 PM NoNukes has responded

Replies to this message:
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NoNukes
Member
Posts: 9993
From: Central NC USA
Joined: 08-13-2010
Member Rating: 2.3


Message 26 of 29 (648142)
01-13-2012 12:01 PM
Reply to: Message 25 by RAZD
01-12-2012 10:34 PM


Re: More thoughts about Gamow's equations or "When nuclides decay"
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.

My point is that once magic is invoked, any and all rules might be broken. I don't see any possible way for binding energy to be changed without some supernatural intervention.


Under a government which imprisons any unjustly, the true place for a just man is also in prison. The proper place to-day, the only place which Massachusetts has provided for her freer and less desponding spirits, is in her prisons, to be put out and locked out of the State by her own act, as they have already put themselves out by their principles. Thoreau: Civil Disobedience (1846)

This message is a reply to:
 Message 25 by RAZD, posted 01-12-2012 10:34 PM RAZD has responded

Replies to this message:
 Message 27 by RAZD, posted 01-13-2012 9:44 PM NoNukes has responded

    
RAZD
Member
Posts: 19079
From: the other end of the sidewalk
Joined: 03-14-2004
Member Rating: 2.6


Message 27 of 29 (648204)
01-13-2012 9:44 PM
Reply to: Message 26 by NoNukes
01-13-2012 12:01 PM


decay energy, the speed of light, the strong force, Uranium haloes and 238U fission
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.


we are limited in our ability to understand
by our ability to understand
Rebel American Zen Deist
... to learn ... to think ... to live ... to laugh ...
to share.


• • • Join the effort to solve medical problems, AIDS/HIV, Cancer and more with Team EvC! (click) • • •

This message is a reply to:
 Message 26 by NoNukes, posted 01-13-2012 12:01 PM NoNukes has responded

Replies to this message:
 Message 28 by NoNukes, posted 01-15-2012 4:56 PM RAZD has not yet responded

  
NoNukes
Member
Posts: 9993
From: Central NC USA
Joined: 08-13-2010
Member Rating: 2.3


Message 28 of 29 (648420)
01-15-2012 4:56 PM
Reply to: Message 27 by RAZD
01-13-2012 9:44 PM


Re: decay energy, the speed of light, the strong force, Uranium haloes and 238U fission
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.

Yes, as best we know. Further, there is no evidence that "c" has ever changed. Thank goodness we foreveryoung isn't dragging us down that rabbit hole.

In my view, the difficult is to deny the link between decay constant and decay energy. Gamow not only shows that they are linked, but it also provides one technique for looking at the strength of the link with other constants (charge on electron, nuclear masses, permittivity, etc.)

But that said, we know that Gamow's relations are based on an approximating model, and we might well question it's predictions based on the equation that are not verified by experiment. For example, Bohr's planetary model of the atom worked pretty well to explain the known spectra of the Hydrogen atom, but there are lots of details regarding even hydrogen that the Bohr model cannot explain. Quantum based models of hydrogen explain essential all of hydrogen's chemical behavior.

Further, a creationist is very unlikely to accept that any of this science means anything. "With man this is impossible, but with God all things are possible."


Under a government which imprisons any unjustly, the true place for a just man is also in prison. The proper place to-day, the only place which Massachusetts has provided for her freer and less desponding spirits, is in her prisons, to be put out and locked out of the State by her own act, as they have already put themselves out by their principles. Thoreau: Civil Disobedience (1846)

This message is a reply to:
 Message 27 by RAZD, posted 01-13-2012 9:44 PM RAZD has not yet responded

    
pandion
Member (Idle past 557 days)
Posts: 166
From: Houston
Joined: 04-06-2009


Message 29 of 29 (648481)
01-16-2012 12:33 AM
Reply to: Message 23 by RAZD
01-12-2012 5:45 PM


Re: More thoughts about Gamow's equations or "When nuclides decay"
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...

This is true of every nuclear fission reaction in the presence of 238U. More than 1/3 of the power from reactors in the U.S. is from the fission of Pu239 that results from neutron capture in 238U.
quote:
...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.

To be honest, I had never thought of the alpha decay of Pu239 as a source of 235U. However, since the Pu239 is generally involved in the reaction almost as fast as it is produced, it doesn't seem possible that it could increase the depleted levels of U235 to levels above that of the surrounding ores.
Zen Deist writes:

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


What? The Oklo reactors were discovered, not because of higher levels of U235, but of lower levels of U235. The natural reactors were confirmed by the presence of fission products.

My source is my son's nuclear engineering text: Raymond L. Murray. Nuclear Energy. 1988. Pergamon Press. New York.

Of course, the time from when the reactors were active to the time when they were discovered has been sufficient for levels of most isotopes of Plutonium to have decayed below levels of detection. I have read that trace amounts of Pu244 have been detected in the Oklo reactors.

The concept of a breeder reactor is not that it produces fissile material from the reaction, but that it produces more fissile material than was consumed in the reaction. Modern breeder reactors accomplish this by surrounding the reactor core with a blanket of U238 that is not part of the core reaction. Neutrons that escape the core produce Pu239 in the blanket. The plutonium is then refined from the blanket and has potential energy more than that produced from the core reaction.

Please correct me if I am wrong. Sources please.


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