A question of force(strong nuclear)

[elurius]

I have a question that I have been working on for some time now. In this effort I have hit a bit of a road block. The question is simple, but I am sure that those of you willing to help me will provide ample complications to my thoughts.

I am looking for a specific value for the strong nuclear force(interaction) for a specific isotope. I am not particular about the isotope, but please let me know which isotope is being used for the force given.

If there is a refference that has the values for the strong nuclear force listed, please let me know. I have had no luck in finding such a refference.

Some background. I lack the higher math skills to use the existing formulae to calculate the strong nuclear force. I am in the process of learning these skills. Additionally, this question is to help me with a personnal project, and is not related to any know studies, or research projects.

Thank you to any who offer their insight, or guidance.

 

[kurros]

Err, I'm afraid that from your post it isn't entirely clear what you want. What kind of "value for the strong nuclear force" are you looking for? Are you interested in the cross-section for some nuclear process?

 

[elurius]

Kurros,
My belief is that there is a value for the strong nuclear force for any given nucleus of an atom that may be represented in classic terms of force(like Newtons, or pounds(f)). The values should be known for isotopes like deuterium, for predictions relating to nuclear fusion. A value for a cross section of absorbtion, or scattering will not give me the information that I need. Which rules out the chart of nuclides as a refference. I will be using the value for some force comparisons that I am working with.

I realize that this is an odd question that shows a certian lack of knowledge on my part. I hesitate to offer the full scope of my project so as not to seem too infantile. But through my project I am learning a great deal.

Thank you very much for your interest, and time. Best wishes.

 

[kurros]

My belief is that there is a value for the strong nuclear force for any given nucleus of an atom that may be represented in classic terms of force(like Newtons, or pounds(f)).

Ahh, I see. Are you thinking along the lines of gravity? Say if you take two objects that are stuck together by gravity and ask what force they exert on each other? There is an answer for this for any two objects, sure, but it depends on the size and masses of the particular objects you have. Is this the kind of thing you are looking for? Say if you take a helium nucleus and ask what force each of the nucleons exert on each other? There is some discussion that could be had about that, although it is much more complicated than the gravity case I described and it wouldn't result in a single number.

If this is not what you want then perhaps you could describe the classical analogue of the thing you are looking for, and then we can decide if such a thing can be transferred into this context or not.

 

[elurius]

Kurros,
I think you are thinking in the same direction that I am. The gravity metaphor is the structural model that I am functioning under. The idea that there would be multiple values for the interaction I assume would be dependant on the masses of the particles involved, and the distance between them.

The helium example is a good place to start. I am wondering how to determine the strong nuclear force between two helium-4 nuclei independant of the obvious electromagnetic repulsion(columb barrier if I understand it correctly) as a function of distance. This offers a consistant mass basis.

I would think that the resultant formula would have a similarity to Newton's law of universal gravitation, though with significant differences. Thus far, I have not found a formula describing the strong nuclear force that has a distance element following the inverse square law. I believe this( 1/d^2) to be a critical element in describing any radial force(such as gravity).

Please forgive my delay in replying. Life has a way of taking up time.
As always, thank you for your help, and guidance.

 

[fzero]

To lowest order, you can model the strong force between nuclei with a Yukawa potential

$$V(r) = C \frac{\hbar c }{r}e^{-m_{\pi^0} c r/\hbar},$$

where $m_{\pi^0}$ is the mass of the neutral pion and $c$ is the speed of light. The coefficient $C$ is of order 1, but I don't know of a good estimate. The proper modeling of the force is rather complicated, as can be seen in a reference like http://arxiv.org/abs/nucl-th/9408016, which is discussing nucleon-nucleon forces. Nucleus-nucleus forces are even more complicated and I don't know of a specific reference.

 

[elurius]

A wonderful formula. The mathematical form seems to reflect what I expected to see.

Now I get to show my lack of knowledge. I don't know the value, and units for the coefficient C. I am also unfamiliar with the crossed h variable. With these two little tidbits I think I can do the calculations that I have been aiming for.

Also, I downloaded the paper that was recomended. At this time I have not finished reading the paper. The detail is well beyond my level of knowledge, but now I have a good direction to continue my reading and learning.

As always, thank you for the help.

 

[Vaibhav089]

The crossed-h or the h-bar is the Reduced Planck's Constant. It is widely used in Quantum Mechanics as it makes mathematical expressions look (a little) less intimidating. Mathematically; the reduced Planck's constant equals Planck's constant divided by (2*pi).
I'm sure you can figure out what the coefficient C represents using the good old Dimensional Analysis. Shouldn't be that hard.