How Accurate is the Nucleus Size Determined from Rutherford Scattering?

[gianeshwar]

By calculating the distance of closest approach, an estimate of the size of nucleus can be made.
I believe it can give only order sequence of sizes of nuclei of different elements and obviously not exact size as electrostatic repulsion is balanced by KE of the incoming alpha particles away from nuclei.
Then how exact size is determined?

 

[DEvens]

The "exact size" of a nucleus depends on how you define it. And it won't be exact because we are dealing with inherently quantum structures here. A nucleus involves a bunch of particles bound together. Even simple Hydrogen, a single proton, has three quarks bound together. So there is always some quantum effects going on.

But basically, the idea is that a nucleus behaves like a clump of bound particles. By scattering particles of different kind and energy, by studying the energy states, and by studying their decay modes, you can get a pretty good idea of how those particles are arranged, what charges (and other quantum numbers) they have, and so on. That let's you get a pretty good idea of their wave function. And that is pretty much all the information you can get about objects of the nature of a nucleus.

So, to state it a different way:
- Measure the scattering behaviour, especially the cross sections
- Observe the energy levels of various nuclei
- Observe the decays
- Build models of the nucleus (for example the "bag model" but it is by no means the only model)
- Do more tests, tweak the model to match the tests, repeat until the model gives good predictions

This is a very non-trivial task. For example, when I was in university there was a model being developed by another research group. It was called the Isgur-Karl bag model. There were something like 12 PhDs written on that model by the time I finished grad school. Another example of a nuclear model is called the "liquid drop" model. There are other models and methods.

Just to give you one idea: A decay that does not happen right away often involves getting through some kind of energy barrier. The particles are at lower energy apart than they are together, but to get apart they have to get through a region of higher energy. Like being caught in a bowl at the top of a hill. First you have to get out of the bowl then you can roll down the hill. The decay rate depends very strongly on the size and shape of that barrier. So if a model gets several decay rates reasonably accurately we tend to have some confidence that it is doing something right.

 

[gianeshwar]

The "exact size" of a nucleus depends on how you define it. And it won't be exact because we are dealing with inherently quantum structures here. A nucleus involves a bunch of particles bound together. Even simple Hydrogen, a single proton, has three quarks bound together. So there is always some quantum effects going on.

But basically, the idea is that a nucleus behaves like a clump of bound particles. By scattering particles of different kind and energy, by studying the energy states, and by studying their decay modes, you can get a pretty good idea of how those particles are arranged, what charges (and other quantum numbers) they have, and so on. That let's you get a pretty good idea of their wave function. And that is pretty much all the information you can get about objects of the nature of a nucleus.

So, to state it a different way:
- Measure the scattering behaviour, especially the cross sections
- Observe the energy levels of various nuclei
- Observe the decays
- Build models of the nucleus (for example the "bag model" but it is by no means the only model)
- Do more tests, tweak the model to match the tests, repeat until the model gives good predictions

This is a very non-trivial task. For example, when I was in university there was a model being developed by another research group. It was called the Isgur-Karl bag model. There were something like 12 PhDs written on that model by the time I finished grad school. Another example of a nuclear model is called the "liquid drop" model. There are other models and methods.

Just to give you one idea: A decay that does not happen right away often involves getting through some kind of energy barrier. The particles are at lower energy apart than they are together, but to get apart they have to get through a region of higher energy. Like being caught in a bowl at the top of a hill. First you have to get out of the bowl then you can roll down the hill. The decay rate depends very strongly on the size and shape of that barrier. So if a model gets several decay rates reasonably accurately we tend to have some confidence that it is doing something right.

Thank you very much DEvens for a sincere answer.I will come back after studying the related details.

 

[stedwards]

You might start with Wikipedia on Rutherford Scattering with comments on why the model doesn't fit the "actual" radius.

 

[gianeshwar]

You might start with Wikipedia on Rutherford Scattering with comments on why the model doesn't fit the "actual" radius.

Thanks stedwarts! I will take some time to study your reference .I could locate answer to my problem.