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### Topic: State of the 51st Proton in Antimony-121  (Read 10551 times)

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#### toluene

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##### State of the 51st Proton in Antimony-121
« on: October 15, 2006, 02:48:21 PM »
Here's my question:

121Sb has a spin of 5/2 and a magnetic moment of 3.36nm. What is the state of the 51st proton. What would the shell model predict?

Presumably the Nilsson model can be used to find the state of the 51st proton, but that requires that the deformation constant be found, and I know of no way to related the information given in the question to the that constant.

Alternatively, one can use the equations j = l + 1/2 and u = lgl + 1/2gs or j = l - 1/2 u = j/(j+1)[l+1gl-1/2gs], and solve a system of equations to find the state (the letter "u" in the preceding equations represent the Greek letter "mu"). However this requires knowing whether the nucleus is j = 1 + 1/2 or j = l - 1/2, which also isn't known. Please advise.

Also, how is nanometers a unit of magnetic moment? I would have expected it in nuclear magnetons or Joules/Tesla.

Thanks

#### Mitch

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##### Re: State of the 51st Proton in Antimony-121
« Reply #1 on: October 15, 2006, 03:33:03 PM »
You can look up deformation parameters from this paper. http://dx.doi.org/10.1016/0092-640X(81)90003-6
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#### Mitch

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##### Re: State of the 51st Proton in Antimony-121
« Reply #2 on: October 15, 2006, 03:33:32 PM »
They should be reported as beta2 values.
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#### toluene

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##### Re: State of the 51st Proton in Antimony-121
« Reply #3 on: October 15, 2006, 03:48:34 PM »
You can look up deformation parameters from this paper. http://dx.doi.org/10.1016/0092-640X(81)90003-6

I can't see the paper. Only the abstract is given with no link to the pdf (though from experience there should be one).

Also, will this be normal, where we have to look elsewhere for information in order complete assigned problems?

#### toluene

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##### Re: State of the 51st Proton in Antimony-121
« Reply #4 on: October 15, 2006, 04:16:48 PM »
I found the website: http://cdfe.sinp.msu.ru/cgi-bin/muh/chartnucl.cgi?zmin=40&zmax=60&zch=1&fz=12&tdata=123 listing the deformation parameters for 40<Z<60 from poking around on google. It seems to be fairly straight forward to use. What do you think of it?

#### Mitch

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##### Re: State of the 51st Proton in Antimony-121
« Reply #5 on: October 15, 2006, 07:02:00 PM »
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#### toluene

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##### Re: State of the 51st Proton in Antimony-121
« Reply #6 on: October 15, 2006, 11:15:51 PM »
Alright, using a deformation parameter of -0.088 as found from .ru website and the Nilsson diagram for protons as found on http://www.pa.uky.edu/~jnorce/Nuclear/node4.html gives a state of 7/2 which disagrees with the 5/2 spin in the problem. Interestingly, if I were to use the Nilsson diagram given for neutrons and fill up to 51, I get a spin of 5/2. Please advise.

Also, I do have the proxy installed on my computer. Though I can see many of the articles provided on Science Direct with the proxy, I can't seem to see the one you provided.