# How is nuclear spin determined?

by bluestar
Tags: determined, nuclear, spin
 P: 245 The nucleons have orbital angular momentum, just as the electrons do. I can't remember off the top of my head but you need to find the orbital ang momentum, l, of the unpaired nucleons, now: $$L = l_{1} + l_{2}...$$ $$S = s_{1} + s_{2}...$$ $$J = L + S$$ where, due to Pauli exclusion priciple : $$Parity = (-1)^{J}$$ PEP defines the allowed values of J as Parity = 1 for Bosons; -1 for ferminons but check it, I'm not 100%. Hope that helps
 P: 73 Yes the Stern-Gerlach experiment was a rather interesting experiment where in applying a longitudinal inhomogeneous magnetic field resulted in the spectra splitting at the nuclear level. Even though I did read several pieces to understand their technique I don’t recall calculations for determining the full range of nuclei spin; although, I will revisit the material. Thanks for the information that not all ‘even’ A type nuclei have 0 spin. This is good information that I had not see yet and hope to pursue it further. *** The formulas $$L = l_{1} + l_{2}...$$ $$S = s_{1} + s_{2}...$$ $$J = L + S$$ were the first things I had considered but I could not achieve the spin numbers for the higher values 55Fe spin 3/2 56Co spin 4 57Co spin 7/2 60Co spin 5 An interesting note is the continuation of the L and S sequence. I had first seen these formulas where the total L or S was equal to just 2 subterms. I took that to mean the single outer most unpaired proton and the single outer most unpaired neutron. If this is not consistent with your understanding I would appreciate your comments. *** I also had considered the “rules” for shell filling where for the 0f shell there are 14 available positions. The first 7 positions would be filled by single nucleons (proton or neutron) and then at the 8 position the nucleon would couple up with the “1st position” with opposing spin directions. Thus the remaining 6 uncoupled nucleons determined the spin for that family of nucleons. However, that sequence didn’t seem to work out either. *** Thanks for the information on “nuclear shell model (Bohr-Mottelson)”. I will start looking for references on this model to see if any calculations are presented to determine nuclear spin. *** In May of last year member “neu”, in the following link, indicated the limiting range of spin nuclear spin was http://www.physicsforums.com/showthread.php?t=56506 $$\vert j_{1} - j_{2}\vert$$ to $$j_{1} + j_{2}$$ In the same note ‘malawi_glenn’ followed with this comment: “Also you must search for every unpaired nucleon in shells, and add their spins according to the formula given by neu. And then multiply each unpaired nucleon parity (parity is given by quantum number l) Then also the shell model just gives you the possible quantum numbers (you do not know witch one is the ground state if you get three possible solutions for a given configuration) the experiment gives you the outcome of this. “ *** I understood that nucleons filled shells from the bottom up, thus the 0s shell is filled before the 0p. Likewise, the 0p is filled before the 0d and so on up the sequence of energy levels for each respective shell. If this be true then all shells below the last nucleon would be filled. So, at most, there would only be 2 nucleons to consider, the last unpaired proton and the last unpaired neutron. So I am unsure if malawi_glenn is referring to more than 2 nucleons; likewise, I am unclear how parity figures into the spin computation. Just like anyone,… I just need a little clarity. Appreciate the tips!