Predicting Nuclear Spin with Shell Model: How is it Calculated and Validated?

[theFuture]

How would one predict the total spin of a nucleus given Z, N and the shell model? Does it have to to do with even-even, even-odd, odd-odd nuclei?

 

[mandril]

Yes, defenetly. In "close to magic numbers" nuclei, one can use the shell model to predict spin and parity of ground states, using pairing techniques. For example, a double magic nuclei, surely has 0+, because all it neutrons and protons are paired, and closing shells. If you add one neutron then spin and parity only depend on the posibilitis of this last one.

 

[neu]

unpaired nucleons determine total nuclear spin.

odd-even or even-odd have presise spin (only 1 unpaire nucleon)

even - even no net spin

odd - odd spin lies in range $$\vert j_{1}-j_{2}\vert$$to $$j_{1}+j_{2}$$

 

[malawi_glenn]

Also you must serach for every unpaired nucleon i shells, and add their spins acording to the forumla given by neu.

And then multiply each unpaired nucelon 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 experient gives you the outcome of this.