Mod-01 Lec-20 Shell model Contd..

Magnetic moment of nucleus that is another parameter, which we can study, which we can test for which the model can be tested, so in this extreme single particle model the magnetic moment that also is given from that pairing thing. So, if it is even nucleus even Z, even N, then all the nucleons are paired, all the

protons are paired, all the neutrons are paired. And for each pair the angular moment are couple to total angular momentum 0, and naturally it is projection also 0, so in any of the level if you have 2 nucleons, 2 protons or 2 neutrons, the angular momentum of this plus angular momentum of this that will add to 0 the angular momentum of this, angular momentum

of this that will add to 0. So, if this I call j 1 this I call j 2, then when these 2 combine, these 2 combine to 0 0, so total j is 0. So, this plus this in general this plus this can be many, other things can come for example, if it is say

3 by 2 p 3 by 2 p 3 by 2 proton, proton in the level p 3 by 2, so 3 by 2 is the j value for first proton, 3 by 2 is the j value for second proton. Then 3 by 2 plus 3 by 2 the total angular momentum quantum number can be if it is 3 by 2, 3 by 2 that can be this

plus this will be 3 and this minus this will be 0, so all these values are possible in general. But, then they are paired; that means, they have chosen to have this angular momentum as 0, so their z components are just opposite each other that is also 0. And therefore, this magnetic moment coming from this pair

is also 0, so when the nucleons are paired each pair contributes 0 magnetic moment. And if each pair contributes 0 magnetic moment then and this is even Z even N, in the total magnetic moment of this nucleus is also 0. So, extreme single particle shell model will predict or will tell that for all even, even nuclei the magnetic moment should be 0, and