Spin and Magnetic Moment | Nuclear and Particle Physics for GATE - GATE Physics PDF Download

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1(c). Spin and Magnetic Moment 
Proton and neutrons, like electrons, are fermions with spin quantum numbers of
2
1
? s . 
This means they have spin angular momenta S of magnitude 
                                     ? ? ? ? ?
2
3
1
2
1
2
1
1 ? ?
?
?
?
?
?
? ? ? ? s s S 
and spin magnetic quantum number of 
2
1
? ?
s
m . 
As in the case of electrons, magnetic moments are associated with the spins of protons 
and neutrons. In nuclear physics magnetic moments are expressed in nuclear 
magnetons ? ?
N
? , where 
Nuclear magneton T eV T J
m
e
p
N
/ 10 152 . 3 / 10 051 . 5
2
8 27 ? ?
? ? ? ? ?
?
? where 
p
m is the 
proton mass. 
In atomic physics we have defined Bohr magneton 
e
B
m
e
2
?
? ?
 
where 
e
m is the electron 
mass. 
The nuclear magneton is smaller than the Bohr magneton by the ratio of the proton mass 
to the electron mass which is 1836. 
                                         1836 ? ?
e
p
N
B
m
m
?
?
. 
The spin magnetic moments of the proton and neutron have components in any direction 
of  
Proton                     
N pz
? ? 793 . 2 ? ? 
Neutron                   
N nz
? ? 913 . 1 ? ? 
Page 2


 
   
 
  
 
    
 
 
1(c). Spin and Magnetic Moment 
Proton and neutrons, like electrons, are fermions with spin quantum numbers of
2
1
? s . 
This means they have spin angular momenta S of magnitude 
                                     ? ? ? ? ?
2
3
1
2
1
2
1
1 ? ?
?
?
?
?
?
? ? ? ? s s S 
and spin magnetic quantum number of 
2
1
? ?
s
m . 
As in the case of electrons, magnetic moments are associated with the spins of protons 
and neutrons. In nuclear physics magnetic moments are expressed in nuclear 
magnetons ? ?
N
? , where 
Nuclear magneton T eV T J
m
e
p
N
/ 10 152 . 3 / 10 051 . 5
2
8 27 ? ?
? ? ? ? ?
?
? where 
p
m is the 
proton mass. 
In atomic physics we have defined Bohr magneton 
e
B
m
e
2
?
? ?
 
where 
e
m is the electron 
mass. 
The nuclear magneton is smaller than the Bohr magneton by the ratio of the proton mass 
to the electron mass which is 1836. 
                                         1836 ? ?
e
p
N
B
m
m
?
?
. 
The spin magnetic moments of the proton and neutron have components in any direction 
of  
Proton                     
N pz
? ? 793 . 2 ? ? 
Neutron                   
N nz
? ? 913 . 1 ? ? 
 
   
 
  
 
    
 
 
There are two possibilities for the signs of 
pz
? and
nz
? , depending on whether
s
m is   
2
1
? or
2
1
? . The ? sign is used for 
pz
? because
pz
? is in the same direction as the spin S , 
whereas ? is used for 
nz
? because
nz
? is opposite to spin S . 
 
 
 
 
 
 
 
Note: For neutron, magnetic moment is expected to be zero as 0 e ? but
N nz
? ? 913 . 1 ? ? . 
At first glance it seems odd that the neutron, with no net charge, has spin magnetic 
moment. But if we assume that the neutron contains equal amounts of positive and 
negative charge, a spin magnetic moment arise if these charges are not uniformly 
distributed. Thus we can say that neutron has physical significance of negative charges 
because magnetic moment is opposite to that of its intrinsic spin angular momentum.  
 
S
p
?
S
n
?
Figure: Spin magnetic moment ( ? ) and spin angular momentum ( S ) 
directions for neutron and protons.