Download Nucleon and Nuclear Angular Momentum

Nucleon and Nuclear
Angular Momentum
Nucleon Angular Momentum
• Inside the nucleus, each nucleon has -– “Orbital” angular momentum
*
L = l(l + 1) h ; l = 0,1,2,...
– Spin angular momentum
*
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†
S = s( s + 1) h ; s = 1 2
Nucleon Angular Momentum
• Inside the nucleus, each nucleon has -– “Orbital” angular momentum - z-axis projection
Lz = ml h ; - l £ ml £ +l ; Dml = 1
– Spin angular momentum
†
h
Sz = sz h ; - s £ sz £ +s ; Sz = ±
2
Nucleon Angular Momentum
• Inside the nucleus, each nucleon has -r r r
– Total angular momentum J = L + S
*
J =
j ( j + 1) h ; l - s £ j £ l + s
– Total angular momentum
z-axis projection
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†
J z = m j h ; - j £ m j £ + j ; j = n 2 n = 1,2,..
Nucleon Wave Functions
• Individual nucleon wavefunctions --
y n,l,m l ,s,sz Æ y n,l,s, j,m j
• Note the appropriate quantum numbers
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Nucleon State Multiplicities
• Individual nucleon wavefunctions --
y n,l,m l ,s,sz Æ
(2l + 1) + (2s + 1)
y n,l,s, j,m j Æ
(2 j + 1)
Nuclear Angular Momentum
• Total nuclear angular momentum is --
r
r
r
I * = I ( I + 1) h ; I = Â J p + Â J n
Z
N
• Nuclear angular momentum z-axis projection
†
Iz = mI h ; - I £ mI £ +I
Nuclear Angular Momentum
• Why is I always even for even-A nuclei?
• Why is I always odd for odd-A nuclei?
– Hint: Consider the z-axis projections of the
nucleons…
Nuclear Angular Momentum
• Total nuclear angular momentum is --
I * = I ( I + 1) h
• Nucear angular momentum z-axis projection
†
†
Iz = mI h ; - I £ mI £ +I