Transcript PowerPoint Presentation - Nucleon and Nuclear Angular Momentum

Nucleon and Nuclear
Angular Momentum

Nucleon Angular Momentum
• Inside the nucleus, each nucleon has -– “Orbital” angular momentum
*
L 

1 ;
 0,1,2,...
– Spin angular momentum
S*  ss 1 ; s  1
2
Nucleon Angular Momentum
• Inside the nucleus, each nucleon has -– “Orbital” angular momentum - z-axis projection
Lz  m
;   m   ; m 1
– Spin angular momentum

Sz  sz ;  s  sz  s ; Sz  
2

Nucleon Angular Momentum
• Inside the nucleus, each nucleon has -– Total angular momentum J  L  S
J  j j 1 ;
*
s  j  s

– Total angular momentum
z-axis projection
Jz  m j ;  j  m j   j ; j  n 2 n 1,2,..
Nucleon Wave Functions
• Individual nucleon wavefunctions --
n,
,m ,s,sz 
n,
,s, j,m j
• Note the appropriate quantum numbers
Nucleon State Multiplicities
• Individual nucleon wavefunctions --
n,
,m ,s,sz 
n,
,s, j,m j
2
1  2s 1
 2 j 1

Nuclear Angular Momentum
• Total nuclear angular momentum is --
I*  II 1 ; I   J p   Jn
Z
N
• Nuclear angular momentum z-axis projection
I z  mI
;  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
• Nucear angular momentum z-axis projection
I z  mI
;  I  mI  I