PowerPoint Presentation - Nucleon and Nuclear Angular Momentum
Download
Report
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* ss 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* II 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* II 1
• Nucear angular momentum z-axis projection
I z mI
; I mI I