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Structures in Micro Objects

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Nuclear Term Schema

The nuclear term schema for an arbitrary nuclide
is obtained by solving the Schrödinger equation
for a modified 3dimensional harmonic oscillator potential.
Taking into account the spin orbit interaction of angular momentum,
Maria GoeppertMayer succeeded in analyzing the structure
of the nuclear shells, interpreting the magic occupation numbers,
and showing that protons and neutrons have slightly different higher terms.
For any nucleon state, we denote by
n ... the principal quantum number (oscillator shells with n = 1,2,...),
l ... the orbital angular momentum (orbitals s,p,... with l = 0,...,n),
s ... the spin quantum number (s = l/2 or +1/2),
j ... the total angular momentum.
Boldface state numbers denote closed neutron shells
and are called nuclear magic numbers.
The schema for protons is similar up to occupation number 82
but differs in higher regions.
# of states  s (l = 0)  p (l = 1)  d (l = 2)  f (l = 3)  g (l = 4)  h (l = 5)  i (l = 6)  j (l = 7)  
184    ___3d(3/2)4       
180  ___4s(1/2)2         
178      ___2g(7/2)8     
170         ___1j(15/2)16  
154        ___1i(11/2)12   
142    ___3d(5/2)6       
136      ___2g(9/2)10     
126   ___3p(1/2)2        
124   ___3p(3/2)4        
120        ___1i(13/2)14   
106     ___2f(5/2)6      
100     ___2f(7/2)8      
92       ___1h(9/2)10    
82  ___3s(1/2)2         
80    ___2d(3/2)4       
76       ___1h(11/2)12    
64    ___2d(5/2)6       
58      ___1g(7/2)8     
50      ___1g(9/2)10     
40   ___2p(1/2)2        
38     ___1f(5/2)6      
32   ___2p(3/2)4        
28     ___1f(7/2)8      
20    ___1d(3/2)4       
16  ___2s(1/2)2         
14    ___1d(5/2)6       
8   ___1p(1/2)2        
6   ___1p(3/2)4        
2  ___1s(1/2)2         

Magic Nucleon Numbers

The table below lists the few stable nuclides with doubly magic nucleon numbers.
_{2}
He
^{4}

_{8}
O
^{16}

_{20}
Ca
^{40}

_{20}
Ca
^{48}

_{82}
Pb
^{208}

_{114}
Uuq
^{298}

_{164}
Uhq
^{482}

References:
Rod Nave, Georgia State University
Jim Branson, University of California, San Diego



