SYMMETRIES in PHYSICS

Symmetry and Spontaneous Symmetry Breaking
Selected Groups and Symmetries
Spontaneous Symmetry Breaking
Nuclear Octahedral Shapes - Proton Spectra
Double group Oh
D has four 2-dimensional and two 4-dimensional
irreducible representations → six distinct families of levels
Proton Energies [MeV]
0
2
-2
-4
-6
-8
-10
-12
160
70 Yb 90
{10}[5,0,5] 11/2
{08}[5,0,3] 7/2
{10}[5,0,3] 7/2
{10}[5,4,1] 3/2
{13}[5,0,5] 11/2
{19}[4,4,0] 1/2
{18}[4,0,2] 3/2
{11}[4,0,0] 1/2
{15}[5,1,4] 7/2
{07}[5,2,3] 5/2
{11}[5,1,2] 5/2
{10}[5,3,2] 5/2
{23}[5,1,4] 9/2
{13}[4,0,4] 7/2
{08}[4,2,2] 3/2
{08}[4,3,1] 1/2
{17}[5,2,3] 7/2
{15}[4,3,1] 1/2
{12}[4,0,2] 5/2
{11}[4,1,3] 5/2
{09}[4,2,0] 1/2
{13}[4,0,4] 9/2
{09}[4,3,1] 3/2
72
58
70
88
52
64
-.35 -.25 -.15 -.05 .05 .15 .25 .35
Octahedral Deformation
82
94
56
88
52
{09}[4,0,2] 5/2
{16}[5,3,2] 5/2
{18}[5,1,4] 9/2
{08}[5,0,5] 9/2
{21}[4,1,3] 5/2
{17}[4,1,3] 7/2
{24}[4,2,2] 3/2
{09}[5,1,2] 5/2
{10}[5,0,5] 9/2
{07}[5,1,0] 1/2
{11}[5,4,1] 3/2
{21}[4,2,0] 1/2
{10}[5,0,5] 11/2
{10}[4,3,1] 1/2
{09}[4,2,2] 3/2
{08}[3,3,0] 1/2
{13}[3,0,1] 3/2
{08}[5,0,3] 7/2
{25}[4,2,2] 5/2
{16}[4,1,3] 7/2
{09}[4,3,1] 3/2
{24}[3,1,2] 3/2
{10}[4,3,1] 1/2
Strasbourg, August 2002 Dirac-Woods-Saxon
α 40(min)=-.350, α40(max)=.350
α 44(min)=-.209, α44(max)=.209
Figure: Full lines correspond to 4-dimensional irreducible representations
- they are marked with double Nilsson labels. Observe huge gap at Z=70.
Jerzy DUDEK
SYMMETRIES in PHYSICS