I Nuclear symmetries and quantum numbers I 1
I. Nuclear symmetries and quantum numbers
I. 1 Fermi statistics Antisymmetric wave function N i Fermi statistics Fermi level
Second quantization: Fermi level
Multi configuration shell model Complete basis Big matrix diagonalization
I. 2 Interactions and symmetries Interaction strong electromag. weak Exchanged boson mesons photon W, Z Translation yes yes Lorentz yes yes Space inversion yes no Rotation yes yes Isorotation yes no no Time reversal yes yes
I. 3 Translational invariance Spatial: Time: Total energy E conserved.
I. 4 Lorentz invariance Low energy – Galilei invariance
High energy – Lorentz invariance Mass spectrograph
The rest mass and rest energy Creation of rest energy (mass) from kinetic energy. A high energy cosmic sulfur nucleus (red) hits an silver nucleus generating a spray of nuclei (blue, green) and pions (yellow).
I. 5 Space inversion invariance Quantum number
1 D 3 D
Parity of electromagnetic dipole decay E 1 p=M 1 p=+
I. 6 Rotational invariance But not spin or orbital separately!
3 D rotations form a non-Abelian group Lie algebra of group
Spherical harmonics eigenfunctions of orbital angular momentum
Spinors
Spectroscopic notation
Alpha decay caused by strong and electromagnetic interaction Way to measure spins and parities of ground and excites states
Angular momentum coupling Bit complicated because of Quantization and noncommuting components
Clebsch-Gordan-Coefficients
Spin orbit coupling
Spin orbit coupling
Hole states Particle states
Two particle states
Selection rules for electromagnetic transitions Multipolarity of the photon l – its angular momentum The transition with the lowest multipole dominates.
Pure M 1 Pure E 1 Pure M 1 Pure E 2 No transition
For alpha decay hold the general rules of angular momentum conservation too.
I. 7 Isorotational invariance Strong interaction same for n-n, p-p, n-p –charge independent. Conservation of isospin (also for particle processes caused by strong interaction).
Same orbital wave state Total state must be antisymmetric.
209 Isobar analogue states
I. 8 Time reversal invariance
differential cross section angle in center of mass system Reaction A+B C+D has same probability as C+D “detailed balance” A+B
Random interaction
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