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I. Nuclear symmetries and quantum numbers

I. Nuclear symmetries and quantum numbers. I.1 Fermi statistics. Fermi statistics. Antisymmetric wave function. Fermi level. N. i. Second quantization:. Fermi level. Multi configuration shell model. Complete basis. Big matrix diagonalization. I.2 Interactions and symmetries.

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I. Nuclear symmetries and quantum numbers

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  1. I. Nuclear symmetries and quantum numbers

  2. I.1 Fermi statistics Fermi statistics Antisymmetric wave function Fermi level N i

  3. Second quantization: Fermi level

  4. Multi configuration shell model Complete basis Big matrix diagonalization

  5. I.2 Interactions and symmetries Interaction strong electromag. weak Exchanged boson mesons photon W,Z Translation yes yes yes Lorentz yes yes yes Space inversion yes yes no Rotation yes yes yes Isorotation yes no no Time reversal yes yes yes

  6. I.3 Translational invariance Spatial: Time: Total energy E conserved.

  7. I.4 Lorentz invariance Low energy – Galilei invariance

  8. Mass spectrograph High energy – Lorentz invariance

  9. 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). The rest mass and rest energy

  10. I.5 Space inversion invariance Quantum number

  11. 1 D 3 D

  12. E1 p=- M1 p=+ Parity of electromagnetic dipole decay

  13. I.6 Rotational invariance But not spin or orbital separately!

  14. 3D rotations form a non-Abelian group Lie algebra of group

  15. Spherical harmonics eigenfunctions of orbital angular momentum

  16. Spinors

  17. Spectroscopic notation

  18. Alpha decay caused by strong and electromagnetic interaction Way to measure spins and parities of ground and excites states

  19. Angular momentum coupling Bit complicated because of Quantization and non-commuting components

  20. Clebsch-Gordan-Coefficients

  21. Spin orbit coupling

  22. Spin orbit coupling

  23. Particle states Hole states

  24. Two particle states

  25. Selection rules for electromagnetictransitions Multipolarity of the photon l – its angular momentum The transition with the lowest multipole dominates.

  26. Pure M1 Pure E1 Pure M1 No transition Pure E2

  27. For alpha decay hold the general rules of angular momentum conservation too.

  28. 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).

  29. Same orbital wave state Total state must be antisymmetric.

  30. 209 Isobar analogue states

  31. I.8 Time reversal invariance

  32. differential cross section angle in center of mass system Reaction A+B C+D has same probability as C+D A+B “detailed balance”

  33. Random interaction

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