individual excitations of nucleons Themes and challenges of Modern Science Complexity out of simplicity – Microscopic How the world, with all its apparent complexity and diversity can be constructed out of a few elementary building blocks and their interactions Simplicity out of complexity – Macroscopic How the world of complex systems can display such remarkable regularity and simplicity individual excitations of nucleons vibration rotation fission

The three faces of the shell model

Experimental single-particle energies γ-spectrum single-particle energies 208Pb → 209Bi Elab = 5 MeV/u 1 h9/2 2 f7/2 1 i13/2 1609 keV 896 keV 0 keV

Experimental single-particle energies γ-spectrum 208Pb → 207Pb Elab = 5 MeV/u single-hole energies 3 p3/2 898 keV 2 f5/2 570 keV 3 p1/2 0 keV

energy of shell closure: Experimental single-particle energies particle states 209Bi 1 i13/2 1609 keV 209Pb 2 f7/2 896 keV 1 h9/2 0 keV energy of shell closure: 207Tl 207Pb hole states protons neutrons

Level scheme of 210Pb 2846 keV 2202 keV 1558 keV 1423 keV 779 keV -1304 keV (pairing energy) M. Rejmund Z.Phys. A359 (1997), 243

Evolution of nuclear structure as a funtion of nucleon number

4+ 2+ 0+ Jπ E ( keV) Experimental observables in even-even nuclei 1000 400 2+ 0+ Jπ E ( keV)

Systematics of the Te isotopes (Z=52) (Z = 52) Neutron number 68 70 72 74 76 78 80 82 Val. Neutr. number 14 12 10 8 6 4 2 0

Systematics of the Te isotopes (Z=52) (Z = 52) 6+ 1.63 4+ 1.69 2+ 1.59 4+ 1.58 2+ 1.16 1.28 2+ 4+ 1.20 0+ 1.10 2+ 0.84 2+ 0.56 0+ 0+ 0+ 120Te 130Te 134Te Case of few valence nucleons: lowering of energies, development of multiplets. R4/2 → ~2-2.4

Electric fields of multipoles (Z = 52) In general the electric potential due to an arbitrary charge distribution is expansion multipole moments special case: electric quadrupole matrixelement special case: electric quadrupole potential B(E2)-value: