Presentation on theme: "Collective properties of even- even nuclei Vibrators and rotors With three Appendices."— Presentation transcript:
Collective properties of even- even nuclei Vibrators and rotors With three Appendices
What happens with both valence neutrons and protons? Case of few valence nucleons: Lowering of energies, development of multiplets. R 4/2 ~2 Vibrational modes, 1- and multi-phonon 2-particle spectra Intermediate
Lots of valence nucleons of both types R 4/2 ~3.33
Broad perspective on structural evolution: R 4/2 Note the characteristic, repeated patterns
Development of collective behavior in nuclei Results primarily from correlations among valence nucleons. Instead of pure “shell model” configurations, the wave functions are mixed – linear combinations of many components. Leads to a lowering of the collective states and to enhanced transition rates as characteristic signatures. How does this happen? Consider mixing of states.
A illustrative special case of fundamental importance T Lowering of one state. Note that the components of its wave function are all equal and in phase Consequences of this: Lower energies for collective states, and enhanced transition rates. Lets look at the latter in a simple model.
0+0+ 2+2+ 4+4+ 6+6+ 8+8+ Rotational states Vibrational excitations Rotational states built on(superposed on) vibrational modes Ground or equilibirum state
Systematics and collectivity of the lowest vibrational modes in deformed nuclei
E2 transitions in deformed nuclei Intraband --- STRONG, typ. ~ 200 W.u. in heavy nuclei Interband --- Collective but much weaker, typ. 5-15 W.u. Which bands are connected? Alaga Rules for Branching ratios