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Collective properties of even- even nuclei Vibrators and rotors With three Appendices

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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

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Lots of valence nucleons of both types R 4/2 ~3.33

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B(E2; 2 + 0 + )

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Broad perspective on structural evolution: R 4/2 Note the characteristic, repeated patterns

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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.

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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.

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W

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Even-even Deformed Nuclei Rotations and vibrations

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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

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Systematics and collectivity of the lowest vibrational modes in deformed nuclei

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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

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Experimental B(E2) values in deformed nuclei

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How to fix the model? Note: the Alaga rules assume that each band is pure – ground or gamma, in character. What about if they MIX ?? Bandmixing formalism

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Mixing of gamma and ground state bands

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Axially Asymmetric Nuclei Two types: “gamma” soft (or “unstable”), and rigid

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First: Gamma soft E ~ ( + 3 ) ~ J max ( J max + 6 ) Note staggering in gamma band energies

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E ~ J ( J + 6 ) E ~ J ~ J ( J + ) E ~ J ( J + 1 ) Overview of yrast energies

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“Gamma” rigid or Davydov model Note opposite staggering in gamma band energies

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Use staggering in gamma band energies as signature for the kind of axial asymmetry

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Appendix A on Intruder States Another form of collective mode that sometimes appears in the low lying spectrum or can even become the ground state equilibrium cofiguration

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The basic idea behind Intruder States: a 2- particle - 2-hole excitation that costs energy but gains it back by added collectivity which increases with increasing valence nucleon number.

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Burcu Cakirli et al. Beta decay exp. + IBA calcs.

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Appendix B on development of collectivity and lowering of collective energies by configuration mixing

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Appendix C on energies and transition rates of 3- phonon states in terms of 2- phonon state anharmonicities

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How nuclei behave: a simple perspective based on symmetry and geometry (with a discussion of the microscopic drivers of structural evolution) R. F. Casten.

How nuclei behave: a simple perspective based on symmetry and geometry (with a discussion of the microscopic drivers of structural evolution) R. F. Casten.

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