Collective properties of even-even nuclei

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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. R4/2 ?
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Vibrational modes, 1- and multi-phonon
2-particle spectra
Intermediate
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Lots of valence nucleons of both types
R4/2 ? 3.33
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B(E2 2 ? 0 )
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Broad perspective on structural evolution R4/2
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
Lowering of one state. Note that the components
of its wave function are all equal and in phase
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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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Even-even Deformed Nuclei

• Rotations and vibrations

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Rotational states built on(superposed on)
vibrational modes
Vibrational excitations
Rotational states
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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0
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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 NucleiTwo types gamma
soft (or unstable), and rigid
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First Gamma soft
E L ( L 3 ) Jmax ( Jmax 6 )
Note staggering in gamma band energies
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Overview of yrast energies
E J ( J 1 )
E J ( J 6 )
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E J J ( J )
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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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