collective properties of even-even nuclei
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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. R4/2 ~2
Vibrational modes, 1- and multi-phonon
2-particle spectra
Intermediate
Lots of valence nucleons of both types
R4/2 ~3.33
B(E2; 2+ 0+ )
Broad perspective on structural evolution: R4/2
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.
W
Even-even Deformed Nuclei
Rotations and vibrations
0+2+4+
6+
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
0
Experimental B(E2) values in deformed nuclei
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
Mixing of gamma and ground state bands
Axially Asymmetric Nuclei
Two types: “gamma” soft (or “unstable”), and rigid
First: Gamma soft
E ~ ( + 3 ) ~ Jmax ( Jmax + 6 )
Note staggering in gamma band
energies
E ~ J ( J + 6 )
E ~ J ~ J ( J + )
E ~ J ( J + 1 )
Overview of yrast energies
“Gamma” rigid or Davydov model
Note opposite staggering in gamma
band energies
Use staggering in gamma band energies as signature for the kind of axial asymmetry
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
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.
Burcu Cakirli et al.Beta decay exp. + IBA calcs.
Appendix B
on development of collectivity
and lowering of collective
energies by configuration
mixing
Appendix C
on energies and transition
rates of 3-phonon states in terms of 2-phonon state
anharmonicities