More General IBA Calculations. Spanning the triangle. How to use the IBA in real life

Transcription

1 More General IBA Calculations Spanning the triangle How to use the IBA in real life

2 Classifying Structure -- The Symmetry Triangle Deformed Sph. Most nuclei do not exhibit the idealized symmetries but rather lie in transitional regions. Mapping the triangle.

3 Mapping the Triangle with a minimum of data -- exploiting an Ising-type Model The IBA Competition between spherical-driving (pairing like nucleon and deformation-driving (esp. p-n interactions H = ah sph bh def Structure ~ a/b Def. Sph.

4 Relation of IBA Hamiltonian to Group Stru We will now see that this same Hamiltonian allows us to calculate the properties of a nucleus ANYWHERE in the triangle simply by choosing appropriate values of the

5 What is the physical meaning of χ Only minimum is at γ = 0 o All γ excursions due to dynamical fluctuations in γ (γ-softness, not to rigid asymmetric shapes. This is confirmed experimentally!!! V (γ vs. χ H = -κ Q Q χ If you think about zero point motion in a potential like this, it is clear that <γ> depends on χ. For a flat potential the nucleus oscillates back and forth from 0 to 60 degrees so <γ> = 30 deg. For, <γ> will be small nucleus is axially symmetric.

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7 Mapping the Entire Triangle with a minimum of data H = ε n d - κ Q Q Parameters:, χ (within Q κ/ε 2 parameters 2-D surface χ κ/ε Use of this form of the Hamiltonian, with T(E2 = aq, is called the Consistent Q Formalism (or CQF. Roughly % of IBA calculations are done this way. Awkward, though that κ/ε varies from 0 to infinity

8 H = c [ Spanning the Triangle ζ ( 1 ζ n d - 4NB Qχ Q χ ] ζ = 1, χ = χ ζ 2γ ζ = 0 ζ = 1, χ =

9 CQF along the leg H = -κ Q Q Only a single parameter, H = ε n d - κ Q Q Two parameters ε /κ and

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11 IBA CQF Predictions for 168 Er g γ

12 Os isotopes from A = 186 to 192: Structure varies from a moderately gamma soft rotor to close to the gammaindependent limit. Describe simply with: H = -κ Q Q : 0 small as A decreases

13 Universal Contour Plots in the CQF χ H = -κ Q Q χ = 0 χ = 7/ 2 = ( 5 χ =

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17 Now, what about more general calculations throughout the triangle Spanning the triangle How do we fix the IBA parameters for any given collective nucleus?

18 164 Er, a typical deformed nucleus

19 H has two parameters. A given observable can only specify one of them. What does this imply? An observable gives a contour of constant values within the triangle R4/2 = 2.9

20 A simple way to pinpoint structure. What do we need? At the basic level : 2 observables (to map any point in the symmetry triangle Preferably with perpendicular trajectories in the triangle Simplest Observable: R 4/2 Only provides a locus of structure 2.5 γ - soft Vibrator Rotor

21 Contour Plots in the Triangle R 4/ E(0 E( E(2 E(2 γ B( E2;2 B( E2;

22 We have a problem What we have: Lots of What we need: Just one Fortunately: E(0 2 E(21 E(2 γ

23 Mapping Structure with Simple Observables Technique of Orthogonal Crossing Contours γ - soft Vibrator E(4 E(2 1 1 Rotor E(0 2 E(2 E(2 1 2 Burcu Cakirli et al. Beta decay exp. IBA calcs.

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25 156 Er E(0 2 E E( R /2 (2 γ = 2.3 = 0.0

26 Trajectories at a Glance E(0 2 E(2 R 4/2 E( γ R 4/2 3.2 Gd N [ E(0 2 - E(2 γ ] / E(2 1

27 Evolution of Structure Complementarity of macroscopic and microscopic approaches. Why do certain nuclei exhibit specific symmetries? Why these evolutionary trajectories? What will happen far from stability in regions of proton-neutron asymmetry and/or weak binding?