Valence p-n interactions, shell model for deformed nuclei and the physics of exotic nuclei. Rick Casten WNSL, Dec 9, 2014

Transcription

1 Valence p-n interactions, shell model for deformed nuclei and the physics of exotic nuclei Rick Casten WNSL, Dec 9, 2014

2 How can we understand nuclear behavior? Two approaches: 1) Nucleons in orbits and their interactions [Independent particle model and shell model] 2) Look at nucleus as an entity in itself a many-body system with shape, symmetries, quantum numbers

3 Doubly magic plus 2 nucleons R 4/2 < 2.0 Vibrator (H.O.) E(J) = n ( ω 0 ) R 4/2 = 2.0 Rotor E(J) ( ħ 2 /2I )J(J+1) R 4/2 = n = n = 1 n = 0

4 Broad perspective on structural evolution Proton Number Neutron Number E(2 1 + ) Proton Number Neutron Number R 4/ The remarkable regularity of these patterns is one of the beauties of nuclear systematics and one of the challenges to nuclear theory. Whether they persist far off stability is one of the fascinating questions for the future

5 Why this behavior? Titanic struggle between good and good - - between the pairing interaction (two nucleons in the same orbit like to couple their angular momenta to zero) and the valence p-n interaction (which drives nuclei to deformed shapes)

6 The idea of both types of nucleons the p-n interaction Sn Magic: no valence p-n interactions Both valence protons and neutrons Lower energies imply correlations and collectivity mixing of IPM wave functions due to residual interactions.

7 Valence p-n interaction: Can we measure it? δvpn (Z,N) = - ¼ [ {B(Z,N) - B(Z, N-2)} - {B(Z-2, N) - B(Z-2, N-2)} ] p n p n p n p n Int. of last two n with Z protons, N-2 neutrons and with each other - Int. of last two n with Z-2 protons, N-2 neutrons and with each other Empirical average interaction of last two neutrons with last two protons

8 How do we expect them to behave? Difficult to calculate in detail but general predictions possible p-n interaction is short range similar orbits give largest p-n interaction LOW j, HIGH n HIGH j, LOW n Largest p-n interactions if proton and neutron shells are filling similar orbits

9 π High j, low n ν Empirical p-n interaction strengths indeed strongest along diagonal. Empirical p-n interaction strengths stronger in like than unlike regions. Direct correlation of observed growth rates of collectivity with empirical p-n interaction strengths

10 What happens to the Independent Particle Model when nuclei are not spherical? Answer: Very interesting things. Lets see what they are

11 Deformed (ellipsoidal) nuclei Nuclear many-body potentials and shapes Nuclear shape defined by two quantities, β, γ. β defines the elongation of the nucleus, γ defines its axial asymmetry. R = R 0 [1 + β cosγ Y 20 (θ,φ) + β sin γ Y 22 (θ,φ)] What are the orbits and energies of individual nucleons around a nucleus like this? In other words, what does the Independent Particle Model look like for deformed nuclei? β, elongation The answer is called the Nilsson model and the result is called a Nilsson diagram (sometimes known as a spaghetti diagram)

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13 The answer: The Nilsson diagram First impression: Aaaarrghh, Ugh, Yuk!!!!! Goal: to understand this diagram, and how to use it, without ANY calculation whatsoever (OK, maybe a sine or cosine), and to be able to construct it for an arbitrary nuclear shape. Need only two ingredients: Nuclear force is short range and attractive Two level mixing

14 First clue: other regions of single particle levels have very similar-looking Nilsson Diagrams. So something must be simple about it. In fact, its utterly simple

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20 This is the essence of the Nilsson model and diagram. Just repeat this idea for EACH j-orbit of the spherical shell model. Voila, the Nilsson Diagram (almost)!!! There is only one other ingredient needed. Note that some of the lines are curved! What does this mean? Where does that come from?

21 Suppose we have a Hamiltonian H = H 0 + H resid. where H 0 has a set of eigenstates X i The eigenstates of H will therefore be mixtures of those of H 0, that is linear combinations of the X i with coefficients C i. (In our case, H 0 will be the Hamiltonian of the SPHERICAL shell model that we have been discussing. H resid. will be the terms that mix different IPM single particle states because the nucleus is deformed.) 2-State mixing (of course, you all know this from Q. Mech brief review of key feature for the Nilsson model)

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26 E(J) ( ħ 2 /2I )J(J+1)

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31 One more example Appendices A and B have other examples you can play with and a more formal derivation of the model.

32 Exotic Nuclei A new era in nuclear structure, reaction, and astrophysics Science, Production, Recent results, and Facilities

33 The scope of Nuclear Structure Physics The Four Frontiers 1. Proton Rich Nuclei 2. Neutron Rich Nuclei 3. Heaviest Nuclei 4. Evolution of structure within these boundaries Terra incognita huge gene pool of new nuclei We can customize our system fabricate designer nuclei to isolate and amplify specific physics or interactions

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35 Major Exotic Beam Facilities Worldwide

36 A field that is energized worldwide Korea -- RISP

37 Some themes in the science of exotic nuclei

38 Physics of exotic, weakly bound nuclei Models Exp. The ultimate goal of the physics of nuclei is to develop a unified, predictive theory of nucleonic matter

39 New Features in Exotic Nuclei V (r) Coupling to open channels r Weak Binding r Spatially extended wave functions Localized nuclear density Low density, diffuse, extended, nearly pure neutron amplitudes Density (log) Halo/Skin Nuclei p-n core 11 Li n-skin Radius (fm) V (r) Diffuse Normal potential Changes in single particle energies, magic numbers New N/Z ranges Interaction-induced changes in SPEs

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42 Recall magic numbers: 2,8,20,50,82,126 Migration of magicity: N = 20 is NOT magic for Mg and N = 28 is NOT magic for Si and S!!!! Evolution of shell structure -- one of the most active, important areas of nuclear structure research today.

43 Neutron skins near the neutron drip line Skins and Skin Modes n np

44 Production and use of Exotic Isotopes High Energy Heavy Ion Driver Intense Stable Ion Beam Fragmentation Target and Ion Separator Exotic Ion Beam Fast Beam Experiments Gas Stopping Stopped Beam Experiments (Traps) High Energy Proton Driver Intense Proton Beam ISOL Target/Ion Extraction Exotic Ions Second Accelerator Exotic Ion Beam Reaccelerated Beam Experiments

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46 The Reach of FRIB Rates are available at isotopes produced at useful rates Slid 46

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48 10 8 to Production of superheavy elements Physics with rare isotopes Physics vs. Intensity With new technology we can now do experiments with orders of magnitude weaker beams than ever before. Particles/sec Physics of Nuclei 10-5 Existence; perhaps half life, decay modes 10-4 to 10-3 Half life, mass, min. structural information 10-2 to 10-1 Some detailed structural information 10 3 Full details of structure >10 5 Astrophysical reaction rates 10 6 Weak interaction strengths

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50 Study of symmetry phases deformation β-decay

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52 Back to the Future Exotic nuclei Similar techniques (as in the old days ): single particle transfer, beta decay, gamma ray spectroscopy, mass measurements, reaction rates on new nuclei New challenges 10 vs p/s

53 Exotic Nuclei Discovery Potential Comprehensive nuclear theory Reaching the limits of nuclear binding Discovery/study of exotic nuclear topologies Discovery of new structural symmetries Study of phases of nuclei and nuclear matter Crucial ingredients for astrophysics Tests of fundamental symmetries Unforeseen Discoveries Spin-offs Applications to medicine, national security, Training the next generation of scientists who know and can exploit the atomic nucleus

54 Themes in Nuclear Structure with exotic nuclei Changing Shell Structure The nucleonic foundation of nuclear behavior changing paradigms after half a century Nucleonic interactions Pairing and p-n: new density regimes and the effects of the continuum. The evolution of structure Symmetries, phase transitions, and critical points in complex nuclei The heaviest nuclei Quantal binding The limits of nuclear existence The links to Astrophysics, and opportunities to test fundamental symmetries

55 Appendix A with more examples of how to use the Nilsson Model in practice

56 On the next slides are other that you can look through and see if you understand.

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63 Appendix B on a more formal derivation of the Nilsson Model with emphasis on the small and large deformation limits and quantum numbers

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