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The proton-neutron interaction and the emergence of collectivity in atomic nuclei

The proton-neutron interaction and the emergence of collectivity in atomic nuclei. R. F. Casten Yale University BNL Colloquium, April 15, 2014. The field of play: Trying to understand how the structure of the nucleus evolves with N and Z, and its drivers.

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The proton-neutron interaction and the emergence of collectivity in atomic nuclei

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  1. The proton-neutron interaction and the emergence of collectivity in atomic nuclei R. F. Casten Yale University BNL Colloquium, April 15, 2014 The field of play: Trying to understand how the structure of the nucleus evolves with N and Z, and its drivers.

  2. Themes and challenges of nuclear structure physics – • common to many areas of Modern Science • Complexity out of simplicity -- Microscopic • How the world, with all its apparent complexity and diversity, can be constructed out of a few elementary building blocks and their interactions • Simplicity out of complexity – Macroscopic • How the world of complex systems* can display such remarkable regularity and simplicity The p-n Interaction Linking the two perspectives What is the force that binds nuclei? Why do nuclei do what they do? What are the simple patterns that emerge in nuclei? What do they tell us about what nuclei do? * Nucleons orbit ~ 10 21 /s , occupy ~ 60% of the nuclear volume; 2 forces

  3. Simple Observables - Even-Even Nuclei 1400 2+ J 1000 4+ Masses 400 2+ B(E2) values ~ transition rates 0 0+ Jπ E (keV)

  4. Ui r Geometric Potentials for Nuclei: 2 typesFor single particle motion and for the many-body system = 0 b b V(b) b

  5. Reminder: Concept of "mean field“ or average potential Ui Vij r = |ri - rj|  r 64  = nl , E = Enl H.O. E = ħ (2n+l) E (n,l) = E (n-1, l+2) E (2s) = E (1d) Simple potentials plus spin-orbit force Clusters of levels  shell structure Pauli Principle (≤ 2j+1 nucleons in orbit with angular momentum j)  Energy gaps, closed shells, magic numbers. Independent Particle Model Inert core of nucleons, Concept of valence nucleons and residual interactions Many-body  few-body: each body counts Change by, say, 2 neutrons in a nucleus with 150 nucleons can drastically alter structure

  6. With many valence nucleons Multiple configurations with the same angular momentum. They mix, produce coherent, collective states l l Doubly magic plus 2 nucleons R4/2< 2.0 Vibrator (H.O.) E(I) = n (0 )R4/2= 2.0 Rotor E(I)  (ħ2/2I )I(I+1) R4/2= 3.33 R4/2 A measure of collectivity A few valence nucleons Many valence nucleons 8+. . . 6+. . . Pairing (sort of…) 2+ n = 2 n = 1 0+ n = 0

  7. Nuclear Shape Evolutionb - nuclear ellipsoidal deformation (b=0 is spherical) Vibrational RegionTransitional RegionRotational Region Critical Point New analytical solutions, E(5) and X(5) R4/2 = 2 R4/2 = 3.33 Few valence nucleonsMany valence Nucleons

  8. The beauty of nuclear structural evolution The remarkable regularity of these patterns is one of the beauties of nuclear structural evolution and one of the challenges to nuclear theory. Whether they persist far off stability is one of the fascinating questions for the future. Cakirli

  9. Structural evolution Complexity and simplicity

  10. BEWARE OF FALSE CORRELATIONS!

  11. Rapid structural changes with N/Z – Quantum Phase Transitions

  12. Quantum phase transitions as a function of proton and neutron number Rotor Transitional Vibrator

  13. Nuclear Shape Evolutionb - nuclear ellipsoidal deformation (b=0 is spherical) Vibrational RegionTransitional RegionRotational Region Critical Point New analytical solutions, E(5) and X(5) R4/2 = 2 R4/2 = 3.33 Few valence nucleonsMany valence Nucleons

  14. X(5) E E 1 2 3 4 β   Critical Point Symmetries First Order Phase Transition – Phase Coexistence Energy surface changes with valence nucleon number Bessel equation Iachello, 2001

  15. 5 3 2

  16. Param-free Remarkable agreement. Discrepancies can be understood in terms of sloped potential wall and the location of the critical point Casten and Zamfir

  17. What drives structural evolution? Valence p-n interactions in competition with pairing Sn – Magic: no valence p-n interactions Both valence protons and neutrons

  18. Seeing structural evolution Different perspectives can yield different insights mid-sh. magic Onset of deformation as a quantum phase transition (convex to concave contours) mediated by a change in proton shell structure as a function of neutron number, hence driven by the p-n interaction Onset of deformation Look at exactly the same data now plotted against Z

  19. Valence p-n interaction: Can we measure it? Vpn (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

  20. Empirical interactions of the last proton with the last neutron dVpn(Z, N) = ¼{[B(Z, N ) – B(Z, N - 2)] - [B(Z - 2, N) – B(Z - 2, N -2)]}

  21. 126 82 LOW j, HIGH n HIGH j, LOW n 50 82 p-n interaction is short range similar orbits give largest p-n interaction Largest p-n interactions if proton and neutron shells are filling similar orbits

  22. Z  82 , N < 126 Z  82 , N < 126 3 1 1 2 3 2 1 126 82 82 50   Z > 82 , N < 126 Z > 82 , N > 126 Low j, high n High j, low n

  23. 208Hg

  24. 82 50 82 126   Empirical p-n interaction strengths indeed strongest along diagonal. Empirical p-n interaction strengths stronger in like regions than unlike regions. Low j, high n High j, low n

  25. p-n interactions and the evolution of structure Direct correlation of observed growth rates of collectivity with empirical p-n interaction strengths

  26. W. Nazarewicz, M. Stoitsov, W. Satula Realistic Calculations Microscopic Density Functional Calculations with Skyrme forces and different treatments of pairing

  27. My understanding of Density Functional Theory Want to see it again?

  28. Comparison of empirical p-n interactions with Density Functional Theory(DFT) with Skyrme forces and surface-volume pairing These DFT calculations accurate only to ~ 1 MeV. dVpn allows one to focus on specific correlations. Recent measurements at ISOLTRAP/ISOLDE test these DFT calculations M. Stoitsov, R. B. Cakirli, R. F. Casten, W. Nazarewicz, and W. Satula PRL 98, 132502 (2007); D. Neidherr et al, Phys. Rev. C80, 044323 (2009)

  29. The competition of pairing and the p-n interaction. A guide to structural evolution.The next slides allow you to estimate the structure of any nucleus by multiplying and dividing two numbers each less than 30(or, if you prefer, you can get the almost as good results from 100 hours of supercomputer time.)

  30. Valence Proton-Neutron Interactions Correlations, collectivity, deformation. Sensitive to magic numbers. NpNn Scheme A refinement to the NpNn Scheme. P = NpNn/(Np+Nn) No. p-n interactions per pairing interaction Highlight deviant nuclei

  31. Competition of p-n interaction with pairing: Simple estimate of evolution of structure with N, Z NpNn p – n = P  Np + Nn pairing p-n / pairing p-n interactions per pairing interaction Pairing int. ~ 1 – 1.5 MeV, p-n ~ 200 - 300 keV Hence takes ~ 5 p-n int. to compete with one pairing int. P ~ 5 Rich searching ground for regions of rapid shape/phase transition far off stability in neutron rich nuclei McCutchan and Zamfir

  32. Comparison with the data

  33. Comparison with R4/2 data: Rare Earth region Deformed nuclei R4/2 data

  34. Special phenomenology of p-n interactions:Implications for the evolution of structure and the onset of deformation in nuclei New result, not recognized before, that shows the effect in purer form

  35. Shell model spherical nuclei Nilsson model Deformed nuclei Deformation Seems complex, huh? Not really. Very simple.

  36. How to understand the Nilsson diagram z Orbit K1 will be lower in energy than orbit K2 where K is the projection of the angular momentum on the symmetry axis Nilsson orbit labels (quantum numbers): K [N nz L ] nzis the number of nodes in the z-direction (extent of the w.f. in z)

  37. This is the essence of the Nilsson model and diagram. Just repeat this idea for EACH j-orbit of the spherical shell model. Look at the left and you will see these patterns. There is only one other ingredient needed. Note that some of the lines are curved . This comes from 2-state mixing of the spherical w.f.’s (not important for present context)

  38. Note: the last filled proton-neutron Nilsson orbitals for the nuclei where dVpn is largest are usually related by: dK[dN,dnz,dΛ]=0[110] 168 Er 7/2[523] 7/2[633]

  39. Specific highly overlapping proton-neutron pairs of orbitals, satisfying0[110], fill almost synchronously in medium mass and heavy nuclei and correlate with changing collectivity 168 Er 7/2[523] 7/2[633] 3/2[422] 3/2[532] 1/2[431] 1/2[541]

  40. Similarity of Nilsson patterns as deformation changes, and high overlaps of 0[110] orbit pairs, leads to maximal collectivity near the Nval ~ Zval line. Synchronized filling of 0[110] proton and neutron orbit combinations and the onset of deformation 0[110]

  41. Summary • Remarkable regularity and simplicity in a complex system • Structural evolution – evidence for quantum phase transitions • Drivers of emergent collectiivity -- valence p-n interaction in competition with pairing • Empirical extraction of valence p-n interactions – sensitivity to orbit overlaps • Enhanced valence p-n interactions for equal numbers of valence protons and neutrons • Key to structural evolution in heavy nuclei – synchronized filling of highly overlapping 0[110] orbits

  42. Principal collaboratorsR. BurcuCakirliDennis BonatsosKlaus BlaumVictor Zamfir Special thanks to Jackie Mooney for decades of collaboration and friendship.

  43. Backups

  44. Competition between valence pairing and the p-n interactions A simple microscopic interpretation of the evolution of structure Partial history: Goldhaber and de Shalit (1953); Talmi (1962); Federman and Pittel ( late 1970’s); Casten et al (1981); Heyde et al (1980’s); Nazarewicz, Dobacewski et al (1980’s); Otsuka et al( 2000’s); Cakirli et al (2000’s); and others.

  45. Shape/ Phase Transition and Critical Point Symmetry

  46. Identifying the nature of the discrepancies. Isolating scale Scaled energes Discrepancies for excited 0+ band are one of scale

  47. A possible explanation Based on idea of Mark Caprio

  48. Discrepancies for transition rates from 0+ band are one of scale

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