Lecture 4 Quantum Phase Transitions and the microscopic drivers of structural evolution

1. Lecture 4Quantum Phase Transitions and the microscopic drivers of structural evolution

2. Quantum phase transitions and structural evolution in nuclei

4. Increasing valence nucleon number E 1 2 3 4 β Quantum phase transitions in equilibrium shapes of nuclei with N, Z Potential as function of the ellipsoidal deformation of the nucleus Transitional Rotor Vibrator For nuclear shape phase transitions the control parameter is nucleon number

6. 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= ~2.0 R4/2= 3.33 Few valence nucleonsMany valence Nucleons

7. 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

9. Casten and Zamfir

10. Comparison of relative energies with X(5)

12. Based on idea of Mark Caprio

13. Flat potentials in b validated by microscopic calculations Li et al, 2009

14. Shimizu et al More neutron holes Potential energy surfaces of 136,134,132Ba 100keV 134Ba 132Ba 136Ba <H> × × × minimum <HPJ=0> × × × (Nn,Np)= (-2,6) (-4,6) (-6,6)

15. Isotope shifts Charlwood et al, 2009 Li et al, 2009

16. Look at other N=90 nulei

17. Where else? In a few minutes I will show some slides that will 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 same result from 10 hours of supercomputer time)

18. Where we stand on QPTs • Muted phase transitional behavior seems established from a number of observables. • Critical point solutions (CPSs) provide extremely simple, parameter-free (except for scales) descriptions that are surprisingly good given their simplicity. • Extensive work exists on refinements to these CPSs. • Microscopic theories have made great strides, and validate the basic idea of flat potentials in b at the critical point. They can also now provide specific predictions for key observables.

19. Proton-neutron interactions A crucial key to structural evolution

20. Microscopic perspective Valence Proton-Neutron Interaction Development of configuration mixing, collectivity and deformation – competition with pairing Changes in single particle energies and magic numbers 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) and many others.

21. Sn – Magic: no valence p-n interactions Both valence protons and neutrons Two effects Configuration mixing, collectivity Changes in single particle energies and shell structure

22. Concept of monopole interaction changing shell structure and inducing collectivity

23. A simple signature of phase transitions MEDIATEDby sub-shell changesBubbles and Crossing patterns

24. Seeing structural evolution Different perspectives can yield different insights Mid-sh. magic Onset of deformation as a phase transition mediated by a change in shell structure Onset of deformation “Crossing” and “Bubble” plots as indicators of phase transitional regions mediated by sub-shell changes

25. Often, esp. in exotic nuclei, R4/2 is not available. A easier-to-obtain observable, E(21+), in the form of 1/ E(21+), can substitute equally well

26. Masses and Nucleonic Interactions Masses: • Shell structure: ~ 1 MeV • Quantum phase transitions: ~ 100s keV • Collective effects ~ 100 keV • Interaction filters ~ 10-15 keV Total mass/binding energy:Sum of all interactions Mass differences:Separation energies shell structure, phase transitions Double differences of masses:Interaction filters Macro Micro

28. Measurements of p-n Interaction Strengths dVpn Average p-n interaction between last protons and last neutrons Double Difference of Binding Energies Vpn (Z,N)  =  ¼ [ {B(Z,N) - B(Z, N-2)}  -  {B(Z-2, N) - B(Z-2, N-2)} ] Ref: J.-y. Zhang and J. D. Garrett

29. 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

30. 82 50 82 126   Orbit dependence of p-n interactions Low j, high n High j, low n

31. 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

32. 208Hg

35. Can we extend these ideas beyond magic regions?

36. 126 82 LOW j, HIGH n HIGH j, LOW n 50 82 Away from closed shells, these simple arguments are too crude. But some general predictions can be made 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

37. 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 New mass data on Xe isotopes at ISOLTRAP – ISOLDE CERN Neidherr et al., PR C, 2009

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

39. Exploiting the p-n interaction • Estimating the structure of any nucleus in a trivial way (example: finding candidat6e for phase transitional behavior) • Testing microscopic calculations

40. A simple microscopic guide to the evolution of structure The NpNn Scheme and the P-factor If the p-n interaction is so important it should be possible to use it to simplify our understanding of how structure evolves. Instead of plotting observables against N or Z or A, plot them against a measure of the p-n interaction. Assume all p-n interactions are equal. How many are there: Answer:Np xNn

41. Compeition between the p-n interaction and pairing: the P-factor General p – n strengths For heavy nuclei can approximate them as all constant. Total number of p – n interactions is NpNn Pairing: each nucleon interacts with ONLY one other – the nucleon of the same type in the same orbit but orbiting in the opposite direction. So, the total number of pairing interactions scales as the number of valence nucleonss.

42. What is the locus of candidates for X(5) NpNn p – n = P  Np + Nn pairing p-n / pairing p-n interactions per pairing interaction Pairing int. ~ 1.5 MeV, p-n ~ 300 keV Hence takes ~ 5 p-n int. to compete with one pairing int. P ~ 5

43. Comparison with the data

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

45. Agreement is remarkable. Especially so since these DFT calculations reproduce known masses only to ~ 1 MeV – yet the double difference embodied in dVpn allows one to focus on sensitive aspects of the wave functions that reflect specific correlations

46. The new Xe mass measurements at ISOLDE give a new test of the DFT

47. dVpn (DFT – Two interactions) SLY4MIX SKPDMIX

48. So, now what? Go out and measure all 4000 unknown nuclei? No way!!! Choose those that tell us some physics, use simple paradigms to get started, use more sophisticated ones to probe more deeply, and study the new physics that emerges. Overall, we understand these beasts (nuclei) only very superficially. Why do this? Ultimately, the goal is to take this quantal, many-body system interacting with at least two forces, consuming 99.9% of visible matter, and understand its structure and symmetries, and its microscopic underpinnings from a fundamental coherent framework. We are progressing. It is your generation that will get us there.

49. The EndThanks for listening

50. Special Thanks to: • Iachello and Arima • Dave Warner, Victor Zamfir, Burcu Cakirli, Stuart Pittel, Kris Heyde and others i9 didn’t have time to type just before the lecture