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Proton-neutron interactions

Proton-neutron interactions. The key to structural evolution. Paradigm Benchmark 700 333 100 0 Rotor J(J + 1). Amplifies structural differences Centrifugal stretching Deviations. 6 + 690. 4 + 330. 2 + 100. 0 + 0. J E (keV).

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Proton-neutron interactions

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  1. Proton-neutron interactions The key to structural evolution

  2. Paradigm Benchmark 700 333 100 0 Rotor J(J + 1) Amplifies structural differences Centrifugal stretching Deviations 6+690 4+330 2+100 0+0 JE (keV) Identify additional degrees of freedom Detour before starting ? Without rotor paradigm

  3. 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.

  4. 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

  5. Microscopic mechanism of first order phase transition (Federman-Pittel, Heyde) Gap obliteration (N ~ 90 ) 1-space 2-space Monopole shift of proton s.p.e. as function of neutron number Can we see this experimentally?

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

  7. 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

  8. A~100

  9. B(E2; 2+ 0+ )

  10. R4/2 Observable E2 Nucleon number, Z or N Sudden changes in R4/2 signify changes in structure, usually from spherical to deformed structure Def. 1/E2 Sph. Onset of deformation

  11. 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

  12. 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

  13. 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

  14. 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

  15. 82 50 82 126   Orbit dependence of p-n interactions Low j, high n High j, low n

  16. Z  82 , N < 126 3 1 2 3 2 1 82 50 82 126   Z > 82 , N < 126 Z > 82 , N > 126 Behavior of p-n interactions

  17. 208Hg

  18. 126 82 LOW j, HIGH n HIGH j, LOW n 50 82 In terms of proton and neutron orbit filling, p-n interaction 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

  19. 82 50 82 126   Empirical p-n interaction strengths indeed strongest along diagonal. Low j, high n High j, low n Neidherr et al, preliminary First direct correlation of observed growth rates of collectivity with empirical p-n interaction strengths

  20. BEWARE OF FALSE CORRELATIONS!

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

  22. Density Functional Theory My understanding of DFT: Would you like to see it again? OK. So, I hope all this is clear. Anyway, Nazarewicz, Stoitsov and Satula calculated masses for over 1000 nuclei across the nuclear chart with several interactions, and, from these masses, computed the p-n interactions using the same double difference expression. Lots of results. A few examples:

  23. http://workshop.turkfizikdernegi.org

  24. Principal Collaborators • Burcu Cakirli (Istanbul) dVpn, Bubbles, Masses • Klaus Blaum (MPI – Heidelberg) Masses • Magda Kowalska (CERN – ISOLDE) Masses • And the GSI Schottky and CERN-ISOLDE mass groups for their measurements of Hg, Rn and Xe masses

  25. Backups

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