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Renormalized Interactions for CI constrained by EDF methods

Renormalized Interactions for CI constrained by EDF methods Alex Brown, Angelo Signoracci and Morten Hjorth -Jensen. Wick’s theorem for a Closed-shell vacuum filled orbitals. Closed-shell vacuum filled orbitals. EDF (Skyrme Phenomenology). Closed-shell vacuum filled orbitals.

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Renormalized Interactions for CI constrained by EDF methods

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  1. Renormalized Interactions for CI constrained by EDF methods Alex Brown, Angelo Signoracci and MortenHjorth-Jensen

  2. Wick’s theorem for a Closed-shell vacuum filled orbitals

  3. Closed-shell vacuum filled orbitals EDF (Skyrme Phenomenology)

  4. Closed-shell vacuum filled orbitals NN potential with V_lowk EDF (Skyrme) phenomenology

  5. Closed-shell vacuum filled orbitals “tuned” valence two-body matrix elements EDF (Skyrme) phenomenology

  6. Closed-shell vacuum filled orbitals Monopole from EDF EDF (Skyrme) phenomenology

  7. Closed-shell vacuum filled orbitals Monopole from EDF A3 A2 A 1

  8. Aspects of evaluating a microscopic two-body Hamiltonian (N3LO + Vlowk+ core-polarization) in a spherical EDF (energy-density functional) basis (i.e. Skyrme HF) TBME (two-body matrix elements): Evaluate N3LO + Vlowk with radial wave functions obtained with EDF. TBME: Evaluate core-polarization with an underlying single-particle spectrum obtained from EDF. TBME: Calculate monopole corrections from EDF that would implicitly include an effective three-body interaction of the valence nucleons with the core. SPE for CI: Use EDF single-particle energies – unless something better is known experimentally.

  9. Why use energy-density functionals (EDF)? Parameters are global and can be extended to nuclear matter. Effort by several groups to improve the understanding and reliability (predictability) of EDF – in particular the UNEDF SciDAC project in the US. This will involve new and extended functionals. With a goal to connect the values of the EDF parameters to the NN and NNN interactions. At this time we have a reasonably good start with some global parameters – for now I will use Skxmb – Skxm from [BAB, Phys. Rev. C58, 220 (1998)] with small adjustment for lowest single-particle states in 209Bi and 209Pb.

  10. Calculations in a spherical basis with no correlations

  11. What do we get out of (spherical) EDF? Binding energy for the closed shell Radial wave functions in a finite-well (expanded in terms of harmonic oscillator). gives single-particle energies for the nucleons constrained to be in orbital (n l j)a where BE(A) is a doubly closed-shell nucleus. 4) gives the monopole two-body matrix element for nucleons constrained to be in orbitals (n l j)a and (n l j)b

  12. EDF core energy and single-particle energy EDF two-body monopole

  13. Theory (ham) from Skxmb with parameters adjusted to reproduce the energy for the 9/2- state plus about 100 other global data.

  14. x = experiment CI with N3LO CI (ham) N3LO with EDF constraint EDF (or CI) with no correlations 208Pb 218U

  15. Skyrme (Skxmb) + Vlow-k N3LO (second order) 210Po

  16. Skyrme (Skxmb) + Vlow-k N3LO (first order) 210Po

  17. Skyrme (Skxmb) + Vlow-k N3LO (second order) 213Fr

  18. 214Ra Skyrme (Skxmb) + Vlow-k N3LO (second order)

  19. EDF core energy and single-particle energy EDF two-body monopole

  20. Theory (ham) from Skxmb with parameters adjusted to reproduce the energy for the 9/2+ state plus about 100 other global data.

  21. 210Pb Skyrme (Skxmb) + Vlow-k N3LO (second order)

  22. 210Bi Skyrme (Skxmb) + Vlow-k N3LO (second order)

  23. 212Po Skyrme (Skxmb) + Vlow-k N3LO (second order)

  24. 210Pb Skyrme (Skxmb) + Vlow-k N3LO (second order)

  25. 210Pb Skyrme (Skxmb) + exp spe Vlow-k N3LO (second order)

  26. Skyrme (Skxmb) for 208Pb (closed shell) + Vlow-k N3LO (second order)

  27. “ab-initio” calculation for absolute energies of 213Fr

  28. Energy of first excited 2+ states

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