1 / 39

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.

dagan
Download Presentation

Renormalized Interactions for CI constrained by EDF methods

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related