1 / 25

Linear response functions in infinite matter with Skyrme-type interactions

Linear response functions in infinite matter with Skyrme-type interactions. Nguyen Van Giai Institut de Physique Nucléaire Université Paris-Sud, Orsay. Outline of talk:. 1 . Self-consistent mean field and RPA linear response 2 . Skyrme interaction and RPA in infinite medium

ddeming
Download Presentation

Linear response functions in infinite matter with Skyrme-type interactions

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. Linear response functions in infinite matter with Skyrme-type interactions Nguyen Van Giai Institut de Physique Nucléaire Université Paris-Sud, Orsay ESNT 2012

  2. Outline of talk: 1. Self-consistent mean field and RPA linear response 2. Skyrme interaction and RPA in infinite medium 3. Closed form expressions of response functions 4. Odd-moment sum rules and instabilities 5. Conclusion ESNT 2012

  3. 1. Self-consistent meanfield and RPA linearresponse • Why are weusing the Random Phase Aproximation? • EnergyDensityFunctionals (EDF) are builtprimarily for predictingground state properties of nuclearsystems, via Hartree-Fockor more generalmeanfieldapproaches • An important class of excitationsconsists of small amplitude vibrations • RPA isthe small amplitude limit of TDHF, and the p-h interaction isuniquelyderivedfrom the EDF: • The sssssss The RPA eigenmodes reflect the Instabilities of the mean field ESNT 2012

  4. Advantages: • - studyground states and excitations of nuclearsystemswithin one framework (EDF) • - the s.c. RPA enables one to evaluatevariousenergy-weightedsumruleswithoutcalculatingdetailedresponsefunctions. • Drawbacks: • In atomicphysics one has theoreticallywellestablished EDF, but not in nuclearphysicswhere applications are donemostlywithSkyrme-type EDF • Why are sumrulemethodsuseful? • One canevaluate the global properties of nuclear excitations without extensive calculations (cf., O. Bohigas, A.M. Lane, J. Martorell, Phys. Rep. 51, 267 (1979); E. Lipparini, S. Stringari, Phys. Rep. 175, 103 (1989) ESNT 2012

  5. - In this presentation we concentrate only on homogeneous nuclear matter in the framework of Skyrme-type EDF, because analytical expressions can be obtained. • - Many RPA studies of finite nuclei have been performed (Skyrme forces, Gogny forces, realistic interactions,…), they will be discussed in this workshop. ESNT 2012

  6. General form of Skyrme-type interaction Central and spin-orbit Tensor ESNT 2012

  7. The free (HF) retarded p-h propagator • (p-h) Green’s function • In the presence of p-h residual interactions the excitations are described by the RPA Green’s function: ESNT 2012

  8. The p-h interaction Momentum transfer along Oz ESNT 2012

  9. Response functions HF RPA Strength distributions ESNT 2012

  10. Explicit form of RPA responsefunctions The special structure of Skyrme V_ph allows to obtain in closed form for infinite medium: - Central interaction: C. Garc’ia-Recio, J. Navarro, NVG, L.L. Salcedo, ANN.Phys.(N.Y.) 214, 293 (1992) S.O. interaction: J. Margueron, NVG, J. Navarro, Phys. Rev. C 74, 015805 (2006) - Tensor interaction: D. Davesne, M. Martini, K. Bennaceur, J. Meyer, Phys. Rev. C 80, 024314 (2009); Erratum Phys. Rev. C 84, 059904 (2011). Sum rules: A. Pastore et al., . arXiv:1204.0336 exte ici ESNT 2012

  11. Generalized Lindhard functions (1) ESNT 2012

  12. GeneralizedLindhardfunctions (2) ESNT 2012

  13. RPA responsefunction in terms of Skyrmeparameters ESNT 2012

  14. Longitudinal RPA response HF response nn Skyrme force: SkM ESNT 2012

  15. Transverse RPA response HF response Skyrme force: SkM ESNT 2012

  16. Inclusion of spin-orbit interaction : The previous expression (p.13) becomes: ESNT 2012

  17. ---- S=0 Effect of spin-orbit interaction - - - S=1 SLy230b - - -- J.Margueron, NVG, J. Navarro, Phys. Rev. C 74, 015805 (2006) ESNT 2012

  18. Excitation operator Sum Rules (1) aaaa ESNT 2012

  19. SumRules (2) Cubic energy-weighted Linear energy-weighted C. Garcia Recio et al, Ann. Phys. (N.Y.) 214, 293 (1992) ESNT 2012

  20. Inverse energy-weighted SumRules (3) Tensor force: see Pastore’s talk ESNT 2012

  21. Polarizability SkM MeM Mean energies : ESNT 2012

  22. Mean energies (SkM) ESNT 2012

  23. EWSR Break down of sum rule if poles! Response function Force: T44 A. Pastore, D. Davesne, Y. Lallouet, M. Martini, K. Bennaceur, J. Meyer, arXiv: 1204.0336 Instabilities in nuclei? ESNT 2012

  24. Summary The Skyrme EDF allows one to carry out detailed analytical calculations of nuclear responses in homogeneous medium one has a practical tool for evaluating strong points/defects of various parametrizations - present studies of effects of tensor component on responses are timely ESNT 2012

  25. Thank You! ESNT 2012

More Related