1. 1 Thomas Duguet FIDIPRO Workshop - Jyvaskyla, Oct 9th-10th 2008 Safe EDF for SR and MR calculations M. Bender, T. Duguet, D. Lacroix FIDIPRO workshop, Jyvaskyla, Oct. 9th-10th 2008

2. 2 Thomas Duguet FIDIPRO Workshop - Jyvaskyla, Oct 9th-10th 2008 Spurious contributions to SR and MR EDF kernels M=9 M=99 Difficulties due to using EDF rather than TRUE Hamiltonian ANY vertex containing at least a density dependence Gogny vertex is already pathological More obviously critical for Skyrme+DDDI Unrecognized spurious contributions to SR calculations Unrecognized to this day but well know in DFT Need to be characterized quantitatively Need to build spuriosity-free SR-EDF (lot to be done) (Now) obvious pathologies of MR calculations (any type) Would NOT exist without spuriosities in SR EDF kernel Combine with MISUSE of GWT to build MR-EDF kernels Can correct for the latter rather “easily” Correctable functional requires  n q with n integer < 4 Everything else is prohibited Bender, Duguet, Int. J. Mod. Phys. E16 (2007) M=9 19 39 59 79 99 Divergence Jump

3. 3 Thomas Duguet FIDIPRO Workshop - Jyvaskyla, Oct 9th-10th 2008 Identification and cure to pathologies (I) Lacroix, et al, General solution to MR pathologies,arXiv/0809.2041 Sources of pathologies Self-Interaction (SR+MR) Not dramatic a priori Need to be characterized SI Self-Pairing (SR+MR) Not dramatic a priori Need to be characterized SP Misuse of Gen. Wick Th. (GWT) within EDF method (MR only) Divergences, sharp steps, smooth steps plus kink Cure to MR Find an Alternative to GWT Identify critical terms Remove pathologies

4. 4 Thomas Duguet FIDIPRO Workshop - Jyvaskyla, Oct 9th-10th 2008  term  term Results Correction is important at but also away from steps Corrected energy curve is smooth Correction is overall small (~1MeV) but of the order of the required mass accuracy or spectroscopy of interest Particle Number Restoration (II) Bender et al, First application to PNR, arXiv/0809.2045

5. 5 Thomas Duguet FIDIPRO Workshop - Jyvaskyla, Oct 9th-10th 2008 Summary and discussion Energy Density Functional methods Specific difficulties to be considered seriously Need a constructive framework for MR-EDF Regularization method valid for any MR calculation (I) Lacroix, et al, General solution to pathologies, arXiv/0809.2041 Need to build (i) Correctable EDF for MR calculations (ii) SI- and SP-free EDF Application to Particle Number Restoration (II) Bender et al, First application to PNR, arXiv/0809.2045 Specific case of fractional power of the density:   (III) Duguet et al, Non-integer powers of density matrices, arXiv/0809.2049 Dobaczewski et al, Identification of problem in PNR, PRC76, 054315 (2007)