Diapositive 1

1
Safe EDF for SR and MR calculations
M. Bender, T. Duguet, D. Lacroix
FIDIPRO workshop, Jyvaskyla, Oct. 9th-10th 2008
2
Spurious contributions to SR and MR EDF kernels

• 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 SkyrmeDDDI
• 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 rnq with n
  integer lt 4
• Everything else is prohibited

3
Identification and cure to pathologies
(I) Lacroix, et al, General solution to MR
pathologies,arXiv/0809.2041

• Self-Interaction (SRMR)
• Not dramatic a priori
• Need to be characterized

• Self-Pairing (SRMR)
• Not dramatic a priori
• Need to be characterized

• Misuse of Gen. Wick Th. (GWT) within EDF method
  (MR only)
• Divergences, sharp steps, smooth steps plus kink

4
Particle Number Restoration
(II) Bender et al, First application to PNR,
arXiv/0809.2045
5
Summary and discussion
Energy Density Functional methods
Dobaczewski et al, Identification of problem in
PNR, PRC76, 054315 (2007)