Safe EDF for SR and MR calculations M. Bender, T. Duguet, D. Lacroix 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
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 rnq 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
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
rr
term kk
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
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: rg (III) Duguet et al, Non-integer powers of density matrices, arXiv/0809.2049 Dobaczewski et al, Identification of problem in PNR, PRC76, 054315 (2007)
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