Transcript Prezentacja programu PowerPoint

Energy Density Functional Methods
in Nuclear Physics
Jacek Dobaczewski
University of Warsaw
University of Jyväskylä
The 18th Jyväskylä Summer School
18th – 22nd August 2008
Jacek Dobaczewski
1. DFT theorems, EFT approach
2. Fermion Fock space, Wick theorem
3. Bogoliubov transformation, density
matrices
4. Group theory, even and odd states
5. Hartree-Fock and Hartree-FockBogoliubov
6. Construction of the energy density
functional
7. Mean fields and single-particle
structure
Home page: http://www.fuw.edu.pl/~dobaczew/
Jacek Dobaczewski
Jacek Dobaczewski:2004 RIA Summer School
http://www.fuw.edu.pl/~dobaczew/RIA.Summer.Lectures/slajd01.html
Jacek Dobaczewski:2005 Ecole Doctorale de Physique, Strasbourg
http://www.fuw.edu.pl/~dobaczew/Strasbourg/slajd01.html
Witek Nazarewicz:2007 Lectures at the University of Knoxville
http://www.phys.utk.edu/witek/NP622/NuclPhys622.html
Jacek Dobaczewski:1986-2005 draft of a book (in Polish)
http://www.fuw.edu.pl/~dobaczew/Czesc057d.pdf
Contents:
Hohenberg-Kohn theorem
Jacek Dobaczewski
Hohenberg-Kohn theorem (trivial version)
Jacek Dobaczewski
Nuclear Energy Density Functional
(physical insight)
Jacek Dobaczewski
Hydrogen atom perturbed near the center
Relative errors in the Swave binding energies
are plotted versus:
(i) the binding energy for
the Coulomb theory
(ii) the Coulomb theory
augmented with a delta
function in first-order
perturbation theory
(iii) the non-perturbative
effective theory through
a2, and
(iv) the effective theory
through a4.
Jacek Dobaczewski
Dimensional analysis - regularization
Jacek Dobaczewski
Dimensional analysis – the hydrogen-like atom
Jacek Dobaczewski
W.C. Haxton, Phys. Rev. C77, 034005 (2008)
N3LO in the chiral perturbation effective field theory
Jacek Dobaczewski
Indistinguishability principle
Jacek Dobaczewski
Fock space
Jacek Dobaczewski
Creation and annihilation operators
Jacek Dobaczewski
Operators in the Fock space
Jacek Dobaczewski
Thouless theorem for even states
Jacek Dobaczewski
Gauss factorization
Jacek Dobaczewski
Hartree-Fock interaction energy
Jacek Dobaczewski
Direct interaction energy
Jacek Dobaczewski
Exchange interaction energy (I)
Jacek Dobaczewski
Exchange interaction energy (II)
Jacek Dobaczewski
Nuclear densities as composite fields
Jacek Dobaczewski
-3
Particle density (fm )
Nuclear densities as composite fields
0.10
100
Sn
(n)
100
Zn
(n)
(p)
(p)
0.05
0.00
0
2
4
6
8
2
4
6
8
10
R (fm)
Modern Mean-Field Theory  Energy Density Functional
r, t,
Hohenberg-Kohn
Kohn-Sham
Negele-Vautherin
Landau-Migdal
Nilsson-Strutinsky
Jacek Dobaczewski

J,

j,

T,

s,

F,
mean field one-body densities
zero range local densities
finite range non-local densities
Local energy
density:
(no isospin,
no pairing)
Jacek Dobaczewski
Complete local energy density
Mean field
Jacek Dobaczewski
Pairing
Mean-field equations
Jacek Dobaczewski
Phenomenological effective interactions
Jacek Dobaczewski
Skyrme-Hartree-Fock
J. Dobaczewski, J. Engel,
Phys. Rev. Lett. 94, 232502 (2005)
Experiment
R.G. Helmer et al., Nucl. Phys. A474 (1987) 77
Jz=1/2
1/2-
b10=0.023
b20=0.161
b30=-0.128
b40=0.091
Jacek Dobaczewski
1/2+
0
55
225Ra