# Course 4: Density functional theory and self-consistent methods

The third edition of Course 4 on
*Density Functional Theory and Self-Consistent Methods* will be held at the
Lawrence Berkeley National Laboratory, in Berkeley, CA, USA.
The dates are July 6 to July 24, 2020.
The principal instructors will be Nicolas Schunck (Lawrence Livermore National Laboratory),
Michael Forbes (Washington State University),
Heiko Hergert (Michigan State University),
and Tomás Rodríguez (Universidad Autonoma de Madrid).

**Contact:** Nicolas Schunck (schunck1@llnl.gov).

Energy density functional (EDF) approaches play a central role in nuclear theory since they offer the only computationally feasible many-body framework capable of describing nuclei across the mass table. EDF approaches to nuclear structure are analogous to electronic DFT in that they map the computationally prohibitive many-body problem onto an effective one-body problem. Besides the obvious computational simplifications, this so-called Kohn-Sham framework provides a mean-field-like description in terms of intrinsic shape and single-particle degrees of freedom that lends itself to simple and physically intuitive interpretations. The price to pay for these simplifications is that the unknown EDF must be approximated with phenomenological functionals (e.g., Skyrme, Gogny, etc.), typically expressed as local powers and gradients of ground state nucleon densities and currents with empirical couplings adjusted to data.

The main goal of the course is to gain an in-depth understanding of the basic concepts, mathematical methods, and computational techniques used to solve the quantum many-body problem within the framework of energy density functional theory. Following the spirit of the TALENT series of lectures, this will be achieved both through regular lectures and the development of a computational project over the duration of the course: Building upon the success of the previous editions of the course, we will offer to solve the spherical Hartree-Fock equation for a schematic energy density functional in the harmonic oscillator basis with an energy functional based on the finite-range two-body Minnesota interaction. To reflect the growing number of applications of time-dependent EDF methods, we will also propose to solve the time-dependent Hartree-Fock equation for a simplified local functional. This will involve a number of coordinate space techniques already presented in the 2016 school for the static case. For students who meet these project goals early, we will offer the option to implement symmetry restoration and/or configuration mixing via the GCM to approach the exact solutions with simple Hamiltonians defined in small valence spaces.

Students should have working proficiency in quantum mechanics. This includes knowledge of the following basic physics concepts and mathematical tools: concept of wave-function, SchrÃ¶dinger equation, spin, Hilbert spaces, linear operators, differential operators, group theory. Students are also expected to have strong operating programming skills in Fortran, C/C++ and/or Python. The target group is students currently pursuing a Master of Science, a Ph.D., as well as early post-doctoral fellows. Students can be either experimentalists or theorists.

The second edition of Course 4 on Density Functional Theory was given at
the University of York in York, UK from July 17 to August 6, 2016. The
principal lecturers were Jacek Dobaczewski (University of York, UK and
Jyvaskyla, Finland), Andrea Idini (University of Surrey, UK), Alessandro
Pastore (University of York, UK), and Nicolas Schunck (Lawrence Livermore
National Laboratory, USA).
The written course materials
and
videos of the lectures
are freely available.

Contact: Jacek Dobaczewski (jacek.dobaczewski@york.ac.uk).

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The course will focus on Energy Density Functional (EDF) theory and its applications to nuclear structure. The core concepts of density functional theory will be introduced covering Hartreeâ€“Fock methods, their extension to symmetry breaking cases (HFB, deformation) and infinite matter, nuclear collective motion and excitations (RPA), and the properties of functionals. Particular emphasis will be placed on guided exercises and on the development of a computer code that can solve a typical (simplified) problem of nuclear density functional theory. The course will run full-time for three weeks and consist of 45h of lectures and directed exercises, about 75h devoted to a computational project, and a final assignment. The total workload will amount to 150 hours, corresponding to 6 ECTS in Europe.

Prospective student participants are expected to have operating programming skills in Fortran or C++ or Python or related programming languages and proficiency in quantum mechanics. Preparatory modules on second quantization, and related fundamental topics, will be provided during the course but students are expected to familiarize with these concepts prior to attendance.

To know more about the course contents and outline, please follow this link.

The first edition of Course 4 on Density Functional Theory ran at the ECT* in Trento, in collaboration with the University of Trento, from July 14 to August 1, 2014. The course materials from the first edition (projects, slides, programs, discussion groups, etc.) can be found here.