As a starting point, we will ask every group of students to write a program (in the language of their choice) solving the Hartree-Fock equations in the spherical harmonic oscillator basis. To facilitate benchmarks, we chose to focus on systems of neutrons that are confined in a harmonic trap and are interacting via a schematic potential called the Minnesota potential. Spherical symmetry will be assumed throughout. Even this simplified system may require a significant effort, so we tried to make your life a little easier.

• We provide most of the necessary background about the harmonic oscillator in this document;
• We give you, without demonstration, the matrix elements of the kinetic energy operator (see the same document);
• Upon request, we can make available to you various Fortran subroutines giving the nodes and weights of the Gauss-Laguerre quadrature. We also will provide DFT solvers that you can use as benchmarks

And of course, we will be around to help you, so don't hesitate to ask if you have questions.

A summary of the characteristics of the system, and of the various steps needed to write a HF code is given in this document.

References

• S. K. Bogner, R. J. Furnstahl, H. Hergert, M. Kortelainen, P. Maris, M. Stoitsov, and J. P. Vary, Testing the density matrix expansion against ab initio calculations of trapped neutron drops, Phys. Rev. C 84, 044306 (2011)