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 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.

In a first step, we will solve the HF equations for the system of N neutrons in a trap interacting with the Minnesota potential in a restricted basis consisting of only l=0 states. This simplifies tremendously the calculation of two-body matrix elements. We broke down the problem into several simple steps that are explained in this document.

To come next week.

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)