Differences

This shows you the differences between two versions of the page.

--- projects [2014/07/16 07:56]
schunck
+++ projects [2014/07/28 07:33] (current)
schunck [3) Possible Extensions for Week 3 and Later]
@@ Line 10: / Line 10: @@
 ==== 1) HF Problem in a Truncated Model Space ====
-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 {{HF_truncated.pdf|document}}.
+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 {{HF_truncated_v2.pdf|document}}.
 ==== 2) HF Problem in the Full Spherical Harmonic Oscillator Basis ====
-To come next week.
+Now that each group (hopefully) has a working HF code for the truncated S-wave model space model, we are ready to attack the general case. Since the generation of two-body matrix elements (TBMEs) is tedious for the general case, we have uploaded a F90 pack to do this for you, see {{:relcom2labsystem.tar.gz|here}}. We will give more explanations on how to use the code in the lectures. Finally, the following document outlines how the HF equations look in spherical symmetry for general model spaces, {{:hf_fullspherical.pdf|}}. We give below a description of what is contained in the files.
+**Single-particle files** - The single-particle files are named **spM.dat** and **spJ.dat** for the M-scheme and coupled J scheme, respectively. The first line (starting with "Legend") gives the meaning of the numbers
+  * For the M-scheme: counter    $n\     l\     2j\   2m_j\   2t_z$
+  * For the J-scheme: counter    $n\     l\     2j\   t_z\    2n+l$
+**Interaction files** - The interaction files are named **VM-scheme.dat** and **VJ-scheme.dat**, respectively (for the M-scheme and the J-scheme).
+  * For the M-scheme: $a\  b\  c\  d\  v_{abcd}$
+  * For the J-scheme: $t_z\ \pi\  2J\  a\  b\  c\  d\ v_{abcd}$
+where $\pi$ is the parity. In each case, the a, b, c, d numbers refer to the counters listed in the single-particle files.
+==== 3) Possible Extensions for Week 3 and Later ====
+Upon completion, the (full) HF code that you have developed can be used to explore various other approximations to the many-body problem. The figure below shows some of the possible extensions, and how one could piece them together (like Lego pieces, ideally).
+{{ :scheme.png?300 |}}
+In this {{HF_extensions.pdf|document}}, we explain in more details how to implement 3 of these extensions, namely (i) the solution of the HFB equations in spherical symmetry, (ii) the solution of the RPA equations in spherical symmetry, and (iii) the solutions of the deformed HF equations. When you are done with the full HF program, you should choose one of these problems and start working on it. We can provide benchmarks for the spherical HFB problem and the deformed HF, not yet for the RPA.
 __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//, [[https://journals.aps.org/prc/abstract/10.1103/PhysRevC.84.044306|Phys. Rev. C 84, 044306 (2011)]]

TalentDFT

User Tools

Site Tools

Differences

Page Tools