NuHamil

This code is to generate the nucleon-nucleon (NN) and three-nucleon (3N) matrix elements. The generated NN and 3N files can be used as inputs of the many-body solvers such as imsrg++ code (https://github.com/ragnarstroberg/imsrg) and HartreeFock code (https://github.com/Takayuki-Miyagi/HartreeFock). It is also possible to compute the few body system with the Jacobi coordinate no-core shell model.

Requirements

• Fortran compiler
• BLAS, LAPACK libraries
• GNU Scientific library
• HDF5 library
• zlib

Installation

Download the code:

cd ~
git clone https://github.com/Takayuki-Miyagi/NuHamil-public.git

(Going to your home directory is not mandatory, but recommended.)

Change the directory and download the submodules:

cd NuHamil
git submodule init
git submodule update

The executable file can be built via make command. By default, it will be compiled with gfortran without MPI. If you want to use the intel compiler and/or turn on the MPI parallelization, please edit the Makefile by yourself.

make -j
make install
echo 'export PATH=$PATH:$HOME/bin' >> $HOME/.bashrc
source $HOME/.bashrc

By default, the symbolic link is created in the HOME/bin directory. If you want to change it, please change the "INSTLDIR" in the Makefile.

Some examples

Running a job is managed by a simple python script. Some example scripts are prepared. Note that you need to change "path_to_nninput" in the python scripts if you did not download the code in your home directory.

• deuteron properties

This should be finished with in a few seconds.

cd $HOME/exe/few-body
python3 deuteron.py

• triton properties

As the $N_{\rm max}$ truncation is sufficiently large $N_{\rm max}=40$, this will take a while. (~ half hour with 16 OpenMP threads on MacBook Pro, 2.3 GHz 8-Core Intel Core i9)

cd $HOME/exe/few-body
python3 triton_helium3.py

• lab-frame HO NN matrix elements

As the $e_{\rm max}$ truncation is reasonably large $e_{\rm max}=14$, this will take a while. (~ 15 min. with 16 OpenMP threads on MacBook Pro, 2.3 GHz 8-Core Intel Core i9)

cd $HOME/exe
python3 NuHamil_2BME.py

• lab-frame HO 3N matrix elements

This will not work on the local machine because of the computational power. I recommend submitting the job to a workstation or supercomputer. You need to edit NuHamil_3BME.py script depending on which job submission system is installed on the machine. This will take ~ 2 days, using 32 OpenMP threads (without MPI). The job is also memory expensive, and you need ~ 200GB RAM.

cd $HOME/exe
python3 NuHamil_3BME.py

Quick benchmarks

Using the NN+3N interaction generated in the above example and the imsrg++ code (https://github.com/ragnarstroberg/imsrg), the ground-state energies of doubly-magic nuclei are the following.

Nucleus	Interaction	$\lambda_{\rm SRG} \ ({\rm fm}^{-1})$	$e_{\rm max}$	$E_{\rm 3max}$	$\hbar\omega \ ({\rm MeV})$	$E_{\rm g.s.} \ ({\rm MeV})$
$^{4}{\rm He}$	${\rm NN-N}^{3}{\rm LO+3N}_{\rm lnl}$	2.0	4	16	16	-27.221
$^{4}{\rm He}$	${\rm NN-N}^{3}{\rm LO+3N}_{\rm lnl}$	2.0	6	16	16	-28.221
$^{4}{\rm He}$	${\rm NN-N}^{3}{\rm LO+3N}_{\rm lnl}$	2.0	8	16	16	-28.569
$^{4}{\rm He}$	${\rm NN-N}^{3}{\rm LO+3N}_{\rm lnl}$	2.0	10	16	16	-28.669
$^{4}{\rm He}$	${\rm NN-N}^{3}{\rm LO+3N}_{\rm lnl}$	2.0	12	16	16	-28.690
$^{16}{\rm O}$	${\rm NN-N}^{3}{\rm LO+3N}_{\rm lnl}$	2.0	4	16	16	-115.540
$^{16}{\rm O}$	${\rm NN-N}^{3}{\rm LO+3N}_{\rm lnl}$	2.0	6	16	16	-123.445
$^{16}{\rm O}$	${\rm NN-N}^{3}{\rm LO+3N}_{\rm lnl}$	2.0	8	16	16	-126.270
$^{16}{\rm O}$	${\rm NN-N}^{3}{\rm LO+3N}_{\rm lnl}$	2.0	10	16	16	-127.016
$^{16}{\rm O}$	${\rm NN-N}^{3}{\rm LO+3N}_{\rm lnl}$	2.0	12	16	16	-127.161
$^{40}{\rm Ca}$	${\rm NN-N}^{3}{\rm LO+3N}_{\rm lnl}$	2.0	4	16	16	-284.589
$^{40}{\rm Ca}$	${\rm NN-N}^{3}{\rm LO+3N}_{\rm lnl}$	2.0	6	16	16	-322.582
$^{40}{\rm Ca}$	${\rm NN-N}^{3}{\rm LO+3N}_{\rm lnl}$	2.0	8	16	16	-336.124
$^{40}{\rm Ca}$	${\rm NN-N}^{3}{\rm LO+3N}_{\rm lnl}$	2.0	10	16	16	-340.546
$^{40}{\rm Ca}$	${\rm NN-N}^{3}{\rm LO+3N}_{\rm lnl}$	2.0	12	16	16	-341.678

Remarks

Unfortunately, non-locally regulated 3N interaction cannot be fully suppported. Feel free to contact me (miyagi@theorie.ikp.physik.tu-darmstadt.de) if you are interested in such interactions. I can provide the HO 3N matrix element files in the Jacobi coordinate or in the laboratory frame.

How to cite

If you use this code in your research, please cite T. Miyagi, Eur. Phys. J. A 59, 150 (2023).

Acknowledgement

NuHamil code is greatly inspired by the manyeff code by P.Navratil and VRenormalize in Computational Environment for Nuclear Structure (CENS) project (https://github.com/ManyBodyPhysics/CENS). The code uses VODE library by G.D.Byrne and S.Thompson. I thank P.Navratil, N.Shimizu, and N.Tsunoda for the discussions, optimizations, and parallelizations. I also thank P.Arthuis, A.Belly, M.Heinz, B.S.Hu, S.R.Stroberg, and A.Tichai for testing the code and useful feedback.