Overview of effective interactions

In this article you’ll find an overview of many effective interactions. My goal is to make nuclear shell model codes more transparent, easily accessible, and user friendly. Doesn’t help that someone made a super performant code if it is not publicly available, difficult to obtain, and / or hard to use! Physicists are notorious when it comes to this, except maybe this one? ;-)

What is an effective interaction?

In the nuclear shell model, effective interactions are a way to simplify the complex forces between nucleons (protons and neutrons). Since dealing with the full interaction between every nucleon in a nucleus is computationally overwhelming, especially for many-body systems, effective interactions are designed to capture the essential parts of these forces within a simplified model space of only the most relevant states.

The idea is to take the full interactions of all possible nucleon interactions and approximate them in a truncated or reduced space. This is done by prohibiting the most bound nucleons from moving about and instead consider them as a single static core. By doing this we of course lose some dynamic in the system, but of course the most bound nucleons are less likely to move compared to the nucleons at the Fermi surface, so in many cases the approximation is quite good!

What parameters are there in an effective interaction?

Practically speaking, an interaction is a text file (or text files) containing single-particle energies (SPEs), two-body matrix elements (TBMEs), and specifications about the model space like $n$, $l$, $j$, $tz$ of all the different orbitals. The exact syntax varies a bit between the different shell model codes (because of tz / np formalism? AS TBMEs?). Various interactions in KSHELL format can be found here.

Overview

Interaction	Range	Model space	Core	$g_{s, p}, g_{s, n}$	$g_s$ quench	Reference
USDA	[$^{17}$O, $^{39}$Ca]	$sd$	$^{16}$O	(5.585, -3.826)	1	Brown et al.
GXPF1A	[$^{41}$Ca, $^{79}$Zr]	$pf$	$^{40}$Ca	(5.027, -3.443)	0.9	Honma et al.
JUN45	[$^{57}$Ni, $^{99}$Sn]	$2p_{3/2}, 1f_{5/2}, 2p_{1/2}, 1g_{9/2}$	$^{56}$Ni	(3.909, -2.678)	0.7	Homna et al.
SDPF-MU	[$^{17}$O, $^{79}$Zr]	$sd, pf$	$^{16}$O	(5.027, -3.443)	0.9	Utsuno et al.
gs8	[$^{17}$O, $^{139}$Yb]	$sd, pf, sdg$	$^{16}$O	(4.189, -2.869)	0.75	Shimizu et al.
GCLSTsdpfsdgix5pn	[$^{17}$O, $^{139}$Yb]	$sd, pf, sdg$	$^{16}$O	(4.189, -2.869)	0.75