SU(3) reduced matrix element package

Abstract
A new SU(3) reduced matrix element package, which exploits logical operations and bit manipulation procedures in implementing a fermion second-quantized formulation for calculating matrix elements of SU(3)-coupled products of creation and annihilation operators (a^† , a^† a^† , a, aa, a^† a, a^† a^† a, a^( †)aa, a^† a^† aa), is introduced. The reduced matrix elements are extracted from full matrix elements of the coupled operators. Since the reduced matrix elements do not depend on the subg...

Title of program: SU3RME
Catalogue Id: ACVI_v1_0

Nature of problem
It is well-known from mean-field studies that a three-dimensional harmonic oscillator is a reasonable zeroth-order approximation for the common potential experienced by nucleons in nuclei. The choice of SU(3) as a basic symmetry is therefore natural since it is the exact symmetry group of the spherical oscillator, and furthermore, it is the dynamical symmetry group of the deformed oscillator when, as is usually the case, the deformation is generated by quadrupole interactions [1-3]. Nonetheless, ...

Versions of this program held in the CPC repository in Mendeley Data
ACVI_v1_0; SU3RME; 10.1016/0010-4655(94)90035-3

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

### 摘要
本文介绍了一款新型SU(3)约化矩阵元（reduced matrix element）程序包，该程序包借助逻辑运算与位操作流程，实现了费米子二次量子化形式，用于计算SU(3)耦合的产生和湮灭算符（creation and annihilation operators）乘积的矩阵元，涉及的算符包括$a^dagger$、$a^dagger a^dagger$、$a$、$aa$、$a^dagger a$、$a^dagger a^dagger a$、$a^dagger aa$、$a^dagger a^dagger aa$。约化矩阵元从耦合算符的完整矩阵元中提取得到。由于约化矩阵元不依赖于子群[原文未完整给出]。

### 程序名称：SU3RME
### 目录编号：ACVI_v1_0

### 问题背景
平均场研究（mean-field studies）已证实，三维谐振子（three-dimensional harmonic oscillator）可作为原子核内核子所受共同势场的合理零级近似（zeroth-order approximation）。因此选择SU(3)作为基本对称性（basic symmetry）是自然的：它既是球谐振子（spherical oscillator）的精确对称群（exact symmetry group），同时在通常由四极相互作用（quadrupole interactions）产生形变的情况下，也是形变谐振子（deformed oscillator）的动力学对称群（dynamical symmetry group）[1-3]。尽管如此，[原文未完整给出]。

### Mendeley数据中CPC库收录的该程序版本
ACVI_v1_0; SU3RME; 10.1016/0010-4655(94)90035-3

本程序源自贝尔法斯特女王大学托管的CPC程序库（1969-2019年）