NUCLEI WITH TETRAHEDRAL SYMMETRY

We discuss a point-group-theory based method of searching for new regions of nuclear stability. We illustrate the related strategy with realistic calculations employing the tetrahedral and the octahedral point groups. In particular, several nuclei in the Rare Earth region appear as excellent candidates to study the new mechanism.

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Isomorphism and matrix representation of point groups

Malaysian Journal of Fundamental and Applied Sciences ◽

10.11113/mjfas.v15n2019.1087 ◽

2019 ◽

Vol 15 (1) ◽

pp. 88-92

Author(s):

Wan Heng Fong ◽

Aqilahfarhana Abdul Rahman ◽

Nor Haniza Sarmin

Keyword(s):

Group Theory ◽

Matrix Representation ◽

Point Group ◽

Multiplication Table ◽

Matrix Representations ◽

The Matrix ◽

Point Groups ◽

Complete Set ◽

Symmetry Of Molecules ◽

Symmetry Operations

In chemistry, point group is a type of group used to describe the symmetry of molecules. It is a collection of symmetry elements controlled by a form or shape which all go through one point in space, which consists of all symmetry operations that are possible for every molecule. Next, a set of number or matrices which assigns to the elements of a group and represents the multiplication of the elements is said to constitute representation of a group. Here, each individual matrix is called a representative that corresponds to the symmetry operations of point groups, and the complete set of matrices is called a matrix representation of the group. This research was aimed to relate the symmetry in point groups with group theory in mathematics using the concept of isomorphism, where elements of point groups and groups were mapped such that the isomorphism properties were fulfilled. Then, matrix representations of point groups were found based on the multiplication table where symmetry operations were represented by matrices. From this research, point groups of order less than eight were shown to be isomorphic with groups in group theory. In addition, the matrix representation corresponding to the symmetry operations of these point groups wasis presented. This research would hence connect the field of mathematics and chemistry, where the relation between groups in group theory and point groups in chemistry were shown.

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SEARCH FOR TETRAHEDRAL SYMMETRY IN NUCLEI: A SHORT OVERVIEW

International Journal of Modern Physics E ◽

10.1142/s0218301311017557 ◽

2011 ◽

Vol 20 (02) ◽

pp. 219-227

Author(s):

◽

D. CURIEN ◽

J. DUDEK ◽

H. MOLIQUE ◽

L. SENGELE ◽

...

Keyword(s):

Rare Earth ◽

Experimental Results ◽

Quadrupole Moments ◽

Vibrational Motion ◽

Octahedral Symmetry ◽

Tetrahedral Symmetry ◽

Experimental Search ◽

Series Of Experiments ◽

Important Progress ◽

The Rare Earth

Following a series of experiments launched by the TetraNuc collaboration to possibly demonstrate the existence of high-rank symmetries in subatomic physics, the first experimental results on the Rare Earth region appear in publications. Meanwhile an important progress has been made on the theory side strongly suggesting that the original criterion of the static tetrahedral symmetry in the form of vanishing quadrupole moments may need to be revised to include explicitly the vibrational motion. The Actinide region seems of particular interest because of the extra stability provided by the octahedral symmetry. In this article a summary of the current experimental efforts on both the Rare-Earth and Actinide regions is given. Finally the ELMA project addressing the experimental search for the symmetries in the Actinides is briefly discussed.

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