| In this paper, we first introduce the basic background of the study of nuclear structure, some elementary knowledge about and the latest achievements in the study of the phenomena of Signature Inversion (SI). Then the description of the two quasi-Particles plus a Rotor Model (PRM) of odd odd nuclei is given. By the Model we perform the practical calculations of the yrast bands of some nuclei in A 100, 130 mass region. Based on the results of these calculations, we discuss some related problems, such as triaxial shape, the phenomena and the mechanism of signature inversion and so on. Some principal conclusions of the theoretical study are as follows: (1). Our practical PRM calculations of the pg 9/2≈nh 11/2yrast bands of some odd odd 98-102 nuclei are performed in A 100 mass region ( Rh) and reproduce the inversion points very well. (2). The calculations further confirm that the competion between the Coriolis force and n-p coupling interaction in the low K space might be the possible dominating mechanism for SI in odd odd nuclei. (3). There exists a deficiency of the axial Symmetry Rotor plus two quasi-Particles Model for odd odd nuclei that the vibration far away from the inversion point is smaller. With the introduction of triaxial shape, the calculated results are remarkably improved. We could draw an elementary conclusion: triaxial shape plays an important role to cause SI in odd odd nuclei and its influence will become stronger in some nuclei which have 100 126 large g deformation, such as Rh and La. (4). We draw an ideal conclusion as well in A 130 mass region and get a confirmation further that triaxial shape is pivotal to influence the vibration. (5). We simply discuss the relations between the angle g of triaxial deformation and SI.
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