Investigation of Isovector Balance and Effective Deformation for 106Mo and 104Zr Isotones within IBM-2 Framework

Abstract

Background: The Interacting boson model (IBM-2) Has been applied to study the effect of nuclear structure properties on the spectral features of   ¹⁰⁶Mo and ¹⁰⁴Zr isotones which have neutron number N=64.

Materials and Methods: The Interacting Boson Model (IBM-2) was applied to analyze the deviation  from ideal behavior, for the U(5) to SU(3) and the weight of each determination in each nucleus. The energy ratio ,  shape coexistence, the effective nuclear deformation parameter  and the isovector balance (IV) have been  determined to confirm the approach to rotational distortion. Electric quadrupole transition probabilities B(E2) and magnetic dipoletransition probabilities B(M1) have been checked.

Results: The effective nuclear deformation parameter , in ¹⁰⁶Mo and¹⁰⁴Zr was negative, stay away from zero. The isovector balance (IV) describes the relationship between the proton  and neutron    parameters within the IBM-2 framework, in ¹⁰⁶Mo and¹⁰⁴Zr, it was found to reinforce the idea of ​​transitioning from vibrational to rotational behavior, this applies perfectly to the results of electrical transition ratios ( , ' and ''). The energy level sequences and ratios indicated that the ¹⁰⁶Mo and ¹⁰⁴Zr are transitional nuclei between vibrational U(5) and rotational SU(3) symmetries. Collective states associated with proton-neutron symmetry and symmetry mixing play an important role in studying collective nuclear properties by changing the Majorana parameter  showed a significant  impact was shown on determining the mixing locations of some levels and  while other levels remained unaffected and their values remained constant at specific values, such as the levels and  in ¹⁰⁶Mo and ¹⁰⁴Zr. No experimental values of the  level are available.

Conclusion: The study shows that the ¹⁰⁶Mo and ¹⁰⁴Zr isotones exhibit transitional behavior between the vibrational and rotational symmetries, with a clear tendency toward rotational deformation. The negative values of the effective nuclear deformation parameter    and the isovector balance emphasize the importance of proton-neutron symmetry in describing the collective properties of these isotones.