Study of The Properties of The Transition Strengths |M(E2)|2 and The Reduced Transition Probabilities B(E2) Of Even-Even Hafnium Hf Nuclei

Abstract

The distribution of matter in the nucleus of an atom is One of the main physical features, and it is the main focus of nuclear physics.Recently, the volume of research specializing in nuclear shapes has been steadily increasing, and large quantities of nuclear building coefficients are being compiled, providing an opportunity to discover new data on many nuclear deformations, especially quadrupole deformations. The nuclei of rare hafnium isotopes in the nuclear diagram are full of distorted nuclei, exhibiting many interesting phenomena related to nuclear structure.

In this research work, the transition Strengths and reduced transition probabilities from the ground state to the first excited state (0⁺ → 2⁺) were calculated for a set of even-even neutron-rich  isotopes.

In addition, the parameters associated with reduced transition probabilities B(E2), such as the quadrupole moment Q₀ and the deformation coefficient β₂ for the  even-even nuclei, were calculated.Since the calculation of the transition Strengths |M(E2)|² depends on the total gamma width Γ of an excited state with a given mean lifetime (τ), We have explained the physics upon which the relationship between (Г) and (τ) depends.Our work has shown that the transition Strengths, transition probability, quadrupole moment, and deformation parameter have relatively lower values ​​for hafnium isotopes that have a neutron number close to the magic number N=82 or N=126.