The systematics of the Grodzins product rule (GPR) is studied from the perspective of the valence-proton and neutron product NpNn in the major shell space Z = 50–82, N = 82–126. The variation of nuclear structure from vibrator to deformed rotor is discussed. The Grodzins product shows more dependence on NpNn in the N ≤ 104 region, as it is a region of deformed nuclei. We present here for the first time the dependence of GPR on the NpNn product.
A systematic dependence of Grodzins product (E( + ) * B(E ) ↑) on the asymmetry parameter γ is studied in the Z = − , N = − major shell space. The Grodzins product provides contributions of E( + ) and B(E ) ↑ simultaneously, which further re ects the shape phase transitions with asymmetry parameter γ . In the region of deformed nuclei, Grodzins product (E( + )*B(E ) ↑) shows direct dependence on the asymmetry parameter γ . We discuss here for the rst time the correlation between Grodzins product (E( + ) * B(E ) ↑) and the asymmetry parameter γ .
The structure of multiphonon K = 4 γγ-band of Ru 112 , Mo 104 , Mo 106 , and Mo 108 nuclei are investigated using the recently proposed modified soft rotor formula (MSRF). The positive values of the moment of inertia and small values of softness parameter are obtained. The calculated values of moment of inertia of γγ-band are almost equal to the moment of inertia of γband, which indeed should be equal to the moment of inertia of ground band. The constant energy parameter EK in the MSRF is also illustrated for K = 4 γγ-band. The staggering pattern in the multiphonon γγ-band is also discussed in detail. The study of one-phonon K = 2 γ-band and two-phonon K = 4 γγ-band using MSRF yields good energy values.
The structure of multiphonon band of 154 Gd nucleus is investigated by using the Modified Soft Rotor Formula (MSRF). The positive values of the moment of inertia and small values of softness parameter are obtained. The calculated value of moment of inertia of γγ-band is almost equal to the moment of inertia of γ-band, which indeed should be equal to the moment of inertia of the ground band. The constant energy parameter EK in the MSRF formula is also illustrated for K=2 βγ-band and K=4 γγ-band. The staggering pattern in the multiphonon γγ-band is also discussed in detail. The study of one-phonon K=2 γ-band, two-phonon K=2 βγ-band and K=4 γγ-band using MSRF formula yield good energy values.
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