No abstract

The well-known Grodzins product [Formula: see text]2, 0[Formula: see text]2[Formula: see text] constancy rule was generalized to the Grodzins linearity relation in our recent work in the form of [Formula: see text] versus [Formula: see text] linear plots. In this form, besides testing the linear relation of [Formula: see text]) and kinetic moment of inertia, it also served as a tool for the study of the spectral details of the nuclei, and for the study of the variation of nuclear structure with [Formula: see text] and [Formula: see text] We now study its extension to the intra band [Formula: see text]2 transition from the higher spins of the ground bands of even [Formula: see text] even [Formula: see text] nuclei of the mid-mass region of Xe–Pt chain of isotopes. We use the plots of [Formula: see text]2, [Formula: see text] versus [Formula: see text] [Formula: see text] and 6[Formula: see text] to test their linear relationship. There seems to be a good correlation of the two entities even at the higher spins for all the nuclei studied here. The deviations from linearity in specific cases can be used for studying the nuclear structures involved.

In the collective spectra of atomic nuclei, the level energy [Formula: see text] varies with atomic number [Formula: see text] and neutron number [Formula: see text]. Also the [Formula: see text]2 decay-reduced transition probability [Formula: see text] is related to the energy [Formula: see text]. The product [Formula: see text] is constant according to Grodzins product rule, independent of the vibration or rotational status of the nucleus. The product rule is often used for determining [Formula: see text] from the known [Formula: see text]. However, the variation of the product with various parameters is also suggested in the literature. Hence, a detailed global study of this rule for [Formula: see text] region is warranted. We use a novel method of displaying the linear relation of [Formula: see text] with [Formula: see text] for the isotopes of each element (Xe–Pt), instead of their variation with [Formula: see text] or [Formula: see text]. Through our work, we firmly establish the global validity of the Grodzins relation of [Formula: see text], being proportional to the moment of inertia, except for the deviation in specific cases. Our [Formula: see text] versus [Formula: see text] plots provide a transparent view of the variation of the low-energy nuclear structure. This gives a new perspective of their nuclear structure. Also the various theoretical interpretations of [Formula: see text]s and the energy [Formula: see text] are reviewed.

The nuclei in the [Formula: see text] [Formula: see text] and [Formula: see text] regions, lying on both sides of the [Formula: see text]-stability line, continue to be of interest for their complex nuclear structures. The Grodzins product rule (GPR) viz. [Formula: see text], for the ground bands of even-[Formula: see text] even-[Formula: see text] nuclei provides a useful approach to study these structures. The utility of our method, displaying the linear relation of [Formula: see text] to [Formula: see text], is illustrated for the [Formula: see text] Zn to [Formula: see text] Cd series of isotopes. The spread of the data on the linear plots enables a quick view of the shape phase transitions. The role of the shells and the subshells, at spherical and deformed shell gaps for neutrons and protons, with their mutual re-inforcement and the shape phase transition are vividly visible on our plots. The development of collectivity in this region is also linked to the effective number of valence nucleons above the magic number of [Formula: see text], and 28 rather than [Formula: see text], for Mo to Cd isotopes for a microscopic calculation.

No abstract

Recently, from the study of the absolute [Formula: see text] values for the ([Formula: see text]–[Formula: see text]) [Formula: see text]2 transitions, the different roles of the triaxiality parameter [Formula: see text] and [Formula: see text] parts were pointed out. Here, the use of the triaxial rotor model expressions for the [Formula: see text]2)s in producing the bell-shaped curve of [Formula: see text] is illustrated. The variation of certain ([Formula: see text]–[Formula: see text]) [Formula: see text] ratios versus [Formula: see text] for the states [Formula: see text] and [Formula: see text] are illustrated, reflecting the two regions of [Formula: see text]. The inter relation of the [Formula: see text] and [Formula: see text] variables is illustrated for the Os isotopes.

The validity of the extended Grodzins product rule (GPR) for higher spins in the ground bands of even [Formula: see text], even [Formula: see text] nuclei of the light mass region of Cd to Zn chain of isotopes is studied. The plots of [Formula: see text]2, [Formula: see text]) versus [1/[Formula: see text]] ([Formula: see text], 6[Formula: see text] provide test of the linear relationship of the two entities. There seems to be a good correlation of the two entities at these higher spin states for most of the nuclei studied here. The deviations from linearity in specific cases are found to be useful for studying the variations in the nuclear structures involved. From these linearity plots, the structural change at higher spin in some nuclei involving subshell gaps, as reflected in the anomalous rise or saturation, leads to further insight into the under lying microscopic structure.

The anharmonicity in the [Formula: see text][Formula: see text]Cd, and [Formula: see text][Formula: see text]Te chain of isotopes, which lie close to magic number [Formula: see text], is analyzed from the study of the correlation of the energy levels in the ground band, and some anomalies in the various entities are pointed out. The split of the degeneracy of the phonon triplet and quintuplet is illustrated. Formation of multiple coexisting phonon multiplets, associated with higher lying excited [Formula: see text] and [Formula: see text] states, and intruder states, including 2p4h excitation, with varying deformations, in [Formula: see text]Cd is discussed. The interacting boson model (IBM) is applied for [Formula: see text] [Formula: see text]Cd. The results of a previous study of [Formula: see text] isotones in the dynamic pairing plus quadrupole model are cited for Cd and Te. The problem of collectivity as reflected in the quadrupole moments and [Formula: see text] values is analyzed. The enigma of deformation features in spherical [Formula: see text]Te, reflected in the transition probability [Formula: see text] is resolved. Charge dependence of [Formula: see text]2 transitions for vibrational nuclei, in producing enhanced [Formula: see text] strengths in Te versus Cd is illustrated.