Problem of energy scale in rigid triaxial rotor model

The problem of mismatching of the level energies, in the ground band and the [Formula: see text]-band of triaxially deformed atomic nuclei, as predicted in the rigid triaxial rotor (RTR) approximation of Davydov and Filippov (DF) model, with experiment, is well known. Here, we illustrate the solutions suggested in the literature, and the deviations observed in the converted energy values, from the experiment. We analyze the source of problem of this mismatch with experiment. This enables a physical picture of the DF (or RTR) model spectra. Our analysis will help in understanding the merits and the limitation of the RTR model in this respect.

Study of the Electric Quadrupole Transitions in 50-51Mn Isotopes by Using F742pn and F7cdpn Interactions

The nuclear shell-model has been used to compute excitation levels of ground band and electric quadrupole transitions for 50-51Mn isotopes in f-shell. In the present study, f742pn and f7cdpn effective interactions have been carried out in full f-shell by using Oxbash Code. The radial wave functions of the single-particle matrix elements have been calculated in terms of the harmonic oscillator (Ho) and Skyrme20 potentials. The predicted theoretical results have been compared with the available experimental data; it has been seen that the predicted results are in agreement with the experimental data. From the current results of the calculations, many predictions of angular momentum and parities of experimental states have been made, and the energy spectra predictions of the ground band and B(E2; ↓) electric quadrupole transitions in 50-51Mn isotopes of the experimental data are not known yet. In the nuclear shell-model calculations framework, energy levels have been determined for 50-51Mn isotopes; new values of electric quadrupole transitions have been predicted in the studied results. This investigation increases the theoretical knowledge of all isotopes with respect to the energy levels and reduced transition probabilities.

Microscopic study of nuclear structure dynamics of neutron-deficient even–even 100–110Cd isotopes within the framework of projected shell model

We have studied the deformation systematics of [Formula: see text] and [Formula: see text] values, yrast spectra, band structure and backbending phenomena in the neutron-deficient even–even [Formula: see text]Cd isotopes within the projected shell model (PSM) framework. The observations of the systematics of [Formula: see text] and [Formula: see text] values for [Formula: see text]Cd isotopes are well reproduced in present calculations. Our observations show that, as we move from [Formula: see text]Cd to [Formula: see text]Cd, the deformation increases and then it reduces up to [Formula: see text]Cd. This gives us a confirmation that [Formula: see text]Cd is the most deformed nucleus in this set of isotopic mass chain. The backbending phenomena is also observed in these isotopes, which can be related to the crossing of ground band (g-band) by 2-quasiparticle (qp) bands or s-bands. The pseudomagic character of [Formula: see text]Cd has also been observed.

Supersolidity of the $\alpha$ cluster structure in the nucleus $^{12}$C

For more than half a century, the structure of $^{12}$C, such as the ground band, has been understood to be well described by the three $\alpha$ cluster model based on a geometrical crystalline picture. On the contrary, recently it has been claimed that the ground state of $^{12}$C is also well described by a nonlocalized cluster model without any of the geometrical configurations originally proposed to explain the dilute gas-like Hoyle state, which is now considered to be a Bose–Einstein condensate of $\alpha$ clusters. The challenging unsolved problem is how we can reconcile the two exclusive $\alpha$ cluster pictures of $^{12}$C, crystalline vs. nonlocalized structure. We show that the crystalline cluster picture and the nonlocalized cluster picture can be reconciled by noticing that they are a manifestation of supersolidity with properties of both crystallinity and superfluidity. This is achieved through a superfluid $\alpha$ cluster model based on effective field theory, which treats the Nambu–Goldstone zero mode rigorously. For several decades, scientists have been searching for a supersolid in nature. Nuclear $\alpha$ cluster structure is considered to be the first confirmed example of a stable supersolid.

Lifetime measurements in 110Cd

Mean lifetimes for the lowest 6 yrast band members have been measured using the Recoil Distance Doppler Shift technique (RDDS). The data have been analyzed via the Differential Decay Curve Method (DDCM). The transition probabilities deduced from the data for the ground band E2 γ-rays are in rather good agreement with the predictions of the U(5)-limit of interacting boson model-1 (IBM-1).

Generalized grodzins relation for ground band

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.

Systematic study of the nature of gamma bands in A = 100–200 mass nuclei

The [Formula: see text]-bands are analyzed through the variation of the energy of the [Formula: see text] excitation and the energies of excited level sequence of [Formula: see text]-bands with respect to various parameters. The shape phase transition observed at N = 88–90 is reviewed through its influence on the energies of [Formula: see text]-band. The correlation of the [Formula: see text] excitation energies with the collective shape signature observable [Formula: see text] indicates a connection with the nuclear equilibrium structure. The study of excited level sequence in the [Formula: see text]-band with respect to the ground band signifies that the two bands differ in deformation.

U(6) dynamical and quasi-dynamical symmetry in strongly deformed heavy nuclei

The low-lying collective states of the ground, β and γ bands in154Sm and238U are investigated within the framework of the microscopic proton-neutron symplectic model (PNSM). For this purpose, the model Hamiltonian is diagonalized in a U(6)-coupled basis, restricted to the symplectic state space spanned by the fully symmetric U(6) vectors. A good description of the energy levels of the three bands under consideration, as well as the intraband B(E2) transition strengths between the states of the ground band is obtained for the two nuclei without the use of an effective charge. The calculations show that when the collective quadrupole dynamics is covered already by the symplectic bandhead structure, as in the case of154Sm, the results show the presence of a very good U(6) dynamical symmetry. In the case of238U, when we have an observed enhancement of the intraband B(E2) transition strengths, then the results show small admixtures from the higher major shells and a highly coherent mixing of different irreps which is manifested by the presence of a good U(6) quasi-dynamical symmetry in the microscopic structure of the collective states under consideration.