Soft Rotor Formula Research Articles

Theoretical study of nuclear collective phenomena and broken SU(3) symmetry of even-even 238−244Pu isotopes

Theoretical nuclear study of the even-even Plutonium Isotopes Pu238−244 was carried out. The positive-parity rotational state band was calculated in the framework of the interacting Boson model-1 (IBM-1) and modified soft rotor formula (MSRF), while the negative-parity band was calculated in the framework of the new modified negative-parity formula (NMF). Furthermore, the energy levels for the β- and γ-vibrational energy bands were calculated. The odd-even staggering effect between the ground and octupole bands, which is a function of spin, was analyzed. The intrinsic coherent state was used to find the potential energy surfaces (PES). In addition, electric transition probabilities B(E1), B(E2), and B(E3) for these isotopes were calculated. The results obtained by applying the IBM-1, MSRF, and the NMF were inferred to be in good agreement with the corresponding experimental data for most of the nuclear states.

Nuclear structure of even-even Ytterbium isotopes 166−176Yb

A nuclear phenomenological study of the even-even Ytterbium Isotopes Yb166−176 was carried out, in the framework of the interacting Boson model-1 (IBM-1) and modified soft rotor formula (MSRF). The energy levels for ground-state, γ- and β-rotational bands were calculated. Also, electric transition probability B (E2) for these isotopes was calculated. Furthermore, the intrinsic coherent state was used to find the potential energy surfaces. The staggering effect of a γ-band, which is a function of spin, was analyzed. The results obtained by applying the IBM-1 and the MSRF are in good agreement with the corresponding experimental data for most of the nuclear states.

A new perspective of ground band energy formulae

A host of alternative energy formulae for the ground bands of even Z even N nuclei are available in the literature. The usual approach is to compare the relative numerical accuracy of the predictions of the level energies by these formulae, for varying deformations of the nuclear core and for high spins. The soft rotor formula and variable moment of inertia model, the ab and pq formulae, the rotation vibration interaction and power index formulae are illustrated. Here, a new perspective is presented, with emphasis on the limitation of the region of their physical validity and on deriving useful meaning of their parameters.

Spins of superdeformed rotational bands in Tl isotopes

The two-parameter model defined for even-even nuclei viz. soft-rotor formula is used to assign the band-head spin of the 17 rotational bands in Tl isotopes. The least-squares fitting method is employed to obtain the spins of these bands in the \(A\sim 190\) mass region. The calculated transition energies are found to depend sensitively on the proposed spin. Whenever a correct spin assignment is made, the calculated and experimental transition energies coincide very well. The dynamic moment of inertia is also calculated and its variation with rotational frequency is explored.

Two-term formula for ground band energy symmetry in low-lying levels of light Mg-Zr nuclei

In this paper, two parameter single-term energy formula [Formula: see text] is used to study the energy spin relationship within the ground bands of even–even Mg-Zr nuclei. The formula works better for the [Formula: see text]-soft nuclei as well as vibrational nuclei. We also compared it with other two-parameter formulas: Ejiri, [Formula: see text], [Formula: see text] and soft rotor formula (SRF). We also study the symmetry of the nuclei in the framework of interacting boson model (IBM-1). The IBM-1 was employed to determine the most appropriate Hamiltonian, the Hamiltonian of the IBM-1 and [Formula: see text](6) symmetry calculation, for the study of these isotopes. We have also calculated energy levels and B(E2) values for number of transitions in these [Formula: see text]Se and [Formula: see text]Kr isotopes and there is a good agreement between the presented results and the previous experimental data.

Study of multiphonon γγ-band in neutron-rich 112Ru nucleus and molybdenum isotopes

The structure of multiphonon K = 4 γγ-band of , , , and 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 γ-band, 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.

ANHARMONICITY VERSUS LINEARITY RELATION AND MALLMANN PLOT

The anharmonity in shape transitional nuclei, observed earlier, is studied and an alternative form is derived. The dichotomy of a constant anharmonicity along with a changing nuclear structure is resolved. The evolution of the collective nuclear structure from the spherical vibrator to the deformed rotor is studied through the variation of energy ratio R10/2(E10/E2) with R4/2, for Ba – Dy and for Dy – Hf (N<104) and R12/2. The role of the Z = 64 subshell and the N = 88–90 shape phase transition are illustrated in the Mallmann plot. The relative merits of the empirical formulae: rotation–vibration linearity model, the soft rotor formula and the power index formula are compared.

New perspective in the use of soft rotor formula for K = 2 γ-band

The use of soft rotor formula (SRF) for the level energies of K = 2 γ -band for the shape transitional even Z even N nuclei in the medium mass region is illustrated. With proper treatment, we obtained positive values of the moment of inertia and softness parameter, as opposed to negative values reported in literature. The moments of inertia of the γ -band are almost equal to the ground state band values. The systematic dependence of the softness parameter on energy ratio R4/2 is studied. The effect of the odd-even spin staggering on these parameters is studied in detail. In deformed nuclei, the same parameters for odd and even spin members yield fair energy values.

Structure and odd--even staggering of Mo, Ru, and Pd even--even nuclei in the framework of IBM-1

In this study, we employed the interacting boson model (IBM-1) to determine the most appropriate Hamiltonian for the study of ^{94-108}Mo, ^{94-110}Ru, and ^{96-114}Pd isotopes in the region A cong 100. The soft rotor formula (SRF) calculation was also done to study these isotopes. Using the best fit values of parameters to construct the Hamiltonian of the IBM-1 we calculated energy levels and B(E2) values for number of transitions in Mo, Ru, and Pd nuclei. The results obtained from the IBM-1 and SRF were compared with experimental data and IBM-2 calculation. On comparing the results it was observed that they were in good agreement with each other. The gamma-band energy staggering in low-spin, back bending effect, low energy spectra of even-even Mo, Ru, and Pd nuclei is also discussed.

The odd-even staggering in 122–124Xe and 124–128Ba nuclei

The γ-band energy staggering in low-spin, low-energy spectra of even-even 122–124Xe and 124–128Ba nuclei are discussed. The energy levels of ground and gamma band are calculated by the Soft Rotor Formula (SRF). The staggering is a function of spin has been analyzed in order to derive the information on the type of triaxiality present in 122–124Xe and 124–128Ba nuclei. The staggering indices of γ-soft and triaxial nuclei are also calculated by this SRF formula. It is found that these staggering indices have opposite signs and provide clear distinction between γ-soft and triaxial nuclei.

Two-parameter formula for ground-band energy spectra of A = 120-200 mass region nuclei

This paper presents a two-parameter formula which works best for an Anharmonic Vibrator (AHV), i.e., soft and rigid rotor nuclei in the A = 120-200 mass region. A comparison with the other two-parameter formulae, i.e., ab, Brentano Soft Rotor Formula (SRF), Ejiri and Variable Moment of Inertia (VMI) model, shows that this formula gives a better fit with the experimental data.