Remarks on the shape transition from spherical to deformed gamma unstable nuclei

Abstract

Energies and transition probabilities for low lying states in134 Ba and 104 Ru were calculated within a hybrid model. The ground and the first 2 + states are described alternatively as a harmonic and anharmonic vibrator states while the remaining states as states with E(5) symmetry. Results for 134 Ba are compared with those predicted by some other methods. One concludes that a gradual setting of the 'critical' potential yields a better agreement with the experimental data. Very good agreement with the data is obtained for 104 Ru. Comparing the present results with those of E(5) symmetry, it is conspicuous that the present formalism add corrections to the E(5) formalism by bringing the predictions closer to the experimental data. Analytical relationship between the states with U (5) symmetry and those given by the E(5) description is established.

Description of the isotope chain180−196Pt within several solvable approaches

“…As a matter of fact this feature is consistent with the results of Ref. [29] saying that not all nuclear properties reach the critical point in a phase transition in the same isotope. We apply the approaches ISWSA and SSA to the mentioned isotopes in order to test their ability to account for these complementary features.…”

Simultaneous description of low-lying positive and negative parity states in spd, sdf and spdf interacting boson model

“…(5) which leads to a set of Bethe ansatz equations (BAE), the c-numbers x i 's are determined in Eq. (38).…”

“…1650089-9 It is worth noting that by omitting the coupling of c f and c p , all relative relations can be expressed as spd and sdf model, respectively. A useful and simple numerical algorithm for solving the BAE (38) and extraction of the constants in comparison with experimental energy spectra of considered nuclei is based on using of Matlab software which will be outlined simultaneously. To determine the roots of the BAE with specified values of ν s , ν p , ν d and ν f , we solve Eq.…”

“…To determine the roots of the BAE with specified values of ν s , ν p , ν d and ν f , we solve Eq. (38) with definite values of α for i = 1 and then use the function "syms-var" in Matlab to obtain all roots. We then repeat this procedure with different α to minimize the root mean square deviation, σ, between the calculated energy spectra and experimental counterparts which explore the quality of extraction processes.…”

Common aspects of -deformed Lie algebras and fractional calculus

“…Critical phase transitions from vibrational to rotational states have been studied for decades using e.g. coherent states formalism or within the framework of the IBA-model [41]- [44]. But in general, within these models, results may be obtained only numerically with extensive effort.…”