[en] Optical dispersive soliton solutions for the fractional Lakshmanan–Porsezian–Daniel equation for optical fibers are studied in this paper considering the M-derivative of order $\mathrm{\chi <!--\; ??\; -->}$. The analytical method considered here is based on the Jacobi elliptic function (JEF) anzätz method. We found new optical soliton solutions that are relevant for the dynamics inside optical fibers. Some constraints conditions arise between the parameters of the JEF soliton solutions. Typical behaviour of the soliton solutions obtained is depicted in some interesting simulations.

[en] The local modified $\exp <!--\; ???\; -->(-<!--\; ???\; -->\mathrm{\Omega <!--\; ??\; -->}(\mathrm{\eta <!--\; ??\; -->}))$-expansion function method is proposed to construct analytical solutions of nonlinear local partial differential equations, involving local M-derivative of order $\mathrm{\alpha <!--\; ??\; -->}$. The modified $\exp <!--\; ???\; -->(-<!--\; ???\; -->\mathrm{\Omega <!--\; ??\; -->}(\mathrm{\eta <!--\; ??\; -->}))$-expansion function method is applied to obtain some solitary wave solutions to the longitudinal wave equation in a magneto electro-elastic circular rod. Some soliton solutions are constructed under some constraint conditions.

[en] The ground state band of the proton-odd Ta isotopes, built on g_7_/_2 orbital, is investigated within the framework of a recently-developed extended Bohr Hamiltonian model. Energy levels of ground state band with their admixture with other possible bands built on g_7_/_2 orbital and B(E2) values inside ground state band are calculated and compared with available experimental data. (author)

[en] Complete text of publication follows. Phase transitions in nuclear systems are of utmost interest. An interesting class of phase transitions can be seen in algebraic models of nuclear structure. They are called shapephase transitions due to the following reason. These models have analytically solvable limiting cases, called dynamical symmetries, which are characterized by a chain of nested subgroups. They correspond to well-defined geometrical shape and behaviour, e.g. to rotation of an ellipsoid, or spherical vibration. The general case of the model, which includes interactions described by more than one groupchain, breaks the symmetry, and changing the relative strengths of these interactions, one can go from one shape to the other. In doing so a phase-transition can be seen. A phase transition is defined as a discontinuity of some quantity as a function of the control parameter, which gives the relative strength of the interactions of different symmetries. Real phase transitions can take place only in infinite systems, like in the classical limits of these algebraic models, when the particle number N is very large: N → ∞. For finite N the discontinuities are smoothed out, nevertheless, some indications of the phase-transitions can still be there. A controlled way of breaking the dynamical symmetries may reveal another very interesting phenomenon, i.e. the appearance of a quasidynamical (or effective) symmetry. This rather general symmetry-concept of quantum mechanics corresponds to a situation, in which the symmetry-breaking interactions are so strong that the energy-eigenfunctions are not symmetric, i.e. are not basis states of an irreducible representation of the symmetry group, rather they are linear combinations of these basis states. However, they are very special linear combinations in the sense that their coefficients are (approximately) identical for states with different spin values. When this is the case, then the underlying intrinsic state is the same, and the states are said to form a (soft) band. The phase-transitions, as well as the persistence of the quasidynamical symmetries in the algebraic models of quadrupole collectivity have extensively been studied. In a recent work [1] we have addressed these questions in relation with another important collectivity of nuclei, i.e. clusterization. Two models were considered, a phenomenological one, containing no Pauli-principle, and a semimicroscopic one, which is based on a microscopically determined model space, being free from the Pauli-forbidden states. The interactions were treated in a phenomenologic and algebraic way in both cases. In this respect the two models have a similar group-structure. We have studied the SU(3) - SO(4) phase transition, related to the description of the relative motion in terms of the vibron model (in its simplest form in the phenomenological model and in a properly truncated form in the semimicroscopic description). The analytical study of the large-N limit of both models shows a first order phase transition. We have carried out numerical calculations as well. Three binary cluster systems were chosen, in which the number of open-shell clusters were zero, one and two, respectively. The numerical studies show that the phase transition is smoothed out for finite N systems, but some fingerprints of it still can be seen. The appearance of the quasidynamical SU(3) symmetry has also been studied, when moving away from the limit of the real SU(3) dynamical symmetry. It turned out that in each case, when there is a real dynamical symmetry in the limiting case (in the sense that a well-defined SU(3) quantum number can be associated to a band), this symmetry survives as quasidynamical symmetry at least up to the critical value of the control parameter. (author)

[en] Complete text of publication follows. There has been much interest recently in phase transitions in various nuclear systems. The phases are defined as (local) minima of the potential energy surface (PES) defined in terms of parameters characterizing the nuclear system. Phase transitions occur when some relevant parameter is changed gradually and the system moves from one phase to another one. In the analysis of such systems the key questions are the number of phases and the order of phase transition between them. Algebraic nuclear structure models are especially interesting from the phase transition point of view, because the different phases may be characterized by different symmetries of the system. Much work has been done recently on models based on the interacting boson approximation (IBA). In these studies the potential energy surface is constructed from the algebraic Hamiltonian by its geometric mapping using the coherent state formalism. Inspired by these studies we performed a similar analysis of a family of algebraic cluster models based on the semimicroscopic algebraic cluster model (SACM). This model has two dynamical symmetries: the SU(3) and SO(4) limits are believed to correspond to vibration around a spherical equilibrium shape and static dipole deformation, respectively. The semimicroscopic nature of this model is reflected by the fact that a fully antisymmetrized microscopic model space is combined with a phenomenologic Hamiltonian that describes excitations of the (typically) two-cluster system. The microscopic model space is necessary to take into account the Pauli exclusion principle acting between the nucleons of the closely interacting clusters. In practice this means that the number of excitation quanta in the relative motion of the clusters has to exceed a certain number n₀ characterizing the system. This is clearly a novelty with respect to other algebraic models, and it complicates the formalism considerably. We thus introduced as a special limit the phenomenologic algebraic cluster model (PACM), in which the n₀ = 0 choice was made. With this choice we ignore a fundamental principle, but in exchange the formalism becomes similar to that of other algebraic models. Our aim was also to explore the consequences of this approximation. In the first step we constructed the PES of the SACM using coherent states. For this we also modified the formalism of the SACM to the present analysis. This included incorporating a third-order term in the Hamiltonian that stabilizes the spectrum for large values of intercluster excitation quanta (π bosons). The parametrization of the Hamiltonian was also changed to allow for a transition between the SU(3) to the SO(4) limits. The results indicated that the effects of the Pauli principle can be simulated in the PACM by incorporating higher-order terms on the Hamiltonian. In the second step we turned to the analysis of phase transitions both in the SACM and the PACM. The potential energy surface typically contained up to two minima, one spherical and one deformed. The analysis identified both first- and second-order phase transitions for the PACM and the SACM, while in the latter case a critical line was also found. The results were illustrated with numerical studies on the ¹⁶O+α and ²⁰Ne+α systems, which correspond to two spherical clusters and to one spherical and one deformed cluster, respectively. The SU(3) limit was found to be the most appropriate one in reproducing the data of the cluster systems. Clear phase transitions were identified in the parameter controlling the transition between the SU(3) and SO(4) limits. It was found that the PACM led to energy spectra that are rather different from the observed physical ones.

[en] Two algebraic cluster models of nuclear structure which use the same Hamiltonian are explored: a Phenomenological Algebraic Cluster Model (PACM), and a Semi-microscopic Algebraic Cluster Model (SACM). The PACM does not incorporate the Pauli exclusion principle, while the SACM does. The Hamiltonian considered is an admixture of three dynamical symmetries; the SU(3), SO(4), and SO(3), with weighting of each determined by parameters. The classical potential is constructed using coherent states, and the model Hilbert space of the SACM is constructed in such a way as to include all shell model states which correspond to the cluster structure of interest. Phase transitions and their orders are investigated for each model, and parameter phase diagrams are presented, wherein it is found that consideration of the Pauli principle has significant consequences. Also shown are fits of Hamiltonian parameters for a nucleus of 2 spherical clusters, when moving between the symmetry limits.

[en] In nuclear cluster systems, a rigorous structural forbiddenness of virtual nuclear division into unexcited fragments is obtained. We re-analyse the concept of forbiddenness, introduced in Smirnov and Tchuvil'sky (1984 Phys. Lett. B 134 25) to understand the structural effects in nuclear cluster physics. We show that the concept is more involved than the one presented previously, where some errors were committed. Due to its importance, it is reanalysed here. In the present contribution a simple way to determine forbiddenness is given, which may easily be extended to any number of clusters, though in this contribution we discuss only two-cluster systems, for illustrative reasons. A simple rule is obtained for the minimization of the forbiddenness, namely to start from a cluster system with a large SU(3) irrep $({\mathrm{\lambda <!--\; ??\; -->}}_c,{\mathrm{\mu <!--\; ??\; -->}}_c)$, but minimizing $({\mathrm{\lambda <!--\; ??\; -->}}_c-<!--\; ???\; -->{\mathrm{\mu <!--\; ??\; -->}}_c)$, i.e., the system has to be oblate. The rule can be easily implemented in structural studies, done up to now with an oversimplified definition of forbiddenness. The new method is applied to various systems of light clusters and to some decay channels of ²³⁶U and ²⁵²Cf. (paper)

[en] We review the concept of forbiddenness as introduced by Smirnov and Yu M. Tchuvil'sky [1], which states that most of the properties of nuclear reactions and cluster structure is based on structural effects (Pauli exclusion principle). This becomes also clear when one tries to obtain the ground state of the united nucleus by two heavy clusters, which is not possible when all excitations are put into the relative motion. Smirnov et al. introduced the concept of forbiddenness, which is defined as the minimal number of relative oscillation quanta which have to be shifted to internal excitations of the clusters, such that the ground state can be reached . We show that Smirnov et al. committed and error in the derivation, leading us to reevaluate the derivation of the forbiddenness. We deduce the correct expression for the forbiddenness, leading to a simple interpretation and implementation in a cluster model and some applications are presented. (paper)

[en] In this work, we revisit the experimental data for elastic, inelastic and α-transfer in the ${}^{12}$C + ${}^{16}$O system at 80 and 84 MeV using the coupled reaction channel method to analyze the angular distributions. The spectroscopic amplitudes relevant for the α-transfer channel have been calculated from the semi-microscopic algebraic cluster model. The imaginary term of the optical potential was fitted to the experimental elastic scattering data at forward angles. Our calculations describe reasonable well the absolute cross sections for the inelastic scattering and α-transfer. We discuss the effect of couplings on the transfer channel.

[en] We present the cranking of the Semimicroscopic Algebraic Cluster Model (SACM) for two spherical clusters. A geometrical mapping is applied and a discussion on phase transition as a function of the cranking parameter is given. This parameter can be related to the average angular momentum of the nucleus. The particular cluster system considered is ¹⁶O+α → ²⁰Ne. We also investigate the phase transition property when the Pauli exclusion principle is not observed. We show that phase transitions may occur within the same dynamical symmetry limit.