The derivative expansion perturbation method is applied to a strongly coupled dusty plasma system consisting of negatively charged dust grains, electrons, and ions. The basic equations are reduced to a nonlinear Schrödinger type equation appropriate for describing the modulated dust acoustic (DA) waves. We have examined the modulation (in) stability and the dependence of the system physical parameters (angular frequency and group velocity) on the polarization force variation. Finally, the extended Poincaré-Lighthill-Kuo technique is employed to investigate the head-on collision (HoC) between two DA dark solitons. The analytical phase shifts and the trajectories of these dark solitons after the collision are derived. The numerical illustrations show that the polarization effect has strong influence on the nature of the phase shifts and the trajectories of the two DA dark solitons after collision.

A systematic calculation of alpha decay half-lives of 347 nuclei is considered in the framework of the Wentzel–Kramers–Brillouin (WKB) approximation using two formulas. A recently proposed barrier penetration formula, with some modified parameters, is used first. Second, a new analytic barrier penetration formula is derived by taking into account the centrifugal potential. A good agreement with experimental data is achieved especially for spherical nuclei. The new formula reproduces experimental alpha decay half-lives with a satisfying accuracy especially for penetration energies much lower than the Coulomb barrier.

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The three-dimensional instability of isothermal ion-acoustic (IIA) solitary waves is examined in a magnetized ultra-relativistic degenerate multicomponent plasma, comprising nondegenerate inertial warm ions and ultra-relativistic degenerate inertialess electrons as well as positrons, by applying a small-k (long wavelength) expansion method. The nonlinear dynamics of IIA solitary waves in such a plasma model are governed by the nonlinear Zakharov–Kuznetsov equation. To perform the analysis, the instability criterion and the growth rate of the instability of IIA solitary waves have been obtained. A careful investigation shows that the amplitude, the width, the growth rate, and the instability of IIA solitary waves increase with the increasing chemical potential of electrons. The stable region of IIA solitary waves increases with the increasing fermion population and the angle between the directions of propagation and the uniform magnetic field. The present study may be helpful for elucidating the physical nature of nonlinear waves in compact objects such as white dwarfs and neutron stars where the concentration of degenerate ultra-relativistic electrons and positrons and their chemical potentials play a crucial role.

In this research, the nonlinear propagation of dust-ion acoustic (DIA) periodic travelling waves in a dusty plasma consisting of cold ions, stationary charged dust grains, and two temperature superthermal electrons is theoretically studied. A nonlinear Zakharov-Kuznetsov equation, which describes nonlinear dust-ion acoustic waves, is derived using a reductive perturbation method. Furthermore, the bifurcation theory has been employed to study the nonlinear propagation of DIA periodic travelling wave solutions. In the proposed model, the co-existence of both compressive and rarefactive DIA periodic travelling waves are found. The numerical investigations illustrate that the characteristics of nonlinear DIA periodic travelling waves strongly depend on the temperature ratio, both the concentration and the superthermality of cold electrons, the ion cyclotron frequency, the direction cosines of wave vector k along z axis, and the concentration of dusty grains. The present investigation can help in better understanding of nonlinear DIA periodic travelling waves in astrophysical environments with two temperature superthermal electrons such as Saturn's magnetosphere.

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Nonlinear rarefactive isothermal ion-acoustic periodic travelling waves (RIIAPTWs) are examined in a magnetized ultrarelativistic degenerate plasma, containing warm fluid ions and ultrarelativistic degenerate inertialess electrons as well as positrons and immobile heavy negative ions. In the linear regime, the excitation of an isothermal ion-acoustic mode and its evolution are investigated. The physical behavior of nonlinear rarefactive isothermal ion-acoustic waves (RIIAWs) in this plasma model is governed by a Zakharov–Kuznetsov (ZK) equation. The analytical solutions for the nonlinear rarefactive isothermal ion-acoustic solitary waves (RIIASWs) and RIIAPTWs are performed by the bifurcation analysis. A careful discussion demonstrates the excitations of RIIASWs and RIIAPTWs are amplified (i.e., the amplitudes become deeper), as the chemical potential (or the Fermi energy at zero temperature) of electrons is decreased. It is found physically that the presence of the ultrarelativistic degenerate positrons and stationary heavy negative ions have strong effects on features of nonlinear RIIASWs and RIIAPTWs. The implications of the present finding in compact astrophysical objects, such as white dwarf stars, have been discussed.

Calculation of alpha particle preformation probabilities for some alpha emitters is considered in the framework of a recent proposed barrier penetration formula, by two different approximations. The behavior of alpha particle preformation probability with the variation of neutron and proton numbers of parent nuclei for isotopes, in the range [Formula: see text], and isotones, in the range [Formula: see text], is investigated. The same correlations are then studied for the alpha decay half-life, the barrier assault frequency, barrier height and barrier penetration probability. Strong correlations are found and in a good agreement with experimental expectations.