Vol. 66 No. 6 Nov-Dec (2020): Revista Mexicana de Física

We describe the importance of charge-exchange reactions, and in particular Gamow-Teller transitions, first to astrophysical processes and double beta decay, and then to the understanding of nuclear structure. In our review of their role in nuclear structure we first provide an overview of some of the key steps in the emergence of our current understanding of the structure of nuclei, including the central role played by the isovector pairing and the quadrupole-quadrupole channels in the description of energy spectra and in the manifestation of collective modes, some associated with deformation of the nuclear shape. We then turned our focus to Gamow-Teller (GT) tran- sitions in relatively light nuclei, especially in the 2p1f shell, where isoscalar pairing may be playing a role in competition with the isovector pairing that dominates in heavier regions. Following a summary of the progress made in recent years on this subject, we report a systematic shell model study aimed at providing further clarification as to how these pairing modes compete. In this study, we use a schematic Hamiltonian that contains a quadrupole- quadrupole interaction as well as both isoscalar and isovector pairing interac- tions. We first find an optimal set of Hamiltonian parameters for the model, to provide a starting point from which to vary the relevant pairing strengths and thus assess how this impacts the behavior of GT transitions and the corresponding energy spectra and rotational properties of the various nuclei involved in the decays. The analysis includes as an important theme a com- parison with experimental data. The need to suppress the isoscalar pairing mode when treating nuclei with a neutron excess to avoid producing spurious results for the ground state spin and parity with the simplified Hamiltonian is highlighted. Varying the strength parameters for the two pairing modes is found to exhibit different but systematic effects on GT transition properties and on the corresponding energy spectra, which are detailed.

In this study, we obtained bound state solutions of the radial Schrödinger equation by the superposition of Hulthén plus Hellmann potential within the framework of Nikiforov-Uvarov (NU) method for an arbitrary  - states. The corresponding normalized wave functions expressed in terms of Jacobi polynomial for a particle exposed to this potential field was also obtained. The numerical energy eigenvalues for different quantum state have been computed. Six special cases are also considered and their energy eigenvalues are obtained. Our results are found to be in good agreement with the results in literature. The behavior of energy in the ground and excited state for different quantum state are studied graphically.

In this study, the Shannon entropy and the Fisher information is investigated with molecular Deng-Fan-Eckart potential for the diatomic molecules  and ScF in position and momentum spaces in three dimensions for the ground and the excited states. The results were numerically obtained for diatomic molecules. Localization is observed for Shannon entropy and delocalization for Fisher information for both molecules in the position and momentum spaces. The uncertainty relations for the selected diatomic molecules were satisfied accordingly.

 

In this present methodical study, on the basis of the density functional theory (DFT), the first-principles calculations have been employed successfully to study the structural and electronic properties of N-acetyl-DL-methionine (C₇H₁₃NO₃S) which is a derivative of DL-methionine which is also known DL-2-amino-4-methyl-thiobutanoic acid. Optimized molecular structure, vibrational frequencies and also ¹³C and ¹H NMR chemical shift values of the title compound are provided in a detailed manner by using B3LYP and HSEH1PBE functionals by applying 6-311++G(d,p) basis set for calculations using Gaussian 09W program. The comparison of the calculated values with the experimental values provides important information about the title compound. In addition, the electronic properties (UV-Vis calculations) of the title compound, such as HOMO-LUMO energy values and energy gap, absorption wavelengths, oscillator strengths were performed basing on the optimized structure in gas phase. Moreover, the molecular electrostatic potential surface, dipole moment, nonlinear optical properties, linear polarizabilities and first hyperpolarizabilities and chemical parameters have also been studied.

We present the analysis of an electroosmotic flow (EOF) of a Newtonian fluid in a wavy-wall microchannel. In order to describe the flow and electrical fields, the lubrication and Debye-Hückel approximations are used. The simplified governing equations of continuity, momentum and Poisson-Boltzmann, together with the boundary conditions are presented in dimensionless form. For solving the mathematical problem, numerical and asymptotic techniques were applied. The asymptotic solution is obtained in the limit of very thin electric double layers (EDLs). We show that the lubrication theory is a powerful technique for solving the hydrodynamic field in electroosmotic flows in microchannels where the amplitude of the waviness changes on the order of the  mean semi-channel height. Approximate analytical expressions for the velocity components and pressure distribution are derived, and a closed formula for the volumetric flow rate is obtained.  The results show that the principal parameters that govern this EOF are the geometrical parameter, ε, which characterizes the waviness of the microchannel and the ratio of the mean semi-channel height to the thickness of the EDL, κ.

In this article, we consider the exact solutions of the Hunter-Saxton and Schrödinger equations defined by Atangana's comformable derivative using the general Kudryashov method. Firstly, Atangana's comformable fractional derivative and its properties are included. Then, by introducing the generalized Kudryashov method, exact solutions of nonlinear fractional partial differential equations (FPDEs), which can be expressed with the comformable derivative of Atangana, are classified. Looking at the results obtained, it is understood that the generalized Kudryashov method can yield important results in obtaining the exact solutions of FPDEs containing beta-derivatives.

The effect of cerium/lanthanum rare earths on the microstructural and mechanical behavior of an automotive grade AA319 aluminum alloy was studied at room and hot working conditions. The microstructural results in the modified AA316 aluminum alloys showed that Ce/La additions formed stable micrometric phases at room and hot working conditions, whilst a reduction
in the total area of the eutectic-Si phase of up to 75\% was observed in comparison with the reference alloy. The effect of the Ce/La addition in the aluminum alloys produced an increment in hardness and UTS under room temperature; however, their mechanical behavior was improved in hot working conditions. This improvement is attained to the presence of well dispersed Ce/La phases increasing the amount of the $\theta$'-phase (Al$_2$Cu) across the aluminum matrix. The $\theta$'-phase (Al$_2$Cu) interferes directly with crack diffusion of the solid in two crystallographic directions. Additionally, it was observed through transmission electron microscopy, that Ce/La presence alters the kinetics of precipitation in the formation of the coherent $\theta$-phase from the $\theta$'-phase.

In this study, we have employed the first-principle methods based on density functional theory to investigate the structural, electronic and optical properties of Al_0.50Ga_0.50N_xSb_1-x in zincblende structure. The exchange and correlation potential is described by the generalized gradient approximation of Perdew, Burke and Ernzerhof (GGA-PBEsol) coupled with TB-mBJ approaches. The studied structures shows that all structures are semiconductors and have a direct bandgap except Al_0.50Ga_0.50N_0.25Sb_0.75 which has a semi-metallic behavior. The optical properties such as refractive index, extinction coefficient and optical conductivity are discussed in detail. Our result shows these materials are considered as promising materials for optoelectronic applications in the visible and infrared region. To our knowledge this is the first time that a study has been done on this alloy and we would like it to serve as a reference for the next studies.

Through computer simulations of Monte Carlo (TOPAS-nBio code), the generation of reactive oxygen species will be analyzed when applying external radiation with electrons which energy is 3 and 5 keV to physical system: composite system and intracellular water. This study of the generation of reactive species was focused exclusively on the interaction between secondary radiation from the composite system and intracellular water.This secondary radiation originates from the platinum atom and oxygens (from the composite system) the influence being greater relative to platinum; which mainly consists of electrons called Auger. In this work, only the influence of these ionizing electrons in intracellular water is considered, leading to the generation of reactive oxygen species. Furthermore, the interaction between the nanoparticle surface and cisplatin was not taken into account.

We aim at finding, from a purely theoretical analysis, the behavior that the refractive index should have within a cylindrical waveguide so that the radiation entering the system in a definite way is guided through it.
Based on the criterion we have set in a previous article applying the Fermat's extremal principle in the framework of the geometrical optics, we depict the radiation confinement regions for refractive index profiles often used in the construction of waveguides, one step, multi-step and parabolic, by drawing upon the Legendre transform space as an intermediate resource in the process.
We have also studied the possibility of performing the reverse path: for a wanted confinement region, to find the parameters defining the refractive index profile of the waveguide to be built. We conclude that such a process is possible as long as we know the shape of the profile.
Under such restriction, our analysis allows us to deduce the characteristics that the guide should have so that the radiation entering with a given angle and at a certain distance from its axis remains confined.
The technique can be used in design processes as a resource to limit the parameters that characterize the system.

In this paper a general study of NV center internal state in diamond is presented. This study is based on experimental and theoretical findings
found in literature. First, a Hamiltonian model for center NV internal state is proposed in terms of a complete set of commuting observables
(CSCO), which consist of angular momentum ^L
, spin momentum ^ S, total angular momentum ^ J = ^L
+ ^ S and spin momentum on z-direction
^ Sz. The second quantization formalism –in steady-state (conservative model)– is used. The creation and annihilation operators are used to
described the steady spin-levels structure and in dynamic-state (non-conservative model) and can also describe the system dynamic between
different spin-levels transitions. Finally, a discussion is presented about the application of this study in the photochromism phenomenon and
solid-state quantum bit (qubit).

Analytical solutions of the Schrödinger equation for the generalized trigonometric Pöschl–Teller potential by using an appropriate approximation to the centrifugal term within the framework of the Functional Analysis Approach have been considered. Using the energy equation obtained, the partition function was calculated and other relevant thermodynamic properties. More so, we use the concept of the superstatistics to also evaluate the thermodynamics properties of the system. It is noted that the well-known normal statistics results are recovered in the absence of the deformation parameter and this is displayed graphically for the clarity of our results. We also obtain analytic forms for the energy eigenvalues and the bound state eigenfunction solutions are obtained in terms of the hypergeometric functions. The numerical energy spectra for different values of the principal and orbital quantum numbers are obtained. To show the accuracy of our results, we discuss some special cases by adjusting some potential parameters and also compute the numerical eigenvalue of the trigonometric Pöschl–Teller potential for comparison sake. However, it was found out that our results agree excellently with the results obtained via other methods

In this article, by applying a preliminary and comprehensive definition of the fractional calculus, the effect of this calculus on the fractional derivatives corresponding to different aspects of physics such as Laplace transforms, Riemann-Liouville and Caputo has been specified. Applications of the fractional calculus in studying the dynamics of particle motion in classical mechanics are investigated analytically. Furthermore, we compare our results with those given in the ordinary condition and we show that this condition is simply found by removing the fractional effects and the expected results are obtained.

The wave equation has very significance role in many area of physics. The paper addresses the
solution of fractional differential equations of electromagnetic wave in plasma and dielectric media with Caputo generalized fractional derivative. The ρ−Laplace transform introduced by Fahd and Thabet was used to obtain the analytic solution of fractional differential equation which arising in electromagnetic fields. We investigate that the wave equation in fractional space can effectively describe the behaviour of space wave and time wave. The results show that the electromagnetic fields change with different fractional orders.

A 2D cellular automata model, which allows a better understanding of the morphogenesis of the avascular tumor pattern formation, is presented. Using thermodynamics formalism of irreversible processes and results of complex systems theory, we propose markers to able to establish, in a quantitative way, the degree of aggressiveness and the malignancy of tumor patterns, such as a fractal dimension and the entropy production rate.

In this paper a stochastic formulation for describing the dynamics of an epidemic is established. We state our model in the language of a compartmental scheme of three sites (susceptible, infected and recovered) SIR, for which the parameters model are extended to be statistical distributions of time. It is established a master equation for governing the dynamics of the probability density P of finding the system in the state characterized by the values of the aleatory variables S, I, R and time t. Our stochastic formalism allow us to recover the associated deterministic model in terms of the expected values of S, I and R; whereas the second momenta of P provide us statistical standard deviations for these three variables which delimit the region in which most of the particular realizations are to be expected. We have applied the analysis developed here, for studying the specific case of the influenza AH1N1 that took place in Mexico in 2009. The reported data by the main Mexican Health institution are in good agreement with the predictions of our model for the standard deviation of the aleatory variables.

The fractional calculus has a very large diversification as it relates to applications from physical interpretations to experimental facts to modeling of new problems in the natural sciences. Within the framework of a recently published article, we obtained the fractional derivative of the variable concentration x (z), the effective mass of the electron dependent on the position m (z) and the potential energy V (z), produced by the confinement of the electron in a semiconductor of type AlxGa1-xAs, with which we can intuit a possible geometric and physical interpretation. As a consequence, it is proposed the existence of three physical and geometric conservative quantities approximate character, associated with each of these parameters of the semiconductor, which add to the many physical magnitudes that already exist in the literature within the context of fractional variation rates. Likewise, we find that the fractional derivatives of these magnitudes, apart from having a common critical point, manifest self-similar behavior, which could characterize them as a type of fractal associated with the type of semiconductor structures under study.