Comparison of potential models of nucleus-nucleus bremsstrahlung

At low photon energies, the potential models of nucleus-nucleus bremsstrahlung are based on electric transition multipole operators, which are derived either only from the nuclear current or only from the charge density by making the long-wavelength approximation and using the Siegert theorem. In the latter case, the bremsstrahlung matrix elements are divergent and some regularization techniques are used to obtain finite values for the bremsstrahlung cross sections. From an extension of the Siegert theorem, which is not based on the long-wavelength approximation, a new potential model of nucleus-nucleus bremsstrahlung is developed. Only convergent integrals are included in this approach. Formal links between bremsstrahlung cross sections obtained in these different models are made. Furthermore, three different ways to calculate the regularized matrix elements are discussed and criticized. Some prescriptions for a proper implementation of the regularization are deduced. A numerical comparison between the different models is done by applying them to the $\alpha+\alpha$ bremsstrahlung.Comment: submitted to Phys. Rev.

Accurate solution of the Dirac equation on Lagrange meshes

The Lagrange-mesh method is an approximate variational method taking the form of equations on a grid because of the use of a Gauss quadrature approximation. With a basis of Lagrange functions involving associated Laguerre polynomials related to the Gauss quadrature, the method is applied to the Dirac equation. The potential may possess a $1/r$ singularity. For hydrogenic atoms, numerically exact energies and wave functions are obtained with small numbers $n+1$ of mesh points, where $n$ is the principal quantum number. Numerically exact mean values of powers $-2$ to 3 of the radial coordinate $r$ can also be obtained with $n+2$ mesh points. For the Yukawa potential, a 15-digit agreement with benchmark energies of the literature is obtained with 50 mesh points or less

Relativistic semiempirical-core-potential calculations in Ca+^+, Sr+^+, and Ba+^+ ions on Lagrange meshes

Relativistic atomic structure calculations are carried out in alkaline-earth-metal ions using a semiempirical-core-potential approach. The systems are partitioned into frozen-core electrons and an active valence electron. The core orbitals are defined by a Dirac-Hartree-Fock calculation using the grasp2k package. The valence electron is described by a Dirac-like Hamiltonian involving a core-polarization potential to simulate the core-valence electron correlation. The associated equation is solved with the Lagrange-mesh method, which is an approximate variational approach having the form of a mesh calculation because of the use of a Gauss quadrature to calculate matrix elements. Properties involving the low-lying metastable $^2D_{3/2,5/2}$ states of Ca$^{+}$, Sr$^{+}$, and Ba$^{+}$ are studied, such as polarizabilities, one- and two-photon decay rates, and lifetimes. Good agreement is found with other theory and observation, which is promising for further applications in alkali-like systems.Comment: 15 pages, accepted for publication in Phys. Rev.

The change in Inequality in the Distribution of Living Standards

This study attempts to carry out a comprehensive analysis of the evolution of inequality trends using CHS I and II collected in 1996 and 2001 respectively. The theoretical decomposition frameworks propelling the study are motivated mainly by the Shapely value while empirical estimates are obtained from DAD 4.4.As concerning the result, we observed the dominant contribution of the Within-group inequality in the distribution of living standard in Cameroon and the Between-group contribution to inequality trends was found to be non negligible. On the global scale, inequality retreated at the national level, Yaounde, Douala and Rural savannah regions in the period 1996-200 and got worse in Rural forest, Rural highlands and other towns. We recommend that, policies and strategies for reducing inequality should place particular emphasis on the countryside (increase employment avenues through potential investment) and on a region-by-region approach (decentralisation, equal distribution of the national cake)

Reconstructing the nucleon-nucleon potential by a new coupled-channel inversion method

A second-order supersymmetric transformation is presented, for the two-channel Schr\"odinger equation with equal thresholds. It adds a Breit-Wigner term to the mixing parameter, without modifying the eigenphase shifts, and modifies the potential matrix analytically. The iteration of a few such transformations allows a precise fit of realistic mixing parameters in terms of a Pade expansion of both the scattering matrix and the effective-range function. The method is applied to build an exactly-solvable potential for the neutron-proton $^3S_1$-$^3D_1$ case.Comment: 4 pages, 4 figure

A Critical Discourse Analysis of COVID-19 in Ethiopia: Rethinking the Past and Defining the Present

The purpose of this study is to unearth the landscape of social media and analyse the contents. Contents of social media, in Ethiopia, are varying over the course of changes in politics, health, socio-economic conditions of the country. Some of the contents are reflected in the forms of narratives, comments, briefings, anecdotes, and verses to list a few. Contents changing the way people interact with each other and share information, personal messages, and opinions about situations, objects, and past experiences- rethinking the past, themes are linked to the present and define the present Ethiopia. In order to attain the stated objective, the researchers developed critical discourse analysis as a research methodology and adapted Norman Fairclough’s model of Analysis as a theoretical framework. Most social media texts are short online conversational posts or comments that do not contain enough information for a full textual analysis. Therefore, using purposive sampling six excerpts were collected from various discourses of the social media platforms, particularly Facebook, Facebook messenger, and YouTube.  Based on the contexts of the discourses, the analysis was categorized thematically. The study concluded that social media users used the platform as a means to reflect both the status quo of the past and linking to the current COVID-19 and its socio-economic impacts. COVID-19 is depicted as a disease, resulting from human wrongdoings, very dangerous which is deadly even to Satan. It is also depicted as a warrior, an extremely hungry predator looking for its prey, ready to eat up human being ravenous without a need for proper chewing

Complex-energy analysis of proton-proton fusion

An analysis of the astrophysical $S$ factor of the proton-proton weak capture ($\mathrm{p}+\mathrm{p}\rightarrow {}^2\mathrm{H}+\mathrm{e}^++\nu_{\mathrm{e}}$) is performed on a large energy range covering solar-core and early Universe temperatures. The measurement of $S$ being physically unachievable, its value relies on the theoretical calculation of the matrix element $\Lambda$. Surprisingly, $\Lambda$ reaches a maximum near $0.13~\mathrm{MeV}$ that has been unexplained until now. A model-independent parametrization of $\Lambda$ valid up to about $5~\mathrm{MeV}$ is established on the basis of recent effective-range functions. It provides an insight into the relationship between the maximum of $\Lambda$ and the proton-proton resonance pole at $(-140-467\,\mathrm{i})~\mathrm{keV}$ from analytic continuation. In addition, this parametrization leads to an accurate evaluation of the derivatives of $\Lambda$, and hence of $S$, in the limit of zero energy.Comment: 13 pages, 9 figures, 43 reference

Multichannel coupling with supersymmetric quantum mechanics and exactly-solvable model for Feshbach resonance

A new type of supersymmetric transformations of the coupled-channel radial Schroedinger equation is introduced, which do not conserve the vanishing behavior of solutions at the origin. Contrary to usual transformations, these ``non-conservative'' transformations allow, in the presence of thresholds, the construction of potentials with coupled scattering matrices from uncoupled potentials. As an example, an exactly-solvable potential matrix is obtained which provides a very simple model of Feshbach-resonance phenomenon.Comment: 10 pages, 2 figure