He23+_2^{3+} and HeH2+^{2+} molecular ions in a strong magnetic field: the Lagrange mesh approach

Accurate calculations for the ground state of the molecular ions He$_2^{3+}$ and HeH$^{2+}$ placed in a strong magnetic field $B\gtrsim 10^{2}$ a.u. ($\approx 2.35 \times 10^{11}$G) using the Lagrange-mesh method are presented. The Born-Oppenheimer approximation of zero order (infinitely massive centers) and the parallel configuration (molecular axis parallel to the magnetic field) are considered. Total energies are found with 9-10 s.d. The obtained results show that the molecular ions He$_2^{3+}$ and HeH$^{2+}$ exist at $B > 100$\,a.u. and $B > 1000$\,a.u., respectively, as predicted in \cite{Tu:2007} while a saddle point in the potential curve appears for the first time at $B \sim 80$ a.u. and $B \sim 740$ a.u., respectively.Comment: 8 pages, 1 figure, 2 tables. arXiv admin note: text overlap with arXiv:0912.104

The R-matrix theory

The different facets of the $R$-matrix method are presented pedagogically in a general framework. Two variants have been developed over the years: $(i)$ The "calculable" $R$-matrix method is a calculational tool to derive scattering properties from the Schr\"odinger equation in a large variety of physical problems. It was developed rather independently in atomic and nuclear physics with too little mutual influence. $(ii)$ The "phenomenological" $R$-matrix method is a technique to parametrize various types of cross sections. It was mainly (or uniquely) used in nuclear physics. Both directions are explained by starting from the simple problem of scattering by a potential. They are illustrated by simple examples in nuclear and atomic physics. In addition to elastic scattering, the $R$-matrix formalism is applied to transfer and radiative-capture reactions. We also present more recent and more ambitious applications of the theory in nuclear physics.Comment: 93 pages, 26 figures. Rep. Prog. Phys., in pres

Exact Configuration of Poverty,Inequality and Polarization Trends in the Distribution of well-being in Cameroon

This study attempts to carry out a comprehensive analysis of poverty, inequality and polarization trends using Cameroon household surveys collected before and during the Heavily Indebted Poor Countries (HIPC) process. The theoretical decomposition frameworks propelling the study are motivated mainly by the Shapley value. Empirical estimates are obtained from the software DAD 4.4 using both money-metric and child nutrition indicators, and poverty lines, with the monetary threshold derived nonparametrically. Effects within-zones account for much of monetary poverty changes than effects between-zones. The findings that inter-zone effects contribute to alleviating rural poverty while aggravating urban poverty, suggests the potential for rural–urban migration to alleviate rural poverty. Changes in money-metric poverty and health deprivation sharply contrast each other. While health poverty deteriorated, income poverty retreated. This is an indication that economic growth may not necessarily engender significant reduction in all dimensions of well-being. Changes in health poverty are driven largely by effects of redistribution, whereas for income poverty the growth component seems to be more important. Both income and non-income dimensions highlight the dominant role of within-group components in accounting for inequality trends. However, while the between-group contributions to inequality are negligible in the health dimension, they are non-negligible in the income space. In terms of levels, polarization and inequality are more of an urban than a rural problem, yet inequality and polarization worsened only in rural areas in the period 1996–2001. As a whole, polarization indices do not give dissimilar trends from standard measures of inequality. The conflicting results from income and health well-being indicators are attributable to the observation that the economic rebound in Cameroon was preceded by fiscal austerity measures embedded in the Structural Adjustment Programmes that engendered a decline in the availability of public goods. Moreover, health indicators are slow-moving compared with income or expenditure, which does not include the quality of service received from social expenditures on health and nutrition. These results have implications for policy making: in terms of income deprivation, emphasis could be on growth-based labour-intensive policies that create opportunities for the rural poor to increase their incomes; and in terms of child health and perhaps general health, emphasis could be on redistribution of health infrastructure and personnel to increase outreach.

Equivalence of the Siegert-pseudostate and Lagrange-mesh R-matrix methods

Siegert pseudostates are purely outgoing states at some fixed point expanded over a finite basis. With discretized variables, they provide an accurate description of scattering in the s wave for short-range potentials with few basis states. The R-matrix method combined with a Lagrange basis, i.e. functions which vanish at all points of a mesh but one, leads to simple mesh-like equations which also allow an accurate description of scattering. These methods are shown to be exactly equivalent for any basis size, with or without discretization. The comparison of their assumptions shows how to accurately derive poles of the scattering matrix in the R-matrix formalism and suggests how to extend the Siegert-pseudostate method to higher partial waves. The different concepts are illustrated with the Bargmann potential and with the centrifugal potential. A simplification of the R-matrix treatment can usefully be extended to the Siegert-pseudostate method.Comment: 19 pages, 1 figur

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.

An explanatory study of 11^{11}Li β\beta decay into 9^9Li and deuteron

The $\beta$-decay of $^{11}$Li into $^9$Li and {\it d} is studied using simple halo wave functions of $^{11}$Li. The sensitivity of the transition probability is elucidated on a description of the halo part and on a choice of the potential between $^9$Li and {\it d} .Comment: 8 pages,revtex,2 figures (available upon request

Time-dependent analysis of the nuclear and Coulomb dissociation of 11Be

The breakup of 11Be on carbon and lead targets around 70 MeV/nucleon is investigated within a semiclassical framework. The role of the 5/2+ resonance is analyzed in both cases. It induces a narrow peak in the nuclear-induced breakup cross section, while its effect on Coulomb breakup is small. The nuclear interactions between the projectile and the target is responsible for the transition toward this resonant state. The influence of the parametrization of the 10Be-n potential that simulates 11Be is also addressed. The breakup calculation is found to be dependent on the potential choice. This leads us to question the reliability of this technique to extract spectroscopic factors.Comment: 9 pages, 6 figures, to be published in the Proceedings of the Second Argonne/MSU/JINA/INT RIA Workshop on Reaction Mechanisms for rare Isotope Beams (2005

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