A Generalized Uhlenbeck and Beth Formula for the Third Cluster Coefficient

Relatively recently (A. Amaya-Tapia, S. Y. Larsen and M. Lassaut. Ann. Phys., vol. 306 (2011) 406), we presented a formula for the evaluation of the third Bose fugacity coefficient - leading to the third virial coefficient - in terms of three-body eigenphase shifts, for particles subject to repulsive forces. An analytical calculation for a 1-dim. model, for which the result is known, confirmed the validity of this approach. We now extend the formalism to particles with attractive forces, and therefore must allow for the possibility that the particles have bound states. We thus obtain a true generalization of the famous formula of Uhlenbeck and Beth (G.E. Uhlenbeck and E. Beth. Physica, vol. 3 (1936) 729; E. Beth and G.E. Uhlenbeck. ibid, vol.4 (1937) 915) (and of Gropper (L. Gropper. Phys. Rev. vol. 50 (1936) 963; ibid vol. 51 (1937) 1108)) for the second virial. We illustrate our formalism by a calculation, in an adiabatic approximation, of the third cluster in one dimension, using McGuire's model as in our previous paper, but with attractive forces. The inclusion of three-body bound states is trivial; taking into account states having asymptotically two particles bound, and one free, is not.Comment: 38 pages, 6 figure

Third Bose Fugacity Coefficient in One Dimension, as a Function of Asymptotic Quantities

In one of the very few exact quantum mechanical calculations of fugacity coefficients, Dodd and Gibbs (\textit{J. Math.Phys}.,\textbf{15}, 41 (1974)) obtained $b_{2}$ and $b_{3}$ for a one dimensional Bose gas, subject to repulsive delta-function interactions, by direct integration of the wave functions. For $b_{2}$, we have shown (\textit{Mol. Phys}.,\textbf{103}, 1301 (2005)) that Dodd and Gibbs' result can be obtained from a phase shift formalism, if one also includes the contribution of oscillating terms, usually contributing only in 1 dimension. Now, we develop an exact expression for $b_{3}-b_{3}^{0}$ (where $b_{3}^{0}$ is the free particle fugacity coefficient) in terms of sums and differences of 3-body eigenphase shifts. Further, we show that if we obtain these eigenphase shifts in a distorted-Born approximation, then, to first order, we reproduce the leading low temperature behaviour, obtained from an expansion of the two-fold integral of Dodd and Gibbs. The contributions of the oscillating terms cancel. The formalism that we propose is not limited to one dimension, but seeks to provide a general method to obtain virial coefficients, fugacity coefficients, in terms of asymptotic quantities. The exact one dimensional results allow us to confirm the validity of our approach in this domain.Comment: 29 page

Urinary Tract Tuberculosis

Urinary tract tuberculosis (UTTB) is an insidious disease with non-specific constitutional symptoms that are often unrecognized and lead to delayed diagnosis. Advanced UTTB may cause loss of kidney function. In the majority of literature, UTTB is reviewed together with genital tuberculosis because often both sites are involved simultaneously; “Genitourinary tuberculosis” (GUTB) is the most common term used in the literature. However, the term may cause confusion because the clinical presentation and diagnosis approach is very different, and does not always occur simultaneously. UTTB is the term used here as we encountered tuberculosis involvement of urinary tract only. This book chapter is a comprehensive review of the epidemiology, pathophysiology, clinical presentation, diagnosis approach, and current treatment of this disease

Second virial coefficient in one dimension, as a function of asymptotic quantities

A result from Dodd and Gibbs[1] for the second virial coefficient of particles in 1 dimension, subject to delta-function interactions, has been obtained by direct integration of the wave functions. It is shown that this result can be obtained from a phase shift formalism, if one includes the contribution of oscillating terms. The result is important in work to follow, for the third virial coefficient, for which a similar formalism is being developed. We examine a number of fine points in the quantum mechanical formalisms.Comment: 7 pages, no figures, submitted to Molecular Physic

S-matrix poles and the second virial coefficient

For cutoff potentials, a condition which is not a limitation for the calculation of physical systems, the S-matrix is meromorphic. We can express it in terms of its poles, and then calculate the quantum mechanical second virial coefficient of a neutral gas. Here, we take another look at this approach, and discuss the feasibility, attraction and problems of the method. Among concerns are the rate of convergence of the 'pole' expansion and the physical significance of the 'higher' poles.Comment: 20 pages, 8 tables, submitted to J. Mol. Phy

Integral representation of one dimensional three particle scattering for delta function interactions

The Schr\"{o}dinger equation, in hyperspherical coordinates, is solved in closed form for a system of three particles on a line, interacting via pair delta functions. This is for the case of equal masses and potential strengths. The interactions are replaced by appropriate boundary conditions. This leads then to requiring the solution of a free-particle Schr\"{o}dinger equation subject to these boundary conditions. A generalized Kontorovich - Lebedev transformation is used to write this solution as an integral involving a product of Bessel functions and pseudo-Sturmian functions. The coefficient of the product is obtained from a three-term recurrence relation, derived from the boundary condition. The contours of the Kontorovich-Lebedev representation are fixed by the asymptotic conditions. The scattering matrix is then derived from the exact solution of the recurrence relation. The wavefunctions that are obtained are shown to be equivalent to those derived by McGuire. The method can clearly be applied to a larger number of particles and hopefully might be useful for unequal masses and potentials.Comment: 18 pages, 2 figures, to be published in J. Math. Phy

Clima organizacional y desempeño laboral de los colaboradores de la Municipalidad Provincial de Pacasmayo, 2022

La investigación tuvo como objetivo determinar la relación entre el clima organizacional y el desempeño laboral de los colaboradores de la municipalidad Provincial de Pacasmayo, 2022; pues se observó que en este organismo público las relaciones entre los colaboradores presentaban dificultades, asimismo ocurría en el desempeño de sus labores. La metodología del estudio es de tipo aplicada, presentando un enfoque cuantitativo, con un diseño no experimental de corte transversal y descriptiva correlacional, La población estuvo constituida por 245 colaboradores y se tomó una muestra de 69 colaboradores entre ellos 34 administrativos y 35 estables. Los resultados mostraron una correlación positiva moderada y significativa entre el clima organizacional y el desempeño laboral con una Rho =0.670 y Sig. (bilateral)= 0,000. En conclusión, se determinó que las variables de este estudio están relacionadas directamente de manera positiva y significativa