Monotonic properties of the shift and penetration factors

We study derivatives of the shift and penetration factors of collision theory with respect to energy, angular momentum, and charge. Definitive results for the signs of these derivatives are found for the repulsive Coulomb case. In particular, we find that the derivative of the shift factor with respect to energy is positive for the repulsive Coulomb case, a long anticipated but heretofore unproven result. These results are closely connected to the properties of the sum of squares of the regular and irregular Coulomb functions; we also present investigations of this quantity.Comment: 13 pages, 1 figur

Empirical Legal Studies Before 1940: A Bibliographic Essay

The modern empirical legal studies movement has well-known antecedents in the law and society and law and economics traditions of the latter half of the 20th century. Less well known is the body of empirical research on legal phenomena from the period prior to World War II. This paper is an extensive bibliographic essay that surveys the English language empirical legal research from approximately 1940 and earlier. The essay is arranged around the themes in the research: criminal justice, civil justice (general studies of civil litigation, auto accident litigation and compensation, divorce, small claims, jurisdiction and procedure, civil juries), debt and bankruptcy, banking, appellate courts, legal needs, legal profession (including legal education), and judicial staffing and selection. Accompanying the essay is an extensive bibliography of research articles, books, and reports