The Relation between Zero-Energy Scattering Phase-Shifts, the Pauli Exclusion Principle and the Number of Composite Bound States TeX Export

@article{citeulike:5848709, abstract = {10.1098/rspa.1955.0031 It is shown that for the interaction of systems described by integro-differential equations, such as the scattering of electrons by atoms or of nucleons by deuterons, tritons and other nuclei, that the zero-energy scattering phase-shift is (n + m) \$\pi \$, where n is the number of composite bound states of the impacted and incident particles, and m is the number of states from which the incident particle is excluded by the Pauli principle. Each of these excluded states corresponds to a solution of the integro-differential equation asymptotic to e\$^{-\gamma r}\$ for which the complete wave function vanishes identically, and which therefore does not represent a bound state. It is possible to predict the zero-energy phase-shift without calculation by a knowledge of the composite bound states and of the distribution and quantum numbers of the elementary particles contained in the impacted and incident systems.}, author = {Swan, P.}, citeulike-article-id = {5848709}, citeulike-linkout-0 = {http://dx.doi.org/10.1098/rspa.1955.0031}, citeulike-linkout-1 = {http://rspa.royalsocietypublishing.org/content/228/1172/10.abstract}, citeulike-linkout-2 = {http://rspa.royalsocietypublishing.org/content/228/1172/10.full.pdf}, day = {15}, doi = {10.1098/rspa.1955.0031}, journal = {Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences}, keywords = {bound, energy, state, zero}, month = {February}, number = {1172}, pages = {10--33}, posted-at = {2009-09-29 09:37:30}, priority = {4}, title = {The Relation between Zero-Energy Scattering Phase-Shifts, the Pauli Exclusion Principle and the Number of Composite Bound States}, url = {http://dx.doi.org/10.1098/rspa.1955.0031}, volume = {228}, year = {1955} }

TY - JOUR ID - citeulike:5848709 L3 - citeulike-article-id:5848709 N2 - 10.1098/rspa.1955.0031 It is shown that for the interaction of systems described by integro-differential equations, such as the scattering of electrons by atoms or of nucleons by deuterons, tritons and other nuclei, that the zero-energy scattering phase-shift is (n + m) $\pi $, where n is the number of composite bound states of the impacted and incident particles, and m is the number of states from which the incident particle is excluded by the Pauli principle. Each of these excluded states corresponds to a solution of the integro-differential equation asymptotic to e$^{-\gamma r}$ for which the complete wave function vanishes identically, and which therefore does not represent a bound state. It is possible to predict the zero-energy phase-shift without calculation by a knowledge of the composite bound states and of the distribution and quantum numbers of the elementary particles contained in the impacted and incident systems. IS - 1172 JF - Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences EP - 33 TI - The Relation between Zero-Energy Scattering Phase-Shifts, the Pauli Exclusion Principle and the Number of Composite Bound States VL - 228 SP - 10 KW - bound KW - energy KW - state KW - zero AU - Swan, P PY - 1955/02/15/ UR - http://dx.doi.org/10.1098/rspa.1955.0031 ER -