2007/05/31 by M. Pavon Valderrama, E. Ruiz Arriola · 1 citation
Physics and Astronomy · #Attractor #Boundary (topology) #Boundary value problem #Fixed point #High-Energy Particle Collisions Research #Limit (mathematics) #Nuclear physics research studies #Observable #Quantum Chromodynamics and Particle Interactions #Renormalization #Renormalization group #Scaling #Scattering #nucl-th
paper · pdf · doi:10.1016/j.aop.2007.08.003
published as AnnalsPhys.323:1037-1086,2008 · 31 pages, 8 figures
arxiv created 2007/08/10 · openalex publication_date 2007/08/27 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We analyze how a short distance boundary condition for the Schrodinger equation must change as a function of the boundary radius by imposing the physical requirement of phase shift independence on the boundary condition. The resulting equation can be interpreted as a variable phase equation of a complementary boundary value problem. We discuss the corresponding infrared fixed points and the perturbative expansion around them generating a short distance modified effective range theory. We also discuss ultraviolet fixed points, limit cycles and attractors with a given fractality which take place for singular attractive potentials at the origin. The scaling behaviour of scattering observables can analytically be determined and is studied with some emphasis on the low energy nucleon-nucleon interaction via singular pion exchange potentials. The generalization to coupled channels is also studied.