2017/08/31 by C. R. Brune, Carl R. Brune, Gerald M. Hale +3
Mathematics · Physics and Astronomy · #Angular momentum #Atomic and Molecular Physics #Collision #Computer science #Coulomb #Coulomb barrier #Coulomb's constant #Economics #Electric potential energy #Electron #Energy (signal processing) #Financial economics #Mathematical analysis #Mathematics #Momentum (technical analysis) #Monotonic function #Nuclear physics research studies #Penetration (warfare) #Physics #Quantum Chromodynamics and Particle Interactions #Quantum electrodynamics #Quantum mechanics #Second derivative #math-ph #math.CA #math.MP #nucl-th #quant-ph
paper · pdf · doi:10.1103/physrevc.97.024603
published as Phys. Rev. C 97, 024603 (2018) · 13 pages, 1 figure
openalex publication_date 2018/02/05 · arxiv created 2018/02/07 · arxiv updated 2018/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.