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Title: Monotonic properties of the shift and penetration factors

Here, 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. In conclusion, 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.
Authors:
 [1] ;  [2] ; ORCiD logo [2]
  1. Ohio Univ., Athens, OH (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Report Number(s):
LA-UR-17-29016
Journal ID: ISSN 2469-9985; PRVCAN
Grant/Contract Number:
AC52-06NA25396; FG02-88ER40387; NA0002905
Type:
Accepted Manuscript
Journal Name:
Physical Review C
Additional Journal Information:
Journal Volume: 97; Journal Issue: 2; Journal ID: ISSN 2469-9985
Publisher:
American Physical Society (APS)
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Atomic and Nuclear Physics; R-matrix theory
OSTI Identifier:
1479931
Alternate Identifier(s):
OSTI ID: 1419605

Brune, Carl Richard, Hale, Gerald M., and Paris, Mark W.. Monotonic properties of the shift and penetration factors. United States: N. p., Web. doi:10.1103/PhysRevC.97.024603.
Brune, Carl Richard, Hale, Gerald M., & Paris, Mark W.. Monotonic properties of the shift and penetration factors. United States. doi:10.1103/PhysRevC.97.024603.
Brune, Carl Richard, Hale, Gerald M., and Paris, Mark W.. 2018. "Monotonic properties of the shift and penetration factors". United States. doi:10.1103/PhysRevC.97.024603.
@article{osti_1479931,
title = {Monotonic properties of the shift and penetration factors},
author = {Brune, Carl Richard and Hale, Gerald M. and Paris, Mark W.},
abstractNote = {Here, 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. In conclusion, 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.},
doi = {10.1103/PhysRevC.97.024603},
journal = {Physical Review C},
number = 2,
volume = 97,
place = {United States},
year = {2018},
month = {2}
}