Abstract
We present a collection of simple derivations for the neutron-induced resonance cross-sections. These formulae are commonly used to experimentally describe the fundamental properties of resonances for neutron-rich nuclei far from stability and to describe unbound nuclei. The main goal of this article is to illustrate their dependencies with basic observables in order to discuss the pertinence of experimental approaches in the derivation of their properties, especially for “N-body” resonances.
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Notes
Riccati-Bessel functions, solutions of the differential equation \( x^2 \frac{d^2 y}{dx^2} + \left[ x^2 - n (n+1)\right] y = 0\). To get back to the present problem simply put \(n=\ell , x=kr\) and \(y=u_\ell \left( kr\right) \).
Except for \(\ell =0\) states, see Sect. 3.2.
Mathematically the moment of order 3 of the reduced centered variable \(\gamma _{1}={\text {E}} \left[ \left( \frac{X-\mu }{\sigma } \right) ^{3}\right] =\frac{\mu _3}{\sigma ^3}\) with \(\mu _{k}={\text {E}} \left[ (X-\mu )^k\right] =\int _{-\infty }^{+\infty }(x-\mu )^k P(x)\textrm{d} x\) and \(^{2} = \mu _{2}\)
References
N. Austern, Direct nuclear reaction theories, in Interscience Monographs and Texts in Physics and Astronomy (Wiley-Interscience, 1970). 30620
J.M. Blatt, V.F. Weisskopf, Theoretical Nuclear Physics (Wiley, New York, 1984)
G.R. Satchler, Introduction to Nuclear Reactions, 2nd edn. (Oxford University Press, Oxford, 1990)
A.M. Lane, R.G. Thomas, \(R\)-matrix theory of nuclear reactions. Rev. Mod. Phys. 30, 257–353 (1958). https://doi.org/10.1103/RevModPhys.30.257
P. Descouvemont, D. Baye, The \(R\)-matrix theory. Rep. Prog. Phys. 73(3), 036,301 (2010)
F. Gunsing, in Joliot-Curie School (2014). https://ejc2014.sciencesconf.org/conference/ejc2014/pages/20150420_ejc2014_gunsing_1_2.pdf
B. Gough, GNU Scientific Library Reference Manual—Third Edition, 3rd edn. (Network Theory Ltd., 2009)
K. McVoy, Virtual states and resonances. Nucl. Phys. A 115(3), 481–494 (1968). https://doi.org/10.1016/0375-9474(68)90741-0
A.M. Lane, Reduced widths of individual nuclear energy levels. Rev. Mod. Phys. 32, 519–566 (1960). https://doi.org/10.1103/RevModPhys.32.519
A. Bohr, B. Mottelson, Nuclear Structure (World Scientific Publishing Company, Inc., London, 1998)
F.C. Barker, \(R\)-matrix formulas for three-body decay widths. Phys. Rev. 68, 054,602 (2003). https://doi.org/10.1103/PhysRevC.68.054602
H.O.U. Fynbo, R. Álvarez-Rodríguez, A.S. Jensen, O.S. Kirsebom, D.V. Fedorov, E. Garrido, Three-body decays and \(R\)-matrix analyses. Phys. Rev. C 79, 054,009 (2009). https://doi.org/10.1103/PhysRevC.79.054009
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Gibelin, J. On the Experimental Description of Neutron Resonances. Few-Body Syst 64, 14 (2023). https://doi.org/10.1007/s00601-023-01798-w
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DOI: https://doi.org/10.1007/s00601-023-01798-w