On Theoretical Methodology of Nuclear Reactions and Outcome of Certain Physical Phenomena from Them. II. To the Space-time Description of Cross Sections and Durations of the Neutron-nucleus Scattering Near 1-2 Resonances in the C- and L-systems

V.S. Olkhovsky^1,

¹Institute for Nuclear Research of NASU, prospekt Nauki, 47, Kiev-03028, Ukraine

Cite this paper

V.S. Olkhovsky. On Theoretical Methodology of Nuclear Reactions and Outcome of Certain Physical Phenomena from Them. II. To the Space-time Description of Cross Sections and Durations of the Neutron-nucleus Scattering Near 1-2 Resonances in the C- and L-systems. American Journal of Applied Mathematics and Statistics. 2015; 3(3):131-141. doi: 10.12691/AJAMS-3-3-6

Abstract

It is already known the appearance of time advance (due to distortion by the non-resonant background) instead of the expected time delay in the region of a compound-nucleus resonance in the center-of-mass (C-) system. Here at the same conditions we study cross sections and durations of the neutron-nucleus scattering in the laboratory (L-) system. Here it is shown that such time advance is a virtual paradox but in the L-system the time-advance phenomenon does not occur and only the trivial time delay is observed. At the same time the transformations from C-system into the L-system appeared to be different from the standard kinematical transformations because in the C-system the motion of a compound nucleus is absent but it is present in the L-system. We analyze the initial wave-packet motion (after the collision origin) and the cross section in the laboratory (L-) system. Also here (as physical revelations of profound general methodic and in very good consistent accordance with the experiment) several results of the calculated cross sections for the neutron-nucleus in comparison with the experimental data in the L-system at the range of one or two overlapped compound resonances are presented. It is shown in the space-time approach that the standard kinematical transformations of cross sections from the C-system to the L-system are not valid because it is necessary to consider the center-of-mass motion in the L-system. Finally on a correct self-consistent base of the space-time description of the nuclear processes in the laboratory system with 3 particles in the final channel, it is shown the validity of the former approach, obtained for the space-time description of the nuclear processes with 2-particle channels earlier.

Keywords

space-time approach to nuclear collision; time delay, time advance, transformations of cross sections from the C-system to the L-system, interference phenomena, recoil system, direct and sequential processes

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References

[1]	Olkhovsky, V.S., Doroshko, N.L., Europhys.Lett., 18 (1992)483.
[2]	D’Arrigo, A., Doroshko, N.L., Eremin, N.V., Olkhovsky, V.S. et al, Nucl.Phys., A,549 (1992)375.
[3]	D’Arrigo, A., Doroshko,N.L., Eremin, N.V.,Olkhovsky, V.S. et al, Nucl.Phys., A, 564(1993)217.
[4]	Kelkar, N.G., J.Phys.G: Nucl.Par.Phys.,29 (2003)L1-L8.
[5]	Kelkar, N.G., Nowakowski, M. and Khemchandani, K.P., Nucl.Phys., A724(2003)357; Kelkar, N.G., Nowakowski,M. and Khemchandani, K.P. and Jain, B.K., Nucl.Phys., A730(2004)121.
[6]	Kelkar, N.G., Khemchandani, K.P. and Jain,B.K.,J.Phys.G: Nucl. Part. Phys.,32:3(2006) L19.
[7]	Prokopets, G.A., Nuclear Physics (Russia), volume 74 (2011), p. 740-746.
[8]	Eremin, N.V., Giardina,G., Olkhovsky,V.S., Omelchenko,S.A., Mod.Phys.Lett.,A,9(1994)2849.
[9]	Olkhovsky, V.S., Dolinska,M.E., Omelchenko,S.A.and Romanyuk, M.V., Internat.J.Mod.Phys. E,19: 5-6 (2010), рр. 1212-1219.
[10]	Olkhovsky,V.S., Dolinska,M.E., Omelchenko,S.A., arXiv.1101.5541v1 [nucl-th], Jan.2011; Appl.Phys.Let., 99(2011) 244103(1-3).
[11]	Olkhovsky,V.S., Dolinska,M.E., Omelchenko,S.A., On the cross section and duration of the neutron-nucleus scattering with a resonance,distorted by a non-resonant background, in the center-of-mass system and laboratory system, Proc. of the 4-th Internat.Conf. Current Problems in Nuclear Physics and Atomic Energy (NPAE-2012, sept.3-7, 2012, Kyiv, Ukraine), Kyiv 2013, pp. 198-201.
[12]	Olkhovsky, V.S., Sov. J. Particles Nucl.(Engl. Transl.);(United States), 1984, v.15, (2),p.130-148; Olkhovsky,V.S., Time as a Quantum Observable, Canonically Conjugated to Energy, and Foundations of Self-Consistent Time Analysis of Quantum Processes, Advances in Math.Phys., vol. 2009 (2009), аrticle ID 859710, 83 pages.
[13]	Olkhovsky, V.S., Doroshko,N.L., Lokotko,T.I., On the cross section and duration of the neutron-nucleus scattering with two overlapped resonances in the center-of-mass system and laboratory system, Proc.of the 4-th Internat. Conf. Current Problems in Nuclear Physics and Atomic Energy (NPAE-2012, sept.3-7, 2012, Kyiv, Ukraine), Kyiv 2013, pp. 192-197.
[14]	The JEFF – 3.1.1. Nuclear Data Library, OECD NEA/NEA2009; EXFOR 13759.002, J.A.Harvey, D.C.Larson, ORNL, 1974.
[15]	Brusegan, A., Rohr, G., Shelley, R., Macavero, E., Van Der Vorst, C., Poortmans, F., Mewissen, I., Vanpraet,G., Very high resolution transmission measurements and resonance parameters of Ni58 and Ni60, 1994.
[16]	Olkhovsky, V.S., Zaichenko, A.K., Phys. Lett.B 272(1991)183-185.
[17]	D’Arrigo, A., Fazio, G., Giardina, G. et al. Progress of Theor. Phys.87 (1992) 1359-1365.
[18]	Kopylov, G.I., Podgoretskij, M.I., Sov. J. Nucl. Phys.15 (1972) 219-223.
[19]	M.L.Goldberger, K.M.Watson, Collision Theory. Wiley J.& Son Inc., 1964.
[20]	A.I.Baz, Ya.B..Zel’dovich, A.M.Perelomov, Scattering, Reaction in Non-Relativistic Quantum Mechanics. Jerusalem, 1969.
[21]	Rosenfeld, L., Nucl. Phys.70 (1965) 1-27.