Analytical version of the resonance coupled-channel model for D + T → 5He** → α + n reaction and its application for the description of low-energy D-T AND D-3He scattering
6/24/2019 2019 - #02 Physics in nuclear power engineering
Godes A.I. Kudriavtseva A.S. Shablov V.L.
The purpose of the present paper is the formulation of the analytical version of the resonance coupled-channel model (RCCM) originally developed for D + T → 5He** → → α + n reaction. The integral in the denominator of the Breit-Wigner type is examined in the expression for S-matrix elements of binary processes in this model. Imaginary part of this integral determines the energy-dependent decay width for the near-threshold channel. It is shown that this integral can be calculated explicitly with the Binet representation for the ψ -function (the logarithmic derivation of the gamma function). As the result the explicit expression for the S-matrix elements in the form of analytical functions of the channel momenta are obtained and the equivalence of the RCCM and the effective range approximation (Landau - Smorodinsky - Bethe approximation) is established on this basis. This allows expressing the parameters of the RCCM through the model independent system characteristics: the complex scattering length and the complex effective range. Several sets of model parameters of both approaches that provide a good description of the measured data on D + T → α + n reaction and D-T elastic scattering are derived. By this means we find the location of the S-matrix poles on different Riemann sheets which corresponds to Jπ = (3/2)+ state of 5He and 5Li. In particular, the location of the resonance (R) and shadow (S) poles is determined: 5He**: ZR = 46.9 – i37.2 (keV) ZS = 81.7 – i3.5 (keV) 5Li**: ZR = 205.7 – i146.8 (keV) ZS = 264.4 + i112.0 (keV).
Our results agree well with previous findings. The possible generalizations of the results obtained are discussed.
- Komarov V. V., Popova A. M., Karmanov F.I, Shablov V. L., Nemets O.F., Pavlenko Yu.N., Pugatch V.M. Scattering properties of two-cluster systems produced in multiparticle nuclear reactions. Soviet Journal of Particles and Nuclei, 1992, v. 23, no. 4, pp. 459-480.
- Fazio G., Giardina G., Karmanov F.I., Shablov V.L. Properties of the resonance scattering in two-fragment systems formed in many-particle nuclear reactions. International Journal of Modern Physics E. 1996, v. 5, no. 1, pp. 175-190.
- Nemets O.F., Pavlenko Yu.N., Shablov V.L., Karmanov F.I., Kiva V.O., Dobrikov V.N., Gorpinich O.K., Kolomiets I.M., Rudenko B.A., Karlishev Yu.A., Voiter A.P., Mazny I.O., Omel’chuk S.E., Rosnuk Yu.S. Angular correlation and decay branching ratio for excited state of 7 Li (7.45 MeV) in reactions 7 Li(α,α)7 Li* . Nuclear Physics and Atomic Energy. 2007, v. 1(19), pp. 36-44.
- Mikhailov A.V., Pavlenko Yu.N., Shablov V.L., Stepaniuk A.V., Tyras I.A. Coulomb interaction effect in many-particle nuclear reaction with two-fragment resonance formation. Nuclear Physics and Atomic Energy. 2014, v. 54, no.4, pp. 334-343.
- Komarov V.V., Green A.M., Popova A.M., Shablov V.L. Dynamics of few quantum particle systems. Moscow. Moscow University Publ., 1996, 335 p. (in Russian).
- Komarov V. V., Green A. M., Popova A. M., Shablov V. L. Coulomb and nuclear field effects on two-body resonances. Modern Physics Letters A. 1987, v. 2, pp. 81-88.
- Pavlenko Yu.N., Dobrikov V.N., Dorosko N.L., Gorpinich O.K., Korzina T.A., Kiva V.O., Shablov V.L., Tyras I.A. Decay properties of short lived resonances of light nuclei in many particle nuclear reactions. International Journal of Modern Physics E. 2010, v. 19, no. 5-6, pp. 1220-1226.
- Wildermuth K., Tang J.C. A Unified Theory of the Nucleus. Vieweg Publ. Braunschweig., 1999, 389 p.
- Nikitiu F. Phase Analysis in Physics of Nuclear Interactions. Moscow. Mir Publ., 1983, 416 p. (in Russian).
- Betan R. M. Id, Kruppa A.I., Vertse T. Shadow poles in coupled-channel problems calculated with Berggren basis. Physical Review C. 2018, v. 97, p. 02437.
- Miaroshi T. Shadow poles. Progress in Theoretical Physics. 1980, v. 64, no. 2, pp. 568-582.
- Arena N., Cavallaro S., Fazio G. Three-body effects in the 7 Li(d,aan) reaction. Physical Review C. 1989, v. 4, no. 1, pp. 55-58.
- Bogdanova L.N., Hale G.M., Markushin V.E. Analytical structure of S-matrix for the coupled channel problem D + T → n + α and the interpretation of the J π = (3/2)+ resonance in the 5 He. Physical Review C. 1991, v. 44, no. 4, pp. 1289-1295.
- Bateman H., Erdelyi A. Higher transcendental functions. Vol. 1. McGrow Hill Book Company Inc. New York Toronto London. 1953, 301 p.
- Karnakov B.M., Mur V.D., Pozdnyakov S.G., Popov V.S. Analytical structure of the d-t scattering amplitude near elastic threshold. Pis’ma v Zhurnal Eksperimental’noj i Teoreticheskoj Fiziki.1990, v. 51, no. 7, pp. 352-355 (in Russian).
- Karnakov B.M., Mur V.D., Pozdnyakov S.G., Popov V.S. Poles and resonances in low-energy scattering of charged particles. Yadernaya fisika. 1991, v. 54, no. 2(8), pp. 400-403 (in Russian).
- Landau L.D., Lifshitz E.M. Course of Theoretical Physics. Vol. 3. Quantum Mechanics. Pergamon Press, Oxford, 1977, 671 p.
- Bosch H.S., Hale G.M. Fusion cross-sections and thermal reactivities. Nuclear Fusion. 1992, v. 32, no. 4, pp. 620-622.
- Balashko Yu.G. Investigations of elastic scattering of charged particles on some light nuclei at low energies. Trudy fizicheskogo instituta im. P.N. Lebedeva Akademii nauk SSSR. 1965, v. 33, pp. 66-126 (in Russian).
thermonuclear reactions resonance coupled channel method effective range approximation S-matrix poles resonance and shadow poles Jπ = (3/2)+ state of the 5He and 5Li
Link for citing the article: Godes A.I., Kudriavtseva A.S., Shablov V.L. Analytical version of the resonance coupled-channel model for D + T → 5He** → α + n reaction and its application for the description of low-energy D-T AND D-3He scattering. Izvestiya vuzov. Yadernaya Energetika. 2019, no. 2, pp. 198-207; DOI: https://doi.org/10.26583/npe.2019.2.17 (in Russian).