Abstract
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 nuclear fusion 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 demonstrated 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 nuclei. 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.
Highlights
Introduction second exited states of 5He** and 5Li** nuclei based on the resonance coupled-channel model for D + T → α + n
The following expression is written for the element of S-matrix S11(E) in effective range approximation instead of (1): Determination of model parameters and positioning of S-matrix poles of D + T → α + n and D + 3He → α + p processes in the neighborhood of resonance energies of 5He(3/2)+ and 5Li(3/2)+ nuclei
Two sets of parameters of the resonance coupled-channel model well matching the cross-section of the thermonuclear fusion D + T → α + n reaction are presented in (Bogdanova et al 1991) for the case of 5He(3/2)+ nucleus with one of the presented sets of parameters in good agreement with measured data on the cross-section of elastic D-T scattering
Summary
Introduction second exited states of5He** and 5Li** nuclei based on the resonance coupled-channel model for D + T → α + nReactions containing in the final state non-stable quantum reaction (Bogdanova et al 1991). Thermonuclear reactions, resonance coupled-channel model, effective range approximation, S-matrix poles, resonance and shadow poles, Jπ = (3/2)+ state of 5He and 5Li nuclei.
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