Analysis of experimental data on doublet neutron-deuteron scattering at energies below the deuteron-breakup threshold on the basis of the pole approximation of the effective-range function

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21.45.+V, 25.10.+S, 25.40.-H, 25.40.Dn, 25.60.Bx, 27.10.+H

Scientific paper

On the basis of the Bargmann representation of the S matrix, the pole approximation is obtained for the effective-range function k cot δ. This approximation is optimal for describing the neutron-deuteron system in the doublet spin state. The values of r 0 = 412.469 fm and v 2 = -35 495.62 fm3 for the doublet low-energy parameters of neutron-deuteron scattering and the value of D = 172.678 fm2 for the respective pole parameter are deduced by using experimental results for the triton binding energy E T , the doublet neutron-deuteron scattering length a 2, and van Oers-Seagrave phase shifts at energies below the deuteron-breakup threshold. With these parameters, the pole approximation of the effective-range function provides a highly precise description (the relative error does not exceed 1%) of the doublet phase shift for neutron-deuteron scattering at energies below the deuteron-breakup threshold. Physical properties of the triton in the ground ( T) and virtual ( v) states are calculated. The results are B v = 0.608 MeV for the virtuallevel position and C {/T 2} = 2.866 and C {/v 2} = 0.0586 for the dimensionless asymptotic normalization constants. It is shown that, in the Whiting-Fuda approximation, the values of physical quantities characterizing the triton virtual state are determined to a high precision by one parameter, the doublet neutron-deuteron scattering length a 2. The effective triton radii in the ground ( ρ T = 1.711 fm) and virtual ( ρ v = 74.184 fm) states are calculated for the first time.

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