$^2{\rm{\vec H(}}\vec d,p{{\rm{)}}^3}{\rm{H}}$ Reaction Calculations at 20–120 keV by the Four-Body Yakubovsky Equations with the Paris Potential

Abstract

We analyze ${}^{2}\text{H(}\vec{d},p{{\text{)}}^{3}}\text{H}$ reaction measurements by using the four-body Yakubovsky integral equations and simple Coulomb correct ion methods. The adopted potential is the Paris-potential (PEST-1) for the ¹ S ₀ and ³ S ₁−³ D ₁ states. The [3+1] and the [2+2] sub-amplitudes are given by the energy dependent pole expansion of rank-3, and also the Hilbert-Schmidt one. We included 1/2⁺ and 1/2⁻ states for ³He and ³H nuclei which may occur in the intermediate subnuclei as part of the four-nucleon system. The angular momentum between two deuterons in the initial state is retained up to 2, and also the maximum value between ³H and p in the final state is 4. Therefore, the total spins and parities of the four-nucleon system are 0⁺, 0⁻, 1⁺, 1⁻, 2⁺, 2⁻, 3⁺, 3⁻, and 4⁺. The calculated total cross section, differential cross section, and tensor analyzing powers at energies from 20 to 120 keV are in very good agreement with the experimental data, but the vector analyzing power is still very small. Ratios of the double polarized deuteron scattering cross sections to the unpolarized one (σ _pol /σ ₀) were calculated. It was found that the cross section is suppressed by a factor one half at higher energies.