Abstract
The two-body threshold behavior at NN′ and π D are investigated by using the multi-channel Lippmann-Schwinger equations with an energy dependent two-body quasi potential, which are analytically continued from the three-body Faddeev equations at the three-body break up threshold. Our calculated NN′ and π D scattering lengths show better agreement with the experimental data for NN and π D systems than those from the original NNπ three-body Faddeev equations.
Highlights
Lovelace’s idea in the early 1960s that the two-body N+N→ N+N reaction should be described by the three-body (N2π)+N1 → N2 + reaction [1], can be accomplished by the introduction of an energy dependent two-body quasi potential (E2Q) below the three-body break up threshold [2]
The second appears in Eq(4), 0 ≤ k21,2 ≤ 2mμ1,2 gives −2mμ1,2 ≤ k12,2 ≤ 0, the integral range of k1,2 is larger than k1,2
A phenomenon at the three-body break up threshold E = 0 gives rise to the Efimov effect [3], with an infinite two-body scattering length, where E = 0 brings about a singular cut which is the same as our Ecm = 0 case just mentioned above [2]
Summary
Lovelace’s idea in the early 1960s that the two-body N+N→ N+N reaction should be described by the three-body (N2π)+N1 → N2 + (πN1) reaction [1], can be accomplished by the introduction of an energy dependent two-body quasi potential (E2Q) below the three-body break up threshold [2]. The nucleon mass m1 = m2 ≡ M, and the three-body total energy is S , DFadd = S − ω1(k1) − ω2(k2) − ω3(k3) = S + m − ω1(k1) − ω2(k2) − ω3(k3) ≡ DE2Q, (1)
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