Solution of the Faddeev equations for the triton problem using local two-particle interactions

Abstract

AbsU'aet: A simple method is described to compute exactly the binding energy (B.E.) of the ground state of three nucleons in the framework of the Faddeev equations. The two-body potentials thereby used are of the local central Yukawa type. The effect of including repulsion in the two-body forces is also studied and it is found to be considerable. As a result of this calculation a value of 8.4 MeV is obtained for the B.E. of triton.

Translationally invariant treatment of pair correlations in nuclei: I. Spin and isospin dependent correlations

“…Using our technology we have set out to calculate the binding energy of 4 the best possible comparison with existing results in the literature we have investigated the Brink-Boeker B1 potential [11], the Afnan-Tang S3 potential [9], the modified S3 (MS3) potential [12], and the Malfliet-Tjon MT I/III and MT V potentials [13]. We have optimised the value of α, the inverse lengthscale of the harmonic oscillator, for the case of the state-independent (SI), purely central (scalar) correlations, i.e., where we restrict the expansion of eq.…”

“…Clearly, one should limit the general form of the correlation so as not to create duplicate basis states, since this will give rise to problems when solving the generalised eigenvalue problem of eq. (13). Specifically, the state-dependent correlation of the V4 type for 4 He should include only the central scalar (Wigner) and spin-exchange (Bartlett) pieces.…”

Approaching Universality in Weakly Bound Three-Body Systems

“…Figure 3 illustrates the correlation for six different families of two-body potentials. The potentials include the TTY potential [6] with an artificial coupling constant, the family of Bargmann potentials [10] with fixed small effective range and a scattering length varying from 2 to 250 atomic units, the Bargmann potential with an effective range simulating the He-He interaction, the family of Bargmann potentials with varying asymptotic normalizing constant, and the MTV potential [11] ("symmetric model" for the triton) with a varying coupling constant. The near-linearity over a wide range of ω is apparent in the figure, though deviations can be seen, especially for small values of the 3−body scattering length, magnified in the inset of Figure 3, where the complexity of the correlation is revealed.…”

Measurement of the neutron (³He) spin structure functions at low Q²: A connection between the Bjorken and gerasimov-drell-hearn sum rule

“…A fit on world calculations of the threenucleon system yields ∆ = 0.07 ± 0.01 and ∆ = 0.014 ± 0.002 [36]. Afnan and Birrell [37] solved the Faddeev equations [38][39][40][41] in momentum space with a unitary pole expansion (UPE) of a Reid soft core (RSC) nucleon-nucleon potential [42] using the partial wave decomposition of Derrick and Blatt [35] involving basis states of definite symmetry (S=symmetric, A=antisymmetric, and M=mixed) for the 3 He wave function. They obtained the percentage probabilities P S = 89.2%, P S = 1.6%, and P D = 9.1% for the three-body system.…”