Application of the method of integral equations for calculating the vertex constants for an α-particle

doi:10.1016/0375-9474(76)90335-3

Nuclear Physics A

Volume 272, Issue 2, 16 November 1976, Pages 327-337

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Abstract

The vertex constants G²_αTN and G²_αdd for the virtual decays α → t(τ) + p(n) and α → d + d are calculated by solving the Faddeev-Yakubovsky equations for four nucleons. A spin-dependent separable potential with the Hulthén form factor is used as the NN interaction. The resonant Hilbert-Schmidt expansion is applied to solve the integral equations. The values obtained G²_αTN = 17.9 ± 1.7 fm and G²_αdd = 18.1 ± 1.3 fm are compared with the phenomenological values extracted from data on nuclear reactions.

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The deuteron momentum distribution ϱ_dd(q) in the ⁴He nucleus has been obtained for the first time from the data on the reaction ⁴Hep → pdd for an incident ⁴He momentum of 2.7 GeV/c at values of the deuteron spectator momentum q ⩽ 0.3 GeV/c using the 2 m hydrogen bubble chamber of ITEP. The criteria of pole dominance are analysed. A lower bound is given on the value of the nuclear vertex constant G_αdd² = (5.97 ± 1.09) fm. The experimental data are compared with the theoretical calculations.
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Integral equations of motion for the system consisting of the four pair-wise interacting nucleons are formulated. The nucleon-nucleon interaction is characterized by a charge-independent, spin-and isospin-exchange central potential of the general (local or non-local) form. The derivation of the equations is performed on the basis of the Faddeev-Yacubovsky method taking the Pauli principle strictly into account. The equations obtained describe all possible processes in the four-nucleon system with the two-fragment initial asymptotic state, as well as the four-nucleon bound states. The calculations of the ⁴He binding energy and the n-³H and n-³He scattering lengths are carried out in the case of the separable rank-1 potentials with the application of the Bateman approximation for the subsystem scattering amplitudes. The correlations between the calculated quantities and their sensitivity to parameters of NN interaction are studied. The results are compared with the available experimental data.
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Nuclear Physics A

Abstract

References (29)

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Phys. Lett.

Nucl. Phys.

JINR preprint P4-8158

Phys. Lett.

Nucl. Phys.

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Yad. Fiz.

Phys. Rev. Lett.

Theory of direct nuclear reactions (in Russian)

Nucl. Phys.

Yad. Fiz.

Nucl. Phys.

Cited by (7)

Determination of the momentum distribution of the deuteron-deuteron relative motion of the α particle from data on the reaction <sup>4</sup>Hep → pdd for an incident α particle momentum of 2.7 GeV/c

Four-nucleon problem in the integral equation approach. The binding energy of <sup>4</sup>He and the n-<sup>3</sup>H and n-<sup>3</sup>He scattering lengths

The use of analyticity in nuclear physics

The contribution of the (t(τ)+N) component to the α-particle wave function from data on the reactions p(α,pp)t and p(α,pn)τ at incident α-particle momentum 5 GeV/c

Analytic and diagram methods in nuclear reaction theory

<sup>4</sup>He fragmentation induced by 46-400 GeV Protons