Asymptotic normalization parameter of the triton

Abstract

On the basis of exact separable potential calculations, we show that there is a significant variation of the asymptotic normalization parameter C, of the triton with its binding energy. We present a partial wave dispersion relation technique for determining this parameter from the triton energy, the doublet n-d scattering length, the doublet, s-wave, n-d inelasticities, and the two-nucleon, on-shell scattering amplitudes. We test the method and find it to be accurate and stable with only low-energy information used as input. For a doublet scattering length of 0.65 fm we obtain C, = 3.3+0.1, where the error limits are determined from uncertainties in the inelasticities and the analytic continuation of the two-nucleon amplitudes to negative energies. I NUCLEAR REACTIONS exact separable potential calculations; partial wave dispersion r'elations for n-d elastic scattering amplitudes.

Model for asymptoticD-state parameters of light nuclei: Application toHe4

“…3 the contribution of the last term on the rhs is expected to be small. The virtual breakup of 4 He first to two deuterons and their eventual breakup to four nucleons to form the four-nucleon-exchange deuteron-deuteron amplitude as in this term is much less probable at negative energies than the virtual breakup of 4 He to a nucleon and a trinucleon and its eventual transformation to the deuteron-deuteron cluster as in the first term on the right-hand side of this equation.…”

“…The values of l 3 = 0, 2 yield the S and D state of 4 He respectively. For evaluating the integral I, we expand the energy propagator in terms of spherical harmonics as below,…”

“…(18) apart from a kinematical factor that takes into account the centrifugal barrier, the form factor is assumed to be independent of the relative momentum of the two components forming the bound state, consistent with the minimal three body model [1]. In particular, the form factors for the formation of 4 He from nucleon(N)−triton(t) channel and from two deuterons(dd) are respectively,…”

“…where B α and B d are the binding energies of 4 He and 2 H respectively and we assumē h = m nucleon = 1.…”

“…In Sec. IV the analytic model for the D state of 4 He is presented. Section V deals with the numerical investigation of our model.…”