Low-energy parameters of neutron-neutron interaction in the effective-range approximation

Abstract

The influence of the mass difference between the charged and neutral pions on the low-energy characteristics of nucleon-nucleon interaction in the 1 S 0 spin-singlet state is studied within the framework of the effective-range approximation. By making use of the experimental singlet neutron-proton scattering parameters and the experimental value of neutron-neutron virtualstate energy, the following values were obtained for the neutron-neutron scattering length and effective range: a nn = −16.59(117) fm, r nn = 2.83(11) fm. The calculated neutron-neutron scattering length a nn is in good agreement with one of the two well known and differing experimental values of this quantity, and the calculated effective range r nn is also in good agreement with present-day experimental results.

Mirror nuclei 3H and 3He binding energies difference and low energy parameters of neutron-neutron scattering

“…This value, however, contradicts a nn = -16.2(3) fm [37] and a nn = -16.5(9) fm [32]. The value of the neutron-neutron scattering length a nn = -16.59(117) fm obtained by us in [29] using experimental results [38], despite large errors, also contradicts the value a nn = -18.38(55) fm calculated in this study. Thus, the values a nn = -16.59(117) fm [29] and a nn = -16.5(9) fm [32] contradict the results obtained based on the analysis of the difference of the mirror nuclei 3 H and 3 He binding energies.…”

“…The examples of such reactions are π -+ d → γ + n + n and n + d → p + n + n. Neutron-neutron scat tering length a nn is usually determined from the analy sis of these reactions. The effective radii of pp and nn scattering are practically equal to each other, since pp and nn interactions take place via the exchange of the same neutral π 0 meson, whose mass determines the interaction radius R. It follows from our study [29] that the effective radii of NN interaction are mainly (90%) determined by the radius of action of nuclear …”

“…For a quantitative evaluation of charge symmetry breaking of nuclear forces in a nucleon-nucleon system, we use the energy differ ence of virtual levels of pp and nn systems ε pp and ε nn , (29) In the assumption of the two particle character of nuclear interaction, the quantities characterizing the charge symmetry breaking in systems of two and three nucleons should be equal to each other in relative units,…”

“…Since similar nucleons (nn and pp) exchange the same neutral π 0 meson, it is natural to assume that the radii of nn and pp interactions are equal to each other [29]:…”

Pseudopotential for the two-dimensional contact interaction

“…Although in this work we have focused on using the pseudopotential to accurately capture the scattering properties of the contact interaction, our formalism allows the further improvement of modeling of quantum gases by calibrating the pseudopotentials to more accurately describe the scattering properties of the underlying Feshbach resonance interaction. To next lowest order in scattering wavevector, this corresponds to including the effective range term essential for describing narrow Feshbach resonances, which may exhibit exotic breached superfluidity [56,57], or other interactions with non-zero effective ranges, which are applicable in the study of nucleon reactions [58]. Rather than a description in terms of the scattering phase shift, the pseudopotentials could instead be calibrated to other scattering properties.…”