Neutron–19C scattering: Towards including realistic interactions

Abstract

Low-energy neutron-19 C scattering is studied in the three-body n + n + 18 C model using a realistic nn potential and a number of shallow and deep n-18 C potentials, the latter supporting deeply-bound Pauli-forbidden states that are projected out. Exact Faddeev-type three-body scattering equations for transition operators including two-and three-body forces are solved in the momentum-space partial-wave framework. Phase shift, inelasticity parameter, and cross sections are calculated. For the elastic n-19 C scattering in the J Π = 0 + partial wave the signatures of the Efimov physics, i.e., the pole in the effective-range expansion and the elastic cross section minimum, are confirmed for both shallow and deep models, but with clear quantitative differences between them, indicating the importance of a proper treatment of deeply-bound Pauli-forbidden states. In contrast, the inelasticity parameter is mostly correlated with the asymptotic normalization coefficient of the 19 C bound state. Finally, in the regime of very weak 19 C binding and near-threshold (bound or virtual) excited 20 C state the standard Efimovian behaviour of the n-19 C scattering length and cross section was confirmed, resolving the discrepancies between earlier studies by other authors [I. Mazumdar, A. R. P. Rau, V. S. Bhasin, Phys. Rev. Lett. 97 (2006) 062503; M. T. Yamashita, T. Frederico, L. Tomio, Phys. Rev. Lett. 99 (2007) 269201].

Probing Efimov discrete scaling in an atom-molecule collision

“…It is tempting to associate the maxima obtained for the cross-section with resonances; however, a calculation by using the complex scaling method [25] for the Gaussian potential, excludes that. These results are also corroborating the conclusions of [18,20] for the neutron-19 C system, where no resonance is found when changing the neutron separation energy in 19 C. By considering different mass-ratios A, varying from 0.01 till 0.08, our results for the cross-sections σ (in arbitrary units) are presented in Fig. 2 for three fixed weaklybound two-body energies B 2 /B 3 =0.01, 0.03 and 0.05.…”

“…It is tempting to associate the maxima obtained for the cross-section with resonances; however, a calculation by using the complex scaling method [25] for the Gaussian potential, excludes that. These results are also corroborating the conclusions of [18,20] for the neutron- 19 C system, where no resonance is found when changing the neutron separation energy in 19 C. FIG. 2: The zero-ranged results for σ (in arbitrary units) as functions of E/B3 are given in eight panels, with mass-ratios A as shown inside the frames.…”

“…Going back in time, what was known theoretically from the pioneer works for the tri-nucleon systems [14][15][16][17], was the existence of a pole in the spin doublet s−wave neutron-deuteron k cot δ 0 , which was associated with a virtual state in the tri-nucleon system. Furthermore, such pole is also present in the neutron-19 C scattering [18][19][20], with a corresponding pronounced minimum of the s−wave elastic cross-section. If the Efimov geometrical factor decreases, which is possible with atomic systems, our expectation for H − (HL) collision is that several minima in the s−wave elastic cross-sections or poles in the k cot δ 0 would emerge from the characteristic log-periodic behavior carried by the wave-function in the region where the Efimov long-range potential is dominant and being reflected in a geometrical law for the spacing of the energies of cross-section minima corresponding to these poles.…”