Movement of Efimov states inC20causing resonance inn−C19scattering near scattering threshold

Abstract

Movement of Efimov states in $^{20}\mathrm{C}$ as a result of increasing the $n\text{\ensuremath{-}}^{18}\mathrm{C}$ binding energy from about $100\phantom{\rule{0.5em}{0ex}}\text{to}\phantom{\rule{0.5em}{0ex}}500\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ is studied in a three body model for $^{20}\mathrm{C}$, assumed to be $n+n+^{18}\mathrm{C}$ system, employing separable potentials for the $n\text{\ensuremath{-}}n$ and $n\text{\ensuremath{-}}^{18}\mathrm{C}$ binary subsystems. The computational analysis shows that for small values of energies ( about $120\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$) which are just necessary to bind the two body $(n\text{\ensuremath{-}}^{18}\mathrm{C})$ system, there could be more than one bound Efimov states. But the states are found to go on disappearing one by one as the binding energy is increased beyond $200\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$. As originally pointed out by Amado and Noble [Phys. Rev. D 5, 1992 (1972)], the Efimov states move into the unphysical sheet associated with the two body unitarity cut on increasing the strength of the binary interaction to bind the two body system. By undertaking a detailed study of the scattering of neutron on a bound $(n\text{\ensuremath{-}}^{18}\mathrm{C})$ system, we find that these states move over to the physical scattering region causing a resonance in $n\text{\ensuremath{-}}^{19}\mathrm{C}$ scattering around neutron incident energy of $1.6\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$, having a width of about $0.25\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$.