Analytic Continuation of Scattering Data to the Region of Negative Energies for Systems That Have One and Two Bound Statesстатья
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Дата последнего поиска статьи во внешних источниках: 28 октября 2016 г.
Аннотация:An exactly solvable potential model is used to study the possibility of deducing information
about the features of bound states for the system under consideration (binding energies and asymptotic
normalization coefficients) on the basis of data on continuum states. The present analysis is based on an
analytic approximation and on the subsequent continuation of a partial-wave scattering function from the
region of positive energies to the region of negative energies. Cases where the system has one or two bound
states are studied. The α+d and α+12C systems are taken as physical examples. In the case of one bound
state, the scattering function is a smooth function of energy, and the procedure of its analytic continuation
for different polynomial approximations leads to close results, which are nearly coincident with exact values.
In the case of two bound states, the scattering function has two poles—one in the region of positive energies
and the other in the region of negative energies between the energies corresponding to the two bound states
in question. Pade´ approximants are used to reproduce these poles. The inclusion of these poles proves to
be necessary for correctly describing the properties of the bound states.