Physics – Atomic Physics
Scientific paper
2010-12-14
Physics
Atomic Physics
21 pages, 7 figures (accepted for publication in Journal of Physics B.)
Scientific paper
The resonance states of one- and two-particle Hamiltonians are studied using variational expansions with real basis-set functions. The resonance energies, $E_r$, and widths, $\Gamma$, are calculated using the density of states and an ${\mathcal L}^2$ golden rule-like formula. We present a recipe to select adequately some solutions of the variational problem. The set of approximate energies obtained shows a very regular behaviour with the basis-set size, $N$. Indeed, these particular variational eigenvalues show a quite simple scaling behaviour and convergence when $N\rightarrow \infty$. Following the same prescription to choose particular solutions of the variational problem we obtain a set of approximate widths. Using the scaling function that characterizes the behaviour of the approximate energies as a guide, it is possible to find a very good approximation to the actual value of the resonance width.
Osenda Omar
Pont Federico M.
Serra Pablo
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