Speaker
Description
A new variation method for solving the bound-state problem for a system of few
particles is proposed. Unlike the traditional variational approach,
where the expectation value of the Hamiltonian is minimized, i.e. just a single
quantity, in the proposed method the approximate solution is constructed by
fitting a continuum of quantities, namely, the entire function that describes
the interaction potential in one of the two-body subsystems. Another
advantage of the new method is that the resulting approximate wave function of
the few-body system satisfies the corresponding Schroedinger equation with a
given (experimental) binding energy. As an example, an approximate analytic
expression of the ground-state wave function of $^9\mathrm{Be}$ nucleus is
obtained. This nucleus is treated as a bound system of two $\alpha$-particles
and one neutron. Within the new variational method the problem is solved by
postulating a trial wave function, using which in the three-body Schroedinger
equation with experimental value of the energy, the corresponding
$\alpha\alpha$-potential is recovered. The parameters of the trial function are
varied in order to minimize the difference between the exact and recovered
$\alpha\alpha$-potentials.
