  A new approximation formalism is applied to study the bound states of the
Hellmann potential, which represents the superposition of the attractive
Coulomb potential $-a/r$ and the Yukawa potential $b\exp (-\delta r)/r$ of
arbitrary strength $b$ and screening parameter $\delta $. Although the analytic
expressions for the energy eigenvalues $E_{n,l\text{}}$ yield quite accurate
results for a wide range of $n,\ell $ in the limit of very weak screening, the
results become gradually worse as the strength $b$ and the screening
coefficient $\delta $ increase. This is because that the expansion parameter is
not sufficiently small enough to guarantee the convergence of the expansion
series for the energy levels.
