  We present a generalization of the perturbative construction of the metric
operator for non-Hermitian Hamiltonians with more than one perturbation
parameter. We use this method to study the non-Hermitian scattering
Hamiltonian: H=p^2/2m+\zeta_-\delta(x+a)+\zeta_+\delta(x-a), where \zeta_\pm
and a are respectively complex and real parameters and \delta(x) is the Dirac
delta function. For regions in the space of coupling constants \zeta_\pm where
H is quasi-Hermitian and there are no complex bound states or spectral
singularities, we construct a (positive-definite) metric operator \eta and the
corresponding equivalent Hermitian Hamiltonian h. \eta turns out to be a
(perturbatively) bounded operator for the cases that the imaginary part of the
coupling constants have opposite sign, \Im(\zeta_+) = -\Im(\zeta_-). This in
particular contains the PT-symmetric case: \zeta_+ = \zeta_-^*. We also
calculate the energy expectation values for certain Gaussian wave packets to
study the nonlocal nature of $\rh$ or equivalently the non-Hermitian nature of
$\rH$. We show that these physical quantities are not directly sensitive to the
presence of PT-symmetry.
