The amazing fact of the reality of the spectra of certain PT -
symmetric (i.e., parity times time-reversal symmetric) quantum
mechanical systems as conjectured by Bessis, Zinn-Justin, Bender and
Boettcher and as first proved by P. Dorey, C. Dunning and R. Tateo
(cf. J. Phys. A: Math. Gen. 34 (2001) 5679–5704) inspired not only a
quick development of the so called  PT - symmetric quantum mechanics
of bound states (cf. [13] or [15] for thorough reviews, or an older
paper [11] for the general theory) but also a disappointing failure
of an attempted extension of this theory to the models of scattering
(cf. [17] and [20] for an explanation).

Two ways our of the difficulty have been proposed. Along one of them
(cf. M. Znojil, ``Scattering theory using smeared non-Hermitian
potentials", Phys. Rev. D. 80 (2009) 045009) one satisfies all of
the standard physical requirements of the causality and unitarity of
the scattering by means of the assumption that the PT - symmetric
potentials must be allowed slightly, selfconsistently non-local.
Alternatively, the parallel path of study of the strictly local PT -
symmetric scattering potentials still survives as a fully legal
means of an effective description of specific open quantum systems
where the necessary loss of unitarity is simply attributed to some
hidden effects of the environment.

The authors proceed along the second, pragmatic line of research.
They extend their results presented in [16] to the relativistic
quantum mechanics. They contemplate the Dirac's equation with
different forms of the potentials (viz., scalars, pseudoscalars or
mixtures of scalars and vectors) and they combine the requirement of
the locality of the interaction with the supplementary requirement
of the PT - symmetry of the related asymptotic wave functions.
Naturally, the resulting scattering is reflectionless but the
absence of the reflection still makes the model asymptotically
meaningful.

The authors indicate that one could also extend the scattering
scenario to certain specific asymptotically large potentials  for
which the reflectionless scattering may proceed along the real axis
in a way shown feasible in [34]. We would like to add that the next
extension of the theory applies to virtually arbitrary
asymptotically large PT - symmetric potentials, requiring only that
the scattering proceeds along certain suitable, asymptotically
complex contours. The first concrete examples of such a type which
parallel the bound-state theory quite closely may be found, e.g., in
G. L\'{e}vai, P. Siegl and M. Znojil, ``Scattering in the
PT-symmetric Coulomb potential", J. Phys. A: Math. Theor. 42 (2009)
295201 or in M. Znojil, ``Spiked potentials and quantum toboggans",
J. Phys. A: Math. Gen. 39 (2006) 13325–13336.

MR2586146 Cannata, Francesco; Ventura, Alberto Reflectionless
$\scr{PT}$-symmetric potentials in the one-dimensional Dirac
equation. J. Phys. A 43 (2010), no. 7, 075305, 19 pp. 81Q12