  A class of one-dimensional reflectionless potentials, an absolute
transparency of which is concerned with their belonging to one SUSY-hierarchy
with a constant potential, is studied. An approach for determination of a
general form of the reflectionless potential on the basis of construction of
such a hierarchy by the recurrent method is proposed. A general form of
interdependence between superpotentials with neighboring numbers of this
hierarchy, opening a possibility to find new reflectionless potentials, have a
simple analytical view and are expressed through finite number of elementary
functions (unlike some reflectionless potentials, which are constructed on the
basis of soliton solutions or are shape invariant in one or many steps with
involving scaling of parameters, and are expressed through series), is
obtained. An analysis of absolute transparency existence for the potential
which has the inverse power dependence on space coordinate (and here tunneling
is possible), i.e. which has the form $V(x) = \pm \alpha / |x-x_{0}|^{n}$
(where $\alpha$ and $x_{0}$ are constants, $n$ is natural number), is
fulfilled. It is shown that such a potential can be reflectionless at n = 2
only. A SUSY-hierarchy of the inverse power reflectionless potentials is
constructed. Isospectral expansions of this hierarchy is analyzed.
