  An impurity in a Bose gas is commonly referred to as Bose polaron. For a
dilute Bose gas its properties are expected to be universal, that is dependent
only on a few parameters characterizing the boson-impurity interactions. When
boson-impurity interactions are weak, it has been known for some time that the
properties of the polaron depend only on the scattering length of these
interactions. In this paper which accompanies and extends Ref. [Phys. Rev.
Lett. 126, 123403 (2021)] (where some of these results have already been
reported) we examine stronger boson-impurity interactions, keeping their range
finite. We demonstrate that for attractive interactions between impurity and
the bosons up to and including the unitary point of these interactions, all
static properties of a Bose polaron in a dilute Bose gas can be calculated in
terms of the scattering length and an additional parameter which characterizes
the range of the impurity-boson interactions. We show that our approach to this
problem is valid if this parameter does not deviate too much from the
scattering length of intra-boson interactions, with the precise criterion given
in the text. We produce explicit expressions for the energy and other
properties of polaron for the case when the impurity-boson scattering length is
tuned to unitarity, and we also provide the first correction away from it.
