  We investigate $IPA$ - real closed fields, that is, real closed fields which
admit an integer part whose non-negative cone is a model of Peano Arithmetic.
We show that the value group of an $IPA$ - real closed field is an exponential
group in the residue field, and that the converse fails in general. As an
application, we classify (up to isomorphism) value groups of countable
recursively saturated exponential real closed fields. We exploit this
characterization to construct countable exponential real closed fields which
are not $IPA$ - real closed fields.
