  We consider one loop quantum corrections to soliton mass for the ${\cal N}=1$
supersymmetric extension of the (1+1)-dimensional scalar field theory with the
potential $U(\phi) = \phi^2 \cos^2\left(\ln \phi^2\right)$. First, we compute
the one loop quantum soliton mass correction of the bosonic sector. To do that,
we regularize implicitly such quantity by subtracting and adding its
corresponding tadpole graph contribution, and use the renormalization
prescription that the added term vanishes with the corresponding counterterms.
As a result we get a finite unambiguous formula for the soliton quantum mass
corrections up to one loop order. Afterwards, the computation for the
supersymmetric case is extended straightforwardly and we obtain for the one
loop quantum correction of the SUSY kink mass the expected value previously
derived for the SUSY sine-Gordon and $\phi^4$ models. However, we also have
found that for a particular value of the parameters, contrary to what was
expected, the introduction of supersymmetry in this model worsens ultraviolet
divergences rather than improving them.
