  In the present work, we examine the role of central (C), spin-orbit (SO) and
tensor (T) components of two-nucleon interaction in the nuclear matrix elements
(NMEs) of the two-neutrino double beta decay ($2\nu\beta\beta$) and the light
neutrino-exchange mechanism of neutrinoless double beta decay
($0\nu\beta\beta$) of $^{48}$Ca in closure approximation and nonclosure
approach. The NMEs are calculated in the nuclear shell-model framework using
two-nucleon effective interaction GXPF1A used for $pf$ shell. The decomposition
of the shell model two-nucleon interaction into its individual components is
performed using the spin-tensor decomposition (STD). The NMEs for
$2\nu\beta\beta$ are calculated in running nonclosure method. The NMEs for
$0\nu\beta\beta$ are calculated with four different methods, namely, closure,
running closure, running nonclosure, and mixed method. Results show that the
magnitude of NMEs for $2\nu\beta\beta$ decreases about 7\% with the C+SO
component of the interaction as compared to the C component. The magnitude of
NMEs is further decreased about 9\% by adding T component to the C+SO
component. The NMEs of $0\nu\beta\beta$ calculated in running nonclosure method
are enhanced by about 8-10\%, 8-10\%, and 9-12\%, respectively, as compared to
corresponding NMEs calculated in running closure method with C, C+SO components
and total (C+SO+T) GXPF1A interaction for different SRC parametrization. For
both $2\nu\beta\beta$ and $0\nu\beta\beta$, the NMEs calculated with C+SO
component is in opposite phase with the NMEs calculated with C component and
the total GXPF1A interaction.
