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In the present work, we examine the role of central (C), spin-orbit (SO) andtensor (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 lightneutrino-exchange mechanism of neutrinoless double beta decay($0\nu\beta\beta$) of $^{48}$Ca in closure approximation and nonclosureapproach. The NMEs are calculated in the nuclear shell-model framework usingtwo-nucleon effective interaction GXPF1A used for $pf$ shell. The decompositionof the shell model two-nucleon interaction into its individual components isperformed 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 themagnitude of NMEs for $2\nu\beta\beta$ decreases about 7\% with the C+SOcomponent of the interaction as compared to the C component. The magnitude ofNMEs is further decreased about 9\% by adding T component to the C+SOcomponent. The NMEs of $0\nu\beta\beta$ calculated in running nonclosure methodare enhanced by about 8-10\%, 8-10\%, and 9-12\%, respectively, as compared tocorresponding NMEs calculated in running closure method with C, C+SO componentsand total (C+SO+T) GXPF1A interaction for different SRC parametrization. Forboth $2\nu\beta\beta$ and $0\nu\beta\beta$, the NMEs calculated with C+SOcomponent is in opposite phase with the NMEs calculated with C component andthe total GXPF1A interaction.

Role of individual components of two-nucleon interaction in nuclear  matrix elements of $2\nu\beta\beta$ and $0\nu\beta\beta$ of $^\textbf{48}$Ca:  Beyond the closure approximation