In this work we study a phenomenological non-gravitational interaction between dark matter and dark energy .
The scenario studied in this work extends the usual interaction model proportional to the derivative of the dark component density adding to the coupling a non-linear term of the form Q = \rho ^ { \prime } / 3 ( \alpha + \beta \rho ) .
This dark sector interaction model could be interpreted as a particular case of a running vacuum model of the type \Lambda ( H ) = n _ { 0 } + n _ { 1 } H ^ { 2 } + n _ { 2 } H ^ { 4 } in which the vacuum decays into dark matter .
For a flat FRW Universe filled with dark energy , dark matter and decoupled baryonic matter and radiation we calculate the energy density evolution equations of the dark sector and solve them .
The different sign combinations of the two parameters of the model show clear qualitative different cosmological scenarios , from basic cosmological insights we discard some of them .
The linear scalar perturbation equations of the dark matter were calculated .
Using the CAMB code we calculate the CMB and matter power spectra for some values of the parameters \alpha and \beta and compare it with \Lambda CDM .
The model modify mainly the lower multipoles of the CMB power spectrum remaining almost the same the high ones .
The matter power spectrum for low wave numbers is not modified by the interaction but after the maximum it is clearly different .
Using observational data from Planck , and various galaxy surveys we obtain the constraints of the parameters , the best fit values obtained are the combinations \alpha = ( 3.7 \pm 7 ) \times 10 ^ { -4 } , - ( 1.5 \times 10 ^ { -5 } { eV } ^ { -1 } ) ^ { 4 } \ll \beta < ( 0.07 { eV } ^ { -1 } ) ^ { 4 } .