  In this work we investigate neutron stars (NS) in $f(\mathtt{R,L_m})$ theory
of gravity for the case $f(\mathtt{R,L_m}) = \mathtt{R} + \mathtt{L_m} +
\sigma\mathtt{R}\mathtt{L_m}$, where $\mathtt{R}$ is the Ricci scalar and
$\mathtt{L_m}$ the Lagrangian matter density. In the term
$\sigma\mathtt{R}\mathtt{L_m}$, $\sigma$ represents the coupling between the
gravitational and particles fields. For the first time the hydrostatic
equilibrium equations in the theory are solved considering realistic equations
of state and NS masses and radii obtained are subject to joint constrains from
massive pulsars, the gravitational wave event GW170817 and from the PSR
J0030+0451 mass-radius from NASA's Neutron Star Interior Composition Explorer
(${\it NICER}$) data. We show that in this theory of gravity, the mass-radius
results can accommodate massive pulsars, while the general theory of relativity
can hardly do it. The theory also can explain the observed NS within the radius
region constrained by the GW170817 and PSR J0030+0451 observations for masses
around $1.4~M_{\odot}$.
