  Type I X-ray bursts are thermonuclear explosions on the neutron star (NS)
surface caused by mass accretion from a companion star. Observations of X-ray
bursts provide valuable information on X-ray binary systems, e.g., binary
parameters, the chemical composition of accreted matter, and the nuclear
equation of state (EOS) of NSs. There have been several theoretical studies to
constrain the physics of X-ray bursters. However, they have mainly focused on
the burning layers above the solid crust of the NS, which brings up issues of
the treatment of NS gravitation and internal energy. In this study, focusing on
the microphysics inside NSs, we calculate a series of X-ray bursts using a
general-relativistic stellar-evolution code with several NS EOSs. We compare
the X-ray-burst models with the burst parameters of a clocked burster
associated with GS 1826-24. We find a monotonic correlation between the NS
radius and the light-curve profile. A larger radius shows a higher recurrence
time and a large peak luminosity. In contrast, the dependence of light curves
on the NS mass becomes more complicated, where the neutrino cooling suppresses
the efficiency of nuclear ignition. We also constrain the EOS and mass of GS
1826-24, i.e., stiffer EOSs, corresponding to larger NS radii, are not
preferred due to too-high peak luminosity. The EOS and the cooling and heating
of NSs are important to discuss the theoretical and observational properties of
X-ray bursts.
