  The Galactic Center has been under intense scrutiny in the recent years thanks to the unprecedented missions aiming at measuring the gas and star dynamics near the supermassive black hole (SMBH) and at finding gravitational wave (GW) signatures of inspiralling stellar black holes. In the crowded environment of galactic nuclei, the two-body interactions alter the distribution of stars on long timescales, making them drift in energy and angular momentum. We present a simplified analytical treatment of the scattering processes in galactic stellar nuclei, assuming all stars have the same mass. We have discussed how the interplay between two-body relaxation and gravitational wave emission modifies the slope of the inner stellar cusp within the SMBH sphere of influence, and calculated the rates of tidal disruption events (TDEs) and main-sequence extreme-mass ratio inspirals (MS-EMRIs) of stars that are tidally disrupted by the SMBH. We find that typically the ratio of the TDE and MS-EMRI rates is the square of the ratio of the tidal and Schwarzschild radii. For our Galaxy, this implies that the rate of MS-EMRIs is just about a percent of the TDE rate. We then consider the role of stars injected on highly eccentric orbits in the vicinity of the SMBH due to Hills binary disruption mechanism, and show that the MS-EMRI rate can almost approach the TDE rate if the binary fraction at the SMBH influence radius is close to unity. Finally, we discuss that physical stellar collisions affect a large area of phase space. 
Tidal disruption events, main-sequence extreme-mass ratio inspirals and   binary star disruptions in galactic nuclei