We discuss the physics potential of intermediate L \sim 20 \div 30 km baseline experiments at reactor facilities , assuming that the solar neutrino oscillation parameters \Delta m ^ { 2 } _ { \odot } and \theta _ { \odot } lie in the high-LMA solution region . We show that such an intermediate baseline reactor experiment can determine both \Delta m ^ { 2 } _ { \odot } and \theta _ { \odot } with a remarkably high precision . We perform also a detailed study of the sensitivity of the indicated experiment to \Delta m ^ { 2 } _ { atm } , which drives the dominant atmospheric \nu _ { \mu } ( \bar { \nu } _ { \mu } ) oscillations , and to \theta - the neutrino mixing angle limited by the data from the CHOOZ and Palo Verde experiments . We find that this experiment can improve the bounds on \sin ^ { 2 } \theta . If the value of \sin ^ { 2 } \theta is large enough , \sin ^ { 2 } \theta \mathrel { \hbox to 0.0 pt { \raise 2.1973 pt \hbox { $ > $ } } { \lower 2.1973 % pt \hbox { $ \sim$ } } } 0.02 , the energy resolution of the detector is sufficiently good and if the statistics is relatively high , it can determine with extremely high precision the value of \Delta m ^ { 2 } _ { atm } . We also explore the potential of the intermediate baseline reactor neutrino experiment for determining the type of the neutrino mass spectrum , which can be with normal or inverted hierarchy . We show that the conditions under which the type of neutrino mass hierarchy can be determined are quite challenging , but are within the reach of the experiment under discussion .