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Ionization injection in a laser-plasma accelerator is studied analytically and by multi-dimensional particle-in-cell (PIC) simulations. To enable the production of low energy spread beams, we consider a short region containing a high atomic number gas (e.g., nitrogen) for ionization-induced trapping, followed by a longer region using a low atomic number gas (e.g., hydrogen), that is, free of additional trapping, for post acceleration. For a broad laser pulse, ionization injection requires a minimum normalized laser field of a0≃1.7, assuming a resonant Gaussian laser pulse. Effects of gas mix parameters, including species, concentration, and length of the mixture region, on the final electron injection number and beam quality are studied. The minimum energy spread is determined by the spread in initial ionized phases of the electrons in the wakefield due to the tunneling ionization process within the laser pulse. Laser polarization and intensity effects on injection number and final electron emittance are examined. Two-dimensional PIC simulations are used to study the ionization injection process and the transverse beam structure. With proper laser-plasma parameters, mono-energetic electron beams with 10 pC charge, a central energy at GeV level, and energy spread less than 1% can be produced in a mixed gas with ionized electron density of 1018cm-3. Lower density can give a higher final accelerated beam energy and reduce the final relative energy spread even further.