NOVELTY - A lithium secondary battery has an active material layer containing active material particles (10) and provided on a collector. The active material particles are secondary particles (14) formed by aggregating primary particles (12) of lithium transition metal oxide. The active material particles have hollow structure with hollow portion (16) formed inside secondary particles, and a shell portion (15). The ratio of the half value width (A) of diffraction peak of plane (003) and half value width (B) of diffraction peak of (104) plane of active material particles is 0.7 or less.    USE - Lithium secondary battery used as power supply for personal computer, portable terminals, electric vehicles and hybrid vehicles.    ADVANTAGE - The lithium secondary battery has high output even in low state of charge (SOC) region.    DETAILED DESCRIPTION - A lithium secondary battery has an active material layer containing active material particles and provided on a collector. The active material particles are secondary particles formed by aggregating two or more primary particles of lithium transition metal oxide. The active material particles have hollow structure with hollow portion formed inside secondary particles, and a shell portion surrounding the hollow portion. A through-hole (18) penetrated from the outside to hollow portion is formed in the secondary particles. The ratio of the half value width (A) of diffraction peak of plane (003) and half value width (B) of diffraction peak of (104) plane of active material particles is 0.7 or less, measured by powder X-ray diffraction. An INDEPENDENT CLAIM is included for manufacture of active material particles. An ammonium ion is supplied to the aqueous solution of transition metal compound. The aqueous solution contains at least one transition metal element, and particles of transition-metal hydroxide are deposited from aqueous solution. The transition-metal hydroxide and lithium compound are mixed and baked at 700-1000 degrees C to obtain active material particles. The molar ratio of lithium and total of other metallic element (M) is 1.05-1.2.    DESCRIPTION OF DRAWING(S) - The drawing shows the sectional view of active material particles.    Active material particles (10)    Primary particles (12)    Secondary particles (14)    Shell portion (15)    Hollow portion (16)    Through-hole (18)