That picture looks like a version of the Ray-O-Vac Sportsman (one of which I am holding now) or its Eveready equivalent. The first Eveready Big Jim was a 5 D-cell light, made in the late 1950's, which was the predecessor of the Mag lites in its style. I still have mine.
The Sportsman-type batteries are still sold, although the prices are a bit steep, running about $25-30 for the Ray-O-Vac version. The Duracell battery uses short "cells", giving less overall lifespan than the Eveready or Ray-O-Vac, which use full size F cells. These lights have long run-times which I haven't measured exactly but exceed two or more hours, with irregular, uneven beam patterns; the battery shelf-life is several years.
This style was an early water-resistant sealed beam light, and mine came with a swiveling, flashing rear bulb, and I have seen some without. Mine has no serial no. except on the battery, which is now made in China.
HAK