Neo 1973 Battery
The battery is a one 3.7V (nominal) cell. It has internal protection circuitry, and a capacity of 1200mAh.
On the battery, which has dimensions of approximately 53mm*38mm*7mm is written "FIC, First International Computer, Model: GTC-01/GTA-01, Standard Battery Pack, 1200mAh Li-ion, Rechargeable Battery: 3.7V".
It is apparently compatible with the Nokia BL-5C See this mailing list post These are available very inexpensively from ebay. Though quality will of course vary. However, currently Neo1973 won't charge BL-C5 batteries.
BL-5C battery will work in Neo, but not the other way around. Battery is too thick for Nokia, and attempting to use Neo battery in nokia will result in Nokia entering strange "test mode". This is because of the pack supervisor chip (the small chip in all Li-* batteries that takes care of charging the pack properly) which also contains some identification data (e.g. serial number, part number etc.), which identification data Nokia uses to perform several tasks, such as entering the aforementioned test mode. If you look in the Nokia service manuals, you will see that the debug rig for mostly all Nokia phones includes a so-called "debug battery adapter" which fits inside the phone, instead of the battery, but replies with a special identification when inquired by the phone upon boot, thus triggering "test mode".
This is also the reason why Nokia phones (and, presumably, all Nokia standalone smart-chargers) will refuse to charge a Neo1973 battery because it does not match the identification code expected by the phone firmware.
Nokia BL-6C is a bit thicker than BL-5C, but (almost?) identical in all other dimensions and electrically. Maybe it'll fit inside Neo too. The original BL-6C is 1070mAh compared to BL-5C 850mAh making it a slightly more interesting replacement battery. Could somebody confirm if it fits?
Neo1973 will happily run off 3 NiMH batteries, with thermistor disconnected.