Accelerator mass spectrometry (AMS) dimension. How come we are in need of AMS?

Accelerator mass spectrometry (AMS) dimension. How come we are in need of AMS? So that you can determine radiocarbon ages it is important to get the level of radiocarbon in an example. This dimension may be made either by calculating the radioactivity for the test (the standard beta-counting technique) or by straight counting the radiocarbon