section_path: Charge radius
section_name: Charge radius
paragraph_text: Charge radius
  
  The CODATA recommended value of a proton's charge radius is 8.4075(64) × 10 m. The radius of the proton is defined by a formula that can be calculated by quantum electrodynamics and be derived from either atomic spectroscopy or by electron–proton scattering. The formula involves a form-factor related to the two-dimensional parton diameter of the proton.
  
  A value from before 2010 is based on scattering electrons from protons followed by complex calculation involving scattering cross section based on Rosenbluth equation for momentum-transfer cross section), and based on studies of the atomic energy levels of hydrogen and deuterium.In 2010 an international research team published a proton charge radius measurement via the Lamb shift in muonic hydrogen (an exotic atom made of a proton and a negatively charged muon). As a muon is 200 times heavier than an electron, resulting in a smaller atomic orbital, it is much more sensitive to the proton's charge radius and thus allows a more precise measurement. Subsequent improved scattering and electron-spectroscopy measurements agree with the new small radius. Work continues to refine and check this new value.