Neutron-star radii provide useful information on the equation of state of neutron rich matter .
Particularly interesting is the density dependence of the equation of state ( EOS ) .
For example , the softening of the EOS at high density , where the pressure rises slower than anticipated , could signal a transition to an exotic phase .
However , extracting the density dependence of the EOS requires measuring the radii of neutron stars for a broad range of masses .
A “ normal ” 1.4 M _ { \odot } ( M _ { \odot } =solar mass ) neutron star has a central density of a few times nuclear-matter saturation density ( \rho _ { 0 } ) .
In contrast , low mass ( \simeq 0.5 M _ { \odot } ) neutron stars have central densities near \rho _ { 0 } so its radius provides information on the EOS at low density .
Unfortunately , low-mass stars are rare because they may be hard to form .
Instead , a precision measurement of nuclear radii on atomic nuclei may contain similar information .
Indeed , we find a strong correlation between the neutron radius of ^ { 208 } Pb and the radius of a 0.5 M _ { \odot } neutron star .
Thus , the radius of a 0.5 M _ { \odot } neutron star can be inferred from a measurement of the the neutron radius of ^ { 208 } Pb .
Comparing this value to the measured radius of a \simeq 1.4 M _ { \odot } neutron star should provide the strongest constraint to date on the density dependence of the equation of state .