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Neutron stars, produced at the death of massive stars, are often regarded asgiant neutron-rich nuclei. This picture is especially relevant for low-mass(below about solar mass) neutron stars, where non-nucleonic components are notexpected to occur. Due to the saturation property of nucleonic matter, leadingto the celebrated liquid-drop picture of atomic nuclei, empirical nuclearmasses and radii can be approximately expressed as function of atomic massnumber. It is, however, not straightforward to express masses and radii ofneutron stars even in the low-mass range where the structure is determined by abalance between the pressure of neutron-rich nucleonic matter and the gravity.Such expressions would be of great use given possible simultaneous mass andradius measurements. Here we successfully construct theoretical formulas forthe masses and radii of low-mass neutron stars from various models that areconsistent with empirical masses and radii of stable nuclei. In this process,we discover a new equation-of-state parameter that characterizes the structureof low-mass neutron stars. This parameter, which plays a key role in connectingthe mass-radius relation of the laboratory nuclei to that of the celestialobjects, could be constrained from future observations of low-mass neutronstars.

Mass and radius formulas for low-mass neutron stars