In nuclear physics, the symmetry energy reflects the variation of the binding energy of the nucleons in the nuclear matter depending on its neutron to proton ratio as a function of baryon density. Symmetry energy is an important parameter in the equation of state describing the nuclear structure of heavy nuclei and neutron stars.
Definition Let n p {\displaystyle n_{p}} and n n {\displaystyle n_{n}} be the number density of protons and neutrons in nuclear matter, and n = n p + n n {\displaystyle n=n_{p}+n_{n}} . Let E 0 ( n ) {\displaystyle E_{0}(n)} be the binding energy per nucleon in symmetric matter, with equally many protons as neutrons, as a function of density. The binding energy per nucleon E {\displaystyle E} of non-symmetric matter is then a function that also depends on the isospin asymmetry,
δ = n p − n n n {\displaystyle \delta ={\frac {n_{p}-n_{n}}{n}}}
so to lowest order the energy per baryon is
E ( n , δ ) = E 0 ( n ) + S ( n ) δ 2 + O ( δ 4 ) , {\displaystyle E(n,\delta )=E_{0}(n)+S(n)\delta ^{2}+O(\delta ^{4}),}
where S {\displaystyle S} is the symmetry energy. There are no odd powers of δ {\displaystyle \delta } in the expansion because the nuclear force acts the same between two protons as between two neutrons. At saturation density n 0 {\displaystyle n_{0}} , the symmetry energy is 32.0±1.1 MeV.
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