Nuclear density

Nuclear density is the density of the nucleons (neutrons and protons) in the nucleus. For heavy nuclei, it is close to the nuclear saturation density n_0=0.15\pm0.01 nucleons/fm 3 , which minimizes the energy density of an infinite nuclear matter. The nuclear saturation mass density is thus \rho_0=n_0 m_{\rm u} \approx 2.5\times10^{17} kg/m 3 , where m u is the atomic mass constant. The descriptive term nuclear density is also applied to situations where similarly high densities occur, such as within neutron stars.

Nuclear density is the density of the nucleons (neutrons and protons) in the nucleus. For heavy nuclei, it is close to the nuclear saturation density n_0=0.15\pm0.01 nucleons/fm 3 , which minimizes the energy density of an infinite nuclear matter. The nuclear saturation mass density is thus \rho_0=n_0 m_{\rm u} \approx 2.5\times10^{17} kg/m 3 , where m u is the atomic mass constant. The descriptive term nuclear density is also applied to situations where similarly high densities occur, such as within neutron stars. R=A^{1/3}R_0 where A is the mass number and R_0 is 1.25 fm, with typical deviations of up to 0.2 fm from this value. The number density of the nucleus is thus: n = \frac{A}{{4\over 3} \pi R^3} The density for any typical nucleus, in terms of mass number, is thus constant, not dependent on A or R, theoretically: n_0^\mathrm{theor} = \frac{A}{{4\over 3} \pi (A^{1/3}R_0)^3} = \frac{3}{4 \pi (1.25\ \mathrm{fm})^3} = 0.122 \ \mathrm{fm}^{-3} = 1.22 \times 10^{44} \ \mathrm{m}^{-3} The experimentally determined value for the nuclear saturation density is n_0^\mathrm{exp}=0.15\pm0.01\ \mathrm{fm}^{-3} = (1.5\pm 0.1)\times 10^{44}\ \mathrm{m}^{-3}. The mass density ρ is the product of the number density n by the particle's mass. The calculated mass density, using a nucleon mass of m n =1.67×10 −27 kg, is thus: \rho_0^\mathrm{theor}=m_\mathrm{n}\,n_0^\mathrm{theor} \approx 2 \times 10^{17} \ \mathrm{kg} \ \mathrm{m}^{-3} (using the theoretical estimate) or \rho_0^\mathrm{exp}=m_\mathrm{n}\,n_0^\mathrm{exp} \approx 2.5 \times 10^{17} \ \mathrm{kg} \ \mathrm{m}^{-3} (using the experimental value). ==See also== ==References== ==External links== (derivation of equations and other mathematical descriptions)

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