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Nuclear density is the density of the nucleus of an atom. For heavy nuclei, it is close to the nuclear saturation density n 0 = 0.15 ± 0.01 {\displaystyle n_{0}=0.15\pm 0.01} nucleons / fm 3 , which minimizes the energy density of an infinite nuclear matter . [ 1 ]
Model-independent analyses of nuclear charge densities for both He-3 and He-4, for example, indicate a significant central depression within a radius of 0.8 fm. [4] Other light nuclides, including carbon-12 and oxygen-16, exhibit similar off-center charge density maxima.
The rms charge radius is a measure of the size of an atomic nucleus, particularly the proton distribution. The proton radius is about one femtometre = 10 −15 metre. It can be measured by the scattering of electrons by the nucleus. Relative changes in the mean squared nuclear charge distribution can be precisely measured with atomic spectroscopy.
The Voronoi cell of atom A is therefore the region of space closer to nucleus A than to any other nucleus. Furthermore, ρ(r) is the electron density of the molecule and Σ B ρ B (r) the superposition of atomic densities ρ B of a fictitious promolecule without chemical interactions that is associated with the situation in which all atoms are ...
The stable nucleus has approximately a constant density and therefore the nuclear radius R can be approximated by the following formula, R = r 0 A 1 / 3 {\displaystyle R=r_{0}A^{1/3}\,} where A = Atomic mass number (the number of protons Z , plus the number of neutrons N ) and r 0 = 1.25 fm = 1.25 × 10 −15 m.
While the total number of "catalytic" nuclei are conserved in the cycle, in stellar evolution the relative proportions of the nuclei are altered. When the cycle is run to equilibrium, the ratio of the carbon-12/carbon-13 nuclei is driven to 3.5, and nitrogen-14 becomes the most numerous nucleus, regardless of initial composition.
However, a helium nucleus weighs less than the sum of the weights of the two heavy hydrogen nuclei which combine to make it. [6] The same is true for carbon, nitrogen and oxygen. For example, the carbon nucleus is slightly lighter than three helium nuclei, which can combine to make a carbon nucleus. This difference is known as the mass defect.
When charged particles move in electric and magnetic fields the following two laws apply: Lorentz force law: = (+),; Newton's second law of motion: = =; where F is the force applied to the ion, m is the mass of the particle, a is the acceleration, Q is the electric charge, E is the electric field, and v × B is the cross product of the ion's velocity and the magnetic flux density.