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The following apply for the nuclear reaction: a + b ↔ R → c in the centre of mass frame , where a and b are the initial species about to collide, c is the final species, and R is the resonant state .
Magic numbers are typically obtained by empirical studies; if the form of the nuclear potential is known, then the Schrödinger equation can be solved for the motion of nucleons and energy levels determined. Nuclear shells are said to occur when the separation between energy levels is significantly greater than the local mean separation.
In nuclear physics, the Bateman equation is a mathematical model describing abundances and activities in a decay chain as a function of time, based on the decay rates and initial abundances. The model was formulated by Ernest Rutherford in 1905 [ 1 ] and the analytical solution was provided by Harry Bateman in 1910.
Nuclear reactions may be shown in a form similar to chemical equations, for which invariant mass must balance for each side of the equation, and in which transformations of particles must follow certain conservation laws, such as conservation of charge and baryon number (total atomic mass number). An example of this notation follows:
Woods–Saxon potential for A = 50, relative to V 0 with a = 0.5 fm and =. The Woods–Saxon potential is a mean field potential for the nucleons (protons and neutrons) inside the atomic nucleus, which is used to describe approximately the forces applied on each nucleon, in the nuclear shell model for the structure of the nucleus.
In physics and chemistry, specifically in nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI), and electron spin resonance (ESR), the Bloch equations are a set of macroscopic equations that are used to calculate the nuclear magnetization M = (M x, M y, M z) as a function of time when relaxation times T 1 and T 2 are present.
In nuclear physics, a decay product (also known as a daughter product, daughter isotope, radio-daughter, or daughter nuclide) is the remaining nuclide left over from radioactive decay. Radioactive decay often proceeds via a sequence of steps ( decay chain ).
A chart or table of nuclides maps the nuclear, or radioactive, behavior of nuclides, as it distinguishes the isotopes of an element.It contrasts with a periodic table, which only maps their chemical behavior, since isotopes (nuclides that are variants of the same element) do not differ chemically to any significant degree, with the exception of hydrogen.