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NMR Conditions and Biological Systems
Published in Andrew A. Marino, Modern Bioelectricity, 2020
E. Aarholt, M. Jaberansari, A.H. Jafary-Asl, P.N. Marsh, C.W. Smith
A fundamental postulate of theoretical physics is that the total angular momentum of an isolated particle can only take on certain discrete values. It is said to be quantized, and can only have values which are integral multiples of the quantity h/2π, often written, where ħ, is Planck’s constant (6.626176 × 10−34 J.sec). The nuclear energy levels are quantized as a direct result of the quantized nature of the nuclear angular momentum. It takes on a series of values corresponding to unity changes in a quantity known as the spin quantum number I, which can range from +I to -I. Since the proton has I = 1/2, only the two values corresponding to I = ±1/2 are allowed. The value of I depends on the particular nucleus. Isotopes with equal numbers of protons and neutrons have I = 0 and isotopes having odd mass numbers tend to have 1/2 integral spin values. The highest value is for the isotope 17671Lu, for which I= 6.
Newton’s laws of motion
Published in Paul Grimshaw, Michael Cole, Adrian Burden, Neil Fowler, Instant Notes in Sport and Exercise Biomechanics, 2019
The angular analogue of Newton’s first law states that the angular momentum of a body will remain constant unless the body is acted upon by an external torque. At this point it is particularly important to stress that angular momentum is related to a particular axis of rotation. If the body that is being considered is made up of several parts, then the total angular momentum is the sum of all the individual momenta of each body part (that is acting about the same axis of rotation).
Fundamentals
Published in Mike Tooley, Lloyd Dingle, Engineering Science, 2020
The law of conservation of angular momentum is given as: The total angular momentum of a mass system, rotating in a particular direction, remains constant; provided that the moments of inertia of the rotating masses remain unaltered and that no external torques act on the system.
The fine and hyperfine structures of the low-n 3Π u Rydberg states of H2 revisited
Published in Molecular Physics, 2022
For non-specialists we recall here that the theory of diatomic molecules frequently refers to the coupling cases (a), (b), (c), (d) and (e) introduced by Hund [15]. These are most easily distinguished by the way the rotational energy levels are arranged in a given electronic state. Thus one has , , , , , respectively, for Hund's cases (a) to (e), where B is the rotational constant and J, N, , and are the total angular momentum of the molecule (exclusive of nuclear spins), the total angular momentum without electron spin, the total angular momentum of the cation without electron spin, and the total angular momentum of the cation including electron spin. Case (c) behaves like case (a), but unlike in case (a), the total electron spin S is not assumed to be a good quantum number.
The interaction of methylene with molecular hydrogen: potential energy surface and inelastic collisions
Published in Molecular Physics, 2021
The fine-structure splittings in CH() are much smaller than the rotational spacings [4]. Hence. we can compute cross sections between the rotational/fine-structure levels by the recoupling method [12,13]. In this approach, T matrix elements for which the electron spin is included are derived from spin-free T matrix elements. We denote the total angular momentum of the collision complex with inclusion of the electron spin ; equals J + s, where J is the total angular momentum excluding the electron spin of the collisioncomplex.
Theoretical approaches for doubly-excited Rydberg states in quasi-two-electron systems: two-electron dynamics far away from the nucleus
Published in Molecular Physics, 2021
Rydberg states are associated with electrons promoted to atomic orbitals that are much larger in size than the residual ion ‘core’. Rydberg electrons are labelled by their principal quantum number n, orbital-angular-momentum quantum number l and total-angular-momentum quantum number j. In the following, we distinguish three different types of Rydberg states: (i) singly-excited Rydberg states, in which one electron is in a Rydberg orbital and the ion core is in its electronic ground state; (ii) core-excited Rydberg states, in which one electron is in a Rydberg orbital and the ion core is in a low-lying excited electronic state; (iii) doubly-excited Rydberg states, where two electrons are in Rydberg orbitals. These three types of Rydberg states possess distinctive physical properties that are detailed below for the case of quasi-two-electron atoms.