Reduced mass definition

We may also apply the above expressions to polyatomic molecular ions. However, the effective reduced mass M of the oscillator in Equation 5 is a function of the definition of normal coordinate, and it is diffi-... 

Reduced mass comes from the definition of moment of inertia, which will be discussed shortly. 

At the same time a definite, radical lowering of the frequency and amplitude of the oscillations was noted. Such reduction in oscillation reduces mass-transfer rates. 

Another contribution due to nuclear properties is the so-called recoil contribution. It takes into account the finite mass of the nucleus even beyond the non-relativistic reduced mass approximation. Up to now there is a lack of calculations non-perturbatively in (Za) which exist only for the QED corrections of order (a/n) up to now but would definitely be required for heavy systems. 

Isotope Effect. When an isotopic substitution is made in a diatomic molecule, the equilibrium bond length and the force constant k are unchanged, since they depend only on the behavior of the bonding electrons. However, the reduced mass ft does change, and this will affect the rotation and vibration of the molecule. In the case of rotation, the isotope effect can be easily stated. From the definitions of B and I, we see that... 

This review shows how the photochemistry of ketones can be rationalized through a single model, the Tunnel Effect Theory (TET), which treats reactions of ketones as radiationless transitions from reactant to product potential energy curves (PEC). Two critical approximations are involved in the development of this theory (i) the representation of reactants and products as diatomic harmonic oscillators of appropriate reduced masses and force constants (ii) the definition of a unidimensional reaction coordinate (RC) as the sum of the reactant and product bond distensions to the transition state. Within these approximations, TET is used to calculate the reactivity parameters of the most important photoreactions of ketones, using only a partially adjustable parameter, whose physical meaning is well understood and which admits only predictable variations. 

The definitions (30,11) and (31.11) also hold for the cross sections of inelastic and reactive scattering in which the particles before and after the collision have different internal states and/or different compositions. Then, the letters i and j may be used to represent two sets of qusmttmi numbers for the initial state (separated reactants) and for the final state (separated products), respectively, in which also the reduced masses i and j ) and the relative velocities (v and v ) are generally different. 

The Schrodinger equation gives only the stationary states (the ground state and the excited ones), which live forever. It cannot describe, therefore, the annihilation process, but it is able to describe the positronium before the annihilation takes place. This equation for the positronium is identical to that for the hydrogen atom, except that the reduced mass changes from /i 1 a.u. to /T = 2 a.u. ( = Y + Y = 2). As a result (see the definition of oq on p. 202), one may say that the size of the orbitals of the positronium doubles when compared to that of the... 

The other main avenue to tackle the A-particle quantum problem with Pis focuses on the so-called pair product actions. These are approaches that have been proven to be very cost effective, as relatively low P discretizations work excellently well. Besides, the use of pair actions has led to a deep understanding of helium and the system of hard spheres at low temperatures [83-108]. Clear indications of how to proceed along this line were given by Barker in his pioneering work on quantum hard spheres (QHS) [24], Klemm and Storer [83], and Ceperley [28]. Essentially, this sort of approach consists of representing the V-particle density matrix through a product of density matrices, which includes those of the free particles and those of the reduced masses of every pair of particles. The potential is assumed pair-wise additive and, for definiteness, P time slices in... 

To understand polymer structure, polymers are often dissolved in appropriate solvents, allowing molecular weight or degree of polymerization to be determined from dilute solution viscosity. The relative viscosity, is the ratio of solution viscosity to that of the solvent. The specific viscosity, is the ratio of the difference in solution and solvent viscosities divided by the solvent viscosity. These dimensionless quantities are often divided by the mass concentration of the polymer to obtain several additional terms that have units of dilution or volume per unit mass concentration the reduced viscosity, which is ratio of the relative viscosity to the concentration the inherent viscosity, which is the ratio of the natural logarithm of the relative viscosity and the intrinsic viscosity, [77], which is the common limiting value of the reduced (Huggins definition) or inherent (Craemer s definition) viscosity at infinite dilution of the polymer. The intrinsic viscosity is a concentration ratio it has been used to estimate molecular... 

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