XXXVII.—The Van der Waals Force between a Proton and a Hydrogen Atom. II. Excited States

1948 ◽  
Vol 62 (3) ◽  
pp. 360-368 ◽  
Author(s):  
C. A. Coulson ◽  
C. M. Gillam
Keyword(s):  
Hydrogen Atom ◽  
Closed Form ◽  
Interaction Energy ◽  
Excited States ◽  
Internuclear Distance ◽  
Van Der Waals ◽  
Quantum States ◽  
Van Der Waals Force ◽  
Image Position

SummaryThe interaction energy, or Van der Waals force, between a proton and a hydrogen atom in any one of its allowed quantum states is calculated in terms of the internuclear distance R by an expansion of the formAll the coefficients up to and including E5 are obtained in closed form. For values of R for which the expansion is valid, the coefficients are determined absolutely, no approximations being introduced.

II.—The Van der Waals Force between a Proton and a Hydrogen Atom

1941 ◽  
Vol 61 (1) ◽  
pp. 20-25 ◽  
Author(s):  
C. A. Coulson
Keyword(s):  
Hydrogen Atom ◽  
Power Series ◽  
Interaction Energy ◽  
Van Der Waals ◽  
Ground States ◽  
Van Der Waals Forces ◽  
Van Der Waals Force ◽  
Hydrogen Atoms ◽  
Nuclear Separation

The calculation of Van der Waals forces has acquired considerable interest recently through the work of Buckingham, Knipp and others (Buckingham, 1937; Knipp, 1939). In these papers the interaction energy between two atoms is expressed as a power series in i/R, where R is the nuclear separation, and the various terms in this series are known as dipole-dipole, dipole-quadrupole, quadrupole-quadrupole, etc… interactions. In most cases only approximate values are obtainable for the coefficients in this series, though for two hydrogen atoms in their ground states, Pauling and Beach (1935) have determined the magnitudes correct to about I in 106. In this paper we discuss the simplest possible problem of this nature, i.e. the force between a bare proton and a normal unexcited hydrogen atom. We shall show that a rigorous determination of the coefficients in the power series can be made.

scholarly journals Oscillator Representation and Generalized van der Waals Hamiltonians

1997 ◽  
Vol 12 (16) ◽  
pp. 1193-1207
Author(s):  
M. Dineykhan
Keyword(s):  
Hydrogen Atom ◽  
Excited States ◽  
Ground State ◽  
Van Der Waals ◽  
Bound State ◽  
Oscillator Strengths ◽  
Uniform Electric Field ◽  
Oscillator Representation ◽  
Representation Method ◽  
Oscillator Representation Method

The oscillator representation method is extended to calculate the energy spectrum of bound state systems described by axially symmetrical potentials in the parabolic system coordinates. In particular, it is applied to calculate the energy of the ground and excited states of the hydrogen atom in the uniform electric field and van der Waals field. The method gives the perturbation formulas for the analytic spectrum of the hydrogen atom in the generalized van der Waals field and defines oscillator strengths for transitions from the ground state to the perturbed manifold n=10, m=0.

scholarly journals On steady states of van der Waals force driven thin film equations

2007 ◽  
Vol 18 (2) ◽  
pp. 153-180 ◽  
Author(s):  
HUIQIANG JIANG ◽  
WEI-MING NI
Keyword(s):  
Continuous Solution ◽  
Van Der Waals ◽  
Neumann Boundary ◽  
Steady States ◽  
Van Der Waals Force ◽  
Smooth Solutions ◽  
Thin Film Equations ◽  
Radially Symmetric Solutions ◽  
Bounded Smooth ◽  
Image Position

Let $\Omega\subset\mathbb{R}^{N}$, N ≥2 be a bounded smooth domain and α > 1. We are interested in the singular elliptic equation with Neumann boundary conditions. In this paper, a complete description of all continuous radially symmetric solutions is given. In particular, we construct nontrivial smooth solutions as well as rupture solutions. Here a continuous solution is said to be a rupture solution if its zero set is nonempty. When N = 2 and α = 3, the equation is used to model steady states of van der Waals force driven thin films of viscous fluids. We also consider the physical problem when total volume of the fluid is prescribed.

scholarly journals First-Principles Study on Graphene/Mg2Si Interface of Selective Laser Melting Graphene/Aluminum Matrix Composites

Metals ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 941
Author(s):  
Zhanyong Zhao ◽  
Shijie Chang ◽  
Jie Wang ◽  
Peikang Bai ◽  
Wenbo Du ◽  
...  
Keyword(s):  
Interfacial Energy ◽  
First Principles ◽  
Lattice Mismatch ◽  
Van Der Waals ◽  
Aluminum Matrix ◽  
Van Der Waals Force ◽  
Aluminum Matrix Composites ◽  
Matrix Composites ◽  
Charge Density Difference ◽  
Interface Charge

The bonding strength of a Gr/Mg2Si interface was calculated by first principles. Graphene can form a stable, completely coherent interface with Mg2Si. When the (0001) Gr/(001) Mg2Si crystal plane is combined, the mismatch degree is 5.394%, which conforms to the two-dimensional lattice mismatch theory. At the interface between Gr/Mg2Si, chemical bonds were not formed, there was only a strong van der Waals force; the interfaces composed of three low index surfaces (001), (011) and (111) of Mg2Si and Gr (0001) have smaller interfacial adhesion work and larger interfacial energy, the interfacial energy of Gr/Mg2Si is much larger than that of α-Al/Al melt and Gr/Al interfacial (0.15 J/m2, 0.16 J/m2), and the interface distance of a stable interface is larger than the bond length of a chemical bond. The interface charge density difference diagram and density of states curve show that there is only strong van der Waals force in a Gr/Mg2Si interface. Therefore, when the Gr/AlSi10Mg composite is stressed and deformed, the Gr/Mg2Si interface in the composite is easy to separate and become the crack propagation source. The Gr/Mg2Si interface should be avoided in the preparation of Gr/AlSi10Mg composite.

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