Two-parameter wave function for the helium sequence

1987 ◽  
Vol 64 (2) ◽  
pp. 128 ◽  
Author(s):  
Wai-Kee Li
Keyword(s):  
Wave Function ◽  
Two Parameter ◽  
Parameter Wave

The Polarizability of Molecular Hydrogen H2

1936 ◽  
Vol 32 (2) ◽  
pp. 260-264 ◽  
Author(s):  
C. E. Easthope
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Molecular Hydrogen ◽  
Applied Field ◽  
Minimum Energy ◽  
Wave Functions ◽  
The Other ◽  
System A ◽  
The One ◽  
Two Parameter

1. The problem of calculating the polarizability of molecular hydrogen has recently been considered by a number of investigators. Steensholt and Hirschfelder use the variational method developed by Hylleras and Hassé. For ψ0, the wave function of the unperturbed molecule when no external field is present, they take either the Rosent or the Wang wave function, while the wave functions of the perturbed molecule were considered in both the one-parameter form, ψ0 [1+A(q1 + q2)] and the two-parameter form, ψ0 [1+A(q1 + q2) + B(r1q1 + r2q2)], where A and B are parameters to be varied so as to give the system a minimum energy, q1 and q2 are the coordinates of the electrons 1 and 2 in the direction of the applied field as measured from the centre of the molecule, and r1 and r2 are their respective distances from the same point. Mrowka, on the other hand, employs a method based on the usual perturbation theory. Their numerical results are given in the following table.

QUARTETTING IN ATTRACTIVE FERMI-SYSTEMS AND ALPHA PARTICLE CONDENSATION IN NUCLEAR SYSTEMS

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2420-2428
Author(s):  
P. SCHUCK ◽  
Y. FUNAKI ◽  
H. HORIUCHI ◽  
G. RÖPKE ◽  
A. TOHSAKI ◽  
...  
Keyword(s):  
Transition Probability ◽  
Adjustable Parameter ◽  
Low Density ◽  
Hoyle State ◽  
Fermi Systems ◽  
Nuclear Systems ◽  
Physical Quantities ◽  
Two Parameter ◽  
Parameter Wave ◽  
Α Particles

The famous Hoyle state (02+ at 7.654 MeV in 12 C ) is identified as being an almost ideal condensate of three α-particles, hold together only by the Coulomb barrier. It, therefore, has a 8 Be -α structure of low density. Transition probability and inelastic form factor together with position and other physical quantities are correctly reproduced without any adjustable parameter from our two parameter wave function of α-particle condensate type. The possibility of the existence of α-particle condensed states in heavier nα nuclei is also discussed.

The interpolation of atomic fields

1955 ◽  
Vol 51 (4) ◽  
pp. 693-701 ◽  
Author(s):  
E. Cicely Ridley
Keyword(s):  
Wave Function ◽  
Atomic Number ◽  
Periodic Table ◽  
Published Data ◽  
Parameter Method ◽  
Screening Constant ◽  
Unknown Structure ◽  
Good For ◽  
Two Parameters ◽  
Two Parameter

ABSTRACTZ(nl; r) is the contribution to Z(r) from an electron in the (nl) wave function. The Z(nl; r) vary systematically with atomic number and, as N becomes large, tend to the corresponding hydrogen-like functions, ZH(nl; r). A two-parameter method of fitting the Z(nl; r) to the ZH(nl; r) is described. This involves a ‘screening constant’ and a ‘slope constant’, both of which are defined. From published data, the two parameters have been obtained as functions of atomic number. The parameters for an unsolved atom can then be found by interpolation and approximate Z(nl; r) derived by appropriate adjustment of the functions for the nearest atom in the periodic table for which they are known. The method has been tested by interpolating for the (3d) function between Cu+ and Rb+ and by preparing estimates of the Z(nl; r) for the unknown structure Mo+. The results were good for all but Z(4d; r) for Mo+, where the number of values of the screening and slope constants already known was insufficient for reliable interpolation.

On the ionization energies of the hydrogen molecule ion in intense magnetic fields

1977 ◽  
Vol 55 (11) ◽  
pp. 1013-1015 ◽  
Author(s):  
C. S. Lai
Keyword(s):  
Wave Function ◽  
Variational Principle ◽  
Magnetic Fields ◽  
Hydrogen Molecule ◽  
Trial Wave Function ◽  
Ionization Energies ◽  
High Fields ◽  
Two Parameter ◽  
Very High

The variational principle with a two-parameter trial wave function is used to determine the ionization energies and equilibrium internuclear separations of a hydrogen molecule ion situated in intense magnetic fields. The results for E1 obtained are improved significantly for fields less than 3 × 1010 G. and they approach the values predicted by de Melo, Ferreira, Brandi, and Miranda for very high fields.

Compact 11S Helium Wave Functions; an 8-Parameter Wave Function and its Sensitivity Analysis

2007 ◽  
Vol 62 (3-4) ◽  
pp. 224-226 ◽  
Author(s):  
Carl W. David
Keyword(s):  
Sensitivity Analysis ◽  
Wave Function ◽  
Wave Functions ◽  
Parameter Wave

A previously obtained approximate non-relativistic Helium wave function is improved significantly coming within 0.02% of the “exact” value with 8 terms. The sensitivity of this final result to the parameters in the wave function is examined.

A unified two-parameter wave spectral model for a general sea state

1981 ◽  
Vol 112 (-1) ◽  
pp. 203 ◽  
Author(s):  
Norden E. Huang ◽  
Steven R. Long ◽  
Chi-Chao Tung ◽  
Yeli Yuen ◽  
Larry F. Bliven
Keyword(s):  
Spectral Model ◽  
Sea State ◽  
Two Parameter ◽  
Parameter Wave

VARIATIONAL CALCULATIONS OF CHARGED EXCITONS IN GaAs QUANTUM-WELL WIRES

2006 ◽  
Vol 20 (13) ◽  
pp. 761-769
Author(s):  
JIAN-JUN LIU ◽  
YAN-XIU SUN
Keyword(s):  
Wave Function ◽  
Quantum Well ◽  
Quantum Wells ◽  
Interparticle Distance ◽  
Binding Energies ◽  
Equivalent Model ◽  
Variational Calculations ◽  
Quantum Well Wires ◽  
The Wire ◽  
Parameter Wave

The binding energy of positively and negatively charged excitons in GaAs quantum-well wires is calculated variationally as a function of the wire width by using a two-parameter wave function and a one-dimensional equivalent model. There is no artificial parameter added in our calculation. It is found that the binding energies are closely correlated to the sizes of the wire, and also that their magnitudes are greater than those in the two-dimensional quantum wells compared. In addition, we also calculate the average interparticle distance and the distribution of the wave function of exciton centre-of-mass as functions of the wires width. The results are discussed in detail.

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