Atomic Hyperfine Structure. II. First-Order Wave Functions for the Ground States of B,C,N,O, and F

1969 ◽  
Vol 181 (1) ◽  
pp. 137-143 ◽  
Author(s):  
Henry F. Schaefer ◽  
Richard A. Klemm ◽  
Frank E. Harris
Keyword(s):  
Hyperfine Structure ◽  
Ground States ◽  
Wave Functions ◽  
First Order

Atomic Hyperfine Structure. I. Polarization Wave Functions for the Ground States of B, C, N, O, and F

1968 ◽  
Vol 176 (1) ◽  
pp. 49-58 ◽  
Author(s):  
Henry F. Schaefer ◽  
Richard A. Klemm ◽  
Frank E. Harris
Keyword(s):  
Hyperfine Structure ◽  
Ground States ◽  
Wave Functions ◽  
Polarization Wave

Eine Approximation der Löwdinschen natürlichen Orbitale für Moleküle mit einer Green-Funktion-Methode

1972 ◽  
Vol 27 (4) ◽  
pp. 545-552 ◽  
Author(s):  
R. Albat
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Mass Operator ◽  
Ground States ◽  
Present Form ◽  
Many Body ◽  
Natural Orbitals ◽  
First Order ◽  
The Many ◽  
Closed Shells

Abstract An Approximation of Löwdin's Natural Orbitals for Molecules with a Green's Function Method The many-body-pertubation theorie of the single-particle Green's function is used to get an approximate first-order density matrix. Slightly modified SCF-orbitals form the basis for the expansion. The mass-operator in Dyson's equation is considered up to second order in the Perturbation. In the present form the method is only applicable to ground states with closed shells. The ground states of the molecules LiH and NH3 serve as examples to demonstrate the usefulness of the directly calculated natural orbitals for application in the C I-method. The natural orbitals give a much better convergence of the C I-expansion than the SCF-orbitals do.

scholarly journals Intercombination Transitions between Levels X1Σg+ and A 3Πu in C2

1987 ◽  
Vol 120 ◽  
pp. 103-105
Author(s):  
J. Le Bourlot ◽  
E. Roueff
Keyword(s):  
Transition Probabilities ◽  
Energy Levels ◽  
Wave Functions ◽  
Spin Orbit Coupling ◽  
Energy Matrix ◽  
First Order ◽  
Emission Transition ◽  
Intercombination Transition ◽  
The One ◽  
Potential Curves

We present a new calculation of intercombination transition probabilities between levels X1Σg+ and a 3Πu of the C2 molecule. Starting from experimental energy levels, we calculate RKR potential curves using Leroy's Near Dissociation Expansion (NDE) method; these curves give us wave functions for all levels of interest. We then compute the energy matrix for the four lowest states of C2, taking into account Spin-Orbit coupling between a 3Πu and A 1Πu on the one hand and X 1Σ+g and b 3Σg− on the other. First order wave functions are then derived by diagonalization. Einstein emission transition probabilities of the Intercombination lines are finally obtained.

The Wave Theory of the Electron

1928 ◽  
Vol 24 (4) ◽  
pp. 501-505 ◽  
Author(s):  
J. M. Whittaker
Keyword(s):  
Wave Function ◽  
Differential Equations ◽  
Fourth Order ◽  
Commutative Algebra ◽  
Wave Theory ◽  
Wave Functions ◽  
Linear Differential Equations ◽  
Wave Mechanics ◽  
First Order ◽  
Linear Differential

In two recent papers Dirac has shown how the “duplexity” phenomena of the atom can be accounted for without recourse to the hypothesis of the spinning electron. The investigation is carried out by the methods of non-commutative algebra, the wave function ψ being a matrix of the fourth order. An alternative presentation of the theory, using the methods of wave mechanics, has been given by Darwin. The four-rowed matrix ψ is replaced by four wave functions ψ1, ψ2, ψ3, ψ4 satisfying four linear differential equations of the first order. These functions are related to one particular direction, and the work can only be given invariance of form at the expense of much additional complication, the four wave functions being replaced by sixteen.

scholarly journals Masses of fully heavy tetraquarks $$QQ {\bar{Q}} {\bar{Q}}$$ in an extended relativized quark model

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Qi-Fang Lü ◽  
Dian-Yong Chen ◽  
Yu-Bing Dong
Keyword(s):  
Quark Model ◽  
Mass Spectra ◽  
Ground States ◽  
Lhcb Collaboration ◽  
Wave Functions ◽  
Recent Measurement ◽  
Heavy Quarkonium ◽  
Radial Excitation ◽  
Broad Structure ◽  
Narrow Structure

AbstractInspired by recent measurement of possible fully charmed tetraquarks in LHCb Collaboration, we investigate the mass spectra of fully heavy tetraquarks $$QQ {\bar{Q}} {\bar{Q}}$$ Q Q Q ¯ Q ¯ in an extended relativized quark model. Our estimations indicate that the broad structure around 6.4 GeV should contain one or more ground states for $$cc {\bar{c}} {\bar{c}}$$ c c c ¯ c ¯ tetraquarks, while the narrow structure near 6.9 GeV can be categorized as the first radial excitation of $$cc {\bar{c}} {\bar{c}}$$ c c c ¯ c ¯ system. Moreover, with the wave functions of the tetraquarks and mesons, the strong decays of tetraquarks into heavy quarkonium pair are qualitatively discussed, which can be further checked by the LHCb and CMS Collaborations.

Substituent effects of rate constants for thermal [4π + 2π] cycloreversion of spiro-fused β-lactam oxadiazolines

1993 ◽  
Vol 71 (6) ◽  
pp. 907-911 ◽  
Author(s):  
Michel Zoghbi ◽  
John Warkentin
Keyword(s):  
Thermal Decomposition ◽  
Rate Constant ◽  
Rate Constants ◽  
Transition States ◽  
Substituent Effects ◽  
Ground States ◽  
Phenyl Substituent ◽  
First Order ◽  
Average Value ◽  
Carbonyl Ylide

Twelve Δ3-1,3,4-oxadiazolines in which C-2 is also C-4 of a β-lactam moiety (spiro-fused β-lactam oxadiazoline system) were thermolyzed as solutions in benzene. Substituents in the β-lactam portion affect the rate constant for thermal decomposition of the oxadiazolines to N2, acetone, and a β-lactam-4-ylidene. The total spread of first-order rate constants at 100 °C was 47-fold and the average value was 6.7 × 10−4 s−1. A phenyl substituent at N-1 or at C-3 was found to be rate enhancing, relative to methyl. At C-3, H and Cl were also rate enhancing, relative to methyl. The data are interpreted in terms of the differential effects of substituents on the stabilities of the ground states, and on the stabilities of corresponding transition states for concerted, suprafacial, [4π + 2π] cycloreversion. The first products, presumably formed irreversibly, are N2 and a carbonyl ylide. The latter subsequently fragments to form acetone (quantitative) and a β-lactam-4-ylidene.

Reply to "A remark on Moore's new method of obtaining approximate solutions of the Dirac equation"

1981 ◽  
Vol 59 (11) ◽  
pp. 1614-1619 ◽  
Author(s):  
R. A. Moore ◽  
Sam Lee
Keyword(s):  
Dirac Equation ◽  
Structure Constant ◽  
Approximate Solutions ◽  
Wave Functions ◽  
Fine Structure Constant ◽  
Energy Calculation ◽  
Calculation Error ◽  
First Order ◽  
The One ◽  
The Individual

This work was written to clarify the use of a recently developed procedure to obtain approximate solutions of the one-particle Dirac equation directly and in response to a recent critique on its application to lowest order. The critique emphasized the fact that when the wave functions are determined only to zero order then a first order energy calculation contains significant errors of the order of α4, α being the fine structure constant, and a matrix element calculation error of order α2. Tomishima re-affirms that higher order solutions are required to obtain accuracy of these orders. In this work the hierarchy of equations occurring in the procedure is extended to first order and it is shown that exact solutions exist for hydrogen-like atoms. It is also shown that the energy in second order contains all of the contributions of order α4. In addition, we illustrate, in detail, that the procedure can be aplied in such a way as to isolate the individual components of the wave functions and energies as power series of α2. This analysis lays the basis for the determination of suitable numerical methods and hence for application to physical systems.

Hyperfine Structure of the Electronic Ground States ofRb85andRb87

1962 ◽  
Vol 127 (2) ◽  
pp. 524-528 ◽  
Author(s):  
S. Penselin ◽  
T. Moran ◽  
V. W. Cohen ◽  
G. Winkler
Keyword(s):  
Hyperfine Structure ◽  
Ground States ◽  
Electronic Ground
Sign in / Sign up

Export Citation Format

Share Document