Ground State D2 Dissociation Energy from the Near-dissociation Behavior of Rotational Level Spacings

1975 ◽  
Vol 53 (19) ◽  
pp. 1983-1990 ◽  
Author(s):  
Robert J. Le Roy ◽  
Margaret G. Barwell
Keyword(s):  
Long Range ◽  
Diatomic Molecule ◽  
Dissociation Energy ◽  
Vibrational Level ◽  
Ground State ◽  
Potential Application ◽  
Rotational Level ◽  
Intermolecular Potential ◽  
Continuum Absorption ◽  
Exact Agreement

A method of determining the dissociation energy of a diatomic molecule from the rotational term value(s)of a single vibrational level lying near dissociation is derived and tested. It is based on expressions relating the characteristic near-dissociation behavior of the rotational constants Bv, Dv, Hv,… etc., to the asymptotically dominant inverse power contribution to the long range intermolecular potential. Application of this procedure to data for ground state D2 yields a dissociation energy of D0 = 36 748.88(±0.3)cm−1, in essentially exact agreement with the value Herzberg determined from the onset of continuum absorption in the vacuum u.v., 36 748.9(±0.4) cm−1. This agreement between results obtained from completely different observables appears to confirm the existence of a small discrepancy between experiment and the most recent theoretical nonadiabatic dissociation energy of Kolos and Wolniewicz, 36 748.2 cm−1.

Directional correlations of gamma rays in 152Sm and 152Gd measured by means of two Ge(Li) counters

1970 ◽  
Vol 48 (17) ◽  
pp. 2011-2022 ◽  
Author(s):  
J. Barrette ◽  
M. Barrette ◽  
A. Boutard ◽  
G. Lamoureux ◽  
S. Monaro
Keyword(s):  
Gamma Rays ◽  
Vibrational Level ◽  
Ground State ◽  
Rotational Level ◽  
Weak Intensity ◽  
Vibrational Levels ◽  
Γ Rays ◽  
Gamma Transitions

Directional correlation measurements have been performed with two Ge(Li) counters on several γ rays in coincidence with the 121.78 and 334.31 keV γ transitions which de-excite the first 2+ levels in 152Sm and 152Gd, respectively. A total of 20 γ−γ directional correlations, 13 in the 152Sm nucleus and 7 in the 152Gd nucleus, was measured simultaneously. Several of the γ−γ directional correlations involved gamma transitions of weak intensity, for example the (688.66−121.78), (1457.4−121.78), and (1528.16−121.78) keV cascades in 152Sm and the (586.29−334.31) and (1089.73−334.31) keV cascades in 152Gd. Among the various results which could be extracted from these measurements, the most interesting appears to be the determination of a nearly pure E2 character for the 688.66, 964.01, 1112.04, and 867.33 keV gamma transitions. The first two γ rays de-excite the 2+ β- and γ-vibrational levels to the 2+ ground-state rotational level at 121.78 keV in 152Sm, whereas the last two γ rays de-excite the3+ γ-vibrational level to the 2+ and 4+ (at 366.44 keV) ground-state rotational levels in 152Sm.

The Resonance Fluorescence Spectrum of Cl2 in the Vacuum Ultraviolet

1975 ◽  
Vol 53 (19) ◽  
pp. 1965-1975 ◽  
Author(s):  
A. E. Douglas ◽  
A. R. Hoy
Keyword(s):  
High Resolution ◽  
Fluorescence Spectrum ◽  
Long Range ◽  
Dissociation Energy ◽  
Ground State ◽  
Vacuum Ultraviolet ◽  
Resonance Fluorescence ◽  
State Potential ◽  
Resonance Fluorescence Spectrum ◽  
Cl Atoms

The resonance fluorescence spectrum of Cl2 first observed by Rao and Venkateswarlu in 1962, has been photographed at high resolution and analyzed. The assignments of the lines have been revised and new resonance series have been observed. It is shown that the ground state of Cl2, dissociates into Cl atoms with no potential hill and that the dissociation energy isD0 = 19 997.28 cm−1.Vibrational and rotational constants and the R.K.R. curve of the ground state of Cl2 have been determined. The long-range portion of the ground state potential of Cl2 has been examined and shown to be consistent with the predictions of theory and measurements from the B3Π0 potential.

Dependence of the Diatomic Rotational Constant Bν on the Long-Range Internuclear Potential

1972 ◽  
Vol 50 (10) ◽  
pp. 953-959 ◽  
Author(s):  
Robert J. Le Roy
Keyword(s):  
Experimental Data ◽  
Long Range ◽  
Diatomic Molecule ◽  
Vibrational Level ◽  
Interatomic Potential ◽  
Rotational Constant ◽  
Simple Expression ◽  
Dissociation Limit ◽  
Range Potential ◽  
Vibrational Levels

A simple expression is derived which explicitly relates the rotational constant Bν for vibrational levels near the dissociation limit D of a diatomic molecule, to the nature of the long-range interatomic potential. Assuming a long-range potential of the form V(R) = D – Cn/Rn, the expression Bν = Qn(νD – ν)[4/(n−2)] is obtained, where νD is the effective vibrational index at the dissociation limit, and Qn is a constant depending only on n, Cn, and the reduced mass. This result is slightly less accurate than an analogous recently developed relation for the vibrational level distribution near D. Its utility and accuracy are demonstrated by application to experimental data for the [Formula: see text] states of Cl2, Br2, and I2.

LONG RANGE FORCES BETWEEN HYDROGEN MOLECULES

1955 ◽  
Vol 33 (11) ◽  
pp. 668-678 ◽  
Author(s):  
F. R. Britton ◽  
D. T. W. Bean
Keyword(s):  
Wave Function ◽  
Long Range ◽  
Ground State ◽  
Close Agreement ◽  
Van Der Waals ◽  
Wave Functions ◽  
Numerical Factor ◽  
Hydrogen Molecules ◽  
Static Quadrupole

Long range forces between two hydrogen molecules are calculated by using methods developed by Massey and Buckingham. Several terms omitted by them and a corrected numerical factor greatly change results for the van der Waals energy but do not affect their results for the static quadrupole–quadrupole energy. By using seven approximate ground state H2 wave functions information is obtained regarding the dependence of the van der Waals energy on the choice of wave function. The value of this energy averaged over all orientations of the molecular axes is found to be approximately −11.0 R−6 atomic units, a result in close agreement with semiempirical values.

scholarly journals Off-Diagonal Long-Range Order in Generalized Hubbard Models

1997 ◽  
Vol 11 (11) ◽  
pp. 1311-1335 ◽  
Author(s):  
Kristel Michielsen ◽  
Hans De Raedt
Keyword(s):  
Density Matrix ◽  
Hubbard Model ◽  
Long Range ◽  
Ground State ◽  
Size Dependence ◽  
State Energy ◽  
System Size ◽  
Range Order ◽  
Long Range Order ◽  
Hubbard Models

We present stochastic diagonalization results for the ground-state energy and the largest eigenvalue of the two-fermion density matrix of the BCS reduced Hamiltonian, the Hubbard model, and the Hubbard model with correlated hopping. The system-size dependence of this eigenvalue is used to study the existence of Off-Diagonal Long-Range Order in these models. We show that the model with correlated hopping and repulsive on-site interaction can exhibit Off-Diagonal Long-Range Order. Analytical results for some special limiting cases indicate that Off-Diagonal Long-Range Order not always implies superconductivity.

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