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Certain, P. R.

Publications and source records attributed to Certain, P. R..

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Degenerate RS perturbation theory

A concise, systematic procedure is given for determining the Rayleigh-Schroedinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n + 1)-th order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite-order operators which are determined by the successive resolution of the space of the zeroth-order functions.

Hirschfelder, J. O.↗
NASA NTRS1974

Rotationsal and vibrational spectra of molecular ions: Feasibility of laboratory and astrophysical observation

The rotational spectra of a number of small molecular ions should be detectable in the microwave or millimeter wave regions in laboratory experiments using currently available techniques. The dipole moments and absorption coefficients of polar diatomics CO(+) and NO(+) as well as asymmetric isotopically enriched species, like O-18O-16(+), NE-20NE-22(+), and OC-18 O-16(+) are calculated to be sufficiently large to allow observation of their spectra. In addition to the detailed molecular structure information which such spectral data would provide, precise knowledge of the transition frequencies would render likely the detection of certain of these ions in the interstellar sources or in planetary atmospheres. All of these ions also possess vibrational spectra which should be detectable in the infrared region in laboratory or astrophysical sources.

Woods, R. C.↗
NASA NTRS1973

Degenerate R-S perturbation theory

A concise, systematic procedure is given for determining the Rayleigh-Schrodinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n+1)st order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite order operators which are determined by the successive resolution of the space of the zeroth order functions.

Hirschfelder, J. O.↗
NASA NTRS1973

On the dipole moment of CO/+/.

Results of self-consistent field calculations on neutral CO, its positive ion, and on neutral CN to verify an earlier estimate of the dipole moment of CO(+) in its ground super 2 Sigma state. Based on the above-mentioned calculations, direct evidence is obtained that the dipole moment (relative to the center of mass) is approximately 2.5 plus or minus 0.5 C, as previously determined by Kopelman and Klemperer (1962).

Certain, P. R.↗
NASA NTRS1970

New partitioning perturbation theory. II

Coupled simple harmonic oscillators with almost degenerate energy levels, comparing partitioning perturbation techniques with Rayleigh- Schroedinger approach

Certain, P. R.↗