K.T. Hecht

The vibration-rotation energies of tetrahedral XY4 molecules : Part I. Theory of spherical top molecules

Abstract The theory of vibration-rotational perturbations in tetrahedral XY 4 molecules has been reexamined in the light of the modern theory of angular momentum coupling. It is shown that, even to third order of approximation, the splitting of a vibration rotation level into its tetrahedral sublevels is governed only by perturbation terms of one basic symmetry in all states in which vibrational quanta of ν 1 , ν 3 , and ν 4 are excited and to a certain approximation in many of the infrared active states in which quanta of both ν 2 and ν 3 or ν 4 are excited. The perturbation term is identified as the tetrahedrally symmetric linear combination of fourth rank spherical tensor operators. In dominant approximation the rotational fine structure splitting patterns are characterized solely by the rotational angular momentum of the state. Only the overall extent of the patterns depends on the vibrational and total angular momentum quantum numbers and the vibrational character of the state. In next approximation the basic splitting patterns are all deformed to a certain extent by matrix elements off-diagonal in the rotational angular momentum quantum number. These cannot be neglected if theory is to account for the modern high resolution spectra. The terms of the vibration-rotation Hamiltonian to third order of approximation are classified according to their symmetry. Explicit expressions are given for the pure vibrational energies of the simpler bands. Explicit numerical values are also given for the matrix elements of the rotational sublevels of types A 1 , A 2 , E , F 1 , and F 2 from which the rotational energies of the vibrational ground state and the infrared active fundamentals can be computed. These matrix elements also give the numbers for the basic splitting patterns of the dominant approximation for any state involving combinations of ν 1 , ν 3 , and ν 4 .

GENERALIZED SENIORITY FOR FAVORED J # 0 PAIRS IN MIXED CONFIGURATIONS

Abstract By assigning a pseudo-spin and pseudo-orbital angular momentum ( b -spin and c -spin) to the single-particle states in a mixed configuration of identical nucleons, it is possible to classify as B = 0 objects both the favored pair operators of the surface delta interaction (SDI) and the multipole moment operators, (the latter under suitable assumptions). The favored pair is defined for each J as the specific superposition of two-particle states acted upon by this separable interaction. The SDI is diagonal in the total B - and C -spins; the eigenvalues of a ( B , C ) multiplet are independent of the total angular momentum J, ( J = B + C ) ; and all states with B = case1 2 v are degenerate ( v = total seniority). For the case of a degenerate doublet of levels ( l j , l +2) j + 1), e.g. ( d 5 2 g 7 2 ) or ( f 7 2 h 9 2 ), the specification, B = 0, defines the fa the number of nucleons not members of favored pairs. Exact calculations for the ( d 5 2 g 7 2 ) system show that states with B 1 2 v cluster closely about their centers of gravity; therefore, to a good approximation the SDI can be replaced by a generalized pairing interaction depending only on B and v . Possible generalizations are discussed for the case of many degenerate single-particle levels, where this generalized pairing interaction is no longer a good approximation.

Internal‐Rotation in Hydrogen Peroxide: The Far‐Infrared Spectrum and the Determination of the Hindering Potential

The torsional oscillation between the two OH groups of the hydrogen peroxide molecule is investigated through a study of the far‐infrared absorption spectrum of the molecule. A 1‐m‐focal‐length vacuum grating monochromator was used to scan the region from 15 to 700 cm−1 with an average resolution of 0.3 cm−1. The observed spectrum contains seven perpendicular‐type bands of which only the Q branches are resolved. The centers of the seven bands are at 11.43, 116.51, 198.57, 242.76, 370.70, 521.68, and 557.84 cm−1. These bands result from transitions between different states of the internal rotation and their identification makes it possible to construct the internal‐rotation energy level scheme through the first five excited states. Relative to the torsional ground state, these levels occur at 11.43, 254.2, 370.7, 569.3, and 775.9 cm−1.A theory of internal rotation in the hydrogen peroxide molecule is developed for use in the analysis of the far‐infrared spectra. In this theory, the Hamiltonian is construct...

Search for a coupling scheme in heavy deformed nuclei: the pseudo SU(3) model.

To test the possible usefulness of the pseudo SU(3) coupling scheme a few nuclear properties are examined which can be expected to be governed largely by the (lg

Hindered Rotation in Molecules with Relatively High Potential Barriers

d~2d+3s+) part of the proton configuration for odd-2 nuclei and the (lh2fs2f*3p+3p+) part of the neutron configuration for odd-N nuclei. The equivalence between these configurations and pseudo oscillator shells (?

SU3 recoupling and fractional parentage in the 2s-1d shell

&&) and (~

Vibration‐Hindered Rotation Interactions in Methyl Alcohol. The J=0→1 Transition

+) is exploited to show that the low-lying natural-parity rotational bands in deformed nuclei can be described approximately by many- particle states which are coupled to leading pseudo SU(3) representation (maximum possible value of 2i+;) of these configurations. The simple model in which the natural-parity part of the proton and neutron configurations are coupled to leading pseudo SU(3) representation predicts ground state magnetic moments in remarkably good agreement with experiment. The strong hindrance factors observed in certain interband Ml transition probabilities are, however, not predicted by this model. The diagonalization of a simple effective interaction within the leading pseudo SU(3) representation leads to spectra with the experimentally observed ordering of the K-bands. (The case of the Eu and Tm isotopes has been examined in some detail since these are expected to have leading pseudo SU(3) representations with the same quantum numbers (&) but with quite different ordering of the K-bands.)

BARYON BARYON SPIN ORBIT AND TENSOR INTERACTIONS FROM QUARK EXCHANGE KERNELS

The theory of hindered rotation has been applied to the type of asymmetric molecule in which the hindering barrier is high enough so that the hindered rotation splittings of the energy levels are small compared with the rotational energies but yet large enough to be observable in the microwave spectrum. The specific type of molecule considered consists of a rigid asymmetric component which may undergo a hindered rotation about the symmetry axis of a rigid symmetric component where the symmetric component is in addition assumed to have threefold symmetry and the asymmetric component at least a plane of symmetry containing the symmetry axis of the symmetric component. An example might be the acetaldehyde molecule, CH3CHO.In principle, the theory developed by Burkhard and Dennison can be used directly but in practice the method is difficult to apply to such a molecule since the matrix elements of the Hamiltonian used previously do not degenerate naturally or easily to those for the rigid asymmetric rotator i...