Parity Splitting Research Articles

Intermolecular vibrations of the hydrogen bonded OH–CO reactant complex

Intermolecular vibrations of the linear OH–CO reactant complex have been observed as combination bands in the OH overtone region using infrared action spectroscopy. Rotational analyses and simulations of the band structures have been carried out for transitions to geared bend, excited spin–orbit, and H-atom bend states with 50–250 cm−1 of intermolecular excitation. The projection quantum number associated with each of these upper states is identified through the intensity profile of the band contour, missing rotational lines, and/or parity splitting of individual rotational lines. Intermolecular states with projection quantum numbers P=1/2 and 5/2 are observed for each of the two bending modes, arising from coupling of the unquenched angular momentum of OH with the vibrational angular momentum associated with the bending motion of the complex. An additional P=1/2 state is attributed to spin–orbit excitation, which shifts to higher energy than in free OH and gains infrared transition strength through the spin-decoupling interaction. The intermolecular energy level pattern is also examined in the context of the Renner-Teller interaction and spin–orbit coupling. The intermolecular bends of the OH–CO complex are of special interest because they probe portions of the reaction path leading to trans-HOCO formation.

Cluster interpretation of parity splitting in alternating parity bands

The parity splitting in actinides is described with a cluster model of oscillations in mass asymmetry coordinate. The spin dependence of the calculated parity splitting is in a good agreement with the experimental data.

Parity splitting in nuclei involving octupole correlations and the alignment of the angular momentum

A rotational model based on a simultaneous analysis of parity splitting and the alignment of the angular momentum is developed to describe high-spin negative-parity states. A simple formula for the energy of these states is proposed. It is shown that negative-parity states exhibit alignment, provided that the ground-state band is aligned and that the two opposite-parity bands can be considered as a single alternating-parity band.

Experimental and theoretical investigation of the rotational structure of the Al–H2/D2 complex

The rotational structure of the Al–H2/D2 complex is investigated in a collaborative experimental and theoretical study. The isotopomeric complexes were prepared in a pulsed supersonic beam, and their 3d←3p and 4p←3d electronic transitions recorded through laser fluorescence excitation spectroscopy. Transitions to quasibound excited vibronic levels were observed by monitoring emission from lower excited Al atomic levels, formed by nonradiative decay of the excited complex. In some bands, the Lorentzian width was sufficiently narrow that resolved rotational lines were observed. Rotational analysis of several bands which typify the two different patterns of observed rotational structure is presented. The derived rotational constants and parity splitting parameters for the ground Al(3p)–oH2/pD2 bend-stretch levels were compared with constants computed from fits to J- and parity-dependent energies calculated with new Al(3p)–H2 potential energy surfaces (PESs), which extend those recently reported by Williams and Alexander [J. Chem. Phys. 112, 5722 (2000)] by inclusion of the dependence on the H2 bond distance. The experimental and computed rotational constants were found to be in very good agreement. This provides strong support for the reliability of the calculated PESs.

Spectroscopy of the A 2Δ–X 2Π transition of CH/D–Ar

The CH(A 2Δ)–Ar van der Waals molecule provides a prototypical example of a Δ2 state complex. The rovibronic structure of CH/D(A)–Ar has been examined by recording rotationally resolved spectra for the A–X transition. The spectra are dominated by vibrational progressions of the intermolecular stretch in combination with two bending states. Rotational energy level patterns were consistent with a linear equilibrium geometry for CH(A)–Ar. Parity splittings resulting from vibronic interactions were below the resolution of the present measurements. Spectra for the A–X transition of CD, recorded incidentally in this study, reveal an error in the previously accepted assignment of the 0–0 band R2(1/2) line.

Infrared spectroscopy of ArOH: A direct probe of the Ar+OH X2Π potential energy surface

An infrared-ultraviolet (IR-UV) double-resonance technique has been implemented to obtain the infrared spectrum of ArOH in the vicinity of the fundamental OH stretch at 2.8 μm. A rotationally resolved spectrum of the fundamental OH stretching band of ArOH is observed at 3567.85(1) cm−1 (origin). A combination band, involving both OH stretch and intermolecular bending excitation, is identified at 3577.00(1) cm−1 (origin). The intermolecular energy of the excited bending state provides a direct measure of the anisotropy of the Ar+OH X2Π interaction potential. The rotational structure of the combination band reveals a large splitting between parity components with the same total angular momentum in the excited bending state [0.69(1) cm−1 for J=32]. The experimentally derived parity splitting is compared with previous experimental and theoretical determinations of this parameter. The parity splitting associated with the excited bending state reflects the change in the intermolecular potential when the pπ orbital containing the unpaired electron of OH lies in or out of the ArOH plane.

Parity splitting in the alternating parity bands of some actinide nuclei

An angular momentum dependence of the parity splitting in the alternating parity bands of nuclei with strong octupole correlations is considered basing on the model of the octupole motion in a one-dimensional potential well conserving axial symmetry. A sign reversal of the parity splitting at higher values of the angular momentum is interpreted as a result of the Coriolis coupling to K=1 octupole mode. New experimental data on the spectra of the alternating parity octupole bands are used.

High resolution electronic spectroscopy of the R⋅SH complexes (R= Ne, Ar, Kr)

The high resolution laser induced fluorescence spectra of the à 2Π3/2 electronic transition of the R⋅SH/D (R= Kr, Ar, Ne) van der Waals (vdW) complexes are reported. Analysis of these bands requires the inclusion of rotation, fine and hyperfine structure, spin-rotation interactions, and parity splittings. A number of molecular parameters are determined, along with internuclear bond distances between the R and the SH moiety. Comparison of the present results for R⋅SH/D is made with the analogous R⋅OH/D species where applicable. In addition, the detailed “rotational” structure and the highly precise determinations of the band origins of the different heavy atom isotopomers are critical for absolute vibrational quantum number assignment in the à state.

Reflection asymmetric deformation and clustering in heavy nuclei

The relationship between the cluster properties of heavy nuclei and the appearance of low-lying collective negative-parity states in these nuclei is discussed. Energies of the cluster typenp-nh particle-hole excited states, wheren is the number of nucleons in a cluster, are calculated. It is shown that the energies of these states take minimal values in nuclei having low-lying collective 1- states and ground-state alternating-parity rotational bands with ΔI = 1. The correlation between the difference of the quadrupole deformations in the potential energy minimum and at the barrier separating two octupole minima and the value of the angular momentum, at which parity splitting disappears, is studied.

Bound rovibronic levels of the [formula omitted] complex

We have used ab initio MRCI (multireference internally contracted configuration interaction) potential energy functions to compute the energies of the bound rovibronic levels of the T-shaped nearly-degenerate electronically excited HeN 2 +(A 2Π) . In these calculations a variational approach which includes the rotation-vibration, the electronic angular and spin momenta couplings has been employed. The wavenumbers for the large amplitude bending and stretching modes have been calculated to lie around 60 and 75 cm −1, respectively. For J = 1 2 , three states with excited bending and one state with excited stretching mode were found to be bound. The weak interaction between He and the N 2 + (A 2Π u) state leads to a spin flip. The inverted doublet in N 2 + (A 2Π u) becomes a normal doublet in the complex. This unusual effect is attributed to large anisotropies and to a large difference potential between the A′ and A″ components, which leads also to the largest known parity splittings in Renner-Teller weakly bound complexes.

Fluorescence depletion spectroscopy of the CH/D–Ne B 2Σ−–X 2Π transition

Fluorescence depletion techniques were used to test vibronic and rotational assignments for the B 2Σ−–X 2Π transition of CH–Ne. Previous vibronic assignments [W. H. Basinger, U. Schnupf, and M. C. Heaven, Faraday Discuss. 97, 351 (1994)] were confirmed, and observations of transitions to dissociation continua provided accurate dissociation energies for the B and X states. Errors in the rotational assignments were discovered. Re analysis of the rotational structure yielded ground state parity splittings and improved rotational constants. Adiabatic model calculations were used to determine approximate angular potential energy curves for the B and X states. These calculations also accounted for the prominent optical activity of internal rotation in the spectrum.

Rotational spectra and parity splitting in nuclei with strong octupole correlations

Abstract A formula is suggested to describe the energies of positive- and negative-parity states belonging to the ground-state alternating-parity rotational bands in nuclei with significant octupole correlations. The agreement with experimental data is quite good for actinide nuclei. This formula corresponds to the parity splitting from a one-dimensional potential well. It leads to a common moment of inertia for both parities at least for low angular momenta. At high angular momenta a slight difference in the moments of inertia is found, which is presumably due to backbending.

Angular momentum dependence of the parity splitting in nuclei with octupole correlations.

Experimental data on the angular momentum dependence of parity splitting of yrast bands in different nuclei are analyzed using a one-dimensional model of octupole motion with axial symmetry. A two parameter formula, based on a solution of the Schroedinger equation with a double-minimum potential, predicts that the parity splitting exponentially decreases with [ital I]([ital I]+1) and gives a good fit to these data. Moreover, it relates the observed parity splitting directly to the internal barrier height of the potential.

Octupole deformation in 149,151Sm nuclei.

Parity doublet states and alternating parity bands in [sup 149,151]Sm nuclei observed in [sup 148,150]Nd ([alpha],3[ital n][gamma]) reactions at [ital E][sub [alpha]]=37 and 35 MeV are presented here. Nineteen new transitions in [sup 149]Sm and sixteen in [sup 151]Sm have been observed in singles and [gamma]-[gamma]-[ital t]-r.f. coincidence experiments. Four alternating parity bands in [sup 149]Sm and two in [sup 151]Sm characterized by simplex quantum numbers are reported. The observed level schemes are interpreted in terms of octupole deformation. The energy difference due to parity splitting, collective rotational parameters, quasiparticle Routhians, single particle angular momentum alignments of bands with simplex quantum number [ital s]=[plus minus][ital i] in [sup 149]Sm and with [ital s]=[minus][ital i] in [sup 151]Sm have been calculated from the experimental results. From the [ital E]1, [ital E]2 branching ratios, the electric dipole moments are deduced to be [l angle][ital D][sub 0][r angle]=0.19[plus minus]0.08 [ital e] fm for [sup 149]Sm and [l angle][ital D][sub 0][r angle]=0.36[plus minus]0.11 [ital e] fm for [sup 151]Sm. The parameter [ital C][sub 1], a function of the symmetry energy coefficient, has been estimated for [sup 149]Sm from the liquid drop model of Strutinsky for deformed nucleus, and has been found to be [italmore » C][sub 1]=0.002003[sub [minus]0.000159][sup +0.000087] fm.« less

High-resolution electronic spectroscopy of the Ne·OH and Ne·OD Ã ← X̃ bands

The high-resolution laser-induced fluorescence spectra of the Ne·OH A˜(0,11,1)←X˜(0,00,0) and Ne·OD A˜(0,00,0)←X˜(0,00,0),A˜(0,00,1)←X˜(0,00,0),A˜(0,10,1)←X˜(0,00,0),A˜(0,11,1)←X˜(0,00,0) transitions were obtained. Analyses of these spectra determine precise bond lengths and reveal interesting spin–rotation and parity structure. In the A (0, 1K=0,1, 1) levels of Ne·OH and Ne·OD, the spin–rotation structure is described with the parameter γ, whose magnitude is larger than in the other observed levels of Ne·OH, Ne·OD, and Ar·OH, and Ar·OD. For the K = 1 level an additional term κ is introduced and is found to be an order of magnitude larger than γ. A model based on perturbation theory is proposed and successfully explains the peculiar spin–rotation structure in the A (0, 1K, 1) levels. In addition, a parity-splitting (P-type doubling) for the X˜(0,00,0) level of Ne·OD was determined to be a factor of 10 larger than that in Ar·OD. The parity splitting (K-type doubling) for the A (0, 11, 1) level of Ne·OH is also observed and measured.

Laser magnetic resonance spectroscopy of the NiD radical in the far- and mid-infrared

The rotational spectrum of NiD in the lowest three vibrational levels (v = 0, 1, 2) of its ground 2Δ state has been studied by far-infrared laser magnetic resonance (LMR). Transitions have been detected for all five isotopes of nickel and within both the lower 2Δ5/2 and upper 2Δ3/2 spin components. The nuclear hyperfine splittings for the 61Ni isotope (I = 3/2) have been resolved. An effective Hamiltonian has been used to fit the data which include the known vibration-rotational transitions within the 2Δ5/2(v = 1 ← v = 0) subsystem and a fine structure transition in the v = 0 level of the 2Δ ground state, recently measured by CO2 LMR. From a parity splitting of the rotational transition within the X 2Δ3/2 spin component we have determined the first Λ-type doubling parameter for the X 2Δ ground state. A set of molecular parameters for NiD in the 2Δ ground state of NiD is given which allows a comparison with the parameter set for the well known NiH radical.

Excitation Spectra of the Two Impurity Anderson Model. I. Critical Transition in the Two Magnetic Impurity Problem and the Roles of the Parity Splitting

Excitation spectra of the two impurity Anderson model are calculated by using the numerical renormalization group method. The critical transition found by Jones et al. is examined based on the model that the parity splitting is induced by the f - f transfer matrix, t . The low energy scale, ω l / T K , is approximately given as (( j - j c )/1.5) 2 +( t /23 T K ) 2 , and thus t suppresses the critical transition, where j is the exchange coupling normalized by the Kondo temperature T K , j c the critical value for the model without t . The γ-coefficient is proportional to ω l -1 , while the antiferromagnetic susceptibility to ln ω l -1 . The phase shift changes continuously near j c . It tends to singular jump as t →0. The parity splitting of the single particle excitation spectrum is enhanced by the exchange coupling.

Excitation Spectra of the Two Impurity Anderson Model. II. Interplay between the Kondo Effect and the Inter Site Interactions

Excitation spectra of the two impurity Anderson model are calculated for various parameter regions of the f-f transfer, t , c-f hybridization and the exchange coupling between local spins. The parity dependent potential scattering suppresses the critical transition pointed out by Jones et al. In the case of small t , the parity splitting of the f-level is given by t / Z , where Z is the enhancement factor of the specific heat in the single impurity problem. In the case of large t , γ of the electronic specific heat decreases drastically and the parity splitting increases largely. The splitting remains to be order of t / Z if the induced kinetic exchange coupling is compensated by other mechanism. The fluctuation of the singlet non-uniform superconductivity is relatively large in the electron-hole asymmetric case, but its intensity is about 1/10 of the antiferromagnetic one.

Parity doubling in open-shell van der Waals complexes

In open-shell van der Waals complexes containing 2Π diatomic molecules, the splitting between states with the same angular momentum quantum numbers but different parity is sensitively dependent on the intermolecular potential. The splitting for states with angular momentum projection quantum number P = ± 1 2 has been investigated previously by Green and Lester, and shown to arise in third-order perturbation theory. We use the same model to calculate the splitting for states with P = ± 3 2 , which arises in fifth order. A formula previously used to estimate the ratio of the parity splittings in P = ± 1 2 and ± 3 2 states (Ohshima et al.) is shown to be incomplete, casting doubt on the resulting claim of compatibility between the measurements of these two splittings.

A perturbation theory guide to open-shell complexes: OH–Ar(X 2Π)

Perturbation theory is used to understand the experimentally observed stimulated emission spectra of OH–Ar(X 2Π). A useful zero-order Hamiltonian for an open-shell van der Waals complex is presented, and the most important perturbation terms are identified: rotational decoupling ( j⋅s), Renner–Teller coupling (V̂2), and a Coriolis interaction (J⋅j). This treatment reveals those parts of the Hamiltonian which are responsible for various unusual features in the spectra of open-shell complexes, such as the large parity splittings in certain vibrational bands and spin–orbit–induced predissociation of the OH–Ar(X 2Π) complex. The magnitude of the parity splitting is shown to be directly proportional to the change in the intermolecular potential when the odd electron in the free radical lies in or out of the O–H–Ar plane, the A′ and A″ surfaces. The measured splitting is used to infer the magnitude of the difference between the A′ and A″ potential-energy surfaces (∼12 cm−1) in the region sampled by the first excited bend.