Rotor Band Research Articles

Mass-23 nuclei in astrophysics

The formation of mass-23 nuclei by radiative capture is of great interest in astrophysics. A topical problem associated with these isobars is the so-called 22Na puzzle of ONe white dwarf novae, where the abundance of 22Na observed is not as is predicted by current stellar models, indicating there is more to learn about how the distribution of elements in the universe occurred. Another concerns unexplained variations in elements abundance on the surface of aging red giant stars. One method for theoretically studying nuclear scattering is the Multi-Channel Algebraic Scattering (MCAS) formalism. Studies to date have used a simple collective-rotor prescription to model the target states which couple to projectile nucleons. While, in general, the target states considered all belong to the ground state rotor band, for some systems it is necessary to include coupling to states outside of this band. Herein we discuss an extension of MCAS to allow coupling of different strengths between such states and the ground state band. This consideration is essential when studying the scattering of neutrons from 22Ne, a necessary step in studying the mass-23 nuclei mentioned above.

Torsion-vibration coupling in S1 toluene: Implications for IVR, the torsional barrier height, and rotational constants.

We have examined the S1←S0 transition of toluene in the region from the 0(0)(0) band to ∼210 cm(-1) above it. The spectrum reveals methyl rotor levels of 0(0) toluene up to m = 6 and of the lowest frequency vibration, 20(1), up to m = 4. The rotor levels of both 20(1) and 0(0) are perturbed by torsion-vibration coupling. The inclusion of torsion-vibration coupling leads to the S1 torsional barrier, V6, being revised from -26.376 cm(-1) to -5.59 cm(-1). The torsion-vibration coupling constant is determined to be 21.1 cm(-1). This situation is the S1 analogue of that recently reported for S0 toluene [Gascooke et al., J. Chem. Phys. 142, 024315 (2015)]. Torsion-vibration coupling alters both the rotor band positions and the rotational contours, which particularly affects the rotational constants associated with motion around the a-axis, about which the methyl group rotates. Every vibrational state (indicated generically by X) will be involved in the corresponding X - X20(1) torsion-vibration coupling; so, this interaction permeates the vib-rotor manifold, providing a mechanism to enhance intramolecular vibrational energy redistribution.

Coupling to two target-state bands in the study of then+Ne22system at low energy

One theoretical method for studying nuclear scattering and resonances is via the multi-channel algebraic scattering (MCAS) formalism. Studies to date with this method have used a simple collective-rotor prescription to model target states with which a nucleon couples. While generally these target states all belong to the same rotational band, for certain systems it is necessary to include coupling to states outside of that main band. Here, we extend MCAS to allow coupling of different strengths between such states and the rotor band. This is an essential consideration in studying the example examined herein, the scattering of neutrons from 22Ne.

The intensity of forbidden torsional transitions in electronic spectra of molecules with a 6-fold barrier: Application to toluenes

Franck-Condon forbidden transitions involving methyl rotor modes are seen in the S1 ← S0 spectrum of toluene and toluene-like molecules. The strongest of these rotor transitions (m″ = 1 → m′ = 2, m″ = 0 → m′ = 3a1″, and m″ = 1 → m′ = 4) have been shown by Walker et al. [J. Chem. Phys. 102, 8718 (1995)] to gain intensity through the rotor equivalent of the Herzberg-Teller mechanism. Despite the m″ = 0 → m′ = 3a2″ transition being forbidden in this formalism, it is sporadically observed. We show that this transition derives oscillator strength from incomplete mixing of the −3 and +3 free rotor basis states due to torsion-rotation coupling. Calculations demonstrate that this mechanism quantitatively explains the intensities observed for toluene, including their temperature dependence. Because the −3/+3 mixing is weakest when the torsional barrier height, V6, is small, the m″ = 0 → m′ = 3a2″ transition increases in intensity as |V6| decreases. The temperature and |V6| dependencies explain why reports of the 0 → 3a2″ transition have been intermittent. The torsion-rotation coupling mechanism is predicted to also give significant intensity to m = 0 → m = 6a2′ transitions relative to m = 0 → m = 6a1′ transitions and to provide intensity to 0 → 3a2 transitions in molecules with a 3-fold (V3) barrier. Comparison between the observed and calculated rotor band contours shows, unexpectedly, that the 3a1″ constants fail to predict the 3a2″ contour despite these two states being derived from the same free rotor basis states. Comparison with the observed spectrum also reveals differences in the separation of the S1 3a2″ and 3a1″ levels. The V6 value determined from analysis of the high resolution, rotationally resolved m″ = 0 → m′ = 3a1″ spectrum overestimates the 3a2″–3a1″ separation by 0.6 cm−1. We postulate that this may be due to torsion-vibration coupling. The observed toluene torsion-rotation contours have been modeled to provide estimates of the rotational constants for several of the torsional states.

Persistence of rotational bands in a coupled SU(3) model

To understand better the emergence of rotational structures in a variety of situations, a model in which two SU(3) irreps are coupled via a quadrupole-quadrupole (Q·Q) interaction is considered. Strong coupling of different SU(3) irreps gives rise to low-lying rotor bands. We study the excited bands that occur and the perturbation effects of the rotational decoupling. Persistence of rotational-like bands for a large range of coupling strengths is observed. However, although for very weak interaction strengths the electromagnetic transition rates are consistent with those of the rotor model, the excitation energy ratios look more vibrational, a phenomenon which has been observed in many nuclei.

Particle-hole excited states in133Te

Excited states in neutron-rich ${}^{133}\mathrm{Te}$ have been identified with the Gamma sphere array by measuring three- and higher-fold prompt coincidence events following spontaneous fission of ${}^{252}\mathrm{Cf}.$ Four types of particle-hole bands built on the known 334.3 keV isomer in ${}^{133}\mathrm{Te}$ are identified. The yrast and near yrast particle-hole states observed up to 6.2 MeV in ${}^{133}\mathrm{Te}$ have characteristics quite similar to those in ${}^{134}\mathrm{Te}.$ These states are interpreted as a result of coupling a neutron $\ensuremath{\nu}{h}_{11/2}$ hole to the ${}^{134}\mathrm{Te}$ core. The group of states observed above 5.214 MeV is the result of a neutron particle-hole excitation of the double magic core nucleus ${}^{132}\mathrm{Sn},$ and is a candidate for a tilted rotor band. Shell-model calculations considering ${}^{132}\mathrm{Sn}$ as a closed core have been performed and have provided guidance to the interpretation of the levels below 4.3 MeV. Very good agreement between theory and experiment is obtained for these states.

FTIR study of the second stretching vibrational overtone system of H370GeD: example of an almost asymmetric rotor band

FTIR study of the second stretching vibrational overtone system of H370GeD: example of an almost asymmetric rotor band

FTIR study of the second stretching vibrational overtone system of H3 70GeD: example of an almost asymmetric rotor band

The FTIR spectrum of monoisotopic H3 70GeD around 6100 cm-1 was recorded with a resolution of about 0·012 cm-1. A perpendicular-type band, v 0(E) = 6129·441 cm-1, is observed, which is unperturbed for K′ ⩽ 1>2. Its rotational analysis reveals, in addition to rovibrational r and q resonance effects within the E vibrational state, a strong rovibrational α resonance perturbation by an almost degenerate perturber of A1 symmetry, v 0 = 6129·434 cm-1. Owing to intensity perturbations the parallel component is very weak in spite of a transition moment ratio M(E)/M(A1) of about -2. The rovibrational energy level pattern is indicative of local mode behaviour of the v (GeH) = 3 state, in which Coriolis effects are almost absent and simple arithmetic relations between vibration-rotation parameters fulfilled as expected. This gives rise to an excited state energy level pattern almost consistent with that of an asymmetric rotor.

Photodissociation dynamics in quantum state-selected clusters: A test of the one-atom cage effect in Ar–H2O

High resolution IR overtone pumping with an injection seeded optical parametric oscillator (OPO) is used in conjunction with excimer laser photolysis to investigate the state-resolved dynamics of quantum state-selected van der Waals clusters in a slit supersonic expansion. The narrow band IR light source (160 MHz, 5 mJ) preselects a specific upper state via the internal rotor band of Ar–H2O which correlates to the ‖03〉−←‖00〉+, 000←101 transition in H2O monomer. At fixed UV photolysis and probe wavelength, scanning the high resolution OPO yields the ‖03〉−←‖00〉+, Σ(000)←Σ(101) overtone action spectrum of Ar–H2O complexes. Conversely, at fixed IR pump wavelength, the state distribution of the OH photoproduct from photolysis of quantum state selected Ar–H2O clusters can be probed by laser induced fluorescence on the A 2Σ+←X 2Π (0,0) band. The OH distributions from H2O monomer vs Ar–H2O photolysis from the same internal rotor state are remarkably similar, though significant anomalies are observed for specific K rotational levels.

Strong coupling and quasispinor representations of the SU(3) rotor model

We define a coupling scheme, in close parallel to the coupling scheme of Elliott and Wilsdon, in which nucleonic intrinsic spins are strongly coupled to SU(3) spatial wave functions. The scheme is proposed for shell-model calculations in strongly deformed nuclei and for semimicroscopic analyses of rotations in odd-mass nuclei and other nuclei for which the spin-orbit interaction is believed to play an important role. The coupling scheme extends the domain of utility of the SU(3) model, and the symplectic model, to heavy nuclei and odd-mass nuclei. It is based on the observation that the low angular-momentum states of an SU(3) irrep have properties that mimic those of a corresponding irrep of the rotor algebra. Thus, we show that strongly coupled spin-SU(3) bands behave like strongly coupled rotor bands with properties that approach those of irreducible representations of the rigid-rotor algebra in the limit of large SU(3) quantum numbers. Moreover, we determine that the low angular-momentum states of a strongly coupled band of states of half-odd integer angular momentum behave to a high degree of accuracy as if they belonged to an SU(3) irrep. These are the quasispinor SU(3) irreps referred to in the title.

The SU(3) structure of rotational states in heavy deformed nuclei

The SU(3) coupling scheme provides an informative basis for the expansion of shell-model wave functions and their interpretation in collective-model terms. We show in this paper that it is possible, using the coupled-rotor-vibrator model, to infer averages of the distributions of SU(3) representation labels in heavy rotational nuclei by direct interpretation of physically observed E2 transition rates and quadrupole moments. We find that the distributions of SU(3) representation labels have nearly constant average values for states belonging to some well-defined rotational bands. These are bands of states having B(E2) values and quadrupole moments that follow the predictions of the rotor model. Such bands are interpreted as soft SU(3) bands in parallel with the concept of a soft rotor band with vibrational-shape fluctuations. The concept of a soft SU(3) band and its implications for beta-vibrational excited bands is developed. The average SU(3) representation labels inferred from experiment are interpreted by calculating those implied by the Nilsson model. An analysis of the SU(3) content of Nilsson wave functions also leads to two remarkable predictions. The first is that, in the asymptotic limit, the Nilsson model implies intrinsic states for a rotor band that are beta rigid. The second is that, although the intrinsic Nilsson state is axially symmetric, it generates a sequence of K = 0,2,4, … bands.

Tunable far infrared laser spectroscopy of van der Waals bonds: The intermolecular stretching vibration and effective radial potentials for Ar–H2O

Measurements of the fundamental van der Waals stretching vibration Σ(000,vs=1) ←Σ(000,vs=0) of Ar–H2O [ν0=907 322.08(94) MHz] and a transition from the lowest excited internal rotor state Σ(101,vs=0) to the Σ(101,vs=1) level [ν0=1019 239.4(1.0) MHz] are presented. A simultaneous rotational analysis of the new stretching data with the internal rotor bands observed by us previously [J. Chem. Phys. 89, 4494 (1988)], including the effects of Coriolis interactions, provides experimental evidence for the new assignment of the internal rotor transitions suggested by Hutson in the accompanying paper. Fits to the rotational term values for the vs=0 states are used to derive effective radial potential energy surfaces for each of the Σ internal rotor states. The results show the well depth (153.4 cm−1) of the effective radial potential for the Σ(101,vs=0) level to be approximately 25 cm−1 deeper than that for the Σ(000,vs=0) ground state of the complex, indicating that the former is stabilized considerably more by the anisotropic intermolecular potential energy surface than is the ground state.

The survival of rotor and SU(3) bands under strong spin-orbit symmetry mixing

The algebraic properties of rotational bands generated using collective models based on dynamical groups are shown to be remarkably resilient to strong symmetry mixing by the spin-orbit interaction. Thus, dynamical groups continue to remain useful for the description of observed bands in spite of strong symmetry breaking. Explicit results are given for the rigid rotor and SU(3) models. The examples provide an illustration of the new group theoretic concept of embedded representations.

Pseudobands in non-SU(3) odd-mass nuclei and coherent state structures of quadrupole phonons

Ground state symmetric rotor bands are described as coherent-state structures of deformation in a quadrupole-phonon model. These structures are shown to be very different from the phonon composition of pseudobands which are culled from the excited state spectrum of nuclei such as75Se,75Kr, and77Kr. The pseudobands are shown to be only a subset of more complete excitation spectra, which occur in most unique-parity odd-nucleon nuclei with a transitional core and can be expected to occur throughout the chart of the nuclides.

Rotational properties of shell-model states infp-shell nuclei

The relation between the microscopic shell model and the collective rotor model is investigated. As the first step an extensive shell-model calculation is performed on about twentyfp-shell nuclei with massA=52–60. It turns out that, with the model space and the effective interaction chosen, the shell model is well able to reproduce the experimental data in this mass region. As the second step the shell-model wavefunctions are used to calculate energies, electromagnetic moments and transition rates of states with spin up toJ=16. As the third step the observables calculated with the shell model are used to investigate whether these microscopic results can be reproduced by a simple rotational model. About twenty pure axially symmetric rotor bands, generated by the shell model, could be localized. Their properties are presented and discussed.

Molecular electronic spectroscopy by Fabry-Perot interferometry: Contour analysis of a band of the 5500 Å absorption system of s-tetrazine vapor

The very sharp, rotational fine structure of the s-tetrazine- d 0 type- C absorption band at 18913 cm −1 has been recorded with a Fabry-Perot interferometer spectrometer for which the instrumental resolving power is 1 300 000. Because of the absence of spectrometer slit distortion, it has been possible to interpret in detail not only peak positions but also their shapes half-widths and relative heights. Molecular parameters that have been well determined by this asymmetric rotor band contour analysis are the band center and five moments of inertia.

Rotational analysis of the 2714 Å band of p-difluorobenzene

The rotational fine structure of the 0-0 band (2714 Å) of the 1B 2u - 1A g transition of p-difluorobenzene was photographed, and analyzed by the asymmetric rotor band contour method. The rotational constants in the 1 B 2 u state were found to be A′ = 0.1778 cm −1, B′ = 0.04798 cm −1, and C′ = 0.03778 cm −1, those in the ground state being taken to be A″ = 0.18956 cm −1, B″ = 0.04776 cm −1, and C″ = 0.03815 cm −1. These values indicate that the CF bond length is shortened in the excited state. The vibrational analysis and the normal coordinate calculation also support this conclusion.

Rotational band contour analyses in the 3062 Å system of p-fluoroaniline and the 2847 Å system of p-fluorophenol

The origin bands of the 3062 a system of p-fluoroaniline and the 2847 a system of p-fluorophenol have been rotationally analysed by the asymmetric rotor band contour method. They are both type B bands of prolate asymmetric tops which require the electronic assignments of the systems to be 1 B 2-A 1. The excited state rotational constants have been obtained in both cases and show that there is a contraction from the ground to the excited state along the long in-plane axis: the contraction is greater in p-fluoroaniline than in p-fluorophenol. The rotational constants of p-fluoroaniline could not be obtained sufficiently accurately to provide any information on the configuration of the amino group. The rotational origin of the 3062 a band of p-fluoroaniline is at 32653·3 ± 0·1 cm-1 and that of the 2847 a band of p-fluorophenol is at 35115·9 ± 0·1 cm-1.

Rotational band contour analysis in the 2700 Å system of chlorobenzene

The origin band of the 2700 A system of chlorobenzene has been rotationally analysed by the asymmetric rotor band contour method. It is shown to be a type B band of a prolate asymmetric top which requires the electronic assignment of the system to be 1 B 2-1 A 1. The excited state rotational constants are: A′=0·1797 ± 0·0001 cm-1, B′=0·05230 ± 0.00002 cm-1, C′=0.040512 ± 0.000007 cm-1. These can be interpreted in terms of a contraction of the C-Cl bond of about 0·04 A and an expansion of the benzene ring similar to that in the 1 B 2u excited state of benzene. The origin of the 2700 A band is shown to be at 37 048·2 ± 0·2 cm−1. Strong type A bands involving the b 2 vibration v 29 are also assigned from their rotational contours. The 291 level is shown to be in Fermi resonance with the 141201 level. Of the eight prominent sequence intervals associated with the origin band, five are interpreted with considerable certainty.

Rotational band contours in electronic spectra of large asymmetric top molecules: the 2750 Å system of phenol

The rotational band contour of the 0–0 band of phenol at 2750 Å has been recorded experimentally with a resolving power of 300000. The contour contains many characteristic features of which a series dependent on K a has been used to obtain trial sets of rotational constants A', B' and C' in the electronically excited state. The excited state was assumed to be planar. These data together with rotational selection rules were used in an asymmetric rotor band contour computer program and the rotational constants varied until the com­puted contour matched the observed. The contours were matched only by using type B selection rules. The electronic assignment is therefore 1 B 2 – 1 A 1 (using the C 2 v point group) and the excited state rotational constants are : A ' = 0·1773 ± 0·0002 cm -1 ; B ' = 0·08751 ± 0·00006 cm -1 ; C ' = 0·05859 ± 0·00001 cm -1 . These constants reflect an appreciable interaction of the hydroxyl group with the ring in the excited state whereas microwave data have shown very little interaction in the ground state. In particular, there is a slight overall contraction of the molecule along the long in-plane inertial axis from the ground to the excited state in contrast to an expected expansion if there were no hydroxyl group interaction. The origin of the 2750 Å 0–0 band is at 36 348·7 ± 0·2 cm -1 .