Level Anticrossings Research Articles

Study of the residual linewidth of the level-anti-crossing signal in p-benzoquinone

The linewidth of the level-anti-crossing (LAC) signal in p-benzoquinone has been examined using optical detection of magnetic resonance between states in the avoided crossing region. The results are used to separate the homogeneous (due to hyperfine coupling) from the inhomogeneous (due to disorder) contribution to the LAC linewidth.

Optically-detected radiofrequency studies of level anticrossings in phosphorescent crystals

Strong radiofrequency transitions between pairs of anticrossing magnetic sublevels of 3(n, π*) benzophenone and three of its isotopically-labeled derivatives in the deep trap host 4,4′-dibromodiphenylether have been observed using optical detection of magnetic resonance methods. An analysis of the frequency dependence of the positions and intensities of these transitions over the range 0.1–500 MHz provides estimates of the magnitudes of the perturbations V which are responsible for both level-anticrossing (LAC) and cross-relaxation (CR) effects in these systems. By comparing the results for different molecules, it is shown that LAC effects are caused by a combination of off-diagonal intramolecular hyperfine and Zeeman terms whereas CR effects are caused by off-diagonal intermolecular hyperfine terms. Typically, V LAC ≥ 10 V CR; hence, the degree of mixing which is associated with each effect is significantly different.

Jahn-Teller parameters of MgO:Cr2+determined using heat pulses

A strong scattering of phonons at level anticrossings in the low-lying states of Cr2+ in MgO has been observed as a function of magnetic fields. The observed spectra was found to be turning points, with respect to strain, of the magnetic fields at which level anti-crossings occurred. The B//(100) data could be accounted for by a computer diagonalization of the lowest fifteen eigenvalues on the basis of the theory of Fletcher and Stevens (1969) the values 3 Lambda =32+or-6 cm-1 are obtained for the tunnelling splitting and D=2.5+or-0.5 cm-1 for the reduced spin-orbit coupling, with the sign of the warping parameter, B positive.

Optische Kernspin Polarisation (ONP) in Anthracen dotiert mit Phenazin im Temperaturbereich 1,4…300 K / Optical Nuclear Polarisation (ONP) in Anthracene doped with Phenazine in the Temperature Range 1.4…300 K

Abstract ONP of proton spins in anthracene doped with 1000 ppm phenazine has been measured as a function of the external magnetic field Hp and its orientation with respect to the crystalline axes for the temperatures: 300, 78, 4.2 and 1.4 K. At 300 K characteristic features in magnetic fields up to 150 G are similar to results observed in doped fluorene crystals. They are interpreted as due to ONP as a consequence of level anti-crossing (LAC) in the triplet state of guest-host complexes. The zero-field splitting tensor is: D*= ±0.0101 (2) cm-1, ∣E*∣≲∣ ± 0.000811 cm-1 with the principal axes z* ∥ b, y* and x* in the ac-plane with ∢ (y*, a) =30 + 1°. No complex formation is observed at or below 78 K. The most prominent feature at all temperatures is the field dependence of ONP when the magnetic field is oriented along the projection of the long molecular in-plane axes of the anthracene molecules. The excitable triplet states in the doped anthracene crystal are discussed in terms of their qualification as ONP-active states.

Optical nuclear polarization as a consequence of the non-crossing rule (level-anti-crossing): II. The influence of electronic relaxation

The theory for Optical Nuclear Polarization (ONP) as a consequence of Level-Anti-Crossing (LAC) as outlined in the first part of this series, is extended by considering the influence of relaxation between the electron spin states T x . T y and T z . Unselective relaxation as defined by equal rates of relaxation among the spin states, T μ, in general reduces the nuclear polarization. In addition, it broadens the shape of the ONP as a function of the magnetic field. Similar destructive effects are found for selective relaxation with the exception of one specific type of selectiveness. It will be referred to as constructive relaxation, because it is even able to enhance ONP by LAC together with a more pronounced broadening of the field dependence. For instance when a polarizing field is taken in the z direction, a large relaxation rate W xy (relaxation between T x and T y ) enhances the effect. Large rates W xz and W yz would reduce the ONP. The constructive relaxation is treated analytically by perturbation theory. From the experimental ONP results one has to conclude that often of the three relaxation rates is considerably larger than the other two.

Optical nuclear polarization as a consequence of the non-crossing rule (Level-Anti-Crossing): III. Experimental results and evidence for guest-host complexes in doped fluorene crystals

Fluorene crystals doped with the guest molecules acridine, phenazine and anthracene have been studied before due to their strong Optical Nuclear Polarization (ONP) in low magnetic fields around 100 gauss. In this paper, these results together with supporting new data are interpreted in terms of ONP as a consequence of Level-Anti-Crossing (LAC) within the excited triplet state of a guest-host complex. The results permit a first detailed check of the theoretical model of ONP by LAC including the influence of electronic relaxation. Furthermore, they render the spectroscopic parameters needed for the characterization of the triplet-state complexes: • The zero-field splitting tensor and the orientation of its principal axes system with respect to the crystalline axes. • The proton hyperfine tensor, which is essentially due to one-proton spin in the CH 2-group of the fluorene host molecule contributing to the complex.

An analysis of the effects of level crossing and anticrossing in the resonant scattering of thermal phonons

An analysis is given of the changes that occur in the thermal conductivity of a solid containing resonant phonon scattering centres when there are crossings or anticrossings of levels involved in the scattering. At a level crossing, the changes are due to interference between the scattering processes involving the two levels. At a level anticrossing, the two levels repel because of the coupling between them and the changes in conductivity are due to the effects of state mixing as well as to interference. The effects of both types of crossing are discussed in the two limiting cases of weak and strong resonant scattering in comparison with the other scattering rates present. Observation of these effects can in principle provide rather accurate spectroscopic information about the positions of energy levels. In addition, information should be obtainable on the eigenstates and on the lifetimes of the levels involved.

Short-Time-Interval Behavior of Photon Echoes in Ruby near Level Crossings

The behavior of photon echoes near level anticrossings is described in terms of the magnetic-field-dependent mixing parameters. The general features of level-crossing behavior are obscured for most cases in dilute ruby and are dominated instead by strong spin-dependent decay resulting from Cr-Al interactions. However, new experiments at short time separation ($\ensuremath{\tau}=32$ nsec) between pulses have permitted observation of the predicted photon-echo anticrossing signals in ruby, and may be applied to other atomic systems.

Molecular Level Anticrossing in the CN Radical

A molecular level anticrossing experiment has been performed on the CN radical. The A2 Π3/2 state is preferentially populated by chemical reaction and various sublevels of this state are crossed with sublevels of the B 2Σ+ state by tuning with a magnetic field. The levels are mixed and anticrossed by application of a perpendicular electric field and the anticrossing resonance is observed by monitoring the emission in the violet bands. A density matrix theory of level crossing and anticrossing has been developed which allows an arbitrary number of molecular states to be included in the computer calculation of the lineshape. This calculation has been carried out for the case of CN in the two and three level limit, and the predicted electric field dependence of the linewidth and intensity agrees with the experimental results.

Level crossings and anticrossings

The level-crossing technique of atomic spectroscopy utilizes the spatial interference in the scattering of resonance radiation which can occur when a Zeeman level of one of the fine (hyperfine) structure levels of an atom is brought into coincidence (“crossed”) with a Zeeman level of a neighboring fine (hyperfine) structure level by the application of an external magnetic field. For most experimental geometries (relative orientations of direction of incident radiation, magnetic field, and direction of scattered radiation), a sharp change in the intensity of the radiation reaching the detector will occur provided the magnetic quantum numbers of the two Zeeman levels are appropriately related. From the strength of the magnetic field at crossing, one can calculate in a straightforward manner the separation of the levels at zero magnetic field, i.e. the fine (hyperfine) structure splitting. Anticrossing refers to the situation where the levels involved are prevented from crossing by the presence of a small interaction which couples the two corresponding states. Instead of crossing, the levels “repel” one another and the wave functions of the two states interchange their identities as the magnetic field is swept through the region of close approach. Though the crossing does not actually occur, it is still possible to observe changes in the resonance fluorescence from these levels due to this state mixing. These changes can be observed even if the energy splitting at closest approach is many times the level width and in situations where a normal level crossing signal is not observable.