Resonance Absorption Line Shape Research Articles

Information Theory Applied to Parameter Inference of Pake Doublet Spectra

Magnetic resonance absorption lineshapes can have subtle dependencies on the model parameters that specify the lineshape. To quantify how the model parameters influence the lineshape, it is useful to study simple model systems for which analytical expressions are available. We propose that information theory is a useful tool to quantify how well model parameters may be inferred from a noisy signal. Information theory also allows us to assess the importance of missing parameters from an incomplete model. We do this by monitoring the magnitude of a partition function determined from a suitably defined probability mass function as the model parameters are varied. The optimum parameter set makes the partition function a maximum, which establishes a computable criterion for determining the best model parameter set. Given the availability of a partition function, one may define thermodynamic functions such as the entropy. The optimum parameter set in this interpretation corresponds to the state of maximum entropy. In this work, we observe that at sufficiently low signal to noise ratio, the entropy landscape has no clear maximum, while a related quantity, the Fisher information, always has a clear minimum at the optimum parameter set. The qualitative information we are able to gather from the entropy landscapes is also difficult to assess when the parameters are far from their optimum values, at least for the model system studied here.

Mobility of inorganic nanoparticles in soft matter

The 100 nm hematite Fe2O3 particles in gelatin gel, dense water solution of sugar, commercial paints, foam, cosmetic cream and friable powder exhibit the mobility in the range of mm/s which was determined from the analysis of the resonance absorption line shape. In the solution of sugar the movement is correlated for particle–particle distance less then 300 nm. The Mossbauer spectroscopy of the iron bearing nanoparticles is proposed as a novel experimental technique for the investigation of the dynamical and structural properties of the soft matter at the mesoscoipic scale.

A new approach to electron-spin resonance absorption line shape function

We derive a new electron-spin resonance spectrum formula utilizing a quantum-statistical projection technique. The line shape factor appearing in the susceptibility tensor contains the many-body effects for electrons more realistically. It thus becomes possible to explain, in an organized way, all electron transitions including spin conserved processes and spin flipped processes.

Anticrossing phenomena in a resonator with 2D electrons on liquid helium

We have investigated the details of the eigenmode for a resonator containing a two-dimensional electron system (2DES) formed on the surface of liquid helium. We show that anticrossing phenomena occur near the crossing point ω0=ωc, where ω0 is the eigenmode of the resonator and ωc is the cyclotron frequency. The structure of the coupling constant is established. It is a flexible parameter, i.e., sensitive especially to magnetic field and electron density. A finite coupling leads to a perturbation, δω, of the eigenmode of the resonator in presence of the 2DES. Corresponding calculations and measurements of δω are presented. The theory fits the experimental data. The influence of anticrossing on the cyclotron resonance absorption line shape is demonstrated.

Low-temperature evolution of the proton magnetic resonance line shape in ?-phase palladium hydride

Measurements of the proton magnetic resonance absorption line shape in β-phase palladium hydride indicate that there is no short-range ordering associated with the order-disorder phase transition that occurs in the neighborhood of 50 K. However, measurements of the line shape in the range 10–30 K show a change from a Gaussian to a non-Gaussian profile. This effect is not related to the order-disorder phase transition. A possible explanation in terms of thermally assisted tunneling is proposed.

Cubic to tetragonal structural phase transition in K2OsCl6as studied by chlorine nuclear quadrupole resonance: precursor effects in the cubic phase

Chlorine nuclear quadrupole resonance absorption lineshapes are reported for powder and single-crystal samples of the antifluorite K2OsCl6 for a range of temperatures above the cubic to tetragonal phase transition. The temperature dependence of the lineshape and its integrated intensity, as well as the isotope independence of the results, provide clear evidence of precursor effects associated with nonlinear anharmonic behaviour. The results suggest that the detailed dynamics associated with the precursor clusters is sensitive to whether point defects or dislocations are dominant as the primary cause of line broadening.

Near-resonance absorption processes: A model study

We construct an exactly soluble model in which an otherwise bound system can make transitions to another channel with a continuous energy spectrum to simulate the decay of an excited atom by the emission of photons. We show that the resonance absorption line shape occurs naturally in such a model.

Theory of intramolecular energy relaxation and vibrational overtone resonance absorption lineshapes of isolated polyatomic molecules

The vibrational dynamics of an isolated polyatomic molecule in interaction with a laser field is treated by using a graphical analysis of the molecular operators. The lineshape arises from any order of the perturbing intramolecular interaction leading to an integral equation for the local mode scattering operator. Explicit calculation indicates that the identity of the local mode and the normal mode quanta can no longer be retained over hopping times which are comparable to mean free times. The renormalization method introduced here is quite capable of probing short time intra-molecular dynamics and improves on the strict Born approximation utilized by Heller and Mukamel earlier. Essential features of the lineshape remain the same except for the generalization to higher order effects and the inclusion of the interference processes.

The 1H–19F coupled nuclear magnetic relaxation in (NH4)2TiF6

Nuclear magnetic resonance absorption line shapes and spin lattice relaxation times have been measured for the proton and fluorine spin systems in (NH4)2TiF6. At liquid helium temperature the ammonium ions are found to exhibit effects of quantum mechanical tunneling between equilibrium orientations. Over the temperature range 40<T<250 K the spin lattice relaxation of both the proton and fluorine spin systems is controlled by the stochastic reorientation of the ammonium ions. The TiF6= ions remain essentially immobile over this region but their thermal reorientations are found to become effective in the relaxation mechanism above 250 K. The results are discussed in terms of nuclear dipole–dipole cross coupling between the 1H and 19F spin systems.

Proton magnetic resonance line shape measurements in solid ethane

The proton magnetic resonance absorption line shape has been measured for solid ethane in the temperature range from 4 K to the melting point. The linewidth and second moment have been derived from the data. The existence of two solid phases has been confirmed; the solid–solid phase transition temperature was determined to be 89.72 ±0.05 K, and the melting point 90.37±0.05 K. The higher temperature solid phase is characterized by a narrow liquidlike resonance line indicating rapid diffusion. In the lower temperature solid phase the linewidth is much greater and it increases in two stages as the temperature is lowered to 4 K. The second moment of the line has been compared with the result of model calculations and the types of molecular motion inferred. Even at the lowest temperatures the observed second moment is much less than would be appropriate for a rigid lattice; this is interpreted in terms of tunneling of the molecules about their threefold symmetry axes.

Nuclear magnetic resonance in solid cycloheptane

Measurements are reported of the nuclear magnetic resonance absorption lineshape and spin-lattice relaxation time of solid cycloheptane from 50K to the melting point of 265K. Considerable molecular motion is found in the various solid phases but conclusions about the types of motion involved are difficult to reach due to a lack of knowledge of the crystal structure. Although the results in phase III can be explained by molecular pseudorotation process with an activation energy of 1.7 kcal mol-1, it is quite possible that the motion of this very flexible molecule is not of a well defined nature but is a complex and irregular mixture of motions which have comparable restricting barriers. In the higher solid phases, it appears that free isotropic molecular rotation commences and that this is followed by a molecular diffusion process approximately 40K below the melting point.

Resonance Absorption Line Shapes in Monatomic Gases: The Role of Off-Diagonal Resolvent Matrix Elements

A new derivation is given for the resonance absorption line shape in monatomic gases in terms of resolvent-operator matrix elements. This derivation is believed to be simpler and more rigorous than the one given previously by Reck, Takebe, and Mead. In contrast to the earlier result, in which only diagonal resolvent matrix elements appeared in the expression for the susceptibility, it is shown that off-diagonal elements also contribute. In the classical path approximation, with neglect of excitation transfer via virtual transverse photons, it is shown that the line shapes for emission and absorption are identical. The effect of the off-diagonal elements on the line shape is calculated for the static (statistical) limit, and it is shown to lead to a shift toward the blue. It was previously shown that the off-diagonal terms cause a red shift in the opposite "impact" limit.

Theory for Ion Cyclotron Resonance Absorption Line Shapes

Explicit expressions have been calculated for the ion cyclotron resonance (ICR) absorption line shapes for reactive and for unreactive ionic species, in terms of ionic mass and charge, applied rf electric field frequency and magnitude, observing magnetic field strength, and electric drift potentials in various parts of the ICR spectrometer cell. The calculations are based on a zero-pressure equation of motion for the velocity of a charged ion which moves under the influence of a static magnetic field perpendicular to a static electric field and a sinusoidal time-varying electric field. The zero-pressure equation is applied only during the time intervals between ion–molecule collisions, and the power absorption contribution from ions in a particular region of the analyzer region of the ICR spectrometer cell is computed. The relative number of ions in a given region of the ICR cell is determined from that set of ion current expressions which follow from a particular specified kinetic scheme. The power absorption contributions from all regions of the analyzer are then summed; the resultant power absorption expression reduces to a Lorentzian line shape for reactive ions in the limit of very large collision frequency. It is shown that any process which interrupts ion power absorption may contribute to the linewidth of the ion cyclotron resonance. Computer-generated absorption and derivative line shapes are displayed for some representative cases, and plots of calculated ICR absorption linewidth vs collision frequency are given for several line-shape models. The relation of the present work to other models for ICR line shape is extensively discussed.

Magnetic Resonance Study of Molecular Motion in Cubic (NH4)2SiF6

Proton, fluorine, and deuteron magnetic resonance absorption line shapes, as well as 1H and 19F spin—lattice relaxation times, have been measured in polycrystalline cubic (NH4)2SiF6 and (ND4)2SiF6 from −170° to +100°C. The results demonstrate that the threefold proton disorder in the NH4 groups is indeed dynamic and not static, and suggest the following mode of reorientation: The NH4 tetrahedron is first excited from the ground torsional—vibrational state to nearly continuous levels above the potential barrier, and after a short interval of nearly free rotation again drops to one of the three possible equilibrium orientations in the ground state. On the average, each proton spends the same amount of time in each of the 12 equilibrium sites. Large-amplitude rotational oscilations in the ground state are also consistent with the experimental data. The existence of a 19F linewidth transition, as well as spin—lattice relaxation data, demonstrate the onset of hindered rotation of the SiF6 ions above room temperature.

Nuclear magnetic resonance spin-spin relaxation

A general method is described for the calculation of the relaxation function G(t) for a macroscopic nuclear magnetization perpendicular to a strong steady magnetic field, under the influence of the nuclear dipole-dipole interaction. This function is the Fourier transform of the nuclear magnetic resonance absorption line shape. Approximations are introduced, the form of which depends upon whether the short-term or the long-term development of G(t) is required. A third type of approximation leads to the equation of Lowe and Norberg. The theory is applied to the case of the fluorine resonance in calcium fluoride with the steady field in the [100] direction. The first approximation gives a curve that differs only slightly from that of Lowe and Norberg over the range of t for which the latter is in good agreement with experiment. For larger t the disagreement with experiment is less severe, the characteristic oscillation of G(t) being present, though with too large an amplitude. In contrast the second approximation gives a curve which though overdamped provides a better description of the approach of the spin system to equilibrium. The theory may be extended to problems in which the dipolar Hamiltonian possesses an explicit time dependence. In this form it is applied to the case of motional narrowing due to rapid rotation of the sample about an axis inclined at 54.7° to the magnetic field, for which the absorption spectrum consists of a narrow central line flanked by an infinite series of sidebands spaced at intervals corresponding to the rotation frequency. It leads to a separation of the two components of the second moment of the spectrum due respectively to the generation of sidebands and to the finite width of the lines. Though the sum of these contributions is invariant to rotation they themselves are not. An assumed form for the shape of the lines leads to a linewidth which for rapid rotation depends inversely on the cube of the rotation frequency and is in substantial agreement with an earlier statistical theory.

Theory of Resonance Absorption Line Shapes in Monatomic Gases

It is pointed out that the usual theories of pressure broadening disagree with direct experimental measurements of the widths of resonance-broadened alkali doublet lines, although the theories are at least qualitatively confirmed for the wings of resonance lines and for foreign-gas broadening. There are also two conflicting sets of experimental data (both in strong disagreement with theory). Some qualitative arguments are given for doubting the validity, near the center of a resonance line, of the "two-body" approximation generally used in theoretical treatments, and some formal objections to the usual procedure are also presented. The basic equation relating the susceptibility to a resolvent operator matrix element is derived from a more fundamental point of view than usual; the result contains in principle all effects due to translational motion, to the quantized nature of the radiation field, and to "spatial dispersion." In the limit of large absorber mass it is proved rigorously that the two-body approximation can never be valid near the center of a line, even for very low densities. By using different approximations for the wings and the line center, we obtain satisfactory agreement with experiments in both regions for the alkali doublet lines. We are also able to decide between the two conflicting experiments, favoring the square-root density dependence of the line-width observed by Lauriston and Welsh.

Magnetic Resonance Line Shapes at the Onset of Saturation

Magnetic resonance absorption line shapes and widths in Li metal and Ca${\mathrm{F}}_{2}$ crystals have been measured as a function of radio-frequency power level. The measurements have been made on the ${\mathrm{Li}}^{7}$ resonance in Li at 77\ifmmode^\circ\else\textdegree\fi{}K and 215\ifmmode^\circ\else\textdegree\fi{}K and on the ${\mathrm{F}}^{19}$ resonance in Ca${\mathrm{F}}_{2}$ at room temperature. The measurements have been made from low rf power into the region of appreciable saturation, but not into the very high saturation region considered by Redfield. A decrease in $\ensuremath{\delta}H$, the peak-to-peak absorption derivative line width, was observed in both systems at sufficiently large values of ${H}_{1}$, the rf magnetic field. The changes of line width in Li at various values of ${T}_{1}$ and of characteristic motional frequency of the nuclei show good qualitative agreement with the criteria proposed in the recent theory of Tomita. Line-width data obtained by Redfield in aluminum are included for comparison. In the case of Ca${\mathrm{F}}_{2}$, where the spin-lattice relaxation proceeds via paramagnetic impurities, the decrease in $\ensuremath{\delta}H$ occurs at appreciably higher saturation levels than is the case in Li and Al.

Spin Resonance in Metals as a Function of the Overhauser Effect

The polarization of the nuclear spin states by saturating the electron spin levels as predicted by Overhauser is shown to alter the electron spin resonance absorption line shape. It is shown that under certain stringent conditions the line shape may depend upon the sweep direction of the magnetic field ${H}_{0}$. The theory is developed under the assumption of no skin-depth broadening.