Bipolar Moment Research Articles

The Properties of the Tilts of Bipolar Solar Regions

We investigate various properties associated with the tilt of isolated magnetic bipoles in magnetograms taken at the solar surface. We show that bipoles can be divided into two groups which have tilts of opposite signs, and reveal similar properties with respect to bipole area, flux and bipolar moment. Detailed comparison of these physical quantities shows that the dividing point between the two types of bipoles corresponds to a bipole area of about 300 millionths of the solar hemisphere (MHS). The time-latitude distribution of small bipoles differs substantially from that for large bipoles. Such behaviour in terms of dynamo theory may indicate that small and large bipoles trace different components of the solar magnetic field. The other possible viewpoint is that the difference in tilt data for small and large bipoles is connected with spectral helicity separation, which results in opposite tilts for small and large bipoles. We note that the data available do not provide convincing reasons to prefer either interpretation.

Stereodynamics of the Photodissociation of Nitromethane at 193 nm: Unravelling the Dissociation Mechanism

The photodissociation of nitromethane at 193 nm is reviewed in terms of new stereodynamical information provided by the measurement of the first four Dixon's bipolar moments, β0(2)(20), β0(0)(22), β0(2)(02), and β0(2)(22), using slice imaging. The measured speed-dependent β0(2)(20) (directly related with the spatial anisotropy parameter β) indicates that after one-photon absorption to the S3(2 (1)A″) state by an allowed perpendicular transition, two reaction pathways can compete with similar probability, a direct dissociation process yielding ground-state CH3 and NO2(1 (2)A2) radicals and a indirect dissociation through conical intersections in which NO2 radicals are formed in lower-lying electronic states. A particularly important result from our measurements is that the low recoil energy part of the methyl fragment translational energy distribution presents a contribution with parallel character, irrespective of the experimental conditions employed, that we attribute to parent cluster dissociation. Moreover, the positive values found for the β0(0)(22) bipolar moment indicates some propensity for the fragment's recoil velocity and angular momentum vectors to be parallel.

A method for the determination of speed-dependent semi-classical vector correlations from sliced image anisotropies

We present analytical expressions relating the bipolar moment β(Q)(K)(k(1)k(2)) parameters of Dixon to the measured anisotropy parameters of different pump/probe geometry sliced ion images. In the semi-classical limit, when there is no significant coherent contribution from multiple excited states to fragment angular momentum polarization, the anisotropy of the images alone is sufficient to extract the β(Q)(K)(k(1)k(2)) parameters with no need to reference relative image intensities. The analysis of sliced images is advantageous since the anisotropy can be directly obtained from the image at any radius without the need for 3D-deconvolution, which is not applicable for most pump/probe geometries. This method is therefore ideally suited for systems which result in a broad distribution of fragment velocities. The bipolar moment parameters are obtained for NO(2) dissociation at 355 nm using these equations, and are compared to the bipolar moment parameters obtained from a proven iterative fitting technique for crushed ion images. Additionally, the utility of these equations in extracting speed-dependent bipolar moments is demonstrated on the recently investigated NO(3) system.

Fourier moment analysis of velocity-map ion images

An alternative to inverse Abel transform and forward convolution methods is presented for extracting dynamical information from velocity-map ion images. Unlike most competing methods, that presented here does not require the probed three-dimensional distribution to possess cylindrical symmetry. The new method involves analysis of the Fourier moments of images measured in different experimental geometries, and allows speed distributions, angular differential cross sections, and angular momentum alignment and orientation to be determined from raw images of the products of photodissociation and photon-initiated bimolecular reactions. The methodology is developed within the semiclassical framework of Dixon’s bipolar moment formalism [R. N. Dixon, J. Chem. Phys. 85, 1866 (1986)], although it is equally applicable to other common formulations of the product scattering distribution. To allow a comparison of the method with the Abel inversion, which requires that the velocity distribution of the probed product has an axis of cylindrical symmetry, the method is applied to newly acquired experimental images of atomic chlorine produced in the photolysis of NOCl. Extraction of product rotational alignment information is illustrated using newly acquired images of rotationally aligned NO formed by NO2 photolysis. Application of the Fourier moment methodology to studies of bimolecular reactions is also demonstrated, using simulated images for the reaction H+D2→HD(v=0,j=0,9)+D.

Measurement of bipolar moments for photofragment angular correlations in ion imaging experiments

A general numerical method is given to extract angular correlations from photodissociation experiments with ion imaging detection. The angular correlations among the transition dipole moment of the parent molecule, μ, the photoproduct recoil velocity, v, and its angular momentum, j, are parametrized analytically using the semiclassical bipolar moment scheme due to Dixon. The method is a forward-convolution scheme which allows quantitative extraction of all measurable bipolar moments and can be applied in experiments with both linearly and circularly polarized probe light. It avoids the cylindrical symmetry limitations of the inverse Abel transform method, traditionally used for extracting photoproduct recoil anisotropy and speed distribution from imaging data. The method presented here also takes into account the possibility of multiple photodissociation channels. The features of the method are illustrated in a two-color 1+1′ REMPI-ion imaging study of the NO photoproduct trajectories resulting from the 650 nm photodissociation of 2-chloro-2-nitrosopropane (CNP). A comparison between experimental and synthetic images is presented for selected experimental geometries. The experimental images for CNP and the results from their fit confirm earlier TOF studies showing that the recoil speed distribution is bimodal with the low and high speed components having average values of approximately 500 and 910 m/s. These components have been previously assigned to dissociation from the S0 and T1 electronic states of the parent molecule, respectively. The experimental results from the current study also confirm that for the high-speed component the product NO velocity vector, v, is preferentially perpendicular to its angular momentum, j [β00(22)=−0.21], and that there is no significant correlation between v and the transition dipole moment μ of the CNP molecule [β02(20)=−0.02].

Determination of μ-v-j vector correlations in photodissociation experiments using 2+n resonance-enhanced multiphoton ionization with time-of-flight mass spectrometer detection

A practical method is described for 2+n resonance-enhanced multiphoton-ionization probing of photofragment μ-v-j correlations arising in molecular photodissociation on a linearly polarized single-photon electric-dipole transition. The scheme uses polarized spectroscopy on the two-photon resonant transition with velocity detection by time-of-flight mass spectrometry. The technique is based on the theory of Kummel, Sitz, and Zare for polarized two-photon detection of angular momentum alignment and orientation and Dixon’s bipolar moment description of vector correlations. Optimal experimental and polarization geometries are described for selective measurement of targeted bipolar moments. The utility of the technique is demonstrated in experiments using 2+1 REMPI to probe methyl radical vector correlations in the 266 nm photodissociation of methyl iodide.

Relationship between bipolar moments and molecule-frame polarization parameters in Doppler photofragment spectroscopy

In terms of the molecular-frame polarization parameters aq(k)(p), an equation is derived that describes the shape of a photofragment Doppler profile as a function of the three angles Γ, Δ, and Φ that specify the photolysis and probe laser polarizations about the detection axis. This expression is specialized to linearly polarized photolysis and probe laser beams. For the particular value of the angle between the probe laser polarization and the detection axis, Δ=π/2, this equation can be reduced to the form of well-known laboratory-frame expressions that use the bipolar moment formalism introduced by Dixon. Comparison of these forms shows the equivalence of the two formalisms and gives the relationships between the bipolar moments βQK(k1k2) and the molecule-frame aq(k)(p) parameters. We show that linear combinations of the bipolar moments completely describe photofragment polarization in the molecular frame and possess distinct quantum mechanical significance. In particular, it is shown that the coherent contribution to the photofragment alignment is proportional to the linear combination (1/5)β02(02)−(1/7)β02(22)−(12/35)β02(42).

Detection of “ended” NO recoil in the 355 nm NO2 photodissociation mechanism

Circularly polarized 1+1′ REMPI with ion imaging detection was used to probe μ–v–j angular correlations of the NO (X 2Π1/2,3/2, v=0) photoproduct from linearly polarized 355 nm photodissociation of NO2 in a molecular beam. Rotational angular momentum orientation was measured for the NO product, with the sense and magnitude of the orientation depending upon the direction of the NO recoil velocity with respect to the polarization vector of the photolysis light. The rotational orientation is shown to originate from the directionality of the torque responsible for NO rotational motion. The experimentally observed sense of rotation in the plane of the NO2 parent molecule is consistent with an effective recoil impulse force applied to the N end of the NO product. A preliminary measure of the bipolar moment associated with this orientation for the j=21.5 and j=36.5 rotational levels gives a value of approximately β02(21)=0.2.

Laser induced fluorescence Doppler profiles of photofragments in the presence of v–J correlation: A density matrix formalism

1+1 LIF Doppler profile functions of photofragments in the presence of v–J correlation are derived in a formalism of density matrix. Radon transforms which are imposed by the resonance condition of Doppler spectroscopy have been implemented exactly. Independent parameters which characterize the angular momentum polarizations of photofragments in a specific state on an expanding Newton sphere have been examined carefully to compare the present treatment with the bipolar moment formalism of Dixon [R. N. Dixon, J. Chem. Phys. 85, 1866 (1986)]. To extract information on speed distributions of photofragments from a combined, isotropic Doppler profile, the proper procedure to take the linear combination of experimental profiles from various detection geometries and rotational branches of transitions has been presented. For future analyses of Doppler spectroscopic measurements of photofragmentation processes, it is recommended that the Doppler profile function in the present framework should be utilized.

NO μ-v-j correlations in the photofragmentation of 2-chloro-2-nitrosopropane

The trajectory of NO X 2ΠΩ=1/2,3/2(v=0) produced after excitation of 2-chloro-2-nitrosopropane S1 Ã 1A″ is studied by polarized 1+1′ resonance-enhanced multiphoton ionization with time-of-flight mass spectrometry detection. The correlations among the NO velocity v, angular momentum j, and the S1 Ã 1A″←S0 X̃ 1A′ [n(N),π*(N=O)] transition dipole μ of the parent molecule are measured. The dissociation occurs by internal conversion to the ground S0 state or intersystem crossing to the T1 ã 3A″ state and the observed speed distribution of the NO fragments is bimodal. There is no evidence for μ-v-j correlations for the products associated with the slow component of the speed distribution. For the higher speed component, the v-j correlation is a function of the NO rotational state, j, and is described by the bipolar moment β00(22). The average value of β00(22) is −0.17(±0.02) at j≊11.5–22.5, more than five times larger than predicted by statistical phase space theory for dissociation on the S0 X̃ 1A′ surface, indicating a moderate preference for a perpendicular orientation of the NO rotational angular momentum and velocity vectors. The v and j vectors are nearly uncorrelated for low NO rotational states (j≤6.5). The μ-v correlation described by the β20(20) bipolar moment does not change with j and its average value is −0.04(±0.01) at j≊12.5–19.5. The average value of the β20(02) bipolar moment describing μ-j correlation is 0.04(±0.02) at j≊7.5–24.5. These results are consistent with a mechanism involving both impulsive force due to a barrier along the reaction coordinate on the T1 ã 3A″ surface and forces resulting from the C–N–O bending and NO torsion about the C–N bond.

The correlated product state distribution of ketene photodissociation at 308 nm

The correlated product state distribution for ketene photodissociation (CH2CO→CH2+CO) at 308 nm has been measured by using quantum-state-specific metastable time-of-flight (TOF) spectroscopy. This distribution is a matrix whose elements are the probability that if CO is produced in the dissociation with quantum-state ‖nCO〉, CH2 will be produced with quantum-state ‖nCH2〉. It was found that ketene photodissociation yields CH2 in three resolved states; the 1A1(000), and 1A1(010) states of CH2 are the major channels, while the 3B1 state is a minor channel. In addition to this scalar distribution, the vector correlations between the recoil velocity and the angular momentum of the CO fragment (v⋅j correlation), expressed by the β00(22) bipolar moment, have also been obtained as a function of the kinetic energy release of the photoreaction. The correlated product state distribution was found not to follow the predictions of phase space theory, suggesting that dynamic hindrances exist in the photoreaction that have not been previously observed. A phase space theory calculation with restricted impact parameter values was also performed and compared to experiment. The impact parameter restricted phase space theory more accurately reproduced all of the correlated product state information obtained in this work as well as previous uncorrelated product state distributions for CH2 and CO. Both the ranges and the values of the allowed impact parameters obtained from these restricted calculations increase as the rotational energy of CO increases. Also, the values of the allowed impact parameters for 1A1(010) CH2 are larger than for 1A1(000) CH2. This strongly suggests that C–C–O bending modes are hindered at the transition state and therefore play an important role in the photodissociation.

NO v–j vector correlations in the photodissociation of 2-chloro-2-nitrosopropane

The correlation between the velocity and angular momentum vectors of the NO X 2ΠΩ=1/2,3/2(v=0) fragment from the photodissociation of 2-chloro-2-nitrosopropane, CH3CCl(NO)CH3, following excitation to the S1Ã 1A″ electronic surface is measured. The experiments are performed in a molecular beam and a scheme for detecting NO by polarized 1+1′ resonance-enhanced multiphoton ionization and pulsed-extraction time-of-flight mass spectrometry is described. The vector correlation is a function of the NO rotational state j, and the bipolar moment describing the correlation has a maximum value of β00(22)=−0.13(±0.01) at j≊18.5–22.5, indicating a preferred perpendicular orientation of the NO angular momentum and velocity vectors. The correlation diminishes as j decreases. This result is consistent with impulsive dissociation from a barrier along the reaction coordinate on the T1ã 3A″ surface, previously postulated to produce the highest angular momentum states of NO.

Photofragment vector correlations measured by sub-doppler 2+1 laser-induced fluorescence spectroscopy

The bipolar moment formalism used by Dixon to discuss the measurement of photofragment vector correlations by sub-Doppler 1+1 laser-induced fluorescence spectroscopy is extended to cover measurements using three photons. The 1+1 and 2+1 LIF methods are compared and the 2+1 LIF approach shown to be more sensitive to some of the higher-order bipolar moments. The usefulness of several special geometries is considered and leads to the conclusion that the LIF technique cannot be used to measure the conventional translational anisotropy parameter directly, nor can it be made to yield an isotropic (flat-topped) lineshape for a single experimental geometry. These limitations are contrasted with the advantages offered by the multiphoton ionisation/time-of-flight technique introduced by Mons and Dimicoli which can achieve both of the above simplifications.

Dynamics of H2O2 photodissociation: OH product state and momentum distribution characterized by sub-Doppler and polarization spectroscopy

Hydrogen peroxide has been optically excited at a wavelength of 266 nm and the OH photofragment completely characterized by Doppler and polarization spectroscopy using the laser-induced fluorescence technique. The entire internal state distribution (vibration, rotation, spin, and Λ components), translational energy, angular distribution, rotational alignment, and vector correlations between rotational and translation motions of OH products is measured. The hydroxyl radicals are formed in the X 2Π3/2,1/2 ground state with 90% of the available energy (248 kJ/mol) being released as OH recoil translation. The angular distribution is nearly a sin2 θ distribution about the electric vector of the photolysis laser. The internal motion of OH is vibrationally cold (no vibrationally excited OH was found) while the rotational excitation in v″=0 can be described by a Boltzmann distribution with a temperature parameter of Trot=(1530±150) K. The two spin states are found to be populated nearly statistically, in contrast to the Λ components which show an increasing inversion with increasing OH rotation. The observed profiles of recoil Doppler broadened spectral lines are strongly dependent on the nature of the transition, the excitation–detection geometry, and the relative polarizations of the dissociating and analyzing laser light. However, the line intensities show only a minor dependence on geometry and polarization indicating a low alignment of OH photofragments (A(2)0≤0.1). For the first time the vector correlation between product rotational and translational motions was analyzed and evaluated in terms of the three bipolar moments β20(20), β00(22), and β20 (22). The bipolar moment β20(20) corresponds to the conventionally defined anisotropy parameter β=2β20(20) =−0.71. The angular distribution peaks in the direction perpendicular to the electric vector of the dissociating laser light, indicating the predominant electronic excited state in H2O2 being of 1A symmetry. The moment β00(22) increases with JOH showing a bias towards vOH and JOH being parallel to one another. The moment β20(22) is a measure of the mutual correlation of the fragment translational and rotational vectors and the transition dipole vector μ in the parent molecule. The positive value of this moment [β20(22)=0.11] indicates that the expectation value of 〈J2y〉 should be very small when μ is parallel to the z axis and vOH perpendicular to μ (x axis). 〈J2x〉 originates in the torsional motion in the H2O2 parent molecule, while 〈J2z〉 reflects the bending vibration of nearly planar H2O2 where the H atoms are in the trans position.