In this article we present a new method for reconstructing three-dimensional ͑3D͒ images with cylindrical symmetry from their two-dimensional projections. The method is based on expanding the projection in a basis set of functions that are analytical projections of known well-behaved functions. The original 3D image can then be reconstructed as a linear combination of these well-behaved functions, which have a Gaussian-like shape, with the same expansion coefficients as the projection. In the process of finding the expansion coefficients, regularization is used to achieve a more reliable reconstruction of noisy projections. The method is efficient and computationally cheap and is particularly well suited for transforming projections obtained in photoion and photoelectron imaging experiments. It can be used for any image with cylindrical symmetry, requires minimal user's input, and provides a reliable reconstruction in certain cases when the commonly used Fourier-Hankel Abel transform method fails.

Angular distributions of state-selected NO and O products in the photoinitiated unimolecular decomposition of jet-cooled NO 2 have been measured by using both the photofragment ion imaging technique with velocity map imaging and ion time-of-flight translational spectroscopy. The recoil anisotropy parameter of the photofragments, ␤, depends strongly on the rotational angular momentum of the photoproduct. O( 3 P jϭ2,0 ) angular distributions are recorded at photolysis wavelengths 371.7, 354.7, and 338.9 nm. At these wavelengths, respectively, vibrational levels v ϭ0, vϭ0,1 and vϭ0 -2 of NO are generated. In addition, ␤ values for NO(vϭ2) in specific high rotational levels are determined at ϳ338 nm. The experimental observations are rationalized with a classical model that takes into account the transverse recoil component mandated by angular momentum conservation. The model is general and applicable in cases where fragment angular momentum is large, i.e., a classical treatment is justified. It is applied here both to the experimental NO 2 results, and results of quantum calculations of the vibrational predissociation of the Ne-ICl van der Waals complex. It is concluded that deviations from the limiting ␤ values should be prominent in fast, barrierless unimolecular decomposition, and in certain dissociation processes where a large fraction of the available energy is deposited in rotational excitation of the diatom. The application of the model to NO 2 dissociation suggests that the nuclear dynamics leading to dissociation involves a decrease in bending angle at short internuclear separations followed by a stretching motion. This interpretation is in accord with recent theoretical calculations.

Angular distributions of selected rotational states of NO(A 2 ⌺ ϩ ,ϭ0) products obtained in the 213 nm photodissociation of (NO) 2 have been determined in a molecular beam by using the photofragment ion imaging technique. Specifically, images of NO(A,ϭ0) products in Nϭ0, 11, and 19 have been recorded, for which the maximum energies available to the NO(X 2 ⌸) products are 2038, 1774, and 1278 cm Ϫ1 , respectively. The recoil anisotropy parameter of the photofragments, ␤ eff , decreases significantly at low center-of-mass translational energies from its maximum value of 1.36Ϯ0.05, and depends strongly on the rotational angular momentum of the photoproducts. This behavior is described well by a classical model that takes into account the transverse recoil component mandated by angular momentum conservation. For each of the observed NO(A) N states, highly rotating NO(X) levels are produced via planar dissociation, and the angular momenta are established at an interfragment separation of about 2.6 Å. For most of the center-of-mass translational energy range, both corotating and counterrotating fragments are produced, but at the lowest energies, only the latter are allowed. The correlated rotational energy distributions exhibit deviations from the behavior predicted by phase space theory, suggesting that exit-channel dynamics beyond the transition state influences the product state distributions. In this study, a new method for image reconstruction is employed, which gives accurate angular distributions throughout the image plane.

The correlated angular and product rotational state distributions obtained in the 221.67 nm photodissociation of (NO) 2 yielding NO(A 2 ⌺ ϩ)ϩNO(X 2 ⌸) have been examined in the molecular beam using the velocity map ion imaging technique. The translational energy and angular distributions of selected rotational states of NO(A 2 ⌺ ϩ) products in Nϭ0, 5, 6 for which the maximum energies available to the NO(X 2 ⌸) products are 202.5, 142.5, and 118.5 cm Ϫ1 , respectively, have been measured. The recoil anisotropy parameter of the photofragments, ␤ eff , is 1.2Ϯ0.1, less than that previously measured at 213 nm ͑1.36Ϯ0.05͒. The correlated product state distributions near dissociation threshold agree with the predictions of phase space theory. These experimental results, as well as those obtained previously at 213 nm, are compared to statistical calculations, including v"J correlations. Application of the ␤-E T correlation model to the 213 nm results indicates that ͓NO(A,N),NO(X,J)͔ pairs with high NO(X,J) rotational levels are produced preferentially via planar dissociation, in contrast to the statistical expectation of the v"J correlation, which reveals no preference for planar dissociation. A mechanism involving vibrational predissociation with restricted intramolecular vibrational energy redistribution can explain both the observed scalar and vector properties. Specifically, the low frequency torsional ͑out-of-plane͒ mode does not couple efficiently to the other modes, especially at higher excess energies when the dissociation is rapid. On the other hand, the long-range attraction between NO(A) and NO(X), which is revealed both in the photodissociation dynamics of the dimer and in the quenching of NO(A) by NO(X), encourages long-range mode couplings and can explain the largely statistical rotational state distributions observed near threshold. From images obtained near threshold, the bond energy of the NO dimer in the ground state is determined to be 710Ϯ10 cm Ϫ1 , in good agreement with previous results.

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