Statistical theory of angular momentum polarization in chemical reactions

A general statistical treatment applicable to any vector property of reactive scattering is derived from angular correlation theory. This pertains to the usual experimental situation in which two or three vector directions are observed but numerous other vectors are random or unobserved, particularly various angular momentum vectors. The dependence of the cross section on the angles relating the observed vectors is expanded as a Legendre polynomial series, with coefficients which represent averages of angular momentum functions over the unobserved vectors. An algorithm for calculating these angular correlation coefficients is provided by the statistical theory. All non-vanishing terms involve only even-order Legendre polynomials. In many experiments, one or two terms are predominant. Classical and quantal versions give the same algorithm in the correspondence principle limit, which often holds for chemical reactions. The angular correlations involving the initial and final relative velocity vector directions [kcirc] and [kcirc]′ and the product rotational angular momentum j′ are treated in detail, including both pairwise and triple correlations. Explicit formulae are given for three choices of the quantization axis : along [kcirc], along [kcirc]′, and along [kcirc] × [kcirc]′. Coefficients for the ([kcirc], [kcirc]′, j′) correlations are tabulated for seven reactions as examples and comparison made with recent experimental measurements of the spatial orientation or polarization of j′ in reactions of alkali atoms with hydrogen halides and with methyl iodide.     

Nuclear spin selection rules in chemical reactions by angular momentum algebra

The detailed selection rules for reactive collisions reported by Quack using molecular symmetry group are derived by using angular momentum algebra. Instead of the representations of the permutation-inversion group for both nuclear spin and rovibronic coordinate wavefunctions, those of the rotation group for nuclear spin wavefunction only are used. The method allows more straightforward derivation of Quack’s results and further extension of the calculation for separating elementary reactions and application to higher proton systems.     

Twin photons entangled in polarization and angular momentum

Quantum states of twin photons entangled in angular momentum and polarization provide new degrees of freedom to researchers in quantum information and imaging. This work discuss these states and also emphasizes differences between two proposed models for twin photons entangled in angular momentum. Answers to the presented questions would contribute to a better understanding of this nonlinear process. Received 30 August 2002 / Received in final form 10 October 2002 Published online 21 January 2003     

Optical orbital angular momentum from the curl of polarization

We predict a new category of optical orbital angular momentum that is associated with the curl of polarization and a kind of vector field with radial-variant hybrid states of polarization that can carry such novel optical orbital angular momentum. We present a scheme for creating the desired vector fields. Optical trapping experiments validate that the vector fields, which have no additional phase vortex, exert torques to drive the orbital motion of the trapped isotropic microspheres.     

Probing the low angular momentum window in fusion reactions

The angular correlation between two alpha particles evaporated from the compound nucleus is sensitive to the initial spin population, and can thus be used to test the possible existence of angular momentum windows in the fusion cross section. A model calculation performed for the ²⁸Si + ²⁸Si fusion reaction at E_cm = 60 MeV is used as an illustration.     

Special topics in the quantum theory of angular momentum

Two special topics in the quantum theory of angular momentum are discussed in this article. They are: (i) the relationship between the coupling and recoupling coefficients (for two and three angular momenta, respectively) and sets of generalized hyper-geometric functions of unit argument; and (ii) the ‘non-trivial’ or polynomial zeros of angular momentum coefficients and their classification.     

The polarization of chemical reactions

Microwaves have been widely used in organic chemical syntheses, but the mechanism is still unclear. The aim of this paper is to study the polarization of polar molecule reactions in the liquid phase. A novel model is proposed to describe the polarization of chemical reactions. In this model, the polarization is expressed by the summation of the orientational polarization of the liquid mixture and the polarization increment due to the chemical process. On the basis of the assumption of local equilibrium, the chemical process is divided into a series of equilibrium systems. We derive the general expression for the polarization increment according to the mass balance equations. By considering a simple chemical process, we give a specific expression for the polarization. Copyright © 2015 John Wiley & Sons, Ltd.     

Study of continuum gamma rays following low angular momentum reactions

The continuum γ-rays following the reaction ¹⁶⁶Er(α, 2n)¹⁶⁸Yb have been studied at bombarding energies of 21, 27 and 36 MeV. The shape of the statistical γ-rays below 1 MeV was deduced. A low energy bump at ～300 keV was observed. This may arise from transitions along bands at and above the pairing gap.     

Zero orbital angular momentum transfer reactions induced by Li ions

An example of a zero orbital angular momentum transfer reaction is the mutual excitation of ⁶Li ions to their T = 1, 0⁺ states at 3.56 MeV. An experimental angular distribution for this reaction is fitted using a distorted-wave theory and also an extension of the adiabatic theory of Austern and Blair. Reasonable fits are obtained in terms of one parameter, the strength of the spin-flip, isospin-flip component of the effective nucleon-nucleon force. Applications of the theory to similar reactions and the inclusion of exchange terms in the amplitude are considered.     

Statistical description of a paired nucleus with the inclusion of angular momentum

The effect of angular momentum on an excited paired nucleus has been studied. The BCS Hamiltonian, modified to include the z-projection of angular momentum has been diagonalized and expressed in terms of the quasiparticle occupation numbers. The grand partition function and all the relevant thermodynamical functions as well as the level-density expression have been derived for the general case of an arbitrary set of single-particle levels. Furthermore, the formalism has been applied to the uniform model and, whenever possible, analytical expressions have been derived. In particular the zero-temperature angular momentum dependence of the gap parameter, the critical angular momentum as well as the yrast line have been calculated. The critical temperature as a function of angular momentum, which defines the phase transition between paired and unpaired systems, has been calculated. A new effect called the thermally assisted pairing correlation, involving an increase of pairing with increasing temperature has been predicted. The completeness of the formalism as applied to spherical or deformed nuclei has been discussed.     

Backscattered polarization patterns, optical vortices, and the angular momentum of light

We demonstrate that the polarization patterns observed in backscattering of linearly polarized light are a manifestation of the conservation of angular momentum of light. We will show that this phenomenon can be described in terms of phase vortices that are acquired by the right and left circularly polarized components. The helicity and orbital angular momentum of these components satisfy the requirement for conservation of angular momentum.     

Evidence for large angular momentum window associated with incomplete fusion reactions

Mean values and variances of the angular momentum window of incomplete fusion reactions induced by¹⁶O on^116–124Sn targets at 90, 100 and 125 MeV have been measured. Theγ multiplicity technique has been used to extract these quantities for each reaction channel identified by discreteγ lines. Incomplete fusion seems to appear in about the same angular momentum window than complete fusion. This is confirmed by the observation of α 2p4n and 2α4n channels appearing at low angular momentum in the 125 MeV reaction.     

Intrinsic angular momentum in HMO

ＩｎｔｒｉｎｓｉｃａｎｇｕｌａｒｍｏｍｅｎｔｕｍｉｎＨＭＯＷＡＮＧＧａｎｇ（ＰｈｙｓｉｃｓＤｅｐａｒｔｍｅｎｔ，ＵｎｉｖｅｒｓｉｔｙｏｆＥｌｅｃｔｒｏｎｉｃＳｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏｇｙｏｆＣｈｉｎａ，Ｃｈｅｎｇｄｕ６１００５４，Ｃｈｉｎａ...