Angular momentum vector correlations

In addition to CO(v = 0—2,7) populations, Houston and Kable recorded CO Doppler profiles to measure the translational energy release, and the vector correlation between the recoil velocity vector and the angular momentum vector of CO. Together, these data paint a compelling picture that two pathways to CH4 + CO are operative. The rotationally hot CO population (85% of total CO)... 

The third technique for establishing a reference axis for angular correlations can be applied to nuclear reactions when the direction of a particle involved in the reaction is detected. This direction provides a reference axis that can be related to the angular momentum axis, but each nuclear reaction has its own pecu-larities and constr aints on the angular momentum vector. For example, the direction of an a particle from a decay process that feeds an excited state can be detected as indicated in Figure 9.7, but, as is discussed in Chapter 7, the energetics of a decay... 

The vector of the electromagnetic field defines a well specified direction in the laboratory frame relative to which all other vectors relevant in photodissociation can be measured. This includes the transition dipole moment, fi, the recoil velocity of the fragments, v, and the angular momentum vector of the products, j. Vector correlations in photodissociation contain a wealth of information about the symmetry of the excited electronic state as well as the dynamics of the fragmentation. Section 11.4 gives a short introduction. Finally, we elucidate in Section 11.5 the correlation between the rotational excitation of the products if the parent molecule breaks up into two diatomic fragments. 

A second correlation exists between the transition dipole moment fi, which is preferentially aligned parallel to Eo, and the angular momentum vector of the photofragment, j. This correlation concerns the direction of the final angular momentum vector j with respect to the space-fixed axis Eo- In quantum mechanics the projection of j on the axis defined by Eo is quantized with quantum numbers mj = —j, + —... 

It is interesting that the normalized memory function for , which has non-Gaussian structure, lies very dose to the normalized correlation function /< I > for the angular momentum vector, while the memory function for the angular momentum is very neariy Gaussian. The former correspondence is not surprising, since the motion of a linear molecule is equival it to that of a particle on a sphere, so that the Kubo-Shimizu consideration of a plane rotation may apply with only the numerical change which makes the relevant correlation function in the exponent of Kubo s formula. 

CO its rotation, must occur such that the angular momentum vector of CO is always perpendicular to the OCS plane, while the recoil direction is always in plane. Therefore, v is perpendicular to j this correlation in OCS photodissociation has in fact been seen [31], The departing CO resembles a tumbling cartwheel. Such vj correlations are very commonly observed. They are expected from the simple impulsive model or indeed from any model where the forces all lie within a plane. Any impulsive force imparted to a diatomic fragment that is directed at a position displaced from the center of mass of the diatomic molecule will lead to both translational and rotational energy and a cartwheeling motion will result. 

The deviations of the Doppler profiles from the behavior predicted by eq.3 are explained in terms of a correlation between the translational and angular momenta of the recoil fragments. If J, L and J are the angular momentum vectors of the parent molecule, the orbital motion of the two fragments and the internal rotational motion of the diatomic fragment respectively, then conservation of angular momentum implies = L + J. If the... 

The complex nature of the slow mode responsible for the long-time behavior of first rank correlation functions for a first rank interaction potential is illustrated by the composition of the eigenvector corresponding to the slow mode 11a in Table XI, for Uj = 3 and o) = 0.5. Note that n 1, tij, ii, J2 describe the magnitudes and the orientations of the momentum vectors Lj and L2 j is referred to the orientation of L, -t- Lj, 7, and J2 are related to the orientations of the two bodies, and the total orientational angular operator defines the quantum number J finally J, which is not included in this table, is the total angular momentum quantum number, and it is always equal to 1 for first rank orientational and momentum correlation functions, and to 2 for second rank correlation functions. In Fig. 11 we show the first rank correlation functions for different collision frequencies of body 1. The second rank correlation function decays are plotted in Fig. 12. The librational motions in the wells are more important than they were in the first rank potential case (since there is now a more accentuated curvature of the potential wells). 

Another important vector correlation in photodissociation is called v-j correlation, which describes the relationship between the recoil velocity and the angular momentum of one of the fragments. This correlation can give important indications about the kinds of torques in effect between the recoiling products during dissociation. These torques can arise from bending and torsional modes in the parent molecule and from exit channel dynamics. 

---