Angular momenta distribution

The most natural method of detecting the optical polarization produced in the excited state consists of using the polarization characteristics of molecular fluorescence from this state in some transition b — c which is convenient for observation see Fig. 1.2. The same radiation, in the cycle a —> b c may also provide information on the initial state a if the process of absorption is non-linear. A more direct way of probing the anisotropy of angular momenta distribution in the ground state consists of monitoring the absorption from this level by means of a test beam. 

In the case of righthanded circular polarized i -type excitation, when orientation of angular momenta takes place and the probability density of the angular momenta distribution is proportional to (1 — cos )2/2 (see (2.13)), only alignment of internuclear axes occurs, described by the probability density, which is proportional to (1/2)[1 + (sin20r)/2j. 

Three components (Q — —1,0,+1) of the multipole moment of rank K = 1 form the cyclic components of the vector. They are proportional to the mean value of the corresponding spherical functions (B.l) for angular momenta distribution in the state of the molecule as described by the probability density p 9,(p). These components of the multipole moments enable us to find the cyclic components of the angular momentum of the molecule ... 

Applying the latest model, the simplest equation for the probability density of angular momenta distribution in the absorbing state a may be written as follows ... 

Fig. 3.2. Isometric projection of the probability density of angular momenta distribution of ground (lower part) and excited (upper part) states (a) Q excitation (6) (P, R) excitation by light with E z.

When molecules arrive at the state with rotation quantum number J" from the state J in the process of spontaneous radiation at rate (see Fig. 3.14), a photon possessing unit spin is emitted in an arbitrary direction. Let us assume that the angular momentum carried away by the emitted photon is small, as compared with both 3 [ and Jr. This means that the angular momentum vector of each separate molecule does not change its value and does not turn in space as a result of the spontaneous transition. Consequently, the angular momenta distribution pji(0,ip) is... 

Effect of external magnetic field on angular momenta distribution... 

We thus see that the purely magnetic evolution (4.11) of the polarization moment is, in essence, a linear change in time of its phase ip according to (4.12), with conservation of the module Mod pq (circle in Fig. 4.1(c)). The factor e1 means that the dependence pq (t) is periodic with a period Tq = 2ir/Qu)ji, i.e. that each transversal component of a polarization moment passes into itself with its own frequency Quj>. This is in full agreement with what has been said before in Section 2.3 on the connection between the coherence and symmetry of p(6,ip). The model presented affords the conservation of the shape of the angular momenta distribution p(0,ip) in the course of precession (see Fig. 4.1(6)). Incidentally, it may not seem quite appropriate in this context to maintain the statement that the magnetic field itself destroys coherency , as described by the transversal components pq, Q 0. Indeed, it follows from (4.11) that at... 

Due to the fact that the effect of a magnetic field on the ground state angular momenta distribution pa(0, ip) causes changes in the excited state distribution pb(9,(p) (see Figs. 4.9 and 4.10), one may expect to observe the ground state Hanle effect in fluorescence intensity difference I — I or in the degree of polarization V B). Indeed, since we have gj"/yK 2>... 

Let us consider the effect of an external magnetic field on the angular momenta distribution at a level populated in the fluorescence process see Section 3.4, Fig. 3.14. In the presence of an external magnetic field the following polarization moments are created on the lower level J" via spontaneous transitions at weak excitation, x — 0 ... 

The photodissociation process takes place most frequently at excitation of the molecule to a non-bonded state, with subsequent dissociation into products. Since the angular part of the transition probability, according to Chapter 2, is still dependent on the mutual orientation of the E-vector of the initiating light beam and on the transition dipole moment d, one may expect spatial anisotropy of angular momenta distribution both in the dissociation products and in the set of molecules which remains undestroyed. 

It was shown in Section 2.3 that for the description of axially symmetric angular momenta distribution the use of only the polarization moments pg where Q = 0 are sufficient. In this case p(d, functions connected with Yko(0,Legendre polynomials [183] Pk(cos 6) which may be easily obtained in explicit form using the formula... 

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