Partial widths

The quantities y4 are related to the partial widths of the resonance according to... 

In this form, which is the more common expression used in numerical fitting, the matrix A is not as simply related to the partial widths. For an INR,... 

Recently, experimental evidence (Achasov,1999) of the G-parity violating (ft W7T0 decay with the partial widths... 

The next diagram (FIG. 3) also does not contribute to the partial width for the 0 — W7r° decay. In this case the Lagrangian of the strong coupling of axial-vector mesons to vector and pseudoscalar mesons is derived in a similar way and has the form (Nasriddinov, 1994)... 

The structure constants of the SU(3) group responsible for this transition are equal to zero /391 = /3i0i = /39s = /3108 = 0. It should be noted that the diagrams 2 and 3 do not contribute to the partial width of the 0 — con0 decay channel which is obvious also due to the hadronic flavor conservation principle. According to the expression (2),also the anomalous diagram (FIG.4.) does not contribute to the partial width of the 0 —> W7T° decay because... 

Finally the diagram with the intermediate oj meson (FIG. 5) does not contribute to the partial width of this decay channel also because of these structure constants. 

Within the method of phenomenological chiral Lagrangians(PCL s), the partial width of the 0 — um° decay is therefore given by the diagrams with 0 — p and to — p mixings (FIG.6 and FIG.7). In this case all the structure constants are equal to zero except... 

N. Moiseyev, Israel J. Chem., 31, 311 (1991). Resonances, Cross Sections and Partial Widths... 

Secondly, the cross section reflects the nature of the dependence of the partial widths on the intermolecular distance R. As expected from Eq. (20), is small for large R and increases gradually with decrease in R. On the other hand, Fgx in its empirical form (Eq. (17)) is extremely small at large distances and increases sharply near the repulsive wall. Therefore, the de-excitation probability due to Penning ionization is determined by the dipole-dipole part of the decay width in collisions with large impact parameter, whereas the probability for Penning ionization is already almost unity by the single contribution... 

The form displayed in eq. (2-40) implies that the ratios of the amplitudes for scattering into different exit channels are independent of the entrance channel. This, of course, will only be true if the resonance is long lived, so that memory of the initial state can be lost. Note that Aga is a symmetric function, which is a consequence of time-reversal invariance. Note also that, within the approximations used, the phase shift associated with a given channel is just the elastic scattering phase shift for that channel. Finally, the partial widths are proportional to the probability of decay from channel fi. Equation (2-41) is, then, merely a statement that the total probability of decay from channel is the sum of the probabilities of decay into individual channels. 

By analogy, the energy uncertainty associated with a given state, AE, through the Heisenberg uncertainty principle can be obtained from the lifetime contributed by each decay mode. If we use the definition AE = T, the level width, then we can express F in terms of the partial widths for each decay mode T, such that... 

Example Problem Consider the nucleus 64Cu (ti/2 = 12.700 h). MCu is known to decay by electron capture (61%) and (3 decay (39%). What are the partial half-lives for EC and (3 decay What is the partial width for EC decay ... 

All naturally occurring radioactive nuclei have extremely small partial widths. Did you notice that 64Cu can decay into 64Zn and 64Ni This is unusual but can occur for certain odd-odd nuclei (see Chapter 2). 

Conversely, a coherent superposition of continuum states with a population closely reproducing an isolated peak in the density of states, which corresponds to a resonance, can be built in such a way to give rise to a localized state. From this localized state, there will be an outward probability density flux, i.e., it will have a finite lifetime. In the limit of a resonance position far from any ionization threshold and a narrow energy width, the decay rate will be exponential with the rate constant T/ft. The decay is to all the available open channels, in proportion to their partial widths. 

C. A. Nicolaides, Th. Mercouris, Partial widths and interchannel coupling in autoionizing states in terms of complex eigenvalues and complex coordinates, Phys. Rev A 32 (1985) 3247. 

A second interesting point is the way in which the partial widths depend on the rotational quantum number j" of the (v" 0) dissociation fragment. For H2- and D2-Ar, the potential energy surface has only X=0 and 2 components, so the initial (v, j )=(1,0) State may only couple directly to products corresponding to j" 0 and... 

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