Weisskopf transition rate

Figure 9.3 Weisskopf single-particle estimates of the transition rates for (a) electric multipoles and (b) magnetic multipoles. From Condon and Odishaw, Handbook on Physics, 2nd Edition. Copyright 1967 hy McGraw-Hill Company, Inc. Reprinted by permission of McGraw-Hill Book Company, Inc.

The Weisskopf estimates are usually good to within a factor of 10, which is remarkable given the large number of orders of magnitude that they span, and provide important references for comparison to the observed transition rates. Notice that if a transition occurs more rapidly than the single-particle rate then... 

TABLE 9.2 Weisskopf Single-Particle Transition Rates (Ey is in MeV)... 

As already mentioned, the Weisskopf estimates are calculated in the single-particle approximation, supposing constant radial wave function. The observed transition rates sometimes strongly deviate from the estimated values. Nevertheless, the Weisskopf units (W. u.) are very useful for comparison. For example, enhanced transition rates (compared to the Weisskopf estimate) signal collectivity. 

Endt (1981) evaluated 1,340 y-ray transitions in A = 91-150 nuclek The transition rates were classified according to electric or magnetic multipole character and were expressed in Weisskopf units. Transitions, which can be mixed in principle, are only listed if the mixing ratio has been measured. The strengths S = Ti Ti) usually scatter appreciably, nevertheless, upper limits could be established fi-om the data. These are 0.01,300,100, and 30 W. u. for El, E2, E3, and E4 and 1, 1, 10, and 30 W. u. for Ml, M2, M3, and M4 radiations, respectively. For upper limits in other regions see (Firestone et al. 1996). The strengths are usually enhanced for E2, and E3, while the El, M2 transitions are usually hindered. 

Example Problem Use the electromagnetic selection rules to identity the character of the isomeric transition from the hrst excited state at 0.439 MeV( + ) in 69Znm with the ground state ( ). Then calculate the Weisskopf single-particle rates for the allowed transitions. 

In heavy elements the El transition probabilities are typically 1.0 x 10"6 Weisskopf units for AK 1 transitions and 1.0 x 10 w.u. for AK-0 transitions. We define fast El transitions as transitions with rates of >1.0 x 10 w.u. Recently we have measured [Ish85] level lifetimes in Z 5Ra and 3Ac which indicte the presence of fast El transitions in these nuclei. 

For the theoretician, clusters are also convenient model systems to evaluate the performance of dissociation rate theories. By comparing the results of numerically exact molecular dynamics (MD) trajectories to the predictions of rate theories, the various approximations inherent to these theories can be unambiguously tested and possibly improved upon. Previous authors have critically discussed how the Rice-Ramsperger-Kassel (RRK), ° Weisskopf, and Phase Space Theory of Light and Pechukas, Nikitin, Klots, Chesnavich and Bowers respectively compare for the thermal evaporation of atomic clusters. This work was subsequently extended by the present authors to rotating and molecular clusters. From these efforts it was concluded that phase space theory (PST), in its orbiting transition state version, was quantitatively able to describe statistical dissociation. This chapter is not devoted to a detailed presentation of phase space theory and the reader is encouraged to consult the cited work. 

---