Fission width

In analogy to chemical reactions, we might expect the probability of fission as expressed in the fission width, Tf(=h/r) to be given as... 

There are three types of resonance widths in the Doppler effect expressions the elastic neutron emission width, the radiative capture or gamma width, and the fission width. The inelastic scattering widths are negligible at the low energies pertinent to Doppler effect. 

In the case of the figures in Table IV should only be regarded as an example of the two methods for estimating v. Recent theoretical and experimental work (43, 44) supports the idea that the two spin states in the Pu compound nucleus may have substantially different mean fission widths. The parameter v may also be different for the two states. It is easy to see that, if the data were actually the superposition of two chi-squared distributions with moderate values of v but widely different values of , the values of v as just calculated for the combined data could be significantly lower than either of the individual v values. This could explain the low value of 0.7 calculated by the moment method. For the recommended parameters, see the following section. 

The most uncertain quantity is the parameter v for the fission width distribution. The values one, two, and three have been recommended by different authors. Garrison (54) finds that a maximum likelihood test of the combined fission width distribution of four fissile isotopes yields V = 2.0, whereas Fischer 32) finds v = 2.2 for and v = 1.2 for... 

For Pu, there is, besides some scant older data, a recent measurement of the fission cross section carried out by Moore et al. (71) at the Rensselaer linear electron accelerator. The experiment covered the range up to 100 eV, and up to 36 eV the accuracy was sufficient to permit multilevel analysis. Twenty-one levels were detected and analyzed between 4 and 36 eV the radiation width was taken to be 40 mV. There is strong evidence that the levels split up in two groups with clearly different average fission widths. 

The complication that the transition state cannot be recrossed was dealt with theoretically by Kramers (1940), where the fission width is reduced relative to the Bohr-Wheeler estimate by saddle recrossing. As the recrossing probability increases with friction, the reduced fission probability can be cast in terms of the friction coefficient y. 

The obtained widths of the peaks show the experimental energy resolution up to about 5.3 MeV. Above this excitation energy, the peaks get increasingly broader due to the increasing fission width when one approaches the top of the fission barrier. The low-energy part of the spectrum, which was analyzed before (Krasznahorkay et al. 1998b), is compared to the one published by Blons et al. (1988) in Fig. 5.20. 

The fusion cross section (Tfus depends on the projectile energy Ep, the height of the fusion barrier E, and the angular momentum I of the system. The survival probability of the compound nucleus is determined by the excitation energy E, which yields the number of evaporated neutrons x For each step of neutron evaporation there is a strong competition between neutron evaporation and fission given by the ratio of neutron to fission width IEf. 

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