Klapdor (1983) has argued that the neglect of any structure within beta-strength functions is an oversimplification that is inconsistent with experimental observations. Structure is found at high-level densities, and can significantly affect the half-lives and branching ratios of P—delayed processes. Klapdor and Metzinger (1982a and 1982b) included this structure when determining the electron and antineutrino spectra generated after the fission process. Their method involved microscopic calculations of Sp(E) for all fission products:

Sp (E) dE=£ Bt (Et) dE / D

i

where B(E) is the reduced beta transition probability to a state at excitation energy Ei in the daughter nucleus, and D is the vector coupling constant. However, a major source of uncertainty in the calculation of the electron and antineutrino spectra is the effect the fission products with unknown or poorly-defined decay schemes will have on the shape of the beta-strength function.

0. 1 1 10

cooling time (s)

Fig. 18. Calculated P-and y-ray components of 235U decay heat compared with experiments at very short cooling times (Yoshida and Tachibana, 2000)

cooling time (s)

Fig. 19. Calculated P — and y-ray components of 238U decay heat compared with
experiments at very short cooling times (Yoshida and Tachibana, 2000)

Despite a lack of reliable decay-scheme data for a significant number of fission — product nuclides, P—spectra have been calculated by Davis et al (1979), Avignone and Greenwood (1980), Kopeykin (1980) and Vogel et al (1981) on the assumption that the resulting beta-strength function is smooth. These particular calculations do not reproduce the precise P-spectrum measurements of the fission products from 235U fission (Schreckenbach et al, 1981). Klapdor and Metzinger (1982b) undertook a microscopic analysis of Sp(E) for all fission products with unknown and uncertain decay schemes: considerable improvement was obtained against the measurements,
with a deviation from experiments of less than 4%. Figs. 20 and 21 compare the electron and antineutrino spectra obtained from the various methods of calculating Sp(E), normalised against the equivalent measurements of Schreckenbach et al (1981); calculation/experiment ratio (C/E = R) for method 4 (i. e., Klapdor and Metzinger, 1982b) is much closer to unity over the full energy range. Table 9 lists the different sets of data as a function of electron and antineutrino energy. Studies have also been made of the thermal fission of 239Pu, with similar results (Klapdor and Metzinger, 1982a).

Further microscopic modelling studies by Hirsch et al (1992) have resulted in the successful use of the proton-neutron quasiparticle random phase approximation (pn — QRPA) to calculate the beta-strength functions. Single particle energies are calculated, taking into account nuclear deformation and pairing interaction; subsequent RPA calculations include proton-neutron residual interactions. The resulting theoretical half-lives and mean beta and gamma energies are in good agreement with experimental measurements across the full range of Z, and these data have been adopted to extend the range of radionuclidic coverage of a number of decay-data libraries.