Sui livelli energetici dei nuclei pesanti

Riassunto

Si calcola la densità dei livelli energetici dei nuclei pesanti tenendo conto delle interazioni nucleari e del loro effetto sulla dipendenza dell'energia di eccitazione dalla temperatura del nucleo.

Summary

The level density of a standard heavy nucleus is calculated taking into account the modifications brought about by nuclear interactions in the Fermi gas model. Their effect on the energy-temperature dependence is evaluated by the aid of the following relation: τ=T+aφ(τ) between the equivalent temperature τ and the true temperatureT. The energy-temperature relation may be derived either on the basis of the exact Fermi expressions for the number of particles and their total energy (Eqs. 4–5) or modifying the coefficientb of the lawE=bT ² (Eqs. 7), which may be written in the formE=B(a, T)T ². The functionB(a, T) depends strongly on the parametera and is slowly varying with temperature (Table I and II) in the energy range 0≤E<10 MeV, whereabout calculations are referred. The parametera is closely related to the thermonuclear energy as expected from Watanabe's ratioK ⁽²⁾/K⁽⁰⁾=0,34. Its value was found to be 0,35 instead of 0,29 as given by this Author; such difference is due to the fact that exact expressions of Fermi statistics have been throughout used instead of the approximated ones in the equivalent temperature region. The energy levels have been calculated with Bethe's formula taking into account modified expressions for the nuclear specific heat and entropy (Eqs. (9)). The mean value ofB(a, T) in the considered energy region is fairly well fitted with Bardeen's previsions, although derived on substancially different assumptions. In Fig. 4 the energy levels calculated with formula (10) are compared with other theoretical predictions (curves 1, 2, 3) and with the experimental values (curve 5) observed for Pd¹⁰³. The agreement between our previsions and those obtained with the liquid drop model is briefly discussed.