Nuclear Reaction Calculations Research Articles

Monte Carlo Calculations of Nuclear Evaporation Processes. III. Applications to Low-Energy Reactions

Monte Carlo calculations of nuclear reactions in the low-energy (E < 50 Mev) region are described. The calculations are based on the nuclear evaporation model of Weisskopf. Continuum theory was used for the calculation of inverse reaction cross sections. In the calculation of the level densities of excited nuclei, pairing and shell energy corrections were used in terms of charactertstic level displacements. The accurate equation rather than the approximate Maxwell distribution was used for the selection of the kinetic energy of the evaporated particle. Experimentally determined Q-values for the various reactions were used. The calculations are compared with experimental measurements for about 60 excitation functions of nuclear reactions in the mass range Cr/sup 50/-Se/sup 74/. Cameron's values for pairing energies were used at the outset; but a new set of pairing and shell energy correction values, which leads to substuntially improved agreement with the experimental curves, Is presented. The procedure which was used to arrive at this set is described and several features of the set are discussed. The need for a further downward correction of the level density of symmetrical (A = 2Z) nuclei is indicated. Computed excitation functions are shown for all the reactions studied as well asmore » for several reactions for which experimental data are not yet available. Further experiments on reaction cross sections are suggested which would allow a unique deterntination of the pairing and shell energy corrections of level densities for any value of Z and N in the region under discussion. The existence of a unique set of these correction terms would provide strong evidence for the validity of evaporation theory for the reactions considered. (auth)« less

Methods of Calculation of Radial Wave Functions and New Tables of Coulomb Functions

In connection with the tabulation of Coulomb wave functions special methods of obtaining numerical results having an accuracy of about one percent have been developed and are reported. Some of the methods are applicable also to other problems. Many of them are concerned with the calculation of the second solution of an ordinary differential equation of second order making use of the first solution. The present paper contains an introduction to the use of new Coulomb Functions tables which cover ranges of parameters required for the calculation of nuclear reactions of protons, deuterons and alpha-particles from hydrogen to oxygen in the energy range of a few Mev. The ranges covered are 0 to 6 for $\ensuremath{\rho}$, 0 to 3.98 for $\ensuremath{\eta}$. For alpha-particles the tables suffice for the treatment of reactions up to about 10 Mev for $Z=9(F) \mathrm{and}5$ Mev for $Z=2(\mathrm{He})$. For protons the tables cover an energy range of roughly 4 times that for alpha-particles.