On The Statistical Theory On Nuclear Reactions

Statistical Models for Nuclear Decay: From Evaporation to Vaporization describes statistical models that are applied to the decay of atomic nuclei, emphasizing highly excited nuclei usually produced using heavy ion collisions. The first two chapters present essential introductions to statistical mechanics and nuclear physics, followed by a description of the historical developments, beginning with the application of the Bohr hypothesis by Weisskopf in 1937. This chapter covers fusion, fission, and the Hauser-Festbach theory. The next chapter applies the Hauser-Festbach theory using Monte Carlo methods and presents important experimental results. Subsequent chapters discuss nuclear decay at high excitation energies, including the theories and experimental results for sequential binary division, multifragmentation, and vaporization. The final chapter provides a short summary and discusses possible paths for further research.

Since the discovery of quantum mechanics,more than fifty years ago,the theory of chemical reactivity has taken the first steps of its development. The knowledge of the electronic structure and the properties of atoms and molecules is the basis for an un derstanding of their interactions in the elementary act of any chemical process. The increasing information in this field during the last decades has stimulated the elaboration of the methods for evaluating the potential energy of the reacting systems as well as the creation of new methods for calculation of reaction probabili ties (or cross sections) and rate constants. An exact solution to these fundamental problems of theoretical chemistry based on quan tum mechanics and statistical physics, however, is still impossible even for the simplest chemical reactions. Therefore,different ap proximations have to be used in order to simplify one or the other side of the problem. At present, the basic approach in the theory of chemical reactivity consists in separating the motions of electrons and nu clei by making use of the Born-Oppenheimer adiabatic approximation to obtain electronic energy as an effective potential for nuclear motion. If the potential energy surface is known, one can calculate, in principle, the reaction probability for any given initial state of the system. The reaction rate is then obtained as an average of the reaction probabilities over all possible initial states of the reacting ~artic1es. In the different stages of this calculational scheme additional approximations are usually introduced.

This volume provides the up-to-date information behind nuclear reactor calculations, focusing on a key role of nuclear reaction data, down to the physics of nuclear interactions. It is divided into three parts. Part 1 deals with nuclear reaction models, including neutron resonances, fission, the optical model, statistical and preequilibrium models as well as nuclear level densities. Part 2 is devoted to nuclear data filling and processing; it includes lectures on nuclear data evaluation and formatting, data libraries and services, with emphasis on nuclear-data-processing codes. Part 3 presents applications in nuclear reactor calculations, emphasizing physics, design and safety.

449 one finds that for y = Fo (e) C= :n; V3 [Po (2'Yj) 3 -kjF(i) + (2'Yj)! Fd (2'Yj) 3 -ijF (·m, } 1 (14.17) C2 = :n; [- (2'Yj)! Fd (2'Yj) 3 -ijF(i) + Fo (2'Yj) 3 -~;r(i)J, and if y is to be Go(e), C and Chave the same form with Go (2'Yj) replacing Po (2'Yj) 1 2 and G~(2'Yj) replacing Fd(2'Yj). The values of the functions at eo =2'Yj may be ob tained from (14.8). 1 J.K. TYSON has employed the modified Hankel functions of order one third 2 as solutions of (13.4) to obtain expressions for the Coulomb functions for L =0 which converge near e =2'Yj. His results appear as linear combinations of the real and imaginary parts of n ~(x) = (12)!e- ;/6 [A;{- x) - iB;( -x)J, (14.18) and its derivatives multiplying power series in x = (e - 2'Yj)j(2'Yj)1. For values 1 away from the turning point for L =0, TYSON has obtained forms for Po{e) and Go(e) which are similar to (13.1) to (13.3). The JWKB approximation is again the leading term, and some higher order corrections are given. Expressions similar to Eqs. (14.11) and (14.12) have been obtained by T.D. 3 NEWTON employing the integral representation of (4.4). His results give re presentations of FL(e), Gde) in the vicinity of e=2'Yj [whereas (14.11), (14.12) converge near e=eLJ when L.

Nuclear Reactions deals with the mechanisms of nuclear reactions and covers topics ranging from quantum mechanics and the compound nucleus to the optical model, nuclear structure and nuclear forces, and direct interactions. The structure of the atomic nucleus and capture of slow neutrons are also discussed, along with nuclear reactions at high energies, neutron capture and nuclear constitution, and elastic and inelastic diffraction scattering. This book is comprised of 17 chapters and begins with an overview of early successes and difficulties experienced by nuclear physics as a discipline, paying particular attention to early applications of quantum mechanics and reactions with neutrons. The next chapter explores the compound nuclear and considers the theory of Breit and Wigner, resonances in nuclear reactions, and the statistical model or compound nucleus model. The reader is methodically introduced to the optical model and elastic scattering experiments; nuclear structure and nuclear forces; and direct interactions. The remaining chapters look at the theory of the effect of resonance levels on artificial disintegration; fluctuations of nuclear reaction widths; scattering of high-energy neutrons by nuclei; and regularities in the total cross-sections for fast neutrons. This monograph will be a useful resource for nuclear scientists and physicists as well as undergraduate students who have taken a first course in quantum mechanics.