Unified Theory Of Nuclear Reactions Research Articles

Generalized reaction theory with cluster structures and channel orthogonality

The unified nuclear reaction theory that employs the channel projection operators is generalized to include explicitly the cluster structures of a many-body system. It facilitates not only the construction of asymptotic boundary conditions, but also the incorporation of the cluster models in the interaction region. A matrix representation of the scattering equations and the multi-component wavefunctions in the cluster channel space naturally resolves the difficulty associated with the non-commuting channel operators for different cluster structures, thus removing the principal limitation of the previous formulation. The critical problems of over-completeness and cluster channel orthogonality inherent in the multi-component formulation are discussed in detail for the first time, providing the essential mathematical basis for the validity of the generalized theory.

Decay and fission of oriented nuclei

The angular distributions of fragments originating from the binary decay of oriented spherical and deformed nuclei are investigated with allowance for correct transformation properties of wave functions under time inversion. It is shown that, as in the case of protonic decay, the adiabatic approximation for collective rotational degrees of freedom of the systems under investigation is inapplicable in describing the angular distributions of fragments of the deep-subbarrier alpha and cluster decays of nuclei. It is demonstrated that this approximation is justified in describing spontaneous and induced low-energy nuclear fission. The dependence of partial fission widths on the orientation of intrinsic axes, spins, and projections of spins and relative orbital angular momenta of fission fragments is analyzed by using the formalism of the unified theory of nuclear reactions and the theory of open Fermi systems. It is shown that the adiabatic approximation leads to the coherent interference between the wave functions for the relative motion of fragments, whereby the universal angular distributions of fission fragments of oriented nuclei is formed. Deviations from the A. Bohr formula are investigated for these distributions.

A Unified Theory of Nuclear Reactions, II

The effective Hamiltonian method for nuclear reactions described in an earlier paper with the same title, part I, is generalized so as to include all possible reaction types, as well as the effects arising from the identity of particles. The principal device employed, as in part I, is the projection operator which selects the open channel components of the wave function. It is found that the formal structure of part I providing a unified description for direct and compound nuclear reactions including the coupled equation description for direct reactions remains valid in this wider context. A Kapur–Peierls expansion may also be readily obtained. The concept of channel radii is not needed nor is any decomposition of the wave function for the system into angular momentum eigenstates required, so that the expressions for transition amplitudes and widths are invariant with respect to the angular momentum coupling scheme. Since the open channels can only be defined in an asymptotic sense, the corresponding projection operators are not unique. As a consequence the projection operator method has a flexibility which in the first place is consonant with the wide range of phenomena which can occur in nuclear reactions and in the second place can effectively exploit an intuitive understanding of the phenomena. Examples of projection operators are obtained including one which leads to the Wigner–Eisenbud formalism, another which is appropriate for the stripping reaction, and, finally, one which takes the Pauli exclusion principle into account. Note that explicit representations of the projection operators are not required for the development of general formal results but are necessary if, eventually, quantitative calculations are made.

Towards a unified description of light ion fusion cross section excitation functions

A description of light heavy-ion fusion, taking into account both entrance-channel characteristics and compound-nucleus properties, is derived within a unified theory of nuclear reactions. The dependence of the imaginary fusion potential on the level density of the compound nucleus is revealed. The12C +12C,12C +14N,10B +16O and16O +16O fusion cross sections are calculated forE cm≤120 MeV and compared with experimental data. The excitation energy dependence of the level-density parameter of24Mg,26Al and32S is inferred below 5 MeV/A. A realistic nuclear level-density model, describing the experimental level-density parameters of highly excited nuclei, is shown to be consistent with both the global features and details of the fusion cross section.12C +12C and16O +12O fusion cross section oscillations are predicted at large excitation energies, reflecting the structure of the level density of the highly excited light compound nuclei. Differences of the12C +14N and10B +16O fusion reaction mechanisms are discussed in terms of specific entrance-channel characteristics.

N-body quantum scattering theory in two Hilbert spaces. IV. Approximate equations

A rigorous mathematical theory of approximations is developed for the time-independent transition operators of N-body multichannel nonrelativistic quantum scattering theory. New basic dynamical equations are derived and shown to specify uniquely the approximate time-independent transition operators. These operator equations represent coupled integral equations with compact kernels, but it is not assumed that the equations that determine the exact transition amplitudes have compact kernels. Convergence of sequences of these approximate time-independent transition operators to the exact transition operator is established in appropriate limits. Stability of the basic dynamical equations is proved. Resolvent-type equations and their relation to the limiting absorption principle are investigated. The relation of this theory to the Petryshyn theory of A-proper operators and to the Feshbach unified theory of nuclear reactions is discussed.

General statements of a unified theory of nuclear reactions in the formalism of the quantum green's functions

General statements of a unified theory of nuclear reactions in the formalism of the quantum green's functions

Unified theory of nuclear reactions

A theory of nuclear reactions and structures is proposed which unifies and generalizes several different approaches, such as the method of coupled reaction channels and the distorted wave Born approximation for rearrangement processes, the method of coupled channels array, the resonating group method, the Feshbach theory for the optical potential, and the multiple scattering formalism for high energy processes. The present theory employs an optical potential which can be systematically improved in a controlled way.

The resonance photoionisation of neon in the vicinity of the 2p-23s3p1P resonance in the close-coupling approximation

The profile of the 2p-2(3P)3p1P resonance in the photoionisation of neon has been calculated in the close-coupling approximation with two open and two closed channels. An integral method of calculating the atomic continuum wavefunction in the vicinity of resonances is used, which is based on Bloch's formulation of the unified nuclear reaction theory. Good agreement with experiment has been obtained for the characteristics of this resonance in the approximation which simulates the violation of the LS coupling for the classification of such states.

Alpha-decay lifetimes of superheavy nuclei

The lifetimes of some superheavy nuclei are calculated using a method based on the unified theory of nuclear reactions which eliminates the use of arbitrary radii and ambuguous potentials. The results are compared with calculations using Gamow theory and also values calculated from semi-empirical formulae.

Isospin symmetry-breaking in compound and precompound nuclear reactions

The preequilbrium formalism of the Unified Theory of Nuclear Reactions serves as the formal framework for studying the consequence of isospin symmetry-breaking. A T-violating generalization of the energy-average fluctuation cross section is obtained by (a) choosing a “chained-partition” representation of the closed-channel Hilbert space, from the “simple” doorway through subspaces of increasing “complexity,” (b) introducing explicitly the symmetry-breaking component of the A-body Hamiltonian, (c) following its effects through the entire formal framework, and (d) applying standard statistical approximations. An isospin-conversion mechanism emerges in an explicit microscopic representation. Its functional relationship to the mean isospin-mixing interaction strength is realized by performing an approximate diagonalization of a realistic subspace and by employing random matrix theory. Our analysis suggests that near “complete” mixing is common in compound as well as some precompound processes and that its energy dependence can be very rapid. Simplifications of the general formula are noted. One by-product is the T-violating version of the Hauser-Feshbach expression involving a single mixing parameter. The relationship of this parameter to the mixing interaction strength is precisely clarified, and an approximate analytic relation is provided. Employing an extended exciton model with isospin properly incorporated, the statistical theory is applied to a comparative study of the photoalpha-particle reactions 28Si( γ, α 0) 24Mg and 30Si( γ, α 0) 30Mg in their giant dipole resonance regions. Although the former is isospin-forbidden, its energy-integrated experimental cross section is about twice that of the latter which is isospin-allowed. This discrepancy is explained.

Unified theory of nuclear reactions based on master equations for finite open systems

It is shown that the use of master equations for finite open systems allows to formulate a unified theory of nuclear reactions, which includes the most frequently used phenomenological models: optical model, DWBA, internuclear cascade and evaporation model.

Generalization of the Feshbach unified nuclear reaction theory to rearrangement collisions

A multipartition version of the Feshbach unified nuclear reaction theory is formulated. The new theory can deal with rearrangement processes as well as with elastic and inelastic processes. The generalization results from replacing the Lippmann-Schwinger equation for the transition operator by the Baer-Kouri or Kouri-Levin coupled integral equations.NUCLEAR REACTIONS Unified nuclear reaction formalism of Feshbach generalized to include rearrangement channels.

Cross section calculations for the photo break-up reaction 6Li( γ, τ) 3H

The photo reaction 6 Li(γ, τ) 3 H which contributes appreciably to the nuclear photo effect for photon energies between 16 and 35 MeV is studied in the framework of the unified theory of nuclear reactions based on cluster representations.

An Approach to the Unified Theory of Nuclear Reactions

An Approach to the Unified Theory of Nuclear Reactions

Examples of a unified nuclear reaction theory

As examples for a new treatment of nuclear reactions in the frame of a unified theory of the nuclei the elastic α-n and α- α-scattering is calculated, in which one splits the wavefunction of the nucleus in an internal and external part. The results are compared with the corresponding resonating group calculations.

Single-particle resonances in the unified theory of nuclear reactions

A method for the treatment of single-particle resonances in the theory of nucleon-nucleus scattering is introduced which finds application in the projection operator theory of Feshbach. The example of the d 3 2 neutron resonance in the scattering from 16O is discussed.

On a Generalized Distribution of the Poles of the Unitary Collision Matrix

An expression for the joint distribution of the complex poles of the unitary collision matrix is derived for the single-channel case, which is valid for all values of the ratio of the width to the spacing. The derivation uses the statistical distribution of the parameters of the real R-matrix theory. We find that unitarity gives rise to the statistical correlations between the width and the spacing of the collision matrix. It is shown that the distribution of the poles of the unitary collision matrix using Feshbach's unified theory of nuclear reactions is the same as the one obtained using R-matrix theory, provided we make a particular choice of the arbitrary boundary condition in the latter theory. A remark is made about the use of the random complex orthogonal matrix in the study of the parameters of the statistical collision matrix.

Singular Lippmann-Schwinger equations and the unified theory of nuclear reactions

State normalization for a special type of singular Lippmann-Schwinger equation is investigated. The unified reaction theory of MacDonald is based on equations of this type. It is shown that the resolvent method cannot be used to obtain the formal solutions of these equations. We further show that the expressions given by MacDonald are valid only in the simple case for which the targets and residual nuclei have a pure shell-model configuration or for elastic scattering.

Interfering Compound-Nucleus Resonances

It is shown that the unitary form of the low-energy collision matrix based on R-matrix theory and Feshbach's unified theory of nuclear reactions can always be put into a well-known pole-resonance form for the elastic scattering, which contains only independent observable resonance parameters. The importance of the unitary resonance form of the collision matrix is discussed in connection with the statistical study of the fluctuations of the cross sections and the intermediate resonances.

Pauli principle and rearrangement collisions in unified theory of nuclear reactions

A new method is suggested to describe rearrangement collisions in the framework of the unified theory of nuclear reactions. This method allows also to take into account the exclusion principle and to treat the reaction with the number of fragments n ⩾ 3. The problem is reduced to the solution of a system of inhomogeneous differential equations and of a simple system of linear algebraic equations. Thus it is possible to investigate the strong coupling between channels with different composition of fragments when perturbation theory is not correct. The well-known difficulty of treating the rearrangement processes is avoided by using a truncation procedure to “undesirable” components of the wavefunction Ψ.