Theory of nuclear reactions and decays with allowance for antisymmetrization effects

On the basis of an explicit implementation of the projection-operator method and with due regard to antisymmetrization effects, formulas are constructed for the amplitudes of elastic and inelastic nuclear reactions induced by nucleons and composite particles and for the widths with respect to the nucleonic, alpha-particle, and cluster decays of nuclei. It is shown that equations governing the behavior of elastic-scattering form factors represent generalizations of the equations of the resonating-group model and coincide, provided that ground-state correlations are taken into account, with the analogous equations in the theory of open Fermi systems. It is demonstrated that the nonretarded part of the effective potential of nucleus-nucleus interaction coincides with the Hartree-Fock potential, which has a deep attractive character in accordance with the Levinson theorem, and that the retarded part of the effective potential is determined by the fragmentation of the initial states of colliding nuclei into compound states. It is revealed that the use of different elastic-form-factor representations associated with taking into account antisymmetrization effects leads to the same results for the amplitudes of elastic and inelastic nuclear reactions. The formulas obtained here for the amplitudes of direct inelastic nuclear reactions are found to differ significantly from the corresponding formulas of the distorted-wave method in the Born approximation. Problems that are concerned with the emergence of potential optical resonances for elastic form factors and with their relation to the shell-model wave functions for a compound system are investigated. A new regime of interpolation for the amplitudes of cluster form factors from the shell to the asymptotic region of a decaying nucleus is found. Implications of this interpolation for the calculated alpha-particle and cluster widths and for understanding the nature of superfluid correlations in nuclei are analyzed.     

Quark antisymmetrization and deep-inelastic scattering II. Nuclear structure functions

We consider the effects of quark antisymmetrization for nuclear structure functions. Antisymmetrizing the naive folding of nuclear wave functions in terms of nucleons and the nucleon wave function in terms of quarks, introduces additional contributions. Using the calculated results on quark three-momentum distributions, we calculate the effects on the deep-inelastic structure functions for s- and p-wave nuclei. The effects of quark antisymmetrization turn out to be small.     

Antiproton-Nucleus Interaction and Coulomb Effect at High Energies

The Coulomb effect in high energy antiproton-nucleus elastic and inelastic scattering from ¹²C and ¹⁶O is studied in the framework of Glauber multiple scattering theory for five kinetic energies ranged from 0.23 to 1.83 GeV. A microscopic shell-model nuclear wave functions, Woods-Saxon single-particle wave functions, and experimental pN amplitudes are used in the calculations. The results show that the Coulomb effect is of paramount importance for filling up the dips of differential cross sections. We claim that the present result for inelastic scattering of antiproton-¹²C is sufficiently reliable to be a guide for measurements in the very near future. We also believe that antiproton nucleus elastic and inelastic scattering may produce new information on both the nuclear structure and the antinucleon-nucleon interaction, in particular the p-neutron interaction.     

Exclusion principle and nuclear reaction mechanism

Effects of the Exclusion Principle in specific reference to direct reactions are studied in detail by formulating a simple one-dimensional model in the two channel approximation. The fact that a target wavefunction can be described by different systems of cluster wavefunctions on account of the indistinguishability of nucleons is exploited to bring out the connections between the various aspects of the reaction mechanism and the forward and the backward reaction amplitudes. The coupled integro-differential equations of the model are solved by a matrix method, and an iteration method respectively for low and high energies of the incident particle in the entrance channel. The exact solution of the coupled integro-differential equations takes into account the Exclusion Principle and the effects of rescattering and target recoil. The result shows that the direct reactions are long distance or “surface” phenomena. An evidence is presented that this is a consequence of the Exclusion Principle. The exact result is compared with various approximate results. The latter include the cases; 1. antisymmetrization is completely neglected; 2. antisymmetrization is performed on the target wavefunctions only; 3. plane wave Born approximation; 4. distorted wave Born approximation. The result obtained by target antisymmetrization coincides with the exact result only for high energies of the incident particle. The practical use of this result obtained by use of the two equivalent clusterwavefunctions which describe the target wavefunction is discussed in connection with heavy particle stripping.     

Damping of high-lying single-particle modes in heavy nuclei

The recent experimental and theoretical results on the damping of high-lying single-particle modes in heavy nuclei are reviewed. In one-nucleon transfer reactions these states manifest themselves as broad “resonance”-like structures superimposed on a large continuum. The advantages and the limitations of the transfer reaction approach will be presented using the results from neutron and proton pick-up and stripping reactions. The problem raised by the subtraction of the underlying background, the assumptions made to describe the reaction process and the method used to extract the strength distributions are presented. The existing empirical systematics is summarized for nuclei ranging from ⁹⁰Zr to ²⁰⁸Pb.The theoretical approaches used to explain the damping of the high-lying single-particle modes are based on the coupling between collective and single-particle degrees of freedom. In a first step the bare single-particle mode is spread over several doorway collective states due to the interaction with surface vibrations. In a second step the doorway states spread their strengths over many other degrees of freedom. These two steps of the damping mechanism are discussed in detail within the framework of the quasiparticle-phonon nuclear model. A large-scale comparison between the measured and calculated average energies, spreading widths and spectroscopic strengths of the high-lying single-particle (hole) states in heavy nuclei is presented. The systematic features of the damping (energy, angular momentum and isotopic dependence) are discussed. Recent advances of the experimental approaches, such as the γ-decay of the high-lying states or the use of heavy-ion transfer reactions at intermediate energies, are outlined.The detailed study of the damping mechanism of high-lying single-particle modes reveals new features and leads us to a new field in nuclear structure: “the spectroscopy of inner and outer subshells”.     

Scaling laws and higher-order effects in Coulomb excitation of neutron halo nuclei

Essential properties of halo nuclei can be described in terms of a few low-energy constants. For neutron halo nuclei, analytical results can be found for wave functions and electromagnetic transition matrix elements in simple but well-adapted models. These wave functions can be used to study nuclear reactions; an especially simple and instructive example is Coulomb excitation. A systematic expansion in terms of small parameters can be given. We present scaling laws for excitation amplitudes and cross-sections. The results can be used to analyze experiments like ¹¹Be Coulomb excitation. They also serve as benchmark tests for more involved reaction theories.     

Quark antisymmetrization and deep-inelastic scattering : I. Nuclear quark momentum distributions

We consider the effects of quark antisymmetrization for quark momentum distributions. The simple convolution of nucleon momentum distributions in a nucleus and quark momentum distribution in a nucleon in general does not satisfy the Pauli principle. Antisymmetrizing the product of wave functions in momentum space introduces additional contributions. This paper extends the results for s-wave nuclei to p-wave nuclei, showing that the effects of antisymmetrization in that case are very small. The extension beyond the simple s-wave nuclei is important for the discussion of the role of antisymmetrization in the ratio of deep-inelastic structure functions for nuclei and nucleons.     

The absorptive part of the nucleus-nucleus potential in a semiclassical approach

The imaginary part of the optical potential for nuclear ion-ion scattering in the energy range 20 MeV ?E/A ? 200 MeV is derived using Feshbach's projection formalism. It is defined as the effective absorptive potential in the projected one-body Schroedinger equation for the relative motion of the colliding nuclei. Calculations are done in the Thomas-Fermi approximation, which accounts in a simple way for all phase-space effects as well as for the finite size of the ions. Intrinsic excitations are considered to be of one particle — one hole type in either of the ions, the other remaining in its ground state. The effective two-body interaction is taken to be of finite range. Further simplifications of the model consist in neglecting antisymmetrization between the mutual wave functions of the two ions and in the omission of the Coulomb energy.     

Dispersion theory of nucleon transfer reactions induced by heavy ions

A new approach, the distorted wave pole approximation (DWPA) with the three-body Coulomb effects, is developed by combining the dispersion method and DWBA to analyse the heavy ion-induced neutron transfer reactions. The influence of the three-body Coulomb dynamics on the peripheral partial wave amplitudes is investigated. Differential cross sections of the neutron transfer reactions are calculated to compare the proposed model with the conventional DWBA. The values of nuclear vertex constants for virtual separation of neutron from various nuclei are obtained. The results of the calculations show that DWPA can be applied to analyse the heavy ion-induced neutron transfer reactions and that the three-body Coulomb effects are taken into account with acceptable accuracy in DWBA.     

On the relativistic description of the nucleus

We present a formalism able to generalise to a relativistically covariant scheme the standard nuclear shell model. We show that, using some generalised nuclear Greens functions and their Lehmann representation we can define the relativistic equivalent of the non-relativistic single-particle wave function (not losing, however, the physical contribution of other degrees of freedom, like mesons and antinucleons). It is shown that the mass operator associated to the nuclear Greens function can be approximated with the equivalent of a shell model potential and that the corresponding single-particle wave functions can be easily derived in a specified frame of reference and then boosted to any other system, thus fully restoring the Lorentz covariance.PACS:   21.60.Cs Shell model     

A two-center-oscillator-basis as an alternative set for heavy ion processes

The two-center-oscillator-basis, which is constructed from harmonic oscillator wave functions developing about two different centers, suffers from numerical problems at small center separations due to the overcompleteness of the set. In order to overcome these problems we admix higher oscillator wave functions before the orthogonalization, or antisymmetrization resp. This yields a numerically stable basis set at each center separation. The results obtained for the potential energy surface are comparable with the results of more elaborate models.     

Tensor optimized antisymmetrized molecular dynamics for relativistic nuclear matter

We apply a newly developed many-body theory, tensor optimized antisymmetrized molecular dynamics (TOAMD), to nuclear matter using a relativistic bare nucleon-nucleon interaction in the relativistic framework. It becomes evident that the tensor interaction plays an important role in nuclear many-body system due to the role of the pion in a strongly interacting system. We take the relativistic nuclear matter (RNM) wave function as a basic state and add tensor and short-range correlation operators in the form of pion and omega-meson correlation functions acting on the RNM wave function using the concept of TOAMD. We use the Monte Carlo (Metropolis) method based on the Gaussian integration and the second quantization method for antisymmetrization to calculate all the matrix elements of the many-body Hamiltonian. We write the whole formula of the TOAMD method for numerical calculations of the nuclear binding and saturation properties of nuclear matter using one-boson exchange potential.     

Asymptotic Normalization Constants in Nuclear Astrophysics

The indirect method of determining astrophysical nuclear reaction rates is discussed. The overall normalization of the astrophysical S-factor for such reactions may be determined from one quantity, the asymptotic normalization coefficient of the overlap function of the bound state wave functions for the initial and final channels. These coefficients can be found also from peripheral transfer reactions whose amplitudes are determined by the same overlap function as the amplitudes of the corresponding astrophysical radiative capture processes. The experimental test of this approach and the last results of S₁₇ measurements are presented.     

Multipole expansion of non-local coupling potentials for cluster transfer and application to 16O(16O, 12C)20Ne

When the transfer of clusters and the symmetrization (antisymmetrization) of scattering wave functions is described by cluster models within the coupled-channel formalism, non-local coupling potentials arise. We suggest a procedure to calculate these potentials by a multipole expansion of all potentials and wave functions which depend on sums of vectors. The expansion coefficients are found by least-squares fit. The method is applied to the ¹⁶O(¹⁶O, ¹²C)²⁰Ne reaction, which is treated in the cluster model with two inert ¹²C- and α-clusters as constituents.     

Cross sections for charmonia dissociation in collisions with pions, rhos and kaons

We calculate the unpolarized cross sections for dissociation reactions of charmonia in collisions with π,ρ and K in a potential that is derived from QCD.The reactions are governed by the quark-interchange processes.The mesonic quark-antiquark relative-motion wave functions are determined by the central spinindependent terms of the potential.The numerical wave functions and cross sections are parametrized.The difference of transition amplitudes in the prior form and in the post form is explored by deriving and examining the transition amplitudes of the one-gluon-exchange spin-spin term of the potential in the two forms.We find that the post-prior discrepancy in meson-meson elastic scattering that is governed by quark-interchange processes depends on the difierence of quark or antiquark masses and of quark-antiquark spatial distributions ofthe two mesons.