The energy dependence of nuclear reaction cross sections

The reaction cross section σ_R^pA(E) for proton-nucleus collisions varies with energy as the total cross section σ_t^pN(E) does for proton-nucleon scattering in the energy regime 100 MeV ? E ?400 GeV. We propose several empirical relations, and test them by a χ² analysis of various data. Within the framework of Glauber theory, the parameters in the relations can be linked to the cross section for a single inelastic collision.     

Some problems in nuclear reaction calculations

Convergence problems arise in nuclear reaction theories when approximate wave functions are used to describe the internal motion of composite particles involved in the reaction. Implications on the results of a reaction calculation are discussed and models with unique solutions are defined. Some tentative criteria are given as to which model might have solutions similar to the ones obtained with exact channel functions. A least-squares method for linear parameter variation which does not show spurious singularities is also discussed.     

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.     

Studies of nuclear second moments for pre-equilibrium nuclear reaction theories

The nuclear second moments, important inputs to pre-equilibrium reaction theories, are evaluated by assuming a simple model. The positive definite nature of the second moments is examined, and the nuclear level densities are calculated using positive definite second moments.     

Charged-particle reaction studies for nuclear astrophysics

The TUDA and TACTIC facilities at TRIUMF provide versatile experimental capabilities for the study of astrophysically important reactions using both direct and indirect techniques. The present work will outline the research programme to date, describe the experimental facilities and discuss recent developments.     

Nuclear reaction matrix calculations with a shell-modelQ

The Barrett-Hewitt-McCarthy (BHM) method for calculating the nuclear reaction matrixG is used to compute shell-model matrix elements forA=18 nuclei. The energy denominators in intermediate states containing one unoccupied single-particle (s.p.) state and one valence s.p. state are treated correctly, in contrast to previous calculations. These corrections are not important for valence-shell matrix elements but are found to lead to relatively large changes in cross-shell matrix elements involved in core-polarization diagrams.     

Dense plasma effects on nuclear reaction rates

Plasma density effects can cause an exponential change in charged particle nuclear reaction rates important in stellar evolution. Reaction rates in dense plasma, with emphasis on quantum aspects, are examined here using path integral Monte Carlo calculations. Quantum mechanics causes a reduction in the many body enhancement of the reaction rate compared to the value for a classical system. This can be attributed to the "quantum smearing" of the short range Coulomb interaction resulting in reduced repulsion between the reacting pair and surrounding particles. Electron screening and ion exchange effects are also examined, with screening reducing and exchange slightly increasing the many body enhancement.     

The singularity subtraction method for extracting spectroscopic information from nuclear reaction data

We propose an exact method for determining the strength of the nearest singularity of the differential cross section and thus getting information on the structure of nuclei in a completely model-independent way. Using this method we have determined the t → d+n vertex constant with an impressively small error. The connection with similar methods is discussed.     

A simple approximation for the nuclear density matrix

We propose a new approximation for the nuclear density matrix based on the Density Matrix Expansion (DME) of Negele and Vautherin. When applied to a number of simple problems it gives better results than the Slater and the truncated DME approximations.     

Iterative solutions to the nuclear reaction problem

An iterative technique is probably the most efficient and practical way to solve the large sets of integro-differential equations resulting from a CRC analysis of the nuclear reaction problem. In this paper we present the theoretical and practical convergence properties of a new and different type of iterative technique, namely the method of moments. In order to show the power of this method we present a comparison with three other well known iterative methods: the Sasakawa method, the Austern-Sasakawa method, and the method of successive approximation. The dependence of the practical convergence on coupling strength and angular momentum is discussed for the case of inelastic scattering. The method of moments emerges as clearly superior according to both the theoretical and practical convergence criteria. Non-local potentials are shown to introduce very little additional computational difficulty when the iterative technique is used within the framework of the plane-wave expansion method. The method of moments was the only technique capable of guaranteeing convergence when non-local interactions were involved. One merely requires a Hilbert-Schmidt kernel in a finite region of space to guarantee convergence at a rate faster than that of any geometric progression.     

The reaction kinetics of NiCl2 in silica-alumina gel matrix

Insitu isothermal reduction of NiCl₂ by dextrose in silica-alumina gel matrix has been carried out between 800 and 950 °C under nitrogen atmosphere. The predominant mechanism of reaction is found to be nucleation and growth. X-ray diffraction (XRD) analyses of reacted samples confirm the presence of metallic Ni, nickel aluminate and finely dispersed alumina in the reacted samples. The average particle size of nickel has been determined by transmission electron micrograph (14 nm) as well as XRD (17±2 nm).     

The short-range reaction matrix in MQDT treatment of dissociative recombination and related processes

We discuss the Lippmann-Schwinger equation which governs the short-range reaction matrix (K-matrix) in the two-step multichannel quantum defect theory (MQDT) of dissociative recombination and related processes. We show that, if the energy dependence of the electronic coupling between the dissociative state and the ionization continua can be neglected, the convergence of the Born expansion of the Lippmann-Schwinger equation is achieved at second order. For the case of energy-dependent interaction, higher order effects are tested using a non-perturbative method for solving the Lippmann-Schwinger equation. Numerical examples are given for the dissociative recombination and vibrational de-excitation of the H₂ ⁺ molecular ion.Received: 18 April 2003, Published online: 5 August 2003PACS: 34.80.Gs Molecular excitation and ionization by electron impact - 34.80.Ht Dissociation and dissociative attachment by electron impact - 34.80.Lx Electron-ion recombination and electron attachment     

Effect of nuclear shell structure on fusion reaction

The dependence of the fusion reaction on the nuclear shell structure was investigated for the two reaction systems ⁸²Se + ¹³⁸Ba and ⁸²Se + ¹³⁴Ba, where the nucleus ¹³⁸Ba has a closed neutron shell N=82, while the nucleus ¹³⁴Ba has a neutron number 78. Evaporation residues for these fusion reactions were measured near the Coulomb barrier region. The measured evaporation residue cross sections for the reaction system ⁸²Se + ¹³⁸Ba were two orders of magnitude larger than those for the reaction system ⁸²Se + ¹³⁴Ba in the excitation energy region of 20–30 MeV. The evaporation residue cross sections were compared with those of the other reaction systems that produce the same compound nucleus as the present systems. It was found that the fusion reaction ⁸²Se + ¹³⁸Ba occurs without hindrance, while that of ⁸²Se + ¹³⁴Ba is considerably hindered, as commonly observed in the massive reaction system with the charge product Z _p Z _t >1800 of projectile and target. This suggests the importance of the shell closure N=82 in the heavy-ion fusion reaction.     

The reconstruction of the relaxation matrix from an incomplete set of nuclear overhauser effects

Internal motions in a macromolecule and indirect magnetization transfers (spin diffusion) prevent simple interpretation of NOE values in terms of structural and dynamic parameters in the course of the study of a macromolecule. A method for separating these two problems by first analyzing the NOES with respect to the relaxation rate constants is proposed. NOE values for 1 D or 2D experiments are obtained as nonlinear functions of the ϱ and σ parameters by solving the Bloch equations. A general least-squares minimization routine that makes use of the Hessian matrix of second derivatives was found to be efficient in determining iteratively the set of parameters that statistically correlates the corresponding calculated NOEs to a set of experimental NOES. The procedure was applied to probe the internal mobility of the deoxyriboses in a self-complementary hexamer, d(CGTACG)₂. It was found that H_2′-H_2″ and H_1′-H_2″-vectors are subject to internal motions whose amplitudes vary as we move along the sequence.     

On microscopic theory of radiative nuclear reaction characteristics

A survey of some results in the modern microscopic theory of properties of nuclear reactions with gamma rays is given. First of all, we discuss the impact of Phonon Coupling (PC) on the Photon Strength Function (PSF) because it represents the most natural physical source of additional strength found for Sn isotopes in recent experiments that could not be explained within the standard HFB + QRPA approach. The self-consistent version of the Extended Theory of Finite Fermi Systems in the Quasiparticle Time Blocking Approximation is applied. It uses the HFB mean field and includes both the QRPA and PC effects on the basis of the SLy4 Skyrme force. With our microscopic E1 PSFs, the following properties have been calculated for many stable and unstable even–even semi-magic Sn and Ni isotopes as well as for double-magic ¹³²Sn and ²⁰⁸Pb using the reaction codes EMPIRE and TALYS with several Nuclear Level Density (NLD) models: (1) the neutron capture cross sections; (2) the corresponding neutron capture gamma spectra; (3) the average radiative widths of neutron resonances. In all the properties considered, the PC contribution turned out to be significant, as compared with the standard QRPA one, and necessary to explain the available experimental data. The results with the phenomenological so-called generalized superfluid NLD model turned out to be worse, on the whole, than those obtained with the microscopic HFB + combinatorial NLD model. The very topical question about the M1 resonance contribution to PSFs is also discussed.     

Measurement of anomalous nuclear reaction in deuterium-loaded metal

This paper reports on an experiment for testing natural nuclear fusion at low temperature searching for evidence of the origin of ³He from natural nuclear fusion in deep Earth. The experiment was carried out using deuterium-loaded titanium foil samples and powder sample. Detection of charged particle was carried out using a low-level charged particle spectrometer. An Al foil was used as an energy absorber for identification of charged particle. Although the counting rate is very low in the experiment, the emission of energetic particle from the sample is observed and the particle is identified as a proton having energy about 2.8 MeV after exiting the titanium sample. This work provides a positive result for the emission of charged particle in the deuterium-loaded titanium foil samples at low temperature, but a negative result for the deuterium-loaded titanium powder sample. The average reaction yield is deduced to be (0.46±0.08) protons/h for the foil samples. With the suggestion that the proton originates from d--d reaction, we calculate the reaction rate for d--d reaction, and the obtained result is 1.4× 10^-24 fusion/d--d\cdot sec. The negative result of the deuterium-loaded titanium powder sample suggests that the reaction yield might be correlated with the density or microscopic variables of deuterium-loaded titanium materials. The negative result also indicates that d--d reaction catalysed by μ-meson from cosmic ray can be excluded in the samples in this experiment.     

A multi-angle magnetic spectrograph for nuclear reaction studies

A multi-angle magnetic spectrograph for recording spectra of charged particles emitted in nuclear reactions has been built. The apparatus and the beam transport system are described and their parameters are discussed.     

Uncertainties in the 0νββ-decay nuclear matrix elements

The nuclear matrix elements M ^0ν of the neutrinoless double-beta decay (0νβ β) of most nuclei with known 2νββ-decay rates are systematically evaluated using the Quasiparticle Random Phase Approximation (QRPA) and Renormalized QRPA (RQRPA). The experimental 2νβ β-decay rate is used to adjust the most relevant parameter, the strength of the particle-particle interaction. With such procedure the M ^0ν values become essentially independent of single-particle basis size, the axial vector quenching factor, etc. Theoretical arguments in favor of the adopted way of determining the interaction parameters are presented. It is suggested that most of the spread among the published M ^0ν ’s can be ascribed to the choices of implicit and explicit parameters, inherent to the QRPA method. Presented by V. Rodin at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September 26–29, 2005.     

Medical and industrial applications of nuclear reaction physics

An understanding of the interactions of neutrons and protons below a few hundred MeV with nuclei is important for a number of applications. In this paper, two new applications are discussed: radiation transport calculations of energy deposition in fast neutron and proton cancer radiotherapy to optimize the dose given to a tumor; and intermediate-energy proton accelerators which are currently being designed for a range of applications including the destruction of long-lived radioactive nuclear waste. We describe nuclear theory calculations of direct, preequilibrium, and compound nucleus reaction mechanisms important for the modeling of these systems.