Direct Reaction Theory Research Articles

Single-particle spectroscopic strength from nucleon transfer reactions with a three-nucleon force contribution

The direct reaction theory widely used to study single-particle spectroscopic strength in nucleon transfer experiments is based on a Hamiltonian with two-nucleon interactions only. We point out that in reactions with a loosely-bound projectile, where clustering and breakup effects are important, an additional three-body force arises due to three-nucleon (3N) interaction between two nucleons belonging to different clusters in the projectile and a target nucleon. We study the effects of this force on nucleon transfer in (d,p) and (d,n) reactions on 56Ni, 48Ca, 26mAl and 24O targets at deuteron incident energies between 4 and 40 MeV/nucleon. Deuteron breakup is treated exactly within a continuum discretized coupled-channel approach. It was found that an additional three-body force can noticeably alter the angular distributions at forward angles, with consequences for spectroscopic factors' studies. Additional study of transfer to 2p continuum in the 25F(p,2p)24O reaction, involving the same overlap function as in the 24O(d,n)25F case, revealed that 3N force affects the (d,n) and (p,2p) reactions in a similar way, increasing the cross sections and decreasing spectroscopic factors, although its influence at the main peak of (p,2p) is weaker. The angle-integrated cross sections are found to be less sensitive to the 3N force contribution, they increase by less than 20%. Including 3N interactions in nucleon removal reactions makes an essential step towards bringing together nuclear structure theory, where 3N force is routinely used, and nuclear direct reaction theory, based on two-nucleon interactions only.

Theory and applications of nuclear direct reactions

These lectures, held at a school at the Galileo Galilei Institute for Theoretical Physics, give a survey of the formalism, the methods and achievements of nuclear direct reaction theory. After recapitulating the principles of quantum scattering theory, projection techniques are used to reduce the complexities of nuclear reactions to the manageable level of a set of a few selected coupled channels interacting via effective operators. Direct reactions are introduced as fast reactions proceeding preferentially through the excitation of doorway components of the nuclear many-body configurations, corresponding to a separation of scales in energy and momentum transfer. The concept of the optical model is introduced and applied to elastic scattering on nuclei. The coupled channel T-matrix formalism is discussed for pion-induced reactions on the nucleon. Applications of direct reaction to theory are illustrated for transfer reactions, inelastic scattering, and single and double charge exchange reactions with light and heavy ions.

A Brief Review on the Development of Theories of Deuteron Stripping Reactions

As one type of single nucleon transfer reactions, deuteron stripping reaction has been playing an important role in the study of the single particle structure of atomic nuclei. Also, as a typical three-body nuclear reaction, deuteron stripping reaction is also an important subject in the development of direct nuclear reaction theories. We briefly review the history of the study of deuteron stripping reactions, focusing on the evolution of its theoretical descriptions, and the differences and the relations of the Plane Wave Born Approximation(PWBA), the distorted wave Born approximation(DWBA), the Continuum Discretized Coupled Channel method(CDCC), the Adiabatic Wave Approximation(ADWA), and the approach based on the Faddeev equations. Some important problems being currently addressed in deuteron stripping reaction theories and those should be addressed in near future are also discussed, including deuteron strippings at intermediate and high energies, theory for transfer to continuum states of the residue nuclei, applications of dispersive optical model potentials and non-local potentials, etc. Some preliminary results of our theoretical calculations for deuteron stripping at intermediate and high energies are presented.

Low energy reactions of halo nuclei

Halo nuclei are extreme nuclear states consisting of one or more weakly-bound valence nucleons spatially decoupled from a tightly bound nuclear core. The weakly bound nature of the halo dominates the reaction probability, but the specific reaction mechanisms depend also on the core and target nuclei. Despite of the inherent complexity of the reaction process, simple two-body models and direct reaction theories can be used to extract useful information of the structure of the halo nucleus and its dynamics. These ideas are discussed using selected experiments of Coulomb barrier reactions with one- and two- neutron halo systems.

Indirect methods constraining nuclear capture - the Trojan Horse Method

Reaction rates of nuclear processes of astrophysical relevance can be inferred using the Trojan Horse Method. This indirect technique is a valid alternative to direct measurements in particular when extremely low cross sections are involved. We will review its basic features in the framework of the theory of direct reactions and address the physics case of the 12C+12C fusion.

Astrophysics studies with the Trojan Horse Method

The Trojan Horse Method represents an indirect approach to investigate reactions of astrophysical relevance at the energies of interest, free of Coulomb suppression and electron screening effects. In this review, we will examine how the Trojan Horse Method has evolved from the study of the quasi-free reaction mechanism. We will first present the basic features of the quasi-free reaction mechanism in the framework of the theory of direct reactions, from quasi-free scattering to quasi-free reactions processes, and its evolution towards the Trojan Horse Method with its modern theory. We will review the validity tests to assess the technique, the procedure to analyze the data and to extract the astrophysical factor. Finally, we will discuss some of the most important experimental results recently published related to nuclear astrophysics and applications.

Inclusive cross sections for one- and multi-nucleon removal from Sn, Sb, and Te projectiles beyond the N = 82 shell closure

Inclusive one- and multi-nucleon removal cross sections have been measured for several Sn, Sb and Te isotopes just beyond the N=82 neutron shell closure. The beams were produced in the projectile fission of a 238U beam at the Radioactive Isotope Beam Factory at RIKEN. The experimental cross sections are compared to predictions from the most recent version of the Liege intranuclear cascade model. Although the overall agreement is good, severe discrepancies are observed for the cases of one- and two-neutron removal from 134Sn and 135Sb projectiles and one-proton knockout from all measured N=84 isotones. These discrepancies, as well as the relevance of quasi-elastic reaction channels to the one-neutron removal cross sections, are discussed. In addition, the measured inclusive one-proton knockout cross section for the semi-magic 134Sn projectile is compared to eikonal direct reaction theory calculations to assess if the suppression factors to these calculated cross sections, deduced from data on reactions of lighter projectile nuclei, are also applicable to heavy nuclei.

Nuclear Physics in Stellar Lifestyles with the Trojan Horse Method

The Trojan Horse Method is an indirect technique to measure nuclear reactions of astrophysical relevance at the energies of interest, free of Coulomb suppression and electron screening effects. Its basic features in the framework of the theory of direct reactions will be discussed and the physics case of the 12C+12C fusion will be addressed.

An Approximation of Cross Sections of Channels of the 9Be(α, n) Reaction on the Basis of the Gamow Interaction Radius

Radiation transport of α-particles requires cross sections of inelastic interaction of α-particles with nuclei. At low energies the inelastic interactions are limited to the 9Be(α, n) reaction, whose channel cross sections are assessed only in the specialized evaluated nuclear data library JENDL/AN-2005. The new TPT (Toolkit for Particle Transport) approximation of the 9Be(α, n) reaction cross sections for different channels takes into account the lowest resonance and, at high energies, relies on the exponential decrease in the S-factor, which is a consequence of the theory of direct nuclear reactions.

Formation of heavy neutron-deficient nuclides in 3He-induced reactions

Reactions of 3He with actinide nuclei are a promising tool for the production of heavy neutrondeficient nuclei, which are of great interest as tracers in environmental studies. In this work, highly enriched 235U targets 1 mg cm–2 thick were irradiated using 3He ions with energies of 20.4–42.0 MeV at the Accelerator Laboratory of University of Jyvaskyla, Finland. The irradiated targets were analyzed with gamma and alpha spectrometers and then dissolved in order to chemically separate Pu and Np from the fission products and the target material. The chemical yields of 234Np and 236Pu were determined by measuring their activities prior to and after chemical separation. Previously unknown excitation functions of the nuclides 234, 236, 237Pu and 234, 235, 236m Np were thus found. The obtained experimental data were analyzed using the direct reaction theory for a model with nuclear friction included in the fission channel and due consideration of the preequilibrium processes.

Systematic uncertainties in direct reaction theories

Nuclear reactions are common probes to study nuclei and in particular, nuclei at the limits of stability. The data from reaction measurements depend strongly on theory for a reliable interpretation. Even when using state-of-the-art reaction theories, there are a number of sources of systematic uncertainties. These uncertainties are often unquantified or estimated in a very crude manner. It is clear that for theory to be useful, a quantitative understanding of the uncertainties is critical. Here, we discuss major sources of uncertainties in a variety of reaction theories used to analyze (d,p) nuclear reactions in the energy range Ed = 10–20 MeV, and we provide a critical view on how these have been handled in the past and how estimates can be improved.

The energy spectra and double-differential cross-sections for p+92,94,95,96,97,98,100Mo reactions at the incident energies from threshold to 200 MeV

The energy spectra and double-differential cross sections of neutron, proton, deuteron, triton, helium and alpha-particle emitted are studied by the exciton model including the improved Iwamoto–Harada model. All cross sections, angular distributions, energy spectra and double-differential cross sections are consistently calculated and analyzed for p+92,94,95,96,97,98,100Mo reactions at the incident proton energies below 200MeV by using nuclear theoretical models which integrate the optical model, the intra-nuclear cascade model, direct, pre-equilibrium and equilibrium reaction theories. The theoretically calculated results are compared with existing experimental data.

The cross sections and energy spectra of the particle emission in proton induced reactions on 209Bi

All cross sections of proton induced reactions, angular distributions, energy spectra and double differential cross sections of neutron, proton, deuteron, triton, helium and alpha-particle emissions for p+209Bi reaction are consistently calculated and analyzed at incident proton energies below 250MeV. The optical model, the intra-nuclear cascade model, direct reaction theories, the unified Hauser–Feshbach and exciton model which includes the improved Iwamoto–Harada model are used. Theoretically calculated results are compared with the existing experimental data.

Double differential cross sections of n + 63,65,nat.Cu reactions

The energy spectra and double differential cross sections of neutron, proton, deuteron, triton, helium and alpha-particle emissions for n + 63,65,nat.Cu reactions are calculated and analyzed at incident neutron energies below 200 MeV. The optical model, the intra-nuclear cascade model, direct reaction theories, the unified Hauser–Feshbach and exciton model which includes the improved Iwamoto–Harada model are used. Theoretically calculated results are compared with the existing experimental data.

Theoretical calculation and analysis of the p+ 59Co reaction

All cross sections, elastic and inelastic scattering angular distributions, energy spectra, and double differential cross sections of neutron, proton, deuteron, triton, helium and alpha particle emission for the p+ 59Co reaction have been calculated and analyzed at incident energies from threshold to 200 MeV. The optical model, the intra-nuclear cascade model, direct, pre-equilibrium and equilibrium reaction theories are used. It is found that the theoretical calculated results are in good agreement with experimental data.

Calculation of cross-sections for p+ 92,94,95,96,97,98,100Mo reactions up to 160 MeV

Proton-induced reactions on 92,94,95,96,97,98,100Mo have been studied in the energy range from threshold to 160 MeV. All cross-sections for neutrons, protons, deuterons, tritons, helium and alpha particles emission have been calculated by using nuclear theoretical models which integrate the optical model, the intra-nuclear cascade model, direct, pre-equilibrium and equilibrium reaction theories. Theoretical calculations have been compared with existing experimental data; in most cases, the calculated results are in good agreement with the experimental data.

Double differential cross sections of light charged particle emission in neutron induced reactions on 54,56,57,58Fe

The energy spectra and double differential cross sections of the light composite particle (deuteron, triton, helium and alpha-particle) emissions for n + 54,56,57,58Fe reaction are studied by integrating the optical model, the intra-nuclear cascade model, direct reaction theories, equilibrium reaction theory and the exciton model which included the improved Iwamoto–Harada model. Theoretical calculated results are compared with existing experimental data.

Light charged particle emission for p+54,56,57,58,natFe reactions

The energy spectra and double differential cross sections of nucleon and the light composite particle (d, t, 3He and α) emissions are studied based on the exciton model included the improved Iwamoto–Harada model. All cross sections of proton induced reactions, angular distributions and energy spectra are consistent calculated and analyzed for 54,56,57,58,natFe at incident proton energies below 250MeV by using nuclear theoretical models which integrate the optical model, the intra-nuclear cascade model, direct, pre-equilibrium and equilibrium reaction theories. Theoretical calculated results are compared with existing experimental data.

Calculation and evaluation of cross-sections for p+54,56,57,58,natFe reactions up to 250 MeV

All cross-sections of proton-induced reactions, angular distributions and the energy spectra of neutron, proton, deuteron, triton, helium and alpha-particle emission are consistent calculated and analyzed for p+54,56,57,58,natFe at incident proton energies below 250MeV by using nuclear theoretical models which integrate the optical model, the intra-nuclear cascade model, direct, preequilibrium and equilibrium reaction theories. Especially, the cross-sections of the light composite particle (d, t, 3He and α) emissions are improved based on the exciton model including the pick-up mechanism. Theoretical calculated results are compared with existing experimental data.

Systematic study of elastic scattering, total reaction, transfer/breakup and fusion cross sections for the system [formula omitted] at energies close to the Coulomb barrier

Using an approach based on the direct reaction theory, simultaneous χ 2-analyses are performed of elastic scattering, total reaction, transfer/breakup and fusion cross section data of the system 8 Li+ 208 Pb for energies around the Coulomb barrier. The transfer/breakup cross section data are identified with the experimental direct reaction cross section while the fusion cross section is determined by a simple subtraction of the total reaction and transfer/breakup data. In the analysis, optical model potentials with volume and surface real and imaginary parts are used. The fitted potential parameters show that no threshold anomaly effect is present for the total potential although the volume part shows it. However, good fits are obtained for all the cross sections at the measured energies.