Describing the processes in stars which produce the chemical elements for planets and life, this book shows how similar processes may be reproduced in laboratories using exotic beams, and how these results can be analyzed. Beginning with one-channel scattering theory, the book builds up to multi-channel reactions. Emphasis is placed on using transfer and breakup reactions to probe structure and predict capture processes, as well as R-matrix methods for modeling compound nucleus dynamics described by Hauser-Feshbach methods. Practical applications are prominent in this book, confronting theory predictions with data throughout. The associated reaction program Fresco is described, allowing readers to apply the methods to practical cases. Each chapter ends with exercises so readers can test their understanding of the materials covered. Supplementary materials at www.cambridge.org/9780521856355 include the Fresco program, input and output files for the examples given in the book, and hints and graphs related to the exercises.

We discuss calculations of three-body observables for the breakup of 8 B on a 58 Ni target at low energy using the coupled discretised continuum channels approach. Calculations of both the angular distribution of the 7 Be fragments and their energy distributions are compared with those measured at several laboratory angles. In these observables there is interference between the breakup amplitudes from different spin-parity excitations of the projectile. The resulting angle and the energy distributions reveal the importance of the higher-order continuum state couplings for an understanding of the measurements.

Atomic nuclei have a shell structure in which nuclei with 'magic numbers' of neutrons and protons are analogous to the noble gases in atomic physics. Only ten nuclei with the standard magic numbers of both neutrons and protons have so far been observed. The nuclear shell model is founded on the precept that neutrons and protons can move as independent particles in orbitals with discrete quantum numbers, subject to a mean field generated by all the other nucleons. Knowledge of the properties of single-particle states outside nuclear shell closures in exotic nuclei is important for a fundamental understanding of nuclear structure and nucleosynthesis (for example the r-process, which is responsible for the production of about half of the heavy elements). However, as a result of their short lifetimes, there is a paucity of knowledge about the nature of single-particle states outside exotic doubly magic nuclei. Here we measure the single-particle character of the levels in (133)Sn that lie outside the double shell closure present at the short-lived nucleus (132)Sn. We use an inverse kinematics technique that involves the transfer of a single nucleon to the nucleus. The purity of the measured single-particle states clearly illustrates the magic nature of (132)Sn.

Background: Deuteron induced reactions serve as surrogates for neutron capture into compound states. Although these reactions are of great applicability, no theoretical efforts have been invested in this direction over the last decade. Purpose: The goal of this work is to establish on firm grounds a theory for deuteron induced neutron capture reactions. This includes formulating elastic and inelastic breakup in a consistent manner. Method: We describe this process both in post and prior form distorted wave Born approximation following previous works and discuss the differences in the formulation. While the convergence issues arising in the post formulation can be overcome in the prior formulation, in this case one still needs to take into account additional terms due to non-orthogonality. Results: We apply our method to the 93 Nb(d,p)X at E d =15 MeV and 25 MeV, and are able to obtain a good description of the data. We look at the various partial wave contributions, as well as elastic versus inelastic contributions. We also connect our formulation with transfer to neutron bound states.Conclusions: Our calculations demonstrate that the non-orthogonality term arising in the prior formulation is significant and is at the heart of the long-standing controversy between the post and the prior formulations of the theory. We also show that the cross sections for these reactions are angular momentum dependent and therefore the commonly used Weisskopf limit is inadequate. Finally we make important predictions for the relative contributions of elastic breakup and non-elastic breakup, and call for elastic breakup measurements to further constrain our model.

No abstract

No abstract

The continuum discretized coupled channels (CDCC) method is compared to the exact solution of the three-body Faddeev equations in momentum space. We present results for: i) elastic and breakup observables of d+ 12 C at E d = 56 MeV, ii) elastic scattering of d+ 58 Ni at E d = 80 MeV, and iii) elastic, breakup and transfer observables for 11 Be+p at E11 Be /A = 38.4 MeV. Our comparative studies show that, in the first two cases, the CDCC method is a good approximation to the full three-body Faddeev solution, but for the 11 Be exotic nucleus, depending on the observable or the kinematic regime, it may miss out some of the dynamic three-body effects that appear through the explicit coupling to the transfer channel.

Background: The triple-alpha reaction is the key to our understanding about the nucleosynthesis and the observed abundance of 12 C in stars. The theory of this process is well established at high temperatures but rather ambiguous in the low temperature regime where measurements are impossible. Purpose: Develop a new three-body method, which tackles properly the scattering boundary condition for three charged particles and takes into account both the resonant and the non-resonant reaction mechanisms on the same footing, to compute the triple-alpha reaction rate at low temperatures. Methods: We combine the R-matrix expansion, the R-matrix propagation method, and the screening technique in the hyperspherical harmonics basis. Results: Both the 2 + 1 bound state and the 0 + 2 resonant state in 12 C are well reproduced. We also study the cluster structure of these states. We calculate the triple-alpha reaction rate for T = 0.01 − 0.1 GK. Conclusions: We obtain the same rate as NACRE for temperatures above 0.07 GK, but the new rate is largely enhanced at lower temperatures (≈ 10 12 at 0.02 GK). The differences are caused by the direct capture contribution to the reaction when three alpha particles can not reach the resonant energies.