The Facility for Rare Isotope Beams (FRIB) will be a world-leading laboratory for the study of nuclear structure, reactions and astrophysics. Experiments with intense beams of rare isotopes produced at FRIB will guide us toward a comprehensive descri
ption of nuclei, elucidate the origin of the elements in the cosmos, help provide an understanding of matter in neutron stars, and establish the scientific foundation for innovative applications of nuclear science to society. FRIB will be essential for gaining access to key regions of the nuclear chart, where the measured nuclear properties will challenge established concepts, and highlight shortcomings and needed modifications to current theory. Conversely, nuclear theory will play a critical role in providing the intellectual framework for the science at FRIB, and will provide invaluable guidance to FRIBs experimental programs. This article overviews the broad scope of the FRIB theory effort, which reaches beyond the traditional fields of nuclear structure and reactions, and nuclear astrophysics, to explore exciting interdisciplinary boundaries with other areas. keywords{Nuclear Structure and Reactions. Nuclear Astrophysics. Fundamental Interactions. High Performance Computing. Rare Isotopes. Radioactive Beams.
Reactions are an important tool to study nuclear structure and for extracting reactions relevant for astrophysics. In this paper we focus on deuteron induced reactions which can provide information on neutron shell evolution as well as neutron captur
e cross sections. We review recent work on the systematic comparison of the continuum discretized coupled channel method, the adiabatic wave approximation and the Faddeev momentum-space approach. We also explore other aspects of the reaction mechanism and discuss in detail difficulties encountered in the calculations.
The Continuum Discretized Coupled Channels (CDCC) method is a well established theory for direct nuclear reactions which includes breakup to all orders. Alternatively, the 3-body problem can be solved exactly within the Faddeev formalism which explic
itly includes breakup and transfer channels to all orders. With the aim to understand how CDCC compares with the exact 3-body Faddeev formulation, we study deuteron induced reactions on: i) $^{10}$Be at $E_{rm d}= 21.4, 40.9 ; {rm and} ; 71$ MeV; ii) $^{12}$C at $E_{rm d} = 12 ; {rm and} ; 56$ MeV; and iii) $^{48}$Ca at $E_{rm d} = 56$ MeV. We calculate elastic, transfer and breakup cross sections. Overall, the discrepancies found for elastic scattering are small with the exception of very backward angles. For transfer cross sections at low energy $sim$10 MeV/u, CDCC is in good agreement with the Faddeev-type results and the discrepancy increases with beam energy. On the contrary, breakup observables obtained with CDCC are in good agreement with Faddeev-type results for all but the lower energies considered here.
A new full three-body method is introduced to compute the rate of the triple-alpha capture reaction which is the primary source of $^{12}$C in stars. In this work, we combine the Faddeev hyperspherical harmonics and the R-matrix method to obtain a fu
ll solution to the three-body $alpha+alpha+alpha$ continuum. Particular attention is paid to the long range effects caused by the pairwise Coulomb interactions. The new rate agrees with the NACRE rate for temperatures greater than 0.07 GK, but a large enhancement at lower temperature is found ($approx 10^{14}$ at 0.02 GK). Our results are compared to previous calculations where additional approximations were made. We show that the new rate does not significantly change the evolution of stars around one solar mass. In particular, such stars still undergo a red-giant phase consistent with observations, and no significant differences are found in the final white dwarfs.
Rare isotopes are most often studied through nuclear reactions. Nuclear reactions can be used to obtain detailed structure information but also in connection to astrophysics to determine specific capture rates. In order to extract the desired informa
tion it is crucial to have a reliable framework that describes the reaction process accurately. A few recent developments for transfer and breakup reactions will be presented. These include recent studies on the reliability of existing theories as well as effort to reduce the ambiguities in the predicted observables.
An improved description of single neutron stripping from $^{34,36,46}$Ar beams at 33 MeV/nucleon by a hydrogen target is presented and the dependence on the neutron-proton asymmetry of the spectroscopic factors is further investigated. A finite range
adiabatic model is used in the analysis and compared to previous zero range and local energy approximations. Full three-body Faddeev calculations are performed to estimate the error in the reaction theory. In addition, errors from the optical potentials are also evaluated. From our new spectroscopic factors extracted from transfer, it is possible to corroborate the neutron-proton asymmetry dependence reported from knockout measurements.
The dispersive optical-model is applied to transfer reactions. A systematic study of $(d,p)$ reactions on closed-shell nuclei using the finite-range adiabatic reaction model is performed at several beam energies and results are compared to data as we
ll as to predictions using a standard global optical-potential. Overall, we find that the dispersive optical-model is able to describe the angular distributions as well as or better than the global parameterization. In addition, it also constrains the overlap function. Spectroscopic factors extracted using the dispersive optical-model are generally lower than those using standard parameters, exhibit a reduced dependence on beam energy, and are more in line with results obtained from $(e,ep)$ measurements.
The finite range adiabatic wave approximation provides a practical method to analyze (d,p) or (p,d) reactions, however until now the level of accuracy obtained in the description of the reaction dynamics has not been determined. In this work, we perf
orm a systematic comparison between the finite range adiabatic wave approximation and the exact Faddeev method. We include studies of $^{11}$Be(p,d)$^{10}$Be(g.s.) at $E_p=$5, 10 and 35 MeV; $^{12}$C(d,p)$^{13}$C(g.s.) at $E_d=$7, 12 and 56 MeV and $^{48}$Ca(d,p)$^{49}$Ca(g.s.) at $E_d=$19, 56 and 100 MeV. Results show that the two methods agree within $approx 5%$ for a range of beam energies ($E_d approx 20-40$ MeV) but differences increase significantly for very low energies and for the highest energies. Our tests show that ADWA agrees best with Faddeev when the angular momentum transfer is small $Delta l=0$ and when the neutron-nucleus system is loosely bound.
Direct neutron capture reactions play an important role in nuclear astrophysics and applied physics. Since for most unstable short-lived nuclei it is not possible to measure the $(n, gamma)$ cross sections, $(d,p)$ reactions have been used as an alte
rnative indirect tool. We analyze simultaneously $^{48}{rm Ca}(d,p)^{49}{rm Ca}$ at deuteron energies $2, 13, 19$ and 56 MeV and the thermal $(n,gamma)$ reaction at 25 meV. We include results for the ground state and the first excited state of $^{49}$Ca. From the low-energy $(d,p)$ reaction, the neutron asymptotic normalization coefficient (ANC) is determined. Using this ANC, we extract the spectroscopic factor (SF) from the higher energy $(d,p)$ data and the $(n, gamma)$ data. The SF obtained through the 56 MeV $(d,p)$ data are less accurate but consistent with those from the thermal capture. We show that to have a similar dependence on the single particle parameters as in the $(n, gamma)$, the (d,p) reaction should be measured at 30 MeV.
