This white paper, directed to the Stars and Stellar Evolution panel, has three objectives: 1) to provide the Astro2010 Decadal Survey with a vista into the goals of the nuclear physics and nuclear astrophysics community; 2) to alert the astronomical community of joint opportunities for discoveries at the interface between nuclear physics and astronomy; and 3) to delineate efforts in nuclear physics and describe the observational and theoretical advances in astrophysics necessary to make progress towards answering the following questions in the Nuclear Science 2007 Long Range Plan: 1) What is the origin and distribution of the elements? 2) What are the nuclear reactions that power stars and stellar explosions? 3) What is the nature of dense matter? The scope of this white paper concerns the specific area of "low energy" nuclear astrophysics We define this as the area of overlap between astrophysics and the study of nuclear structure and reactions Of the questions listed above, two -- What is the origin of the elements? and What is the nature of dense matter? -- were specifically listed in the National Academies Study, "Connecting Quarks with the Cosmos"

Nuclei in the Cosmos

A comprehensive account of the theoretical analyses of the Efimov effect and the universal properties of three-body bound states is provided. Recent experimental studies are reviewed and shown how the few-body analysis also yields insights into many-body phenomena, accessible by the experimental ability to tune the range and strength of the forces between cold atoms.

Universal few-body physics and cluster formation

Electron-impact ionization of the hydrogen atom is the prototypical three-body Coulomb breakup problem in quantum mechanics. The combination of subtle correlation effects and the difficult boundary conditions required to describe two electrons in the continuum have made this one of the outstanding challenges of atomic physics. A complete solution of this problem in the form of a 'reduction to computation' of all aspects of the physics is given by the application of exterior complex scaling, a modern variant of the mathematical tool of analytic continuation of the electronic coordinates into the complex plane that was used historically to establish the formal analytic properties of the scattering matrix. This review first discusses the essential difficulties of the three-body Coulomb breakup problem in quantum mechanics. It then describes the formal basis of exterior complex scaling of electronic coordinates as well as the details of its numerical implementation using a variety of methods including finite difference, finite elements, discrete variable representations and B-splines. Given these numerical implementations of exterior complex scaling, the scattering wavefunction can be generated with arbitrary accuracy on any finite volume in the space of electronic coordinates, but there remains the fundamental problem of extracting the breakup amplitudes from it. Methods are described for evaluating these amplitudes. The question of the volume-dependent overall phase that appears in the formal theory of ionization is resolved. A summary is presented of accurate results that have been obtained for the case of electron-impact ionization of hydrogen as well as a discussion of applications to the double photoionization of helium.

/pdf/solving-the-three-body-coulomb-breakup-problem-using-4pawo1mjbq.pdf

Solving the three-body Coulomb breakup problem using exterior complex scaling

In this review, we discuss the present status of three indirect techniques that are used to determine reaction rates for stellar burning processes, asymptotic normalization coefficients, the Trojan Horse method and Coulomb dissociation. A comprehensive review of the theory behind each of these techniques is presented. This is followed by an overview of the experiments that have been carried out using these indirect approaches.

https://iopscience.iop.org/article/10.1088/0034-4885/77/10/106901/pdf

Indirect techniques in nuclear astrophysics: a review

The Coulomb interaction between two protons is included in the calculation of proton-deuteron elastic scattering, radiative proton-deuteron capture, and two-body electromagnetic disintegration of $^{3}\mathrm{He}$. The hadron dynamics is based on the purely nucleonic charge-dependent (CD) Bonn potential and its realistic extension CD Bonn $+\phantom{\rule{0.3em}{0ex}}\ensuremath{\Delta}$ to a coupled-channel two-baryon potential, allowing for single virtual $\ensuremath{\Delta}$-isobar excitation. Calculations are done using integral equations in momentum space. The screening and renormalization approach is employed for including the Coulomb interaction. Convergence of the procedure is found at moderate screening radii. The reliability of the method is demonstrated. The Coulomb effect on observables is seen at low energies for the entire kinematic regime. In proton-deuteron elastic scattering at higher energies the Coulomb effect is confined to forward scattering angles; the $\ensuremath{\Delta}$-isobar effect found previously remains unchanged by the Coulomb effect. In electromagnetic reactions the Coulomb effect competes with other effects in a complicated way.

/pdf/momentum-space-treatment-of-the-coulomb-interaction-in-three-csdncvb9xk.pdf

Momentum-space treatment of the Coulomb interaction in three-nucleon reactions with two protons

Nuclear reaction rates are among the most important input for understanding the primordial nucleosynthesis and therefore for a quantitative description of the early Universe. An up-to-date compilation of direct cross sections of 2 H(d,p) 3 H, 2 H(d,n) 3 He, 7 Li(p, ) 4 He and 3 He(d,p) 4 He reactions is given. These are among the most uncertain cross sections used and input for Big Bang nucleosynthesis calculations. Their measurements through the Trojan Horse Method (THM) are also reviewed and compared with direct data. The reaction rates and the corresponding recommended errors in this work were used as input for primordial nucleosynthesis calculations to evaluate their impact on the 2 H, 3;4 He and 7 Li primordial abundances, which are then compared

/pdf/big-bang-nucleosynthesis-revisited-via-trojan-horse-method-5trpa5jhj7.pdf

Big bang nucleosynthesis revisited via trojan horse method measurements

Surface-integral formulation of scattering theory

Nuclear reaction rates are among the most important input for understanding the primordial nucleosynthesis and therefore for a quantitative description of the early Universe. An up-to-date compilation of direct cross sections of 2H(d,p)3H, 2H(d,n)3He, 7Li(p,alpha)4He and 3He(d,p)4He reactions is given. These are among the most uncertain cross sections used and input for Big Bang nucleosynthesis calculations. Their measurements through the Trojan Horse Method (THM) are also reviewed and compared with direct data. The reaction rates and the corresponding recommended errors in this work were used as input for primordial nucleosynthesis calculations to evaluate their impact on the 2H, 3,4He and 7Li primordial abundances, which are then compared with observations.

/pdf/big-bang-nucleosynthesis-revisited-via-trojan-horse-method-4ukxaojq1s.pdf

Big Bang nucleosynthesis revisited via Trojan Horse Method measurements

Off-energy-shell effects in p-p scattering have been investigated at p-p relative energies from 600 down to 80 keV applying the Trojan horse method (THM) to the p+d{yields}p+p+n reaction at 5 MeV. In contrast with the on-energy-shell case, no Coulomb-nuclear interference minimum has been found in the extracted THM p-p cross section, due to the suppression of the Coulomb amplitude as predicted by the half-off-energy shell calculations. This hypothesis is strengthened by the agreement between THM p-p data and calculated on-energy-shell n+n, n+p and nuclear p+p cross sections.

Suppression of the Coulomb interaction in the off-energy-shell p - p scattering from the p + d --> p + p + n reaction.

Asymptotic forms of the scattered wave for a system of three arbitrary charged particles valid in all domains relevant to breakup are derived. The derivations are based on the relationship between the total wave function of a breakup process in a three-body system with Coulomb interactions and the wave function of the process of scattering of all three particles of the system in the continuum. The results are free from amplitude-phase ambiguity problems associated with previously known forms. A similar technique is used to obtain asymptotic forms of the three-body Coulomb Green's function.

/pdf/asymptotic-behavior-of-the-coulomb-three-body-scattered-wave-3grkgfagll.pdf

A. M. Mukhamedzhanov

Papers

Big bang nucleosynthesis revisited via trojan horse method measurements

Surface-integral formulation of scattering theory

Big Bang nucleosynthesis revisited via Trojan Horse Method measurements

Suppression of the Coulomb interaction in the off-energy-shell p - p scattering from the p + d --> p + p + n reaction.

Asymptotic behavior of the Coulomb three-body scattered wave