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 compression-mode giant resonances and nuclear incompressibility

The ${}^{16}\mathrm{O}{(}^{3}\mathrm{He}{,d)}^{17}\mathrm{F}$ reaction has been used to determine asymptotic normalization coefficients for transitions to the ground and first excited states of ${}^{17}\mathrm{F}.$ The coefficients provide the normalization for the tails of the overlap functions for ${}^{17}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{F}}}^{16}\mathrm{O}+p$ and allow us to calculate the S factors for ${}^{16}\mathrm{O}(p,\ensuremath{\gamma}{)}^{17}\mathrm{F}$ at astrophysical energies. The calculated S factors are compared to measurements and found to be in very good agreement. This provides a test of this indirect method to determine astrophysical direct capture rates using transfer reactions. In addition, our results yield $S(0)$ for capture to the ground and first excited states in ${}^{17}\mathrm{F},$ without the uncertainty associated with extrapolation from higher energies.

/pdf/tests-of-transfer-reaction-determinations-of-astrophysical-s-2xg68vua73.pdf

Tests of transfer reaction determinations of astrophysical S factors

The compression-mode giant resonances, namely the isoscalar giant monopole and isoscalar giant dipole modes, are examples of collective nuclear motion. Their main interest stems from the fact that one hopes to extrapolate from their properties the incompressibility of uniform nuclear matter, which is a key parameter of the nuclear Equation of State (EoS). Our understanding of these issues has undergone two major jumps, one in the late 1970s when the Isoscalar Giant Monopole Resonance (ISGMR) was experimentally identified, and another around the turn of the millennium since when theory has been able to start giving reliable error bars to the incompressibility. However, mainly magic nuclei have been involved in the deduction of the incompressibility from the vibrations of finite nuclei. The present review deals with the developments beyond all this. Experimental techniques have been improved, and new open-shell, and deformed, nuclei have been investigated. The associated changes in our understanding of the problem of the nuclear incompressibility are discussed. New theoretical models, decay measurements, and the search for the evolution of compressional modes in exotic nuclei are also discussed.

The Compression-Mode Giant Resonances and Nuclear Incompressibility

The ion optics of large-acceptance magnetic spectrometers are discussed. General techniques based on a minimum of multi-purpose magnetic elements are described. The aberrations should be minimised by shaping the entrance and exit effective field boundaries of bending magnets, the residual terms being corrected by software. Field clamps, shims and surface coils (the latter to provide kinematic compensation) are also discussed. The results and formulae which we obtain are applied to the case of the large-acceptance (∼50 msr) high-resolution magnetic spectrometer “MAGNEX” at INFN-LNS Catania.

Ion optics for large-acceptance magnetic spectrometers: application to the MAGNEX spectrometer

A new high resolution magnetic spectrometer — the Oxford MDM-2 spectrometer — has been designed, installed and tested. The layout of the magnetic elements is in the order: entrance sextupole and multipole, gradient-field dipole and exit multipole. The device has a “normal” focal plane, and the 1.6 m radius dipole magnet has a maximum mass-energy product of 315 MeV amu. At the maximum solid angle of 8 msr, the ratio of energies that can be accepted by the spectrometer (Emax/Emin) is 1.31. Precide measurements have been performed on the magnetic elements. The dipole magnet has very low hysteresis and field integral errors that amount to less than 1 part in 104. After some in situ modifications the field distributions of the magnets closely approximated the original design specifications. On-line tests with various ion-beams have revealed the optimum setting for each element. These are close to theoretical predictions from the program RAYTRACE, incorporating the parameterised results of the magnetic measurements. An aberration limited resolution (E/ΔE) of greater than 3000 has been observed at 8 msr solid angle.

J.H. Coupland

Papers

The oxford MDM-2 magnetic spectrometer