Nuclear structure  How to Proceed  Neutron beams

Radioactive beams

In explosive astrophysical environments nuclear burning times are (much) shorter than seconds and unstable nuclei will undergo further reactions. Among charged-particle reactions $(p,\gamma$) and $(\alpha,\gamma)$ capture reactions dominate. Due to the high temperatures, the relevant thermal energies E_o are close to the Coulomb barrier E_c, where $\sigma(E)$ is often of the order of $\mu$b and more. For short-lived nuclides, the only direct method for $\sigma(E)$ measurements is the production of radioactive nuclides in a first reaction, separation of the relevant nuclei, and acceleration of a radioactive ion beam (RIB) with typically 1 pA currents, interacting with hydrogen or helium gas targets (inverse kinematics). A 10 pA RIB current, a cross section of 10$\mu$b, and a gas target density of 10¹⁹ atoms/cm² cause 23 capture reactions per hour. A growing number of laboratories have already produced low energy RIB's of astrophysical interest or are in the stage of technical development: ARENAS/Louvain-la-Neuve, SPIRAL/GANIL, REX-ISOLDE/    CERN, EXCYT/Catania, PIAFE/ILL, TWINSOL/    Notre Dame, HRIBF/ORNL, ISAC/TRIUMF, ATLAS/ANL.

Figure: The hot CNO-cycle with breakout reactions to Ne. From Ne to Ca similar hot cycles exist, based always on alpha-nuclei like ²⁰Ne, ²⁴Mg etc.

 

In inverse kinematics, the detection of the capture $\gamma$-rays or of the residual nuclides (via their radioactive decay signals) leads in general to efficiencies far below 100%. In addition, radioactivity hampers seriously the detection methods. Only p(¹³N, $\gamma)^{14}$O has been successfully studied so far via $\gamma$-ray spectroscopy (using an array of Ge detectors at Louvain-la-Neuve) because of an exceptionally large cross section due to a strong and broad resonance. For all other capture reactions studied so far, only upper limits could be derived at the relevant energies, predominantly due to a more typical (i.e. small) cross section. The measurements require a significantly improved detection efficiency, achievable by recoil mass separators (RMS) which filter the RIB from the recoil capture nuclides and focus all recoils for their identification. The RIB-suppression factor must be 10^-10 or better (e.g. 10^-16 for $\sigma(E)$= 1 pb). The potential use of a RMS was successfully exploited in the study of p(¹²C, $\gamma)^{13}$N and p(⁷Be,$\gamma)^8$B [27] at Naples, and beam suppression factors up to 10^-16 (European Recoil separator for Nuclear Astrophysics, ERNA) seem feasible. Going beyond radiative captures will require RIB facilities with detection systems for protons and neutrons. Efficient detection systems for charged particles have been developed in recent years, with a high suppression of the background created by RIB's (e.g. LEDA, the Louvain-Edinburgh-Detector-Array). It should be pointed out that the capture reactions ¹³N( $p,\gamma)^{14}$O and ⁷Be( $p,\gamma)^8$B have also been studied using the method of Coulomb dissociation at RIKEN and GSI. The measurements via ¹⁴O( $\gamma,p)^{13}$N and ⁸B( $\gamma,p)^{7}$Be provide information of the radiative-capture cross section to the ground-state of the compound nucleus [28]. The first reaction, which led to a precise result, represents (again) an "ideal" case due to a broad and strong resonance excited to 100% by E1-radiation. There exist still uncertainties about the obtainable precision. Experimental as well as theoretical problems (high energy resolution of the RIB, nuclear interference and post-acceleration effects) might ask first for a test and calibration of this method with reactions, where high accuracy direct measurements are already known. Because of its strong potential for reactions where direct cross section measurements are extremely difficult, this method should be further explored, also making use of different RIB energies. Some reactions can only be studied via the Coulomb dissociation method. Examples are the sequence of two capture reactions with an intermediate particle-unstable nucleus, similar to the triple alpha process ⁴He( $2\alpha,\gamma)^{12}$C in He-burning. $(2p,\gamma$) reactions can permit a faster reaction flow at high stellar densities by connecting "peninsulas" of the proton-drip line [15]. Others are the ⁴He( $\alpha n,\gamma)^9$Be and ⁴He( $2n,\gamma)^6$He( $2n,\gamma)^8$He reactions, bridging the mass 5 and 8 instability gaps. Similarly, the study of $(n,\gamma)$ reactions on unstable nuclides is another unique application.