Screening effects  How to Proceed  Cosmic ray observations

Stable beams

The cross section $\sigma(E)$ of charged-particle-induced reactions drops nearly exponentially below the Coulomb barrier, E_c. Important reactions, like ⁷Be( $p,\gamma)^8$B, ²⁵Mg( $p,\gamma)^{26}$Al, or ¹²C( $\alpha,\gamma)^{16}$O, are known down to limiting energies E_l of 120keV, 190keV or 1MeV (mainly due to background effects of cosmic rays) and are applied to astrophysics at the relevant stellar thermal energy E_o of 19keV, 39keV or 300keV [6]. The danger of such extrapolations down to e.g. $\approx 0.01E_c$ was demonstrated impressively in the case of ²H( $d,\gamma)^4$He, where new low-energy data changed the extrapolated values by a factor of 1000; other cases are ⁹Be( $p,\alpha)^6$Li (factor 50) and ¹⁰B( $p,\alpha)^7$Be (factor 200). Quite a number of $\sigma(E)$ measurements for the reactions in the pp-chain, the CNO-cycles, the NeNa- and MgAl-cycles in H-burning, alpha-induced reactions in He-burning and the s-process and heavy ion fusion reactions for the late phases of stellar evolution and type I supernova dynamics, have not yet reached the low-energy limit E_l, dictated by the cosmic ray background. These reactions can only be reliably investigated at high intensity, low energy accelerators with new and improved detection facilities, especially large, high granularity detector arrays for gammas and particle reaction products in conjunction with recoil separators.  

Figure: The astrophysical S-factor for the reaction ³He(³He,2p)⁴He. The filled circles were obtained by an underground pilot experiment (LUNA) at the Gran Sasso facility. The solid or dashed curves indicate the inclusion (non-inclusion) of screening corrections. The Gamov peak marks the energy range probed under solar burning conditions, reached for the very first time by experiment [23].

 

If E_l is reached experimentally and an extrapolation down to E_o is uncertain, background free experimental facilities are needed. Passive shielding around the detectors provides a reduction of cosmic ray gammas and neutrons, but it produces an increase of gammas and neutrons due to the cosmic-ray interactions in the shielding itself. A 4$\pi$ active shielding can only partially reduce the problem of cosmic ray activation. The background can be considerably reduced in a deep underground laboratory, like the existing solar neutrino experiments with similar counting rates of the order of 1 event per day or less. The world-wide first pilot experiment (LUNA, a Laboratory Underground for Nuclear Astrophysics) with a 50 kV accelerator at LNGS (Laboratori Nazionale del Gran Sasso, Italy) investigates presently the pp-chain reaction ³He(³He,2p)⁴He within the energy region of the solar Gamov peak (here E_o= 21 keV). The studies [23] provided for the first time data within the Gamov peak. Based on its success, larger accelerator facilities, ranging from a 200-400 kV single-ended accelerator up to a 2 MV tandem would offer the opportunity to investigate a wider energy range and spectrum of reactions. To cope with and make a most efficient use of the low counting rates requires the knowledge of resonance properties, obtainable via single or few particle transfer reactions, a task ideally suited for tandem accelerator facilities.