Tools and technologies in mathematical didactics

This short paper provides an overview of recent European research about the use and impact of tools and technologies in mathematical didactics. Such research is categorised as focusing on theoretical ideas, on algebraic knowledge when using spreadsheet and computer algebra (CAS), and on dynamic geometry software (DGS). The paper reveals the variety of software technologies, education levels, and methodologies utitised in European research

Revision of the 15N(p,{\gamma})16O reaction rate and oxygen abundance in H-burning zones

The NO cycle takes place in the deepest layer of a H-burning core or shell, when the temperature exceeds T {\simeq} 30 {\cdot} 106 K. The O depletion observed in some globular cluster giant stars, always associated with a Na enhancement, may be due to either a deep mixing during the RGB (red giant branch) phase of the star or to the pollution of the primordial gas by an early population of massive AGB (asymptotic giant branch) stars, whose chemical composition was modified by the hot bottom burning. In both cases, the NO cycle is responsible for the O depletion. The activation of this cycle depends on the rate of the 15N(p,{\gamma})16O reaction. A precise evaluation of this reaction rate at temperatures as low as experienced in H-burning zones in stellar interiors is mandatory to understand the observed O abundances. We present a new measurement of the 15N(p,{\gamma})16O reaction performed at LUNA covering for the first time the center of mass energy range 70-370 keV, which corresponds to stellar temperatures between 65 {\cdot} 106 K and 780 {\cdot}106 K. This range includes the 15N(p,{\gamma})16O Gamow-peak energy of explosive H-burning taking place in the external layer of a nova and the one of the hot bottom burning (HBB) nucleosynthesis occurring in massive AGB stars. With the present data, we are also able to confirm the result of the previous R-matrix extrapolation. In particular, in the temperature range of astrophysical interest, the new rate is about a factor of 2 smaller than reported in the widely adopted compilation of reaction rates (NACRE or CF88) and the uncertainty is now reduced down to the 10% level.Comment: 6 pages, 5 figure

Neutron-induced background by an alpha-beam incident on a deuterium gas target and its implications for the study of the 2H(alpha,gamma)6Li reaction at LUNA

The production of the stable isotope Li-6 in standard Big Bang nucleosynthesis has recently attracted much interest. Recent observations in metal-poor stars suggest that a cosmological Li-6 plateau may exist. If true, this plateau would come in addition to the well-known Spite plateau of Li-7 abundances and would point to a predominantly primordial origin of Li-6, contrary to the results of standard Big Bang nucleosynthesis calculations. Therefore, the nuclear physics underlying Big Bang Li-6 production must be revisited. The main production channel for Li-6 in the Big Bang is the 2H(alpha,gamma)6Li reaction. The present work reports on neutron-induced effects in a high-purity germanium detector that were encountered in a new study of this reaction. In the experiment, an {\alpha}-beam from the underground accelerator LUNA in Gran Sasso, Italy, and a windowless deuterium gas target are used. A low neutron flux is induced by energetic deuterons from elastic scattering and, subsequently, the 2H(d,n)3He reaction. Due to the ultra-low laboratory neutron background at LUNA, the effect of this weak flux of 2-3 MeV neutrons on well-shielded high-purity germanium detectors has been studied in detail. Data have been taken at 280 and 400 keV alpha-beam energy and for comparison also using an americium-beryllium neutron source.Comment: Submitted to EPJA; 13 pages, 8 figure

The 3He(alpha,gamma)7Be S-factor at solar energies: the prompt gamma experiment at LUNA

The 3He(alpha,gamma)7Be process is a key reaction in both Big-Bang nucleosynthesis and p-p chain of Hydrogen Burning in Stars. A new measurement of the 3He(alpha,gamma)7Be cross section has been performed at the INFN Gran Sasso underground laboratory by both the activation and the prompt gamma detection methods. The present work reports full details of the prompt gamma detection experiment, focusing on the determination of the systematic uncertainty. The final data, including activation measurements at LUNA, are compared with the results of the last generation experiments and two different theoretical models are used to obtain the S-factor at solar energies.Comment: Accepted for publication in Nucl. Phys.