For charged-particle induced reactions occurring in astrophysical scenarios, projectile energies are usually well below the Coulomb barrier of the reacting system. Hence, extremely small cross section reactions pose a difficult task for laboratory measurements. Most commonly, these energy-dependent cross sections are studied by detecting the emitted prompt gamma rays following the de-excitation of the produced compound nucleus. In this work we propose an alternative way for the measurement of the extremely small cross sections of the 25 Mg(p,γ) 26 Al resonant reaction, namely the use of the Accelerator Mass Spectrometry (AMS) technique.
I IntroductionIn the understanding of the nucleosynthesis of the elements in stars, one of the most important quantities is the reaction rate. This quantity must be evaluated in terms of the stellar temperature T, and its determination involves the knowledge of the excitation function σ(E) of the specific nuclear reaction leading to the final nucleus. The particular case of proton capture reactions plays an important role in stellar process of intermediate-mass elements.In several cases, the formation of a compound nucleus is dominated by a resonant process: the entrance channel, formed by a projectile P impinging on a target nucleus A, evolves into an excited state of a compound nucleus B = P + A, which ultimately decays into lower-lying states with the subsequent emission of gamma rays. This process occurs at well-defined center of mass (CM) energies, E CM = E X − Q, where E X is the energy of the excited states of the compound nucleus B and Q is the Q-value of the reaction [1].In a stellar environment, the reaction rate per particle pair is calculated as [2]where σ is the energy-dependent reaction cross section, v the relative velocity between the reacting particles and φ(v) is the velocity distribution of these particles in the stellar plasma. Nuclei participating in thermonuclear reactions can be considered as non-relativistic and non-degenerate ones, therefore, their velocities v (and hence their energies E) follow a Maxwell-Boltzmann distribution,where E = 1 2 mv 2 represents the kinetic energy of the nucleus with mass m, and T refers to the temperature of the gas. This distribution reaches a maximum value at E = kT. The second term defining the reaction rate is the cross section for the compound nucleus formation. This can be described by three factors: a geometrical one, σ = πλ / 2 ∝ E −1 ; a second one resembling the exponential behavior for tunneling through a Coulomb barrier, σ ∝ exp(−Z P Z A e 2 / v); and finally by a nuclear S-factor, S(E), which depicts the specific nuclear characteristics of the particular reaction. Therefore, the reaction rate per particle pair can also be expressed as