Determining astrophysical three-body radiative capture reaction rates from inclusive Coulomb break-up measurements

Abstract

A relationship between the Coulomb inclusive break-up probability and the radiative capture reaction rate for weakly bound three-body systems is established. This direct link provides a robust procedure to estimate the reaction rate for nuclei of astrophysical interest by measuring inclusive break-up processes at different energies and angles. This might be an advantageous alternative to the determination of reaction rates from the measurement of B(E1) distributions through exclusive Coulomb break-up experiments. In addition, it provides a reference to assess the validity of different theoretical approaches that have been used to calculate reaction rates. The procedure is applied to 11 Li ( 9 Li + n + n) and 6 He ( 4 He + n + n) three-body systems for which some data exist.DOI: 10.1103/PhysRevC.93.041602Nucleosynthesis occurs in stellar environments, following a complex network of reactions in which heavier nuclei are formed by proton, neutron, or α radiative capture by a lighter nucleus. The knowledge of these radiative capture reaction rates is crucial for the stellar models aiming to describe the evolution in composition, energy production, and temperature structure of different stellar environments (see, for example, Ref.[1] and references therein). The direct experimental measurement of the relevant cross sections is, in principle, possible for two-body reactions [2,3]. In many interesting cases, however, reaction cross sections cannot be measured directly. This may occur if the initial nucleus is short-lived [4] or when the capture process is a three-body reaction [5]. In this case, the inverse reaction to radiative capture, photodissociation, could be measured [4]. Reaction rates are then obtained by integrating the photodissociation cross section for the compound nucleus, weighted with the Maxwell-Boltzmann energy distribution and the relevant phase space factors, from the corresponding energy threshold [6,7]. Direct photodissociation measurements can be done only for stable nuclei, e.g., 12 C [8], sometimes with important discrepancies among different experiments, e.g., 9 Be [5,9]. Thus, for many relevant cases this technique is not feasible (e.g., 17 Ne [10]). In addition, to obtain the reaction rate from experimental photodissociation measurements usually requires, for three-body systems, a sequential description of the formation process, which is questionable at low temperatures if the particles do not have enough energy to populate intermediate resonances [11].At first order, the energy distribution of the photodissociation cross section is determined by the B(E1) distribution, of the compound nucleus, into the continuum of its fragments [12]. Hence, an alternative to obtain this cross section, when the nucleus is short-lived, is to perform exclusive Coulomb breakup experiments at intermediate energies (∼100 MeV/nucleon) on heavy targets, at very forward angles [13,14]. From the exclusive break-up cross section, the B(E1) is extracted * jcasal@us.es assuming Coulomb is dominant at those angles. Howe...

Radiative capture reaction forNe17formation within a full three-body model

“…Thus, for reactions involving unstable nuclei, this technique is not feasible. Recently, an alternative procedure was proposed to obtain three-body radiative capture reaction rates from experimental information on inclusive break-up reactions at low energies [23]. No such data are available in the literature for 17 Ne, so theoretical models to describe its structure are in order.…”

Dineutron correlations in knockout reactions with Borromean halo nuclei

“…The three-body ground-state wave function Φ gs (x, y) can be obtained within the hyperspherical formalism [1], provided that reliable core-n and n-n interactions are available. In particular, the analytical transformed harmonic oscillator method is adopted [26,27] to build the wave function in the so-called Jacobi-T representation, where the two valence neutrons are related by the x coordinate. Then, a transformation to the Jacobi-Y coordinates shown in Fig.…”

Structural effects of $^{34}$Na in the $^{33}$Na(n,$γ)^{34}$Na radiative capture reaction

“…( 4), ( 5) and ( 6), we can easily calculate reaction rates of stellar reactions in this elegant indirect manner [29,42]. Such indirect approaches are used quite extensively in nuclear astrophysics for studying a diversity of nuclear reactions and obtaining information about the events occurring in the stellar plasma [43][44][45]. They are essential because given the experimental technologies available, the direct measurement of radiative capture cross-sections, σ (n,γ) (E bc ), for most astrophysical sites is difficult at such low ranges of relative energy (E bc ∼ 10 −3 -1 MeV).…”