Analytical transformed harmonic oscillator basis for three-body nuclei of astrophysical interest: Application to6He

Abstract

Recently, a square-integrable discrete basis, obtained performing a simple analytical local scale transformation to the harmonic oscillator basis, has been proposed and successfully applied to study the properties of two-body systems. Here, the method is generalized to study three-body systems. To test the goodness of the formalism and establish its applicability and limitations, the capture reaction rate for the nucleosynthesis of the Borromean nucleus 6 He ( 4 He + n + n) is addressed. Results are compared with previous publications and with calculations based on actual three-body continuum wave functions, which can be generated for this simple case. The obtained results encourage the application to other Borromean nuclei of astrophysical interest such as 9 Be and 12 C, for which actual three-body continuum calculations are very involved.

Astrophysical reaction rate forBe9formation within a three-body approach

“…[19], where it is applied to a system with a single charged particle. In this section, we summarize the main features of the formalism and we derive the electromagnetic transition probabilities B(Oλ) for the case of a system with two identical charged particles, such as 9 Be (α + α + n).…”

“…Furthermore, in the analytical THO method, the parameters of the transformation govern the radial extension of the THO basis. This provides the advantage of allowing the construction of an optimal basis for each observable of interest [19,21,22]. The analytical THO basis can describe very accurately the strength functions in the low-energy range, providing a good description of the radiative capture reactions.…”

“…The asymptotic behavior of continuum states for systems with several charged particles is not known in general, and very involved procedures are needed to deal with this problem [16][17][18]. In a recent work [19,20] we presented a pseudostate (PS) method based on an analytical local scale transformation (LST) of the harmonic oscillator (HO) basis, the transformed harmonic oscillator (THO) method. We generalized the analytical THO method for three-body systems and successfully applied to the Borromean nucleus 6 He (α+n+n) system.…”

Continuum discretised BCS approach for weakly bound nuclei

“…The prescription used here will be that of Karataglidis et al [37] rather than that of the original work by Stoitsov et al [38]. This THO basis has been shown to reduce the computational cost in nuclear reactions within three-and four-body formalisms [8][9][10]39]. This, together with the flexibility of the THO basis shown in [5,37] is crucial here for exploring the role of the continuum when a nucleus becomes more and more weakly bound.…”

“…The treatment of the continuum represents a challenge on both theoretical and computational grounds. Different representations of the continuum have been used and compared with few-body models [1][2][3][4][5][6][7][8][9]. These models are accurate in nuclei with a strong clusterization into few stable fragments as it occurs in the light region of the Segrè Chart.…”