Exploring continuum structures with a pseudo-state basis

Abstract

The ability of a recently developed square-integrable discrete basis to represent the properties of the continuum of a two-body system is investigated. The basis is obtained performing a simple analytic local scale transformation to the harmonic oscillator basis. Scattering phase-shifts and the electric transition probabilities B(E1) and B(E2) have been evaluated for several potentials using the proposed basis. Both quantities are found to be in excellent agreement with the exact values calculated from the true scattering states. The basis has been applied to describe the projectile continuum in the 6 He scattering by 12 C and 208 Pb targets at 240 MeV/nucleon and the 11 Be scattering by 12 C at 67 MeV/nucleon. The calculated breakup differential cross sections are found to be in very good agreement with the available experimental data for these reactions.

Astrophysical reaction rate forBe9formation within a three-body approach

“…Therefore, the ratio γ/b governs the asymptotic behavior of the THO functions: as γ/b increases, the hyper-radial extension of the basis decreases and some of the eigenvalues obtained by diagonalizing the Hamiltonian explore higher energies [21]. That is, γ/b determines the density of PSs as a function of the energy.…”

“…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.…”

Continuum discretised BCS approach for weakly bound nuclei

“…The CSPLD renormalizes the pairing strength and also prevents according to [24,25] occupations larger than the expected degeneracy in the continuum. PS have been shown to carry the information about the single-particle level density [5,39] which can be reobtained from the overlap of the PS with the actual scattering wave-functions. As seen in section 3.1.1, it is not compulsory to impose externally a level density.…”

“…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. Another important fact is the possibility of treating both resonant and non-resonant part of the continuum in a natural way and on the same footing.…”

“…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.…”