New treatment of breakup continuum in the method of continuum discretized coupled channels

Abstract

A new method of pseudostate discretization is proposed for the method of continuum discretized coupled channels to deal with three-body breakup processes. In the method, discrete S-matrix elements to the pseudo (discretized) continuum states are transformed into smooth ones to the exact continuum states of the projectile. As for the basis functions for describing pseudostate wave functions, we take real-and complex-range Gaussian functions, which form in good approximation a complete set in a finite configuration space being important for breakup processes. This "approximate-completeness" property is essential to make transformed S-matrix elements accurate. Moreover, the use of these Gaussian bases is expected to be very useful to describe four-body breakup processes. Accuracy of the method is tested quantitatively for two realistic examples: elastic and projectile-breakup processes in d+ 58 Ni scattering at 80 MeV and those in 6 Li+ 40 Ca at 156 MeV.

Analytical transformed harmonic oscillator basis for continuum discretized coupled channels calculations

“…[7] and recently employed in a previous application of the THO method [17]. In this method, the breakup S-matrix elements S α :α (k), which depend on both the continuous variable k and the initial and final angular momenta, are obtained by an appropriate superposition of the discrete S-matrix elementsŜ α :α (k i ) resulting from the solution of the coupled-channels equations, as [7,15] …”

“…The 6 Li nucleus is assumed here to be composed of two fragments, α + d, as has usually been done in previous studies (see, for example, Refs. [6][7][8][9]). An important difference with respect to the deuteron case is the presence of a d-wave resonance in the 6 Li continuum.…”

“…Although originally designed to account for the effect of the breakup channels in direct nuclear reactions involving deuterons [1][2][3], it soon proved to be a useful tool to describe reactions induced by other weakly bound nuclei that could be to some extent described within a two-cluster model such as 6 Li [4][5][6][7][8][9] or 7 Li [9][10][11][12][13] and, more recently, the scattering of exotic nuclei such as 8 B [14][15][16][17], 7 Be [13], or 11 Be [18,19]. The CDCC method has been extended lately to describe the scattering of three-body projectiles and has successfully described the elastic scattering of 6 He [20][21][22][23].…”

Four-body continuum-discretized coupled-channels calculations

“…An alternative to the binning procedure is to represent the continuum spectrum by the eigenstates of the internal Hamiltonian in a basis of square integrable (or L 2 ) functions, such as Laguerre [6][7][8], Gaussian [9,10], or Sturmian [11][12][13][14] functions. In practice, the diagonalization is performed in a finite (truncated) set of states and the resulting eigenstates, also known as pseudostates (PS), are regarded as a finite and discrete representation of the spectrum of the system.…”

Breakup and Finite-Range Effects on the 8B(d,n)9C Reaction

“…The pseudostate method with the real-range Gaussian basis functions [14] is used for obtaining the discretized-continuum states of d; we include the s and d states and neglect the intrinsic spin of d. The number of basis functions taken is 20, and the minimum (maximum) range parameter of the Gaussian is 1.0 (30.0) fm. We include in the CDCC pseudostates with ε i pn < 65 MeV and ε i pn < 80 MeV for the s and d states, respectively.…”