Tests of anL2Discretization Procedure for Approximating Three-Body Breakup Effects

Continuum discretization methods in a composite particle scattering off a nucleus: Benchmark calculations

“…Thus, in this approach, solving the three-body LS equation is reduced to the solution of the simple matrix equation (12). 6 The composite-particle elastic scattering amplitude can now be written formally as the diagonal (on-shell) matrix element…”

“…Historically, the main progress in studying elastic and inelastic (breakup) composite projectile scattering off a heavy target was made within the continuum-discretized coupledchannel (CDCC) method [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] in the framework of the Schrödinger coupled-channel scheme. In the CDCC approach, the total three-body scattering wave function (initial versions of the method assumed the projectile to be a two-fragment nucleus) is expanded in a complete basis of the fragment relative motion of the projectile, and the unknown three-dimensional elastic and breakup channel wave functions of the projectile c.m.…”

“…motion are obtained by solving a set of coupled-channel equations. This approach has been successfully applied in the field of nuclear reactions to find the scattering amplitudes of many particular processes for various types of projectiles such as deuterons, 6 Li, 6 He, 7 Li, 12 C, etc. However, a strong discussion about the validity of the method arose [16][17][18] because of some unclear issues related to the treatment of the total wave function breakup components in the asymptotic region.…”

“…This reaction has been also used to compare the CDCC and Faddeev approaches in a recent work [24], showing very good agreement between both methods. It will be vividly demonstrated that the contribution of the closed channels, which are commonly neglected in CDCC calculations [1][2][3][4][5][6][7][8][9]12], increases essentially when the projectile energy gets low. In principle, closed channels can be incorporated within the CDCC scheme; however, in this case the solution of the coupled equations becomes numerically unstable.…”

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.…”