A break-up model solved in hyperspherical coordinates

L.U. ANCARANI, G. GASANEO, AND D.M. MITNIK

Caen

Conferencia; 22nd International Symposium on Ions Atom Collisions; 2011

ISIAC

One way to describe ion-atom break-up processes consists in splitting the total wave functionas     + =     0+    +sc, where     0 is an asymptotically prepared initial state and     +sc is thescattering solution. Adequate asymptotic behavior should be imposed, and hypersphericalcoordinates (; ) are well adapted for this purpose. A Sturmian approach in these coordinates[1] may be used to solve the scattering problem. In principle, a good convergence ratecan be fullled by providing to the basis functions the appropriate physical information ofthe problem (e.g. by diagonalizing part of the interaction appearing in the full Hamiltonian)and the correct asymptotic behavior: in this way, the expansion is restricted to the regionwhere the interaction between the particles takes place.To test numerically the proposed Sturmian-hyperspherical approach we make use of ananalytically solvable model for three particles break up processes [2], as was done, e.g.,within the exterior complex scaling method [3]. In our fragmentation/ionization model,the scattering process is represented by a non-homogeneous Coulomb Schrodinger equationwhere the driven term is given by a Yukawa-like -dependent interaction multiplied by theproduct of a continuum wave function and a bound state in the particles coordinates r1 andr2. The scattering function     +sc is the solution of the following driven equation:[T 􀀀Z 􀀀 E]    +sc = 􀀀W    0; (1)where T is the kinetic energy, and W is the left-out interaction. Closed forms in hypersphericalcoordinates are derived for the solution with outgoing wave behavior and for thescattering transition amplitude. They compare very well with numerical results validatingthe use of the proposed Sturmian hyperspherical approach. Moreover, as all the Sturmianbasis functions possess the correct outgoing Coulombic asymptotic behavior and diagonalizenot only the kinetic energy but also the Coulomb interaction 􀀀Z=, the convergence rate isstrongly accelerated: only a few SF are necessary to reproduce the analytical solutions forboth the scattering wave function and the transition amplitude.References[1] G. Gasaneo et al, J. Phys. Chem. A 113? 14573 (2009).[2] G. Gasaneo, L.U. Ancarani and D. M. Mitnik (to be submitted)[3] C. W. McCurdy and T. N. Rescigno, Phys. Rev. A 56, R4369 (1997).