Particle motion in a deformed potential using a transformed oscillator basis

The quantum description of a particle moving in a deformed potential is investigated. A pseudostate (PS) basis is used to represent the states of the composite system. This PS basis is obtained by diagonalizing the system Hamiltonian in a family of square integrable functions. In this work the transformed harmonic oscillator (THO) functions, obtained from the solutions of the harmonic oscillator using a local scale transformation (LST), are used. The proposed method is applied to the ¹¹Be nucleus, treated in a two-body model (¹⁰Be+n). Structure observables have been studied. Wave functions and energies obtained for the bound states and some low-lying resonances are compared with those obtained by direct integration of the Schr\"odinger equation. The dipole and quadrupole electric transition probabilities for the low-energy continuum have been calculated in the THO basis, and compared with the exact distributions obtained with the scattering states.