Particle motion in a deformed potential using a transformed oscillator basis

Abstract

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 11 Be nucleus, treated in a two-body model ( 10 Be + 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 Schrödinger 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.

Core excitations in the structure and reactions of halo nuclei

“…In order to estimate the error bars, we look for an increase of 1 in the χ 2 /n value, being n the number of experimental points. The results will also depend on the ground state wavefunction, for which we adopt that from the PRM calculation [1]. Following this prescription, we find for the 5/2 + resonance the coefficients a 2 = 0.55 ± 0.15, b 2 = 0.30 ± 0.15 and a renormalization factor N=0.50 ± 0.04.…”

“…[5] (model Be12-b) we obtain the following spectroscopic decomposition for the ground state and the the first 5/2 + and 3/2 + resonances [1]:…”

“…In a recent work [1] we have generalized the Transformed Harmonic Oscillator (THO) basis in order to include the excitations of the core in a simple particle-rotor model. Diagonalizing the Hamiltonian in a square-integrable basis, the eigenstates obtained or pseudo-states (PS) are a finite approximation of the bound and unbound states of the nucleus.…”

“…For each channel we construct a THO set of functions. We then diagonalize the Hamiltonian so that the final PS will be a linear combination of the corresponding THO functions [1].…”

Continuum discretised BCS approach for weakly bound nuclei

“…The prescription used here will be that of Karataglidis et al [37] rather than that of the original work by Stoitsov et al [38]. 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.…”