Finite Size Scaling for Critical Conditions for Stable Multipole-Bound Negative Ions

ALEJANDRO FERRÓN; PABLO SERRA

Poco de Caldas

Congreso; XXVII Encontro Nacional de Física da Materia Condensada; 2004

Sociedad Brasilera de Física

Recently there has been increasing interest in multipole-bound negative ions.For the case of dipole-bound negative ions, the outer electron is weaklybound by the dipole moment of a neutral molecule in a diffuse orbital localizedat the positive end of the dipole.A similar situation occurs when we examine the possibility of one electronbinding by molecules with significant quadrupole moments and vanishing dipolemoments.In this work we present a finite-size scaling approach for the calculationsof the critical parameters for binding electrons to  a  finitemultipole field.The model Hamiltonian consists of a  charge $Q$ located at the originof the coordinates and$k$ charges $-Q/k$ located at distances $\vec{R_{i}}\;;i=1,\ldots,k$.After  proper scaling of distances and energies, the rescaled Hamiltoniandepends only on one free parameter  $q=Q\,R$. Critical parameters $q_c$ and$\alpha$ are defined by the near-threshold condition $E_0 \sim (q-q_c)^{\alpha}$.The finite-size scaling approach gives very accurate results for thecritical parametersby using  a systematic expansion in a finite basis set.We obtain accurate values for the  critical charge for several finite quadrupole potentials. For the critical exponentour results support the assumption that our model has the same value $\alpha=2$ that the exponent for  the ground-state energyfor the  Hamiltonian with a spherical potential that goes to infinite as$1/r^{3}$.In addition we presentsome rigorous results that show the possibility or not of bindingextra electrons to $n$-polar molecules.