45 research outputs found
Universal description of three two-component fermions
A quantum mechanical three-body problem for two identical fermions of mass
and a distinct particle of mass in the universal limit of zero-range
two-body interaction is studied. For the unambiguous formulation of the problem
in the interval ( and ) an additional parameter determining the wave function near
the triple-collision point is introduced; thus, a one-parameter family of
self-adjoint Hamiltonians is defined. The dependence of the bound-state
energies on and in the sector of angular momentum and parity is calculated and analysed with the aid of a simple model
Universal description of the rotational-vibrational spectrum of three particles with zero-range interactions
A comprehensive universal description of the rotational-vibrational spectrum
for two identical particles of mass and the third particle of the mass
in the zero-range limit of the interaction between different particles is
given for arbitrary values of the mass ratio and the total angular
momentum . If the two-body scattering length is positive, a number of
vibrational states is finite for , zero for
, and infinite for . If the two-body scattering
length is negative, a number of states is either zero for or
infinite for . For a finite number of vibrational states, all the
binding energies are described by the universal function , where ,
,and is the vibrational
quantum number. This scaling dependence is in agreement with the numerical
calculations for and only slightly deviates from those for .
The universal description implies that the critical values and
increase as and ,
respectively, while a number of vibrational states for is
within the range
Low-energy three-body dynamics in binary quantum gases
The universal three-body dynamics in ultra-cold binary Fermi and Fermi-Bose
mixtures is studied. Two identical fermions of the mass and a particle of
the mass with the zero-range two-body interaction in the states of the
total angular momentum L=1 are considered. Using the boundary condition model
for the s-wave interaction of different particles, both eigenvalue and
scattering problems are treated by solving hyper-radial equations, whose terms
are derived analytically. The dependencies of the three-body binding energies
on the mass ratio for the positive two-body scattering length are
calculated; it is shown that the ground and excited states arise at and ,
respectively. For m/m_1 \alt \lambda_1 and m/m_1 \alt \lambda_2, the
relevant bound states turn to narrow resonances, whose positions and widths are
calculated. The 2 + 1 elastic scattering and the three-body recombination near
the three-body threshold are studied and it is shown that a two-hump structure
in the mass-ratio dependencies of the cross sections is connected with arising
of the bound states.Comment: 16 page
Universal low-energy properties of three two-dimensional particles
Universal low-energy properties are studied for three identical bosons
confined in two dimensions. The short-range pair-wise interaction in the
low-energy limit is described by means of the boundary condition model. The
wave function is expanded in a set of eigenfunctions on the hypersphere and the
system of hyper-radial equations is used to obtain analytical and numerical
results. Within the framework of this method, exact analytical expressions are
derived for the eigenpotentials and the coupling terms of hyper-radial
equations. The derivation of the coupling terms is generally applicable to a
variety of three-body problems provided the interaction is described by the
boundary condition model. The asymptotic form of the total wave function at a
small and a large hyper-radius is studied and the universal logarithmic
dependence in the vicinity of the triple-collision point is
derived. Precise three-body binding energies and the scattering length
are calculated.Comment: 30 pages with 13 figure