We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Universal description of the rotational-vibrational spectrum of three particles with zero-range interactions.
- Authors
Kartavtsev, O. I.; Malykh, A. V.
- Abstract
A comprehensive universal description of the rotational-vibrational spectrum for two identical particles of mass m and a third particle of mass m 1 in the zero-range limit of the interaction between different particles is given for arbitrary values of the mass ratio m/m 1 and the total angular momentum L. It is found that the number of vibrational states is determined by the functions L c( m/m 1) and L b( m/m 1). Explicitly, if the two-body scattering length is positive, the number of states is finite for L c( m/m 1) ≤ L ≤ L b( m/m 1), zero for L > L b( m/m 1), and infinite for L < L c( m/m 1). If the two-body scattering length is negative, the number of states is zero for L ≥ L c( m/m 1) and infinite for L < L c( m/m 1). For the finite number of vibrational states, all the binding energies are described by the universal function ɛLN( m/m 1) = [Figure not available: see fulltext.](ξ, η), where ξ = ( N − 1/2)/√ L( L + 1), η = √ m/[ m 1 L( L + 1)], and N is the vibrational quantum number. This scaling dependence is in agreement with the numerical calculations for L > 2 and only slightly deviates from those for L = 1, 2. The universal description implies that the critical values L c( m/m 1) and L b( m/m 1) increase as 0.401 √ m/m 1 and 0.563 √ m/m 1, respectively, while the number of vibrational states for L ≥ L c( m/m 1) is within the range N ≤ N max ≈ 1.1√ L( L + 1) + 1/2.
- Subjects
VIBRATIONAL spectra; PARTICLES (Nuclear physics); MOMENTUM (Mechanics); SCATTERING (Physics); MOLECULAR spectra
- Publication
JETP Letters, 2008, Vol 86, Issue 10, p625
- ISSN
0021-3640
- Publication type
Article
- DOI
10.1134/S002136400722002X