
VOLUME 86  ISSUE 10 
PAGE 713

Universal description of the rotationalvibrational spectrum of three particles with zerorange interactions

O. I. Kartavtsev, A. V. Malykh
Joint Institute for Nuclear Research, 141980 Dubna, Russia

PACS: 03.65.Ge, 03.75.Ss, 21.45.+v, 36.90.+f

Abstract
A comprehensive universal description of the rotationalvibrational spectrum for two identical particles of mass m and the third particle of mass m_{1} in the zerorange 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 twobody scattering length is positive, the number of states is finite for , zero for L > L_{b}(m/m_{1}), and infinite for L < L_{c}(m/m_{1}). If the twobody scattering length is negative, the number of states is zero for 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 , where , , 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 and , respectively, while the number of vibrational states for is within the range .


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