Efimov states of three unequal bosons in non-integer dimensions

Abstract

The Efimov effect for three bosons in three dimensions requires two infinitely large $s$-wave scattering lengths. We assume two identical particles with very large scattering lengths interacting with a third particle. We use a novel mathematical technique where the centrifugal barrier contains an effective dimension parameter, which allows efficient calculations precisely as in ordinary three spatial dimensions. We investigate properties and occurrence conditions of Efimov states for such systems as functions of the third scattering length, the non-integer dimension parameter, mass ratio between unequal particles, and total angular momentum. We focus on the practical interest of the existence, number of Efimov states and their scaling properties. Decreasing the dimension parameter from $3$ towards $2$ the Efimov effect and states disappear for critical values of mass ratio, angular momentum and scattering length parameter. We investigate the relations between the four variables and extract details of where and how the states disappear. Finally, we supply a qualitative relation between the dimension parameter and an external field used to squeeze a genuine three dimensional system.

arXiv commentTo be published in Few-body Systems

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Cited by in corpus (9)

• Few-body quantum method in a $d$-dimensional space
• Efimov effect in a $D$-dimensional Born-Oppenheimer approach
• Efimov effect in non-integer dimensions induced by an external field
• Three-body continuum states and Efimov physics in non-integer geometry
• Confinement of $N$-body systems and non-integer dimensions
• Dimensional effects in Efimov physics
• Two-body continuum states in non-integer geometry
• Energetics of three interacting mass-imbalanced bodies in a three-dimensional spherical harmonic trap
• Reliability of the Born-Oppenheimer approximation in noninteger dimensions