Geometric progression of molecules: experimental evidence for the Efimov effect

Scientists from the University of Chicago experimentally obtained an exotic state of particles, known as the Efimov effect , on behalf of the Russian physicist Vitaly Efimov, who predicted this quantum phenomenon in 1970.

As a result of the interference of unbound states of particles and quasi-bound states, the triatomic molecules fit into each other like a nested doll. The illustration above shows the ratio of the size of molecules, between which the geometric proportion must be strictly observed. Surprisingly, even complex natural phenomena obey simple mathematical rules.
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“This is a new chemical law that the size of molecules can correspond to a geometric progression, like 1, 2, 4, 8 ...,” said Cheng Chin, a professor of physics at the University of Chicago. “In our case, we found three molecular states in this sequence, where one molecular state is always 4.88 times the previous one.”

The results of scientific work published in the journal Physical Review Letters.



A group of physicists from Chicago managed to observe three molecules in this sequence, consisting of one lithium atom and two cesium atoms (a mixture of ⁶ LI- ¹³³ Ce was used) at a temperature of about 200 nanogelvins, that is, slightly above absolute zero.

To obtain molecules, it was necessary to cool the atoms of cesium and lithium separately, and then gently mix them, exploiting the Feshbach resonance .

Theoretically, based on the hypothesis of the infinity of the Universe, the number of states in this geometric progression can be infinitely large. The effect is observed for molecules of three atoms, but is unattainable for molecules of two or four atoms.

In the ⁶ LI- ¹³³ Ce system, the size of the molecules was 17, 86 and 415 nanometers, respectively, which almost exactly corresponds to the geometric progression and theoretically predicted values.