Physics rule of thumb gets thumbs down.

When intellectual giant Niels Bohr offered a striking new atomic theory in 1913, he and the field of physics unwittingly benefited from a large dollop of dumb luck, physicists say. Bohr analyzed energy levels of the hydrogen atom, which consists of two charged particles. For interactions of such particles, the quantum mechanics theory that Bohr was helping to establish happens to yield predictions that at high energies match exactly those of classical physics.

Now, a theorist has explored the quantum-classical connection for interactions between neutral atoms chilled nearly to absolute zero. Bo Gao of the University of Toledo in Ohio finds that a principle developed by Bohr to help quantum pioneers develop a theory that dovetailed with classical physics gets left out in the cold.

Bohr proposed a rule of thumb called the correspondence principle (SN: 1/11/86, p. 26). A form of the principle widely repeated in textbooks and lecture halls states that predictions of quantum mechanics and classical physics should match for the most energetic cases.

In the Nov. 22 PHYSICAL REVIEW LETTERS, Gao calculates possible energy states of any chilled, two-atom molecule, such as sodium, that's vibrating and rotating almost to the breaking point. He performs the calculations via quantum mechanical and so-called semiclassical methods and compares the results. Instead of the results agreeing better for increasingly energetic states, the opposite happens.

According to quantum mechanics, Gao explains, atoms behave as both particles and waves. As scientists make atoms colder and more sluggish, the particles' wave nature spreads over a larger space.

For charged particles in high-energy states, this wave property remains small enough that the correspondence principle holds. For neutral atoms, however, which have different forces between them, the wave aspect can't be ignored. As long as the particles' wave nature re mains noticeable, quantum and classical pictures can't look the same.

"This is not to say that anything in quantum mechanics is incorrect," Gao notes. It's "just that some particular formulations of this quantum-classical correspondence are wrong."

"It would be nice if this permeates into the quantum mechanics textbooks," comments Chris Greene of the University of Colorado at Boulder. But don't expect a big impact on research, he cautions. Quantum mechanics specialists have recognized since at least the 1930s that both the correspondence principle and classically based approximations of quantum mechanics can only be trusted to a limited extent, he says.

Gao agrees that the Nov. 22 report mainly sends a message to teachers and textbook writers. He told SCIENCE NEWS, however, that in unpublished work he extends his ideas into a new mathematical description of ultracold atoms that are colliding or weakly bound to each other. This broader theory should strongly affect both atomic physics and chemistry, he says.

For now, researchers rely on computers to predict the behavior of atoms in ultracold gases (SN: 9/11/99, p. 166) such as Bose-Einstein condensates or to model strained bonds in cold but excited molecules. However, for each type of atom, say sodium or rubidium, researchers must generate a different set of equations and numerical solutions, Gao says.

By contrast, his unpublished theory unifies the mathematics so that properties of the ultracold atoms emerge from relatively simple equations that can be solved on paper, he says.

While Gao's new theory is promising, the brute-force computers have become so fast that the numerical approach is already beginning to succeed, Greene contends. At the same time, a shortage of experimentally determined parameters hobbles on-paper solutions, he adds.