# UC Researchers Unravel Physics Mystery

Wednesday, January 19, 2000

Category: Sci/Tech

Scientists working at UC-run laboratories have employed supercomputers to solve one of quantum physics' principal questions.

The question of how charged particles separate has baffled researchers for more than 50 years. Since the 1920s, scientists have known the Shroedinger equation, which is designed to explain the way different elements interact to form chemicals. But researchers have been unable to employ the bulky equations because they are extremely difficult to use and solve.

"It is difficult to even formulate the problem," said Tom Rescigno, a researcher working at Lawrence Livermore National Laboratory and a collaborator on the project. "We had to find a mathematical trick that would allow the computer to handle it."

The scientists studied the simplest case, in which an electron hits a hydrogen atom that is made up of a fused proton and electron.

"The problem we solved has been an outstanding question in quantum physics since the 1920s," said Bill McCurdy, an associate laboratory director at Lawrence Berkeley National Laboratories and an adjunct professor in the UC Berkeley chemistry department.

Electrons and protons, which are both charged particles, exert forces on each other that fall off proportional to one over the square of the distance between the particles - the same manner in which the force of gravity falls off.

"Haley's comet returns back every 70 years," McCurdy said. "That is essentially forever, but the nature of gravity is such that, after a certain distance, the comet comes back."

A similar thing happens on the molecular level, McCurdy said. The behavior of the forces presents mathematical problems that are very difficult to solve.

"In quantum physics, that problem for breakup has deep mathematical difficulties," McCurdy said. "The answer to that problem was the supercomputer."

Because the behavior of charged particles is central to developing new technologies, many researchers have performed experiments that can predict the particles' behavior in energy-specific regions.

Although these experiments aid technology development, they do not paint a complete picture of the way these particles interact.

In order to determine how these particles act in a larger range of environments, McCurdy, Rescigno and their team of scientists worked to create a working mathematical model.

The researchers found that, in regions where accurate experiments have been performed, their results match closely, indicating that the mathematical model is viable.

Experiments designed to test the way charged particles behave can be performed in ordinary physics laboratories, McCurdy said.

Researchers make a beam with a carefully controlled electrical field and then select a specific energy at which to spit electrons into an empty tube. They then introduce several hydrogen atoms into a vacuum and study the way the atoms behave after they have been bombarded with the electrons, McCurdy said.

The new information permits scientists to predict what would happen in areas where the experiment is overly sensitive and difficult to complete, McCurdy said.

"There were no big and deep surprises," he said. "We had a good idea of what would happen, but there was no theory in place that could predict the behavior of these particles."

The team of scientists believes that its technique, which used more than one month of computer time on supercomputers, will provide a framework for solving future equations, McCurdy said.

Knowing could speed technology development, such as plasma-etching on silicon chips and the design of fluorescent lights, McCurdy said.

After consulting many computer and linear algebra experts and proposing different computer programs, the team of scientists designed a method that could produce a viable result.

"After trying hundreds of methods for solving the problem, we finally came up with a trick that permitted us to solve all of those equations," McCurdy said.

Rescigno said that the calculations required to complete the problem are so extensive, they would have been unimaginable 10 years ago.

"This required 5 million equations in 5 million unknowns for every energy, Rescingo said. "In order to piece together the answer, you have to do on the order of 100 calculations."

The energy of an electron depends upon its speed and "excitedness."

The scientists had to complete the calculation for many energies so they could determine how the particles behaved, depending on the amount of energy the electrons have.

"You have to do the calculation for many different energies in order to calculate the probability that, if it is struck, the bombarding electron will kick out the other electron and you'll end up with a bare proton."

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