From: Spudboy100@aol.com
Date: Fri Dec 24 1999 - 12:57:35 MST
Does this have any meaning to Extropianism and the Universe? What about the
quote about Coulomb Interactions are Forever?
http://www.sciencedaily.com/releases/1999/12/991224091255.htm
Source: Lawrence Berkeley National Laboratory (http://www.lbl.gov)
Date: Posted 12/24/99
After 50 Years, Fundamental Problem Of Quantum Physics Solved At Last
BERKELEY, CA -- For over half a century, theorists have tried and failed to
provide a complete solution to scattering in a quantum system of three
charged particles, one of the most fundamental phenomena in atomic physics.
Such interactions are everywhere; ionization by electron impact, for example,
is responsible for the glow of fluorescent lights and for the ion beams that
engrave silicon chips.
Now, collaborators at the Department of Energy's Lawrence Berkeley National
Laboratory, Lawrence Livermore National Laboratory, and the University of
California at Davis have used supercomputers to obtain a complete solution of
the ionization of a hydrogen atom by collision with an electron, the simplest
nontrivial example of the problem's last unsolved component. They report
their findings in the 24 December, 1999, issue of Science magazine.
Their breakthrough employs a mathematical transformation of the Schrödinger
wave equation that makes it possible to treat the outgoing particles not as
if their wave functions extend to infinity -- as they must be treated
conventionally -- but instead as if they simply vanish at large distances
from the nucleus.
"Using this transformation we compute accurate solutions of the
quantum-mechanical wave function of the outgoing particles, and from these
solutions we extract all the dynamical information of the interaction," says
Bill McCurdy, Berkeley Lab's Associate Laboratory Director for Computing
Sciences and a principal author of the Science article.
McCurdy and his longtime collaborator Thomas Rescigno, a staff physicist at
Livermore Lab, and their co-authors, doctoral candidate Mark Baertschy of UC
Davis and postdoctoral fellow William Isaacs at Berkeley Lab, used the
SGI/Cray T3E at the National Energy Research Scientific Computing Center
(NERSC) at Berkeley Lab and the IBM Blue Pacific computer at Livermore Lab
for their solution of the three-charged-body scattering problem.
"An exact first-principles solution of the wave function for the hydrogen
atom was vital to establishing the new quantum theory in the 1920s," says
Rescigno. "But even today, for systems with three or more charged particles,
no analytic solutions exist" -- that is, there are no explicit solutions to
the Schrödinger equation for such systems.
Rescigno points out that "it wasn't until the late 1950s, using early
computers, that accurate solutions were obtained even for the bound states of
helium," an atom with two electrons closely orbiting the nucleus. "Scattering
problems are a lot more difficult."
As with all scattering problems, the electron-ionization of a hydrogen atom
begins with a particle incoming at a certain velocity. This electron
interacts with the atom, and two electrons fly out at an angle to each other,
leaving the proton behind. The likelihood that a specific incoming state will
result in an outgoing state with the particles at specific angles and
energies is the "cross section" for that result.
Cross sections of quantum-mechanical processes are derived from the system's
wave function, solutions of the Schrödinger equation which yield
probabilities of finding the entities involved in a certain state. In
scattering problems, wave functions are not localized but extend over all
space.
Moreover, says McCurdy of the electromagnetic forces between charged
particles, "Coulomb interactions are forever." These infinities make it
impossible to define the final state of scattering exactly. "The form of the
wave function where all three particles are widely separated is so
intractable that no computer-aided numerical approach has been able to
incorporate it explicitly."
But, Rescigno notes, "this obviously hasn't stopped people from working with
plasmas and other ionization phenomena. Mathematically, they've come up with
incredibly artful dodges, and some of them even seem to work."
Earlier this year, however, in the Proceedings of the Royal Society, Colm T.
Whelan of Cambridge University and his colleagues published their conclusion
that all such approximations perform inconsistently and that those few cases
which appear to yield good agreement with experiment "are largely
fortuitous."
By contrast, the method developed by McCurdy and Rescigno and their
co-authors allows the calculation of a highly accurate wave function for the
outgoing state that can be interrogated for details of the incoming state and
interaction in the same way an experimenter would interrogate a physical
system.
They begin with a transformation of the Schrödinger equation called "exterior
complex scaling," invented by Caltech's Barry Simon in 1979 to prove formal
theorems in scattering theory. The transformation leaves the solution
unchanged in regions which correspond to physical reality, producing the
correct outgoing waveform based upon the angular separation and distances of
two electrons far from the nucleus.
Once the wave function has been calculated, it must be analyzed by computing
the "quantum mechanical flux," a means of finding the distribution of
probability densities that dates from the 1920s. This computationally
intensive process can yield the probability of producing electrons at
specific energies and directions from the ionized atom. (Because electrons
are identical, there is no way to distinguish between the initially bound and
initially free electron).
The researchers acknowledge important advances made earlier by others such as
Igor Bray and Andres Stelbovics, whose methods could give the total cross
section for ionization of a scattering reaction but could not give specifics
such as the directions or energies of outgoing electrons. By contrast, says
Rescigno, "Our work produces absolute answers at the ultimate level of
detail."
Comparison with real scattering experiments, such as those recently published
by J. Röder et al, who scattered incoming 17.6 electron-volt electrons from
hydrogen atoms and measured the angles and energies of the outgoing
electrons, prove the accuracy of the new method. The experimental data points
match the graph of the cross sections calculated by Rescigno, Baertschy,
Isaacs, and McCurdy with astonishing exactitude.
"Even if the specific methods have changed, quantum chemistry was founded
when the helium atom with two bound electrons was solved -- it showed that
these problems were in principle solvable," McCurdy says. "What we have done
is analogous. The details of our method probably won't survive, but we've
taken a big step toward treating ionizing collisions of electrons with more
complicated atoms and molecules."
"Collisional breakup in a quantum system of three charged particles," by T.N.
Rescigno, M. Baertschy, W.A. Isaacs, and C.W. McCurdy appears in Science
magazine, 24 December 1999. The authors conclude by noting that the same
computing power and tools necessary for investigating the complexity of
increasingly larger systems are also needed "to answer a basic physics
question for one of the simplest systems imaginable in physics and
chemistry."
###
The Berkeley Lab is a U.S. Department of Energy national laboratory located
in Berkeley, California. It conducts unclassified scientific research and is
managed by the University of California. Visit our website at
http://www.lbl.gov.
Editor's Note: The original news release can be found at
http://www.lbl.gov/Science-Articles/Archive/quantum-scattering.html
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