Star Trek: Science Today

An occasional e-zine by Robert Muratore

"Captain, we're being scanned."

On "Starship Down", an episode of Star Trek: Deep Space 9 shown in April 1996, Kira suggests a method of scanning in an atmosphere, using a "trick" she learned in the resistance: active scanning. In fact, much of the scanning in Star Trek seems to be or to require active scanning, that is, some sort of radiation or particle sent out from the ship with a careful eye on how the target of the scan reacts. What is especially nice about the "Starship Down" episode was the central role played by chance.

On "Maneuvers", an epsiode of Star Trek: Voyager, B'Elanna Torres reminisces with Chakotay about a Maquis trick: "Seska modified an antiproton beam to penetrate the shields."

In this installment, I will describe a form of active scanning that could conceivably be used in the Star Trek universe, and that is actually in use today. Furthermore, the technique relies heavily on chance, that is, on the statistical distribution of many subatomic particles. And the particles in question are dear to the hearts of the Star Trek crew: antiprotons.


Outline

  1. Antiprotons are made at the home of the World Wide Web
  2. How does antiproton imaging work?
  3. What are the limiting errors?
  4. The interaction of antiprotons with matter
  5. The capture of antiprotons by matter
  6. Annihilation
  7. Reconstructing the target
  8. Summary

Antiprotons are made at the home of the World Wide Web

>>>> Outline | Next

Antiprotons are produced at large accelerators such as those at CERN (also the birthplace of the World Wide Web), Fermilab, and Brookhaven. They are as massive and stable as protons, and are oppositely charged. As charged stable particles, they are readily formed into beams of well characterized energy. These beams can be directed at targets, and insofar as the physics of interaction between antiproton beam and target is understood, the results of the interactions will yield information about the target.

Paraffin, a hydrocarbon and thus rich in hydrogen, is vaporized and ionized (stripped of electrons). In this way, many protons are freed. These are shepherded by magnetic fields around a cyclotron, accelerated to high speed. A thin dense target is then bombarded with the protons. Through the mass-energy equivalence, various subatomic particles are created from the energy of the impact; among these are antiprotons.


How does antiproton imaging work?

>>>> Outline | Previous | Next

Until they have nearly stopped, antiprotons interact with matter mainly through the electromagnetic interaction. They lose energy in collisions with electrons. Just prior to annihilation, the negatively charged antiproton orbits a nucleus, forming an antiprotonic atom. The antiproton cascades down energy levels, emitting x-rays, and finally annihilates on a neutron or proton. Products of the annihilation go streaming outward from the annihilation point or vertex; many escape the target. By detecting escaped annihilation products, and extrapolating back along their tracks, the vertex can be inferred.

Now suppose that a pencil beam of antiprotons of energy E1 is sent into a target and stops about a position or vertex R1 (the distribution about R1 is approximately Gaussian). Another beam of antiprotons of energy E2 stops about R2. The difference in the average stopping positions in the target relative to the difference in a water target yields the density. The farther apart stopping positions are, the lower the average target density between the stopping positions.


What are the limiting errors?

>>>> Outline | Previous | Next

There are uncertainties in the behavior of antiprotons that introduce error into this technique. In particular, the rate of energy loss is subject to quantum fluctuations, resulting in a variation in the stopping position called straggling. Furthermore, there is multiple elastic scattering from nuclei which results in displacement of the antiproton perpendicular to its initial direction. This is called lateral scattering. Straggling and lateral scattering of antiprotons, and lateral scattering of charged annihilation products (pions) are the chief sources of error. These errors can be characterized in detail, and techniques worked out to minimize them. For example, straggling can be overcome by finding the mean stopping position of many antiprotons of a given energy. But antiprotons are expensive and in large numbers can damage the target. So there is a tradeoff.


The interaction of antiprotons with matter

>>>> Outline | Previous | Next

Except for the annihilation process itself, the interaction of interest between moderate-energy heavy charged particles and the ambient target is the electromagnetic (Coulomb) interaction. Interaction with electrons results primarily in a loss of kinetic energy to the particle of concern. Because the particle is much more massive than the electron, it is not deflected very much by these collisions. On the other hand, Coulomb interaction with nuclei is elastic scattering, which results in enough deflection of the antiprotons and pions to become a limiting factor in precision.

The kinetic energy loss of the antiproton flying through the target depends upon the density of electrons in the target and on the speed of the antiproton. The rate of energy loss is called the stopping power of the medium. The stopping power decreases as the speed of the particle increases. (One would have a better chance at survival running rather than crawling across a highway.) This is shown in Figure 1. The range that an antiproton will travel in a target, R, is proportional to the kinetic energy of the particle as it enters the target, E, raised to the power 1.77. This is shown in Figure 2. The straggling, or uncertainty in the range, is about 1% of the range.



EXERCISE
You are on the bridge, and asked to scan a nearby piece of debris. The object is known to be roughly spherical with a radius of 20 meters. Engineering is able to give you antiprotons of varying speed. Figure the speed of the antiprotons so that they stop within the target. HINT: use the graph of range vs energy in Figure 2, and the formula for kinetic energy E = 0.5 mv**2.

The deflection of the antiprotons by the nuclei (that gives rise to the lateral scattering) is caused by the Coulomb force. Classically, this is the same thing that deflects the electron beams in the cathode ray tube that most likely is the screen upon which you are reading this. Each time he antiproton passes by a nucleus, it is deflected a small bit just like an electron passing through deflector plates. The net result of all of these microscopic "collisions" is a slightly random path through the target. Several such paths are shown in Figure 3.

Occasionally, a large angle deflection occurs which throws the antiproton so far off course that it is useless for measurement purposes. The probability of this occurring is fairly low in practice.


The capture of antiprotons by matter

>>>> Outline | Previous | Next

An antiproton, being negatively charged, is captured in an electron-like orbit about a nucleus, forming an antiprotonic atom. It makes transitions to lower energy orbits, emitting photons that are characteristic of the nucleus. This process is analogous to electronic photoemission. However, x-rays rather than visible photons are emitted. This is easily understood in terms of the Bohr model, in which particles orbit the nucleus in fixed orbits. The frequency of radiation corresponding to orbital transitions in the Bohr model is proportional to the mass of the orbiting particle. Since the mass of an antiproton is 2000 that of an electron, the frequency of emitted light will be 2000 greater in an antiprotonic than in a conventional atom. Electronic transitions are visible; 2000 greater frequency is in the x-ray range.

X-rays have been detected from antiprotonic atoms from a wide range of elements. Detailed spectra have been obtained for many of these antiprotonic atoms. These x-rays, with energies between 90 and 200 KeV, might make it possible to detect elemental distributions in the body.

Furthermore, deviations in the numbers of antiprotons captured are caused in part by the "chemical effect". This is a wonderful influence of the macroscopic upon the microscopic. The molecular environment of the nuclei exerts a large influence on the capture probability of an antiproton. Thus, it is speculated that chemistry could be imaged with antiprotons.

How do we know where the antiprotons stop? We know that from what happens when the antiproton annihilates.


Annihilation

>>>> Outline | Previous | Next

Most antiprotons annihilate when they are at rest with respect to matter. The annihilation process liberates a host of subatomic particles and energy which goes streaming outward in every direction.

The chief products of annihilation are charged and neutral pions, nuclear gamma-rays, and nuclear fragments. A typical annihilation is shown in Figure 4. Antiprotons enter the left of this deuterium bubble chamber; extending outward from the annihilation sites are pion and nuclear fragment tracks.

Figure 5 is a cartoon of a typical annihilation event or star, with nuclear gamma-rays, charged pions, and heavy fragments streaming outward from the annihilation vertex.

The numbers of charged pions is known to be about 3 per annihilation. The energy of the pions is also known to be about 145MeV. But the direction of the pions is completely random: they stream outward in all directions.

The annihilation of antiprotons in matter upon stopping is the key feature that makes the detection of the stopping position of each antiproton possible.

If antiprotons are beamed into a target at the correct speed, most will stop within the target, and most will annihilate when they stop. (A few will annihilate as they travel; this number is computable increases with the penetration depth into the target.)


Reconstructing the target

>>>> Outline | Previous | Next

The detection of the exiting charged pions and x-rays and gamma-rays is crucial to understanding the target. So if a target is far away, or if it is small, the numbers of detected annihilation products is small. In turn, this means that greater numbers of antiprotons are needed to get sufficient information about the target.


Summary

>>>> Outline | Previous

To summarize, the stopping position of antiprotons of a given energy yields a density profile of the target. The x-rays emitted as the captured antiprotons lose orbital energy and the gamma-rays emitted as the antiprotons annihilate reveal the elemental makeup of the target. And deviations in the number of antiprotons captured hints at the chemistry or molecular makeup of the target.


copyright © 1996 Robert Muratore
quantumNOW
webmaster@quantumnow.com
URL http://quantumnow.com/trek/pbar.html