SOLUTIONS FOR HOMEWORK 10

1. Name five different forms of matter, starting with gas.

   The answers discussed in class were:

   1. GAS: This is a fluid in which the volume of a given amount of gas decreases substantially as pressure increases, and increases substantially as temperature increases. The gas consists of molecules flying around freely with occasional bounces off other molecules. An example is water vapor, which is invisible.
   2. LIQUID: This again is a fluid, but now nearly incompressible, so volume decreases only very slightly as pressure increases, and increases only very slightly as temperature increases Now the molecules are in constant contact with their near neighbors. An example is liquid water , which actually goes DOWN in volume as temperature increases between freezing (0 degrees Celsius) and +4 degrees Celsius! This fact is behind a remarkable phenomenon that occurs twice a year in northern lakes. The water at the bottom and the water at the top exchange places.
   3. SOLID: This not only is hard to compress, but also hard to twist. Now the atoms or molecules are arranged in a regular crystal structure.
   4. PLASMA: This is a gas in which atoms are ionized, so electrons and positive ions can fly freely through the system. which therefore conducts electricity. The plasma also can 'freeze' magnetic fields, so that the field lines move along if the bulk plasma moves, as happens with the solar wind, which is a plasma coming out of the sun and flowing away past the earth and other planets.
   5. SUPERFLUID: This is a system which has the kind of quantum coherence we associate with a wave like the electron in the lowest state of hydrogen, but existing over large distances and including huge numbers of atoms. In superfluid helium one sees phenomena like frictionless flow, so that a in a rotating pail the fluid can sit still, or in a still pail the fluid can go round for a long time. In a superconductor, where 'atoms' that flow may be thought of as pairs of electrons, the system can support a steady current that does not decrease even over times as long as a year, or even much, much longer. In 'Bose-Einstein' condensates individual atoms having integer spin become part of one big wave function, which exhibits coherence features much like those in superfluid helium or superconductors. The general belief is that the essential feature which makes a superfluid happen is a Bose-Einstein condensate. Even though originally this concept was introduced for particles with negligible interaction, it makes sense that superfluidity could hold even when there is substantial interaction, and nature seems to bear that out.

2. Explain the word 'plasma' in 'quark-gluon' plasma.

   Just as in ordinary plasma electrons and ions travel freely and electric currents can flow, so in QGP quarks and gluons travel freely, no longer trapped in hadrons (particles like protons and pi mesons), and one expects that color currents can flow. Thus hadrons which would decay slowly if at all in empty space might quickly dissolve if placed in a quark-gluon plasma, just as ordinary atoms dissociate into electrons and ions when they are in plasma.

3. Why are there magnets in RHIC experiments?

   Charged particles go in circles in a magnetic field, showing the sign of each charge and the corresponding momentum value. This allows particle identification and helps reconstruct how the particles were produced. Thus all the detectors need this kind of information. In addition, magnets are crucial in keeping the beams going around in RHIC, so they can collide repeatedly at the locations of the various detectors.

4. What do the acronyms of RHIC detectors represent?

   Acronyms can be useful shorthand for important features of some program or device. In the case of the detectors at RHIC (which itself is an acronym for Relativistic Heavy Ion Collider) the names vary from descriptive to fancy.

   BRAHMS stands for Broad RAnge Hadron Magnetic Spectrometer. This describes realistically the fact that the detector looks at particles coming out with a broad range of speed along the beam direction, whose tracks are bent by a magnet so one can figure out what they are and how their motion perpendicular to the beam direction compares to that in the parallel direction.

   PHENIX stands for Pioneering High Energy Nuclear Interaction eXperiment, which certainly indicates an experiment at a facility like RHIC, but otherwise doesn't tell you much about it. This detector may have more different systems than any of the others, and in particular is specially suited to looking for muons and electrons, which can give direct diagnostic information on what goes on in the period after a collision when a quark-gluon plasma might exist. That's why its spokesman used the phrase 'X-raying the plasma'.

   Phobos is the name for a moon of Mars, and the detector at one point was supposed to be called MARS -- Modular Array for RHIC spectra. Phobos is a scaled-down version of MARS; hence the name. This detector, like BRAHMS, is a bit smaller than the others, and again emphasizes looking at rather small numbers of particles in each event.. This allows very rapid collection of events and therefore locating simple patterns.

   STAR stands for Solenoidal Tracker At RHIC: A huge magnet has currents going around the direction of the beam, producing a magnetic field lined up parallel to the beam. This means that particles coming out of a collision with some momentum perpendicular to the beam direction will curve in a direction depending on their charge, with the radius of curvature proportional to the momentum, so faster particles curve less. They all are seen in a giant detector called a Time Proportional Chamber, where the time it takes a pulse of ionization to get from a track to a wire current accumulator is a measure of how far the track is from that wire. This locates the track in space so a computer can reconstruct a picture of all the charged-particle tracks.

5. What should QGP do to 'jets' from RHIC?

   When a collision with a fast electron knocks a quark out of a proton, the quark produces a wake or jet of quark-antiquark pairs trailing behind it. This feature has been verified many times in electron-proton and also proton-proton collisions. However, if an electron or quark hit a quark in QGP, then the knocked out quark could react with many quarks and gluons in the plasma, and so get slowed down. This means no jet, and therefore jet quenching could be a signal of the plasma.

   However, any process producing a much higher density of material than in conventional nuclei could lead to the same effect. Therefore this signal does not uniquely pick out QGP.

6. What makes detection of QGP so hard?

   As mentioned just above, for any particular signal, even if it comes out the way QGP said, it still could be explained in other ways. The main reason is that in the

   end one does not see the plasma directly, because all observed strongly interacting particles must be conventional baryons and mesons. This means there has to be a lot of guessing about what happened before these particles came out, and therefore one needs many different approaches and a lot of patience to verify a clear pattern which demonstrates the existence of the plasma.