Expansion

To obtain good pictures, Wilson specified the operating conditions :

The essential conditions to be fulfilled if good pictures of the tracks are to be obtained are mainly these. The expansion must be effected without stirring up the gas; this condition is secured by using a wide, shallow cloud chamber of which the floor can be made to drop suddenly and so produce the desired increase of volume. The cloud chamber must be freed not only from « dust » particles, but from ions other than those produced by the ionizing particles under observation; an electric field maintained between the roof and floor of the cloud chamber serves this purpose. For the purpose of obtaining sharp pictures of the tracks, the order of operations has to be: firstly, the production of the necessary supersaturation by sudden expansion of the gas; secondly, the passage of the ionizing particles through the supersaturated gas.

 

Working principle of the Wilson cloud chamber : We know that dust or ions act as nucleation site, these are « trigger » which facilitate the transition of state of matter. These nucleation sites can be dust, aerosols, ions, or just a foreign material. For example, we know that it’s better to make astronomy after a rain because the sky is free of dust or pollutant. Water vapor condense on theses atmospheric nucleation sites and haul them to the ground within the droplets. These particles may be responsible for the climate change, with the cosmics rays (as they produce ions in the atmosphere and thus can produce more cloud).  Another example of the actions of nucleation site is the supercooling or superheating (check youtube), the coke-menthos effect, the use of seed crystal in industry…

If we zoom into a particle’s track in an expansion cloud chamber, we will always see a pair of water droplets (picture from 1923) : 

pair-creation-cloud-chamber2

These 2 droplets, come from water vapor which condensed into 2 nucleation site present in the air of chamber. As the initial air of the chamber was free of nucleation sites, theses two nucleation sites can only come from the action of a charged particle travelling in the air of the chamber. Indeed, as this particle is charged, it ionizes a molecule of air into a positive and negative ion. For example, it could be the positive ion N2and the oxygen O2-  (the latter has captured the ejected electron from nitrogen). As ions are nucleation site, the water vapor condense immediately into these ions once formed, making two droplets. But the condensation of vapor can happens only if the water vapor is in an unstable thermodynamic state. It’s the resulting expansion of the volume of the chamber which make water vapor unstable. When the expansion occurs, a sudden increase of volume is offered to the moist air (in vapor state) : it’s temperature drop rapidly and the vapor should transform into liquid, a more stable state for this low temperature. But it’s not sufficient : to go to the stable liquid form, it’s necessary for vapor to low the energetic barrier of the transition state, and only a nucleation site can do this. If no nucleation site is present, the unstable vapor rest in it’s unstable form until a perturbation can help it to change it’s state.

In the above picture we see that each pair of droplet, which was in fact the positive and negative ions left by the particle prior to expansion, are spaced from each other. This is due to the action of electric field in the cloud chamber which separate the ions. With no electric field, the pair of ions are created in the exact same location of ionization by the particle. When water start to condense into an ion, this one lose it’s mobility (as the droplet is neutral thus insensible to the electric field). The droplet gain in size with time as more water vapor condense on it then fall in the bottom of the chamber by gravity.  Each tracks is thus composed of thousands of pair of droplets rebuilding the path followed by the particle in matter. The number of droplets (density) in a track is directly linked to the nature of the particle so we can determinate it’s speed, mass and electrical charge.

condensation droplet

Zoom of cosmic rays tracks in an expansion cloud chamber. Each track is made of thousands of droplets about 0,2 to 0,4 mm diameter. The expansion take place after the passage of theses particles as the ions had time to diffuse with the electric field and produced large track (real thickness about 5 mm). At the far right we can see a sudden increase of droplets on the track : it happens that the particle can give a high amount of energy to the ionized electron. This one can then ionize other molecules, creating more ions and thus droplets. If the energy given to the electron is even more, this one can make his own track and is called a delta ray.

Wilson stated during his Nobel lecture that to have good viewing conditions i’s necessary that the initial air inside the chamber is free of any nucleation site.  The initial cleaning can be achieved with several « rain » in the chamber by doing multiples expansions, so all dust or neutral nucleation site are removed. The charged nucleation site (ions) continuously created by cosmic rays in the chamber will be collected by an electric field present in the chamber. If the chamber is not clean of nucleation site prior to expansion, we will observe a dense cloud in the chamber hiding any particle’s tracks (as vapor water condensed into all the nucleation site). 

Obviously, the quantity of supersaturated vapor molecule after expansion is limited. To achieve the best photograph of a radioactive source of interest, the most supersaturated vapor should be available for the studied particle. If the chamber is not enough cleaned prior to expansion, a big quantity of supersaturated vapor will be consumed by parasitic nucleation site to the detriment of the ions left by the particle. So, the tracks will appear with a low density of droplets and can’t be photographed easily (the brightness of the track is higher when then is more droplets doing refection of the light source). Several particle can appear near the same location and nearly in the same time. In the immediate neighborhood of the cloud already condensed on an older track, the supersaturation remaining may be insufficient to cause condensation, although elsewhere the particle may leave a visible track. 

Action of the electric field : it’s important to note the action of the electric field on ions during the operation of cloud chamber, which directly influence the sharpness of the tracks. The electric field is always present in the chamber : before and after the expansion. Suppose that long before the expansion, a particle pass trough the air of a cloud chamber. The particle leaves ions on it’s trail. As the electric field is present, the ions are attracted towards the electrodes of the chamber. So the ions are mobile and can travel a long distance in the chamber the more they are exposed to the action of electric field. Then we realize the expansion : the supersaturated vapor condense into the ions cancelling any mobility (the droplet of water have an overall neutral charge and thus are insensible to the electric field). As the positive and negative ions moved in their respective directions during a long time, we will observe two independent tracks after the expansion : a track of droplets which condensed into the negative ions and another track on the positive ions. We call these « diffuse and parallel tracks » because the density of droplet is low : only one half of the ions produced by the particle serve for one track and the diffuseness is large. The diffuseness is due to self repulsion of the ions in the tracks and to gaseous collisions of different kinds during the motion of the ions. You can see two separate tracks in the 3rd picture above, when Wilson photographed an X ray beam which traversed the chamber before the expansion. 

If a particle pass just before the expansion, the ions don’t have time to separate a lot : after the expansion, we will observe a unique but diffuse track (fat track). If a particle pass after the expansion, during the few seconds of duration of the supersaturated state, the ions left don’t have time to travel in the chamber even if the electric field is still present : unstable vapor immediately condense on them. The result is a sharp track, with a great density of droplets (as there is positive and negative ions in the same space). So the sharpness of a track is directly related to the age of the particle from the moment when the expansion takes place : the ions which stay the lowest time in the chamber will give sharper tracks.

We now may explain what happens in a particular picture that Wilson took in 1922.

wilson 1922 on alpha track

 The picture reproduced is four time the scale of the original object. The cloud condensed on the ions as a result of sudden expansion of the air were photographed through the side of the cloud chamber. At point b and b’, are visible two inclined diffuse cloud tracks : an alpha particle had passed through the air before the expansion occured and had left a trail of free positive and negative ions ; these have been separated by the electric field before being rendered immobile by condensed water, after expansion of the chamber. The alpha particle had traversed the whole height of the cloud chamber along the path AA’. The positive ions goes upwards, negative downwards. From the amount of the vertical separation of the tracks, it follow that the alpha particle traversed the air 1/30 of a second before the expansion.

The other events of which the picture gives a record occurred after the expansion. At point g, a Radon 220 nucleus ejected an alpha particle (named event 1) going to point c. The ions liberated have been fixed by condensation of water so that a sharply defined cloud track is formed : the alpha particle thus was emitted after the expansion. Rn 220 transmuted into Po 216 after the ejection of the alpha particle, this nucleus is at the head of the alpha track in point g. After this reaction, within a small fraction of a second, the Po 216 ejected a second alpha particle coming in a nearly horizontal direction from g to d (named event 2).

In the immediate neighborhood of the lower end of the diffuse cloud b, already condensed on the positive ions of the older track described above, the new alpha particle finds the air robbed of a considerable portion of its water vapor ; In consequence no condensation here takes place on the ions liberated by it until they have been carried by the electric field into a region where the necessary supersaturation still exists. In the present case the negative ions moving down under the action of the field have fairly soon reached a region where the water vapor is still sufficiently supersaturated to condense upon them ; the V shaped diversion in the otherwise straight track is thus easily explained. The positive ions have been carried further into the old cloud by the action of the field and have thus left no track, except for a short distance above the two upper ends of the V.

Again, ions formed along the initial portion of the alpha-ray from Po 216 were liberated within or very near the cloud which had already condensed along the track of the original alpha-particle from Rn 220. Condensation on these ions, positive or negative, could thus only take place when they had been carried sufficiently far up or down to enter regions in which the critical supersaturation was still exceeded (as there is no supersaturated cloud in this region, ions are free to move according to the electric field even if the expansion was made). The initial portion of the cloud track actually left by the alpha-particle from the Po 216 atom is therefore pincer-shaped, and the head of the original alpha-ray track from the emanation atom lies midway between the jaws of the pincers.  The lack of a supersaturated region in the beginning of this alpha tracks mean that the vapor was consumed by condensation on ions from a prior event. Thus the event 2 comes after event 1. 

 

We will then analyse 2 pictures from 1927 to show the usefulness of the electric field. The conditions of experiment is the same as previously. The camera photographed through the side of the cloud chamber, and a vertical electric field is set between the roof and bottom of the chamber. The positive ions goes upwards, negative downwards. The cloud chamber contained Rn 219 which decayed into Po 215 emitting an alpha particle, then the Po 215 shortly emitted a another alpha particle to transmute into Pb 211.

We said previously that a sharp track mean that the negative and positive ions are in the same location because they don’t have been spread by the action of electric field, so they are produced after the expansion as water immediately condense  onto them. Diffuse tracks are always  parallel, they comes from a single column of ion of the same sign. Positive and negative ion columns were separated by the electric field, indicating that the particle which created theses ions traveled in the chamber before the expansion. In the 2 pictures, we can clearly distinguish diffuse parallel tracks and sharp tracks. This pictures can tell that the recoiling atom (Po 215) is charged or not during the emission of the second alpha particle. Indeed the recoil atom may loose momentarily it’s electronic cloud during the process of disintegration. As a ion, the recoil nucleus is thus capable of making it’s own tracks, ionizing matter during it’s displacement. But in these conditions of experiment, the pressure is too high (27 cm Hg) so we can’t see the tracks of the recoiling nucleus (about 0,5 mm). This tracks is neglected (but can be observed if the pressure is at 1 cm Hg !). But we can show with theses original pictures following that the nucleus is charged… or not, during the alpha decay process.  

mobilty recoil atom Po 219 1927 cloud chamber

Let’s consider the case 1. For this case let’s take an hypothesis where the single ions (+ or -) and the charged recoil atom Po 215 have the same mobility under the influence of the electric field (in fact there is some variations due to mass but this is not perceptible in pictures). We are in the time before the expansion in the chamber : at A, the Rn 219 nucleus decay into an alpha particle. This particle goes in the direction indicated by the red arrow, and leave positive and negative ions along it’s path. The electric field move upward the positive ions and downward the negative ions. But the Po 215 in this process is left positively charged so it follow, under the influence of electric field, the same direction as the positive ions. This nucleus moves from A to B. Then the expansion occur, and the supersaturation fix all the ions and the recoil atom in their positions (condensation of droplets occurs on them) : we see the two diffuse tracks of the first alpha particle from Rn 219. During the supersaturation state, the nucleus Po 215 emit the second alpha particle to become Pb 211. This alpha particle provide a sharp track because it travel during the supersaturation state of the chamber (the ions left by it instantly becomes droplets as they don’t have time to moves by the electric field).

Let’s consider the case 2. It’s identical to the case 1, but this time the sharp track is precisely emitted between the two column of ions. In the first alpha decay process, the Po 215 recoil nucleus was uncharged. So it was not sensible to the electric field and didn’t move. Then, after expansion, it decayed into Pb 211 giving a sharp alpha track.  The author said in his article that about 84 % of Po 215 recoils atom where positively charged, the other being neutral.