APPENDIX 1. METHODS OF OBSERVING FAST PARTICLES FROM NUCLEAR REACTIONS

In Chapter I we pointed out the importance of ionization in the study of radioactivity and mentioned the electroscope. In this appendix we shall mention one method of historical importance comparable with the electroscope but no longer used, and then we shall review the various methods now in use for observing alpha particles, beta particles (or positrons), gamma rays, and neutrons, or their effects.

SCINTILLATIONS

The closest approach that can be made to "seeing" an atom is to see the bright flash of light that an alpha particle or high-speed proton makes when it strikes a fluorescent screen. All that is required is a piece of glass covered with zinc sulphide, a low power microscope, a dark room, a well-rested eye, and a source of alpha particles. Most of Rutherford's famous experiments, including that mentioned in paragraph 1.17, involved "counting" scintillations but the method is tedious and, as far as the author knows, has been entirely superseded by electrical methods.

THE PROCESS OF IONIZATON

When a high-speed charged particle like an alpha particle or a high-speed electron passes through matter, it disrupts the mole-cules that it strikes by reason of the electrical forces between the charged particle and the electrons in the molecule. If the material is gaseous, the resultant fragments or ions may move apart and, if there is an electric field present, the electrons knocked out of the molecules move in one direction and the residual positive ions in another direction. A beta particle with a million electron volts energy will produce some 18,000 ionized atoms before it is stopped completely since on the average it uses up about 60 volts energy in each ionizing collision. Since each ionization process gives both a positive and a negative ion, there is a total of 36,000 charges set free by one high-speed electron, but since each charge is only 1.6 x l0^-l9 coulomb, the total is only about 6 X l0^-15 coulomb and is still very minute. The best galvanometer can be made to measure a charge of about 10^-10 coulomb. It is possible to push the sensitivity of an electrometer to about 10^-l6 coulomb but the electrometer is a very inconvenient instrument to use. An alpha particle produces amounts of ionization comparable with the beta particle. It is stopped more rapidly, but it produces more ions per unit of path. A gamma ray is much less efficient as an ionizer since the process is quite different. It does occa-sionally set free an electron from a molecule by Compton scatter-ing or the photoelectric effect, and this secondary electron has enough energy to produce ionization. A neutron, as we have already mentioned in the text, produces ionization only indirectly by giving high velocity to a nucleus by elastic collision, or by disrupting a nucleus with resultant ionization by the fragments. If we are to detect the ionizing effects of these particles, we must evidently use the resultant effect of a great many particles or have very sensitive means of measuring electric currents.

THE ELECTROSCOPE

Essentially the electroscope determines to what degree the air immediately around it has become conducting as the result of the ions produced in it.

The simplest form of electroscope is a strip of gold leaf a few centimeters long, suspended by a hinge from a vertical insulated rod. If the rod is charged, the gold leaf also takes up the same charge and stands out at an angle as a result of the repulsion of like charges. As the charge leaks away, the leaf gradually swings down against the rod, and the rate at which it moves is a measure of the conductivity of the air surrounding it.

A more rugged form of electroscope was devised by C. C Lauritsen, who substituted a quartz fiber for the gold leaf and used the elasticity of the fiber as the restoring force instead of gravity. The fiber is made conducting by a thin coating of metal. Again the instrument is charged, and the fiber, after initial deflection, gradually comes back to its uncharged position. The position of the fiber is read in a low-power microscope. These instruments can be made portable and rugged and fairly sensi-tive. They are the standard field instrument for testing the level of gamma radiation, particularly as a safeguard against dangerous exposure.

IONIZATION CHAMBERS

An ionization chamber measures the total number of ions produced directly in it. It usually consists of two plane electrodes between which there is a strong enough electric field to draw all the ions to the electrodes before they recombine but not strong enough to produce secondary ions as in the instruments we shall describe presently. By careful design and the use of sensitive amplifiers an ionization chamber can measure a number of ions as low as that pro-duced by a single alpha particle, or it can be used much like an electroscope to measure the total amount of ionizing radiation present instantaneously, or it can be arranged to give the total amount of ionization that has occurred over a period of time.

PROPORTIONAL COUNTERS

While ionization chambers can be made which will respond to single alpha particles, it is far more convenient to use a self--amplifying device, that is, to make the ions originally produced make other ions in the same region so that the amplifier circuits need not be so sensitive.

In a proportional counter one of the electrodes is a fine wire along the axis of the second electrode, which is a hollow cylinder. The effect of the wire is to give strong electric field strengths close to it even for relatively small potential differences between it and the other electrode. This strong field quickly accelerates the primary ions formed by the alpha or beta particle or photon, and these accelerated primary ions (particularly the electrons) in turn form secondary ions in the gas with which the counter is filled so that the total pulse of current is much increased. It is possible to design and operate such counters in such a way that the total number of ions formed is proportional to the num-ber of primary ions formed. Thus after amplification a current pulse can be seen on an oscilloscope, the height of which will indicate how effective an ionizer the initial particle was. It is quite easy to distinguish in this way between alpha particles and beta particles and photons, and the circuits can be arranged to count only the pulses of greater than a chosen magnitude. Thus a proportional counter can count alpha particles against a background of betas or can even count only the alpha particles having more than a certain energy.

GEIGER-MULLER COUNTERS

If the voltage on a proportional counter is raised, there comes a point when the primary ions from a single alpha particle, beta particle, or photon will set off a discharge through the whole counter, not merely multiply the number of primary ions in the region where they are produced. This is a trigger action and the current is independent of the number of ions produced; furthermore, the current would continue indefinitely if no steps were taken to quench it. Quenching can be achieved entirely by arranging the external circuits so that the voltage drops as soon as current passes or by using a mixture of gases in the counter which "poison" the electrode surface as soon as the discharge passes and temporarily prevent the further emission of electrons, or by combining both methods.

The Geiger-Muller counter was developed before the propor-tional counter and remains the most sensitive instrument for detecting ionizing radiation, but all it does is "count" any ionizing radiation that passes through it whether it be an alpha particle, proton, electron, or photon.

THE ART 0F COUNTER MEASUREMENTS

It is one thing to describe the principles of various ionization chambers, counters, and the like; quite another to construct and operate them successfully.

First of all, the walls of the counter chamber must allow the particles to enter the counter. For gamma rays this is a minor problem, but for relatively low-speed electrons or positrons or for alpha particles the walls of the counter must be very thin or there must be thin windows.

Then there are great variations in the details of the counter itself, spacing and size of electrodes, nature of the gas filling the chamber, its pressure, and so on.

Finally, the interpretation of the resultant data is a tricky business. The absorption of the counter walls and of any external absorbers must be taken into account; the geometry of the counter with relation to the source must be estimated to translate observed counts into actual number of nuclear events; last but not always least, statistical fluctuations must be considered since all nuclear reactions are governed by probability laws.

THE WILSON CLOUD CHAMBER

There is one method of observing nuclear particles that depends directly on ionization but is not an electrical method. It uses the fact that supersaturated vapor will condense more readily on ions than on neutral molecules. If air saturated with water vapor is cooled by expansion just after an alpha particle has passed through it, tiny drops of water condense on the ions formed by the alpha particle and will reflect a bright light strongly enough to be seen or photographed so that the actual path of the alpha particle is recorded.

This method developed by C. T. R. Wilson in Cambridge, England, about 1912 has been enormously useful in studying the behavior of individual particles, alphas, protons, electrons, positrons, mesons, photons, and the fast atoms caused by collisions with alphas, protons or neutrons. Unlike the scintilla-tion method, its companion tool for many years, it has not been superseded and is still used extensively, particularly to study details of collisions between nuclear particles and atoms.

THE PHOTOGRAPHIC METHOD

The tracks of individual particles passing through matter can also be observed in photographic emulsions, but the lengths of path are so small that they must be observed under a microscope, where they appear as a series of developed grains marking the passage of the particle. This method of observation requires practically no equipment but is tedious and of limited usefulness. It is possible, however, to use the general blackening of a photographic film as a measure of total exposure to radiation, a procedure that has been used to supplement or to replace electroscopes for safety control in many parts of the project.

THE OBSERVATION AND MEASUREMENT OF NEUTRONS

None of the methods we have described is directly applicable to neutrons, but all of them are indirectly applicable since neu-trons produce ions indirectly. This happens in two ways - by elastic collision and by nuclear reaction. As we have already described, a fast neutron in passing through matter occasionally approaches an atomic nucleus so closely as to impart to it a large amount of momentum and energy according to the laws of elastic collision. The nucleus thereby becomes a high-speed charged particle which will produce ionization in an ionization chamber, counter, or cloud chamber. But if the neutron has low speed, e.g., thermal, the struck nucleus will not get enough energy to cause ionization. If, on the other hand, the neutron is absorbed and the resultant nucleus breaks up with the release of energy, ionization will be produced. Thus, for the detection of high-speed neutrons one has a choice between elastic collisions and nuclear reaction, but for thermal speeds only nuclear reaction will serve.

The reaction most commonly used is the B10(n, \alpha)Li7 reaction which releases about 2.5 MeV energy shared between the resultant alpha particle and Li7 nucleus. This is ample to produce ioniza-tion. This reaction is used by filling an ionization chamber or proportional counter with boron trifluoride gas so that the reac-tion occurs in the region where ionization is wanted; as an alterna-tive the interior of the chamber or counter is lined with boron. The ionization chamber then serves as an instrument to measure overall neutron flux while the proportional counter records numbers of individual neutrons.

One of the most valuable methods of measuring neutron densi-ties by nuclear reactions depends on the production of artificial radioactive nuclei. A foil known to be made radioactive by neu-tron bombardment is inserted at a point where the neutron intensity is wanted. After a given time it is removed and its activity measured by an electroscope or counter. The degree of activity that has been built up is then a measure of the number of neutrons that have been absorbed. This method has the obvious disadvantage that it does not give an instantaneous response as do the ionization chamber and counter. One of the most interesting methods developed on the project is to use the fission of uranium as the nuclear reaction for neutron detection. Furthermore, by separating the isotopes, fast and slow neutrons can be differentiated.

Since the probability of a neutron reaction occurring is dif-ferent for every reaction and for every neutron speed, difficulties of translating counts or current measurements into numbers and speeds of neutrons present are even greater than for other nuclear particles. No one need be surprised if two able investigators give different numbers for supposedly the same nuclear constant. It is only by an intricate series of interlocking experiments carefully compared and interpreted that the fundamental facts can be untangled from experimental and instrumental variables.

APPENDIX 3. DELAYED NEUTRONS FROM URANIUM FISSION

As was pointed out in Chapter VI, the control of a chain -reacting pile is greatly facilitated by the fact that some of the neutrons resulting from uranium fission are not emitted until more than a second after fission occurs. It was therefore important to study this effect experimentally. Such experiments were described by Snell, Nedzel and lbser in a report dated May 15, 1942 from which we quote as follows:

"The present experiment consists of two interrelated parts - one concerned with the decay curve, and one concerned with the intensity of the delayed neutrons measured in terms of that of the 'instantaneous' fission neutrons.

THE DECAY CURVE OF THE DELAYED NEUTRONS

"The neutron source was the beryllium target of the University of Chicago cyclotron struck by a beam of up to 20 microA of 8 MeV deuterons. Near the target was placed a hollow shell made of tinned iron and containing 106 lbs. of U3O8. This was surrounded by about 2" of paraffin. The interior of the shell was filled with paraffin, except for an axial hole which accommodated a BF3-filled proportional counter. The counter was connected through an amplifier to a scaling circuit ('scale of 64') equipped with inter-polating lights and a Cenco impulse counter. A tenth-second timer, driven by a synchronous motor, and hundredth-second stop watch were mounted on the panel of the scaler, close to the interpolating lights and impulse counter. This group of dials and lights was photographed at an appropriately varying rate by a Sept camera which was actuated by hand. The result was a record on movie film of times and counts, from which the decay curves were plotted.

"The actual procedure was as follows: During bombardment the stop watch was started and the timer was running con-tinuously; the counter and amplifier were on, but the pulses leaving the amplifier were grounded. The scaler was set at zero. After a warning signal the cyclotron was shut off by one operator, while another operator switched the output of the amplifier from ground into the scaler, and started taking photographs. It was easy to take the first photograph within half a second of turning off the cyclotron. Sixty to a hundred photographs were taken during a typical run. The necessity of using both a stop watch and a timer arose from the fact that the hundredth-second pre-cision of the stop watch was needed for the small time intervals between photographs during the initial part of the run, but the watch ran down and stopped before the counting was complete. The timer then gave sufficient precision for the later time intervals.

"Some forty runs were taken under varying experimental con-ditions. Short activations of one or two seconds were given for best resolution of the short periods. Long, intense bombardments lasting 15-20 minutes, as close as possible to the target, were made to make the long period activities show up with a maximum intensity. Some 5-minute bombardments were made, keeping the cyclotron beam as steady as possible, to study the relative satura-tion intensities of the various activities; in these activations the cyclotron beam was reduced to 1 or 2 * A to prevent the initial counting rate from becoming too high for a counter (300 per sec. was taken as a reasonable upper limit for reliable counting). Two BF3 counters were available, one having a thermal neutron cross section of 2.66 sq. cm., and the other 0.43 sq. cm. After a strong activation, we could follow the decay of the delayed neutrons for some 13 minutes. Background counts (presumably chiefly due to spontaneous fission neutrons) were taken and were sub-tracted from the readings. They amounted to about 0.4 counts per sec. for the large counter.

"A study of all the decay curves gives the following as a general picture of the neutron-emitting activities present:

          HALF-LIFE     RELATIVE INITIAL INTENSITY
                        ACTIVATED TO SATURATION
          57 +/- 3 sec.     0.135
          24 +/- 2 sec.     1.0
          7 sec.            1.2
          2.5 sec.          1.2

"Any activity of period longer than 57 sec. failed to appear even after the most intense bombardment we could give, lasting 20 minutes. The relative initial intensities given are the average values obtained from three curves.

"These results give the following equation for the decay curve, of the delayed neutrons after activation to saturation:

Activity = constant [1.2e^(-0.28t) + 1.2e^(-0.0 99t + 1.0e^(-0.029t) + 0.135e^(-0.012t)]

where t is in seconds."

The second part of the experiment measured the total number of neutrons emitted in the time interval 0.01 sec. to 2.0 min. after the cyclotron was turned off. Assuming that all the delayed neutrons observed were in the four groups measured in the first part of the experiment, this second result indicated that 1.0 +/- 0.2 per cent of the neutrons emitted in uranium fission are delayed by at least 0.01 sec. and that about 0.07 per cent are delayed by as much as a minute. By designing the effective value of k, the multiplication factor, for a typical operating pile to be only 1.01 with all the controls removed and the total variation in k from one control rod to be 0.002, the number of delayed neutrons is sufficient to allow easy control.

APPENDIX 4. THE FIRST SELF-SUSTAINING CHAIN REACTION PILE

In Chapter VI the construction and operation of the first self-sustaining chain-reacting pile were described briefly. Though details must still be withheld for security reasons, the following paragraphs give a somewhat fuller description based on a report by Fermi. This pile was erected by Fermi and his collaborators in the fall of 1942.

DESCRIPTION OF THE PILE

The original plan called for an approximately spherical pile with the best materials near the center. Actually control measure-ments showed that the critical size had been reached before the sphere was complete, and the construction was modified accord-ingly. The final structure may be roughly described as an oblate spheroid flattened at the top, i.e., like a door knob. It was desired to have the uranium or uranium oxide lumps spaced in a cubic Iattice imbedded in graphite. Consequently, the graphite was cut in bricks and built up in layers, alternate ones of which con-tained lumps of uranium at the corners of squares. The critical size was reached when the pile had been built to a height only three quarters of that needed according to the most cautious estimates. Consequently only one more layer was added. The graphite used was chiefly from the National Carbon Company and the Speer Carbon Company. The pile contained 12,400 lbs. of metal, part of which was supplied by Westinghouse, part by Metal Hydrides, and part by Ames. Since there were many more lattice points than lumps of metal, the remaining ones were filled with pressed oxide lumps.

For purposes of control and experiment there were ten slots passing completely through the pile. Three of those near the center were used for control and safety rods. Further to facilitate experiment, particularly the removal of samples, one row of graphite bricks carrying uranium and passing near the center of the pile was arranged so that it could be pushed completely out of the pile.

This whole graphite sphere was supported by a timber frame-work resting on the floor of a squash court under the West Stands of Stagg Field.

PREDICTED PERFORMANCE OF THE PILE

The metal lattice at the center of the pile and the two other major lattices making up the bulk of the rest of the pile had each been studied separately in exponential experiments #18, #27, and #29. These had given a multiplication factor of 1.07 for the metal lattice and 1.04 and 1.03 for the oxide lattices, the difference in the last two resulting from difference in the grade of graphite used. It is to be remembered that these figures are multiplication factors for lattices of infinite size. Therefore a prediction of the actual effective multiplication factor k_eff for the pile as constructed depended on the validity of the deduction of k from the ex-ponential experiments, on a proper averaging for the different lattices, and on a proper deduction of k_eff from the average k for infinite size. Although the original design of the pile had been deliberately generous, its success when only partly completed indicated that the values of the multiplication factors as calculated from exponential experiments had been too low. The observed effective multiplication factor of the part of the planned structure actually built was about 1.0006 when all neutron absorbers were removed.

MEASUREMENTS PERFORMED DURING CONSTRUCTION

A series of measurements was made while the pile was being assembled in order to be sure that the critical dimensions were not reached inadvertently. These measurements served also to check the neutron multiplication properties of the structure during assembly, making possible a prediction of where the critical point would be reached.

In general, any detector of neutrons or gamma radiation can be used for measuring the intensity of the reaction. Neutron detectors are somewhat preferable since they give response more quickly and are not affected by fission-product radiations after shut down. Actually both neutron detectors (boron trifluoride counters) and gamma-ray ionization chambers were distributed in and around the pile. Certain of the ionization chambers were used to operate recording instruments and automatic safety controls.

In the pile itself measurements were made with two types of detector. A boron trifluoride counter was inserted in a slot about 43" from the ground and its readings taken at frequent intervals. In addition, an indium foil was irradiated every night in a posi-tion as close as possible to the effective center of the pile, and its induced activity was measured the following morning and compared with the readings of the boron trifluoride counter.

The results of such measurements can be expressed in two ways. Since the number of secondary neutrons produced by fission will increase steadily as the pile is constructed, the activity A induced in a standard indium foil at the center will increase steadily as the number of layers of the pile is increased. Once the effective multiplication factor is above one, A would theoretically increase to infinity. Such an approach to infinity is hard to observe, so a second way of expressing the results was used. Suppose the lattice spacing and purity of materials of a graphite-uranium structure are such that the multiplication factor would be exactly one if the structure were a sphere of infinite radius. Then, for an actual sphere of similar construction but finite radius, the activation of a detector placed at the center would be proportional to the square of the radius. It was possible to determine a corresponding effective radius R_eff for the real pile in each of its various stages. It followed, therefore, that, if the factor k_infinity were precisely one on the average for the lattice in the pile, the activity A of the detector at the center should increase with increasing R_eff in such a way that (R_eff)^2/A remained constant, but, if k_infinity for the lattice were greater than one, then as the pile size approached the critical value, that is, as k_infinity approached one, A should approach infinity and therefore (R_eff)^2/A approach zero. Therefore by extra-polating a curve of (R_eff)^2/A vs. size of the pile i.e., number of layers to where it cut the axis, it was possible to predict at what layer k_eff would become one. Such a curve indicated at what layer the critical size would be reached. The less useful but more direct and dramatic way of recording the results is just a graph of counts/minute vs. number of completed layers, which shows the growth of the neutron activity of the pile as layers were added.

During the construction, appreciably before reaching this critical layer, some cadmium strips were inserted in suitable slots. They were removed once every day with the proper precautions in order to check the approach to the critical conditions. The construction was carried in this way to the critical layer.

CONTROL

The reaction was controlled by inserting in the pile some strips of neutron-absorbing material - cadmium or boron steel. When the pile was not in operation, several such cadmium strips were inserted in a number of slots, bringing the effective multiplication factor considerably below one. In fact, any one of the cadmium strips alone was sufficient to bring the pile below the critical condition. Besides cadmium strips that could be used for manual operation of the pile, two safety rods and one automatic control rod were provided. The automatic control rod was operated by two electric motors responding to an ionization chamber and amplifying system so that, if the intensity of the reaction increased above the desired level, the rod was pushed in, and vice versa. [If the motor failed, a man with an axe cut a rope, releasing a control rod into the pile.]

OPERATION OF THE PILE

To operate the pile all but one of the cadmium strips were taken out. The remaining one was then slowly pulled out. As the critical conditions were approached, the intensity of the neutrons emitted by the pile began to increase rapidly. It should be noticed, however, that, when this last strip of cadmium was so far inside the pile that the effective multiplication factor was just below one, it took a rather long time for the intensity to reach the saturation value. Similarly, if the cadmium strip was just far enough out to make k_eff greater than one, the intensity rose at a rather slow rate. For example, if one rod is only 1 cm. out from the critical position, the "relaxation time," i.e., the time for the intensity to double, is about four hours. These long "relaxation times" were the result of the small percentage of delayed neutrons which have been discussed in Appendix 3, and make it relatively easy to keep the pile operating at a constant level of intensity. The pile was first operated on December 2, 1942 to a maximum energy production of about 1/2 watt. On December 12th the intensity was run up to about 200 watts, but it was not felt safe to go higher because of the danger of the radiation to personnel in and around the building. During this high intensity run, measurements were made of radiation intensity beside the pile, in the building, and on the sidewalk outside.