2/12/06 clc

 

Photon and Charged Particle Detectors

 

            In this experiment you will gain some experience with various types of detectors used to detect energetic (keV to MeV) photons and heavy particles.  There is an introduction to this subject given by Melissinos, pp. 150-174.  We give here abbreviated descriptions relevant to specific detectors.  Look for further detail in Melissinos.

 

The apparatus includes:

 

A.  Surface Barrier Detector (Melissinos, pp. 208-217)

 

            When a charged particle passes through matter it loses energy, primarily by ejecting electrons from the stationary atoms of the material, and eventually comes to rest.  The number of electrons ejected per unit energy loss depends on the material.  In a typical gas counter, (proportional counter or Geiger counter) this will be of the order of 30 eV per electron, so a 5 MeV -particle will produce some 160,000 electrons.  Since a gas is not dense, however, the particle will travel a long distance before stopping, requiring a large detector volume.  In a solid, such as silicon, the average electron ejection energy is only 3 eV and the stopping distance, or range, of a 5 MeV -particle is only 25 .  Thus a solid-state detector is physically small and capable of generating more electron-hole pairs per unit energy loss.

            The detector you will use is a surface-barrier detector.  It consists of a wafer of silicon (n-type) on the surface of which is evaporated a thin layer of gold (p-type).  The junction forms a diode which will conduct only if a positive voltage is applied to the gold.  If the positive voltage (bias) is applied to the silicon, a region develops near the junction which is depleted of charge carriers.  The depth of this depletion region increases with bias voltage.  When a charge particle enters this region it generates a number of electron-hole pairs equal to the energy loss/2.8 eV.  If the particle stops in the region the number of electron-hole pairs will be strictly proportional to the particle energy.  The electrons and holes then drift to the positive and negative sides of the depletion region (typical collection times  sec) where they cause a pulse of charge to appear.  This pulse is then amplified and analyzed, giving a signal proportional to the particle energy.

            The circuitry suggested is:

 

Part 1:  Fooling around.  Set the scope sensitivity to observe noise from the detector and turn up detector bias.  A slight decrease in noise level should occur, due to the increase in depletion depth and corresponding decrease in input capacitance to preamp.  Allow a small amount of light to fall on the detector.  Is it light sensitive?  Why?  Place the 241Am source near the detector and find the signals.  Note that their height varies with bias voltage.  Why?  Use the scope to observe the signal at the input as well as output of the amplifier.  Change the distance between source and target.  The pulse height changes.  Why?  The counting rate changes.  Why?

 

Part 2:  Measuring the range and stopping power of  5.4 MeV -particles in air.  Read Mellissinos, pp. 155-157 and the appendix on stopping powers given at the end of this writeup.  You are provided with a vacuum chamber to house the source and detector and a pump to evacuate it.  Your instructor will show you how to use this.

 

            Set the source at a distance from the detector such that no signal is observed (several cm).  As you evacuate the chamber you will now see the signal reappear as the number of molecules/cm2 of air traversed by the -particles in getting to the detector decreases.

            Using the PHA, make measurements of

            a)  counts/min, and

            b)  -particle energy at the detector as a function of the effective distance in air at atmospheric pressure.  This distance is varied by changing the pressure in the chamber rather than by moving the source, since this arrangement keeps the solid angle subtended by the detector constant.

            From (a), deduce the range of a 5.4 MeV -particle in air.  From (b) deduce the energy loss  as a function of effective path length.  Since each additional path length results in an additional energy loss at a particle energy corresponding to that seen at the detector, a curve of energy loss per unit length in air (stopping power) may be found by differentiating this curve.  Do this and plot dE/dx versus E.  Is the energy loss rate greater for higher and lower -particle energy?  Why?

 

            Using  known stopping powers, measure the thickness of the gold foil provided. If you do the Rutherford scattering experiment, you will use this thickness later in analyzing the data from that experiment.

Q:  Deduce from your dE/dx curves for ’s dE/dx curves for protons.

Hint:  See Melissinos, p. 157.  You need only re-label the axes appropriately.

Q:  Why are gold and air different in their dE/dx curves?  Be quantitative.

            If you measure x in mg/cm2 rather than cm, they will not be so different.  Do this, and explain why gold  and air are so close when plotted this way.  (Hint:  See Melissinos, p. 161.)

Q:  How far will 5 MeV -particles penetrate into your skin (estimate this from the results of your experiment)?

 

B.  Scintillation Detector (Melissinos, pp. 194-208)

 

            Scintillation detectors are now used primarily to detect higher energy photons, though they can be, and once were often, used to detect charged particles as well.  This scintillator you will use is the common Na I.  The chain of events is the following:  A photon enters the crystal and interacts, via Compton scattering, photoelectric effect or electron-positron pair production, with an atom/electron in the crystal.  The energy deposited is now in the form of electron kinetic energy.  This electron, in the process of stopping in the crystal, transfers a relatively constant fraction of its energy into visible light, whose intensity is proportional to the energy lost by the electron, and which is allowed to fall on the surface of a photomultipler tube.  Here is a number of photoelectrons are emitted from the photocathode (perhaps several hundred only) and multiplied in the tube into a charge pulse of detectable size.  This charge can be quite large and further amplification need not be as great as that required, e.g., for the surface barrier detector.  However, since the number of photoelectrons is small, statistical fluctuations in this number will severely limit the resolution of the system.

            The signal finally obtained measures the energy deposited in the scintillator, which is not necessarily the full primary photon energy.  Read Melissinos, pp. 165-168.  At low energies, below a few hundred keV, the major interaction is via the photoelectric effect which deposits the entire photon energy in the crystal, thus giving a single pulse height proportional to primary photon energy.  For intermediate energies, a few MeV, the Compton effect takes over.  If the scattered photon escapes from the crystal, this energy is lost from the signal.  Since there is a distribution of Compton scattered photon energies, one will obtain a continuous distribution of pulse heights extending up to the “Compton edge,” the energy corresponding to 180o scattering of the primary photon.  Of course if the scattered photon is also captured by the crystal, one will again obtain the full energy signal.  For high energy -rays, pair production becomes important.  Annihilation of the positron with an electron in the crystal produces two photons of .511 MeV each.  If one or both of these escapes the crystal, single or double escape peaks may appear in the pulse height spectrum.

Q:  Would you expect the relative number of counts in the Compton shoulder and the full energy peak (photopeak) to depend on the crystal size?  How?  Why?

Your experimental arrangement is:

 

Part I:  Fooling around.  Place the 137Cs source near the detector and set the HV to +900V.  Observe signals from preamp and amplifier.  How does the pulse height depend on HV?  (Do not exceed 900 V).  Set the HV or fine gain controls to keep the larger pulse height signal from the source just below amplifier saturation.

            Take a spectrum with the source using the subtract mode of the PHA to subtract background.  Explain all features in the spectrum qualitatively.  Place a slab of Al or Pb directly behind (away from NaI) the source and take a spectrum. Then situate it as far from other materials as possible and take another spectrum.  Compare the two spectra.  Why are they different?  How should you place the signal for the rest of the experiment?

 

Part II:  Using the 22Na source (.511 MeV photopeak ) to calibrate the system, find the energies of the other g-ray in the 22Na spectrum and the  g-ray (s) from the 60Co source.

 

Part III:  Photons traversing matter either interact or they don’t ; they do not continuously lose energy, as do charged particles.  A beam of photons of intensity Io will thus emerge from passes through a slab of material of thickness x with an intensity  where the attenuation constant  depends on the photon energy and material.

            Integrating the photonpeak only, measure m for lead and aluminum at the 137Cs -energy by measuring counts versus absorber thickness.  Some thought must be given to relative positions of source, absorber and detector.

Q:  Why?  Q:  Why is m  different for Pb and Al?

 

Part IV:  Statistics of random event counting:  Using the computer in the MCS (multiscaling) mode, so that it counts for some period of time in each channel then advances to the next channel, etc., do a series of “counting” experiments such that the average number of counts per channel is ~100 .  Plot a histogram of the frequency versus number of times that number of counts occurred, using a bin width of one. Probably the easiest way to make a histogram is to put out your “spectrum” in ascii format to a disk, take it over to the networked computers and import it into Excel, and use the histogram feature in Excel.  (You may not wish to use all 512 to 1024 data points, but use enough to get a good histogram.)  Repeat for ~10 counts/channels.  Compare the results with normal distributions, and calculate  for each case.  Is ?

 

C.  Proportional Counter:  (Melissinos, pp. 181-183)

 

            A common configuration for a gas-filled counter is shown below:

 

 

            A charged particle, either a primary one or an electron created by photon interactions in the gas, produces electron-ion pairs in the gas.  The details of what happens are complex, but a simplified description is given here.  The electrons migrate to the positively charged anode.  As they near the wire, the electric field becomes high enough so that they will gain enough energy over one mean-free-path to further ionize the gas themselves, thus multiplying the size of the charge pulse appearing on the anode.  As long as this multiplication is kept low enough, (high voltage kept low enough) the charge pulse will remain proportional to the initial number of electrons produced, which in turn provides a measure of the total energy left in the gas by the primary radiation.  At higher voltages the tube turns into a Geiger tube whose pulse height is independent of the primary charge.

            The detector is especially useful for low-energy photons whose major interaction with the gas is via photo-ionization.  Since the density of the gas is so low, however, it is easy to lose secondary radiation, such as x-rays which result from filling ionized inner shells in the gas.  These losses may give rise to a type of escape peak similar to that seen in NaI detectors for high photon energies.

            The tube you will use is Kr or Xe-filled at 1 atmosphere of pressure.  A rare gas is used because of the long electron mean-free-path.  Xe is better than cheaper Ar for higher energy photons.

Q:  Why?

A small quantity of CO2 is added to the tube to “quench” soft photon emission, thereby keeping the tube from becoming a Geiger tube.  The entrance window is 0.010 inch (ugh) Be.

Q:  Why Be instead of, say, Al?

            The electronics are similar to those used for the NaI detector except that a low-noise, high-gain preamp is used.

 

Part I.  Fooling around:  Place the 55Fe source near the entrance window and find the pulses.  Do not exceed 1800 V on the tube.  These x-rays follow the decay of 55Fe to 55Mn and are 55Mn K-x-rays, mean energies of 5.9 keV and 6.5 keV.  The lower energy x-ray is 7 times more intense.  Observe the variation of pulse height with HV.

 

Part II.  Exploring spectrum from 57Co source.  Using the 55Fe source as calibration, locate x-rays from the 57Co source of 5.5, 14 and 122 keV.  The nuclear decay scheme of 57Co is shown below.

 

Q:  Where does the ~6 keV radiation come from?

 

Part III.  Measure the attenuation of the 14 keV and 5.5 keV x-rays from 57Co in Al, and find the mass absorption coefficients.

 

Q:  Why are they so different for the two energies?

 

You might wish to try the 57Co source on the NaI detector to seek the 136/122 keV lines.  Why are these photons hard to detect with the proportional counter?

 

D.  Optional Additional Experiments using X-ray Machine plus X-ray Sources

 

            In addition to photographic techniques used in conjunction with x-ray crystal analyzers, there are single photon detection methods of obtaining x-ray spectra.  These techniques are generally not as high in energy resolution, but are high in efficiency.  These devices can thus be used to do many x-ray measurements in a short time period.  To become familiar with these pulse-counting techniques we will use a sealed proportional counter to observe directly the spectrum from the x-ray tube.

 

 

            This experiment uses both a NIM BIN  and associated electronics and the Teltronics X-ray apparatus.  You will have to transport one or the other of these to the table of the other. Discuss this with your instructor.

 

(1)  Once the electronics has been assembled, place the 55Fe source in front of proportional counter and obtain a spectrum in the MCA.  Repeat with the 57Co source and obtain an energy calibration (i.e., energy as a function of channel number:  E=Mx+Eo).  Obtain the values of  (FWHM) and  for the Fe and Co source spectra.  Do not change any gains or other settings on the preamp, amp, delay ADC etc. electronics.

 

(2)  Place the proportional counter in front of the x-ray tube and obtain a primary x-ray spectrum.  The x-ray tube must be shielded with a lead cover with a small hole for the x-rays.  The tube puts out a great deal of radiation.  BE CAREFUL!  Using your energy calibration identify x-rays in this spectrum.  Obtain  from this spectrum.  If you have already done the X-ray experiment, compare this with the resolution you obtained using the Bragg spectrometer.  What is the continuum in the spectrum?  What does the maximum energy correspond to?  Vary the voltage on the tube and see if this end point energy changes.

 

(3)  Determine the absorption coefficients m of x-rays in Al for the tube source.   which Io is intensity entering absorber and I is the intensity exciting the absorber.   is the absorption coefficient and x is the absorber thickness).   Measure the intensity of the x-rays as a function of the thickness of the Al.  Use the absorbers given in the lab set.  You may also use Ni.

Q:  Why is Ni special for this tube?

 

Appendix A: Stopping Powers

 

            When a charged particle (called the projectile) travels through a medium (called the target), the projectile loses energy to the target via four types of mechanisms.   The first mechanism is called "electronic" or "inelastic" energy loss and is due to electron excitation or ionization of the target atoms.  "Electronic" energy loss is the principal mechanism for energy loss. The second mechanism is called "nuclear" or "elastic" energy loss and occurs via momentum transfer from the projectile to the recoiling target nuclei in elastic collisions.  "Nuclear" energy loss is important at low projectile velocities.  The third mechanism is energy loss from the generation of photons (bremsstrahlung).  The energy loss from photon emission only occurs at relativistic velocities. The fourth mechanism is from nuclear reactions which also occurs at high velocity.  We will be doing experiments in the velocity region where "electronic" energy loss is dominant.

 

            In the above experiments you will determine or use the energy loss ΔE of a beam of alpha particles from a radioactive source after traversing matter.  We will designate the distance the alpha particle travels through  matter by  ΔX.  This thickness of foils is usually expressed as either NΔX or ρΔX, rather than ΔX, where N is the number density and ρ is the mass density.  These two quantities are related by the formula

                                                                1                                                           (1)

 

N0 and M2 are Avogadro's number and the mass number of the target, respectively.

 

            The stopping power is the specific rate of energy loss of a projectile at a given energy and is denoted by the symbol ε.  In view of the above definitions we can write the stopping power in three different sets of units

 

                               dE/dX :     eV/Å,  MeV/cm

                               dE/ dX:     eV/(g/cm2) , keV/(g/cm2) , MeV/(g/cm2)

                    ε =  dE/NdX:       eV/(atom/cm2) , ev-cm2

 

ε is usually  reserved for the latter quantity, i.e., dE/NdX in ev/(atom/cm2).  We can easily convert from one form to another using eq. 1.  For example

 

            dE/ρdX = N0/M2  *  dE/NdX.

Fig. 1 shows the stopping power for protons on silicon.

 

 

 

 

            For this case we see from the figure that for the proton energy region above about 0.1 MeV and below about 1000 MeV the stopping power can be calculated by perturbation theory.  This is in the region where "electronic" stopping is dominant and can be calculated fairly well with the Bethe formula which is given below. 

 

                             2                        (2)

 

            m = mass of electron                             Z2 = Z of target

            v = velocity of projectile                                    e = charge of the electron

            Z1 = Z of projectile                                           I = mean excitation and ionization energy

 

The two terms containing the v2/c2 are relativistic correction terms.  The term C/Z2 is a velocity dependent term, significant only at low velocities and due to non-participating inner-shell electrons, and δ/2 is only important at ultra high velocities.  

 

            We can use this formula to calculate the stopping power in the present experiment.  Fig. 2 below shows a calculation of the "electronic" stopping power for alpha particles on gold calculated using equation (2) with C = 0, δ = 0, and neglecting the v2/c2 terms.  The results of this calculation are compared with tabulated stopping powers.  The value of I was taken from the approximate relation

 

 

                                                           3                                                      (3)

 

 

 

 

 

 

 

 

            Fig.2.

 
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Figure 3 shows the ratio of I/Z vs. Z from calculation and stopping power measurements.  For elements above Z of 20 the above relation holds fairly well.

 

 

Appendix B: Basics of pulse electrons with detectors

 

Preamp

 

            The major role of the preamplifier for each of your three detectors is to accept a charge pulse and produce a voltage pulse of reasonable size with a low output impedance (capable of driving a long 100 cable for example).  The simplest preamp is simply an emitter (or cathode) follower (E), a device with a high input impedance and a low output impedance.  For example, for a photomultiplier tube, a preamp could be

 

 

            If E has input impedance Rin and gain of unity, a charge pulse q produces a pulse of height  (c includes cable capacitance, etc.). The charge-sensitive preamps used with the surface barrier detector and proportional counter incorporate additional active amplifying stages.

            As a function of time the voltage out will look like

 

 

            The rise time  is determined by the detector (or circuitry of E, whichever is slower).  For the NaI,  nsec and is limited by the lifetimes of the light-emitting excitations in the crystal.  For the proportional counter and surface barrier detector  is dictated by charge collection times in the detectors and is too short for you to observe with your preamps provided.  The fall time, , is given by , which is why  must be large.  Typically  is designed to be about 50sec.  The preamps you have are somewhat more sophisticated but produce pulses with the same characteristics as those shown above.

 

Amplifier

 

            The amplifier must accept these low-level, rather long, pulses and amplify them further for analysis by the PHA (to a few volts, say).  It must also cut off the long tails on the pulses to prevent pileup of one pulse on another at high count rates.  The shaping can be done either by an integration-differentiation network such as shown below: