Detection and measurement of gamma-radiation by gammaspectroscopy Gamma-radiation is electromagnetic radiation having speed equal to the light in vacuum. As reaching a matter it interact with the different parts of that, namely 1./ with nuclei 2. / with electrons 3./ with nuclear field. The most important interactions: 1./ photoelectric effect, 2./ Compton scattering 3./ pair formation. The intensity of a parallel gamma beam with an initial intensity I o after crossing a layer of matter with surface thickness d (in g cm -2 ) can be expressed as I = I o e -d (1) where the mass absorption coefficient, dimension is cm 2 g -1. According the three types of interactions - can be the sum of three members: = f + C + p (2) where f. C and p are the absorption coefficients characteristic of the photoelectric effect, the Compton scattering and the pair formation, respectively. The relation between the cross section of the processes ( f, C and p ) and the mass absorption coefficients ( f, C and p ) is as follows: NZ A 2 1 cm g (3) where N is the Avogadro number, A is the atomic mass; Z is the atomic number of the absorber. The cross section of the three processes depends on the atomic number and the gammaenergy in a very complicated manner, so they are discussed separately. Photoelectric effect: an electron of the atom absorbs the gamma quantum and takes up its total energy. The electron releases and obtains kinetic energy E e, expressed as E e = E - E bind (4) where E e and E are the energies of the electron and the photon, E bind is the binding energy of the electron. The cross-section of the process for the K electron shell is
2 1/ 2 5 mc. Z k Konst (5) E The cross-section of the photoelectric effect is much smaller for the other electron shells. The total cross-section of the photoelectric effect is: 5 f K (6) 4 The released electron is broken down in the matter and gives its total energy (E e ) to the matter, While E bind << E this energy is considered to be equal to the energy of gamma-photon. So, the impulses formed in the matter of a gamma-detector are a well-defined value, proportional to the gamma-energy. Compton-scattering: the process is the scattering of -rays on the electrons of the atom (Fig.1). Compton scattering h 0 h electron E e h 0 Pair formation positron h 0 E k Photoelectric effect Fig. 1: Scattering processes of gamma-radiation The energy of the scattered photon:
the energy of the electron: h o h ' (7) 1(1 cos ) Eo E e (1 cos ) (8) 1(1 cos ) where o is the initial frequency of the photon, h = o, 2 mc the frequency of the scattered photon the angle of the scattering. the energy of the primary photon in units mc 2 (9) The relation of the cross-section and the energy for one electron by Klein-Nishina equation: meg. for one atom ' 1 2( 1) 1 4 1 c K 1 lg(2 1) 2 (10) 2 2 2(2 1) (11) c ' Z c The scattered photon usually releases from the absorbent and takes a part of the energy with itself. The part of the energy of the primary photon given to the electron remains in the absorbent. The ratio of the energy of the electron and the scattered photon depends on the scattering angle, so the impulses formed in a gamma detector by Compton scattering are different, they show a continuous pattern. The minimal and maximal vales can be calculated from Eq. 8. Pair-formation: a gamma-quantum with energy E > 2 mc 2 (12) forms an electron and a positron in the nuclear field. In Eq. 12 2 mc 2 is the energy equivalent with the mass of the positron and electron (1.02 MeV), E is the energy of the primary photon. The total kinetic energy of the positron-electron pair (E kin ) is as follows: E kin = E - 1.02 MeV (13) The cross-section of pair formation, p, depends on Z 2. The cross-section of the three processes as a function of gamma-energy for two substances is shown in Fig.2.
Absorption coefficient 10-3 (cm -1 ) Absorption coefficient 10-3 (10 cm -1 ) 1.0E+04 1.0E+03 total Comptonscattering Comptonscattering 1.0E+02 Photoelectric effect Pair-formation 1.0E+01 1.0E+01 1.0E+02 1.0E+03 1.0E+04 E (kev) Fig. A: Absorption coefficients of germanium as a function of gamma-energy 1.0E+06 1.0E+05 Photoelectric effect 1.0E+04 total 1.0E+03 Pair-formation 1.0E+02 1.0E+01 1.0E+01 1.0E+02 1.0E+03 1.0E+04 E (kev) Fig. B: Absorption coefficients of NaI crystal as a function of gamma-energy Fig. 2: Absorption coefficients of different interactions as a function of gamma-energy
Gamma detectors contain scintillating crystals (Fig. 2B) or semi-conductive materials (Fig.2A). The semi-conductive detectors are solid ionization chambers, so the formation of electric impulses is similar to gas ionization detectors. In scintillation detectors the scintillation forms in the following way: the fast electrons producing in the absorption processes excite the electrons of the absorber substance (e.g. NaI), then the excited electrons go back to the basic electron levels, emitting photons in the range of the visible light. In this way the energy of gamma-photons is transformed to light, and then the light is transformed to electric energy in a photomultiplier, also on the basis of the photoelectric effect. The scheme of a scintillation counter is shown in Fig. 3. The pattern of the electric impulses formed by the absorption of monoenergetic gamma-radiation is shown in Fig.4. Fig.3: Scheme of a scintillation counter imp/s in a unit energy interval Theoretical Practical Energy (MeV) Fig. 4: Theoretical and practical gamma-spectrum in NaI scintillation detector E 0
As seen in Fig. 4 the peak E o caused by the gamma-photons absorbed via photoelectric effects... The energy range from E =0 to a maximum, the so-called Compton edge results in the Compton scattering. The theoretical sharp line is broadening because of the statistical processes in the crystal. The resolution of the detector (W) is defined by the relative half-width of the peak: E W=. 100 % (14) E The meaning of E is illustrated in Fig.5. n n/2 E Fig.5. Interpretation of half-width The resolution of the detector depends on the quality and size of the detector, the energy of the radiation and the electric properties of the photomultiplier. A typical value for the 662 kev line of 137m Ba isotope is about 7-10 %. The resolution of Ge(Li) semi-conductive detectors is much better than that of scintillation detectors, it is 2-3 kev, that is W<0,5 % for the same peak of 137m Ba. Fig. 6 shows the gamma-spectra of 226 Ra and its daughter elements obtained by NaI and Ge(Li) detectors, clearly illustrating the advantages of semi-conductive detectors in gammaspectroscopy.
Intensity Spectrum by semi-conductive detector Spectrum by scintillation detector Energy Fig.6: Spectra of 226 Ra and daughter elements The amplitude of the electric impulses of the photoelectric peak depends on the energy of gamma-photons, the voltage of the photomultiplier, and the electric amplifier. Keeping the electric parameters (voltage and amplifier) as constant values there is a linear relationship between the amplitude and the gamma-energy. So the energy of gamma-radiation can be determined. The measurement of the absolute intensity of a gamma source requires the knowledge of the efficiency of the detector. The efficiency is the ratio of the observed intensity and the number of particles reaching the detector. This value depends on the energy, so the efficiency has to be determined as a function of energy. The spherical angle of detection has to be known, too. When the absolute intensity has been measured, the activity of the gamma-source is also given when the relative abundance of the gamma line is taken into account. The relative abundance means how many per cent of the decays give the measured gamma line. Gamma-spectra can be taken by one-channel and multi-channel amplitude analyzers. In a one-channel analyzer the impulses coming from the detector are separated by a differential discriminator, It is a filter allowing the impulses within a voltage range V D V D going through. V D is the basic level, V D is the width, and they are variable. When varying V D, the gammaspectrum can be taken up range by range. The advantage of the multi-channel amplitude analyzers is that the total spectrum is taken up at the same time. It saves time and makes easier the measurement of samples with short halflife and low activity.
The impulses coming from the amplifier of the detector go to an analog-digital converter (ADC). The condensate in ADC charges up, the charge is determined by the amplitude. Then the condensate losses a part of the stored charge, meanwhile an oscillator sends impulses with constant frequency. The number of impulses during the discharge of the condensate is proportional to the amplitude originally arrived at the ADC or to the energy of the gamma radiation. The number of the signals coming from the oscillator determines the places of the input signals in the magnetic memory. One position of the memory belongs to the input signals with different energy, and its content increases by one if the signal arriving at ADC has the same energy. The output of the data stored in the magnetic memory is done by two digital-analog converters (DAC) and an oscilloscope. One of the DAC s refers to the memory positions which determine the place of the electron beam along the x axis of the oscilloscope. The other DAC shows the number of signals causing the deviation of the electron beam from the x axis. In this way, the amplitude spectrum is continuously present on the screen. The multi-channel analyzer makes possible the arithmetical treatment of the stored data. For example, the background spectrum can automatically subtracted from the spectrum of a sample, the peak areas of the photoelectric effects may be determined. A spectrum stored in a part of the memory can be transferred into another part of memory; the spectra can be summarized or subtracted. It is useful for the analysis of samples containing more radionuclides. Tasks 1. Measurement by a semi-conductive /Ge(Li)/ detector, 8192-channel gamma spectrometer: The spectra of different radioactive isotopes ( 60 Co, 65 Zn, 85 Sr, 108m Ag, 137 Cs, and 226Ra ) are taken with the given measuring time. An energy calibration is done by the aid of literature data. On the basis of energy calibration, unknown samples are identified. 2. Determination of the effectivity of the instrument by the lines of isotopes 226 Ra and 60 Co. The activity of 60 Co is known at a certain time, so the actual activity can be calculated on the basis of the decay law. Take into account the abundance of the different gamma-lines! Plot the effectivity as a function of energy! Note the half-width of the peaks! 3. Measurement by NaI(Tl) scintillation detector, 2-channel analyzer: The efficiency and halfwidth of one line of 60 Co is determined. Take the spectrum of 137 Cs; determine the half-width of the photoelectric peak! Compare the resolution and effectivity of the two detectors!