Which of the following electron transitions results in the most useful Bremsstrahlung x ray

I.B.3.a Bremsstrahlung

Bremsstrahlung (or “braking radiation”) is the radiation given off by free electrons that are deflected (i.e., accelerated) in the electric fields of charged particles and the nuclei of atoms. Thermal bremsstrahlung is the emission given off by an ionized gas of plasma in thermal equilibrium at a particular temperature, where the distribution of electron velocities follows the well-known Maxwellian distribution. Relativistic electrons, whose distribution of energies often follows a power-law shape in astrophysical settings, give rise to relativistic bremsstrahlung radiation that is also of power-law shape with the same spectral index as the emitting electrons.

F. Bremsstrahlung

Bremsstrahlung is electromagnetic radiation similar to x-radiation. It is emitted by a charged particle as it decelerates in a series of collisions with atomic particles. This mechanism is illustrated in Fig. 1.25, where a beta particle traveling through matter approaches a nucleus and is deflected by it. This deflection causes a deceleration of the beta particle and consequently a reduction in its kinetic energy with the emission of energy as a photon of bremsstrahlung or “braking radiation.” The phenomenon is described by

(1.98)hv=Ei−Ef

where hv is the energy of the photon of bremsstrahlung, Ei is the initial kinetic energy of the beta particle prior to collision or deflection, producing a final kinetic energy Ef of the electron. When beta particles from a particular radionuclide source strike an absorber material a wide spectrum of bremsstrahlung photon wavelengths (or energies) will be produced. The broad spectrum of bremsstrahlung is due to the broad possibilities of different interactions, i.e., deflections or collisions, that the beta particles can have with atomic nuclei of the absorber and the broad spectrum of beta-particle energies emitted from any given radionuclide. In a given spectrum of bremsstrahlung the shortest wavelength, λmin, is observed when a beta particle or electron undergoes a direct collision with the nucleus of an atom and loses all of its kinetic energy, hvmax, as bremsstrahlung or x-radiation according to the relation

(1.99)hvmax= hcλmin,

which follows the energy-wavelength relation previously described by Eq. 1.86.

Let us consider an example of a 1710 keV beta particle from 32P (Emax = 1.71 MeV) striking a nucleus of Pb in a lead–glass shield. If the beta particle loses all of its energy in the collision, the wavelength of the bremsstrahlung emitted from this interaction according to Eq. 1.99 would be

λ=hchvmax=12.4keVAo1710keV=0.00725Ao

See Eq. 1.94 for the conversion of the constant hc to convenient units of eV m or eV Å. Bremsstrahlung production by high-energy beta particles in absorber material of high atomic number is significant (see Section V). Consequently to avoid the production of bremsstrahlung in radiation shielding against the harmful effects of high-energy beta particles, an absorber of low atomic number (e.g., plastic) may be preferred over one of high atomic number (e.g., Pb-glass).

An apparatus used to artificially produce x-rays such as those employed in medical diagnosis or x-ray diffraction functions on a similar principle of bremsstrahlung described previously. The x-ray tube consists of an evacuated tube containing a cathode filament and a metal anode target such as tungsten (A = 74). A voltage potential is applied to the tube so that electrons emitted from the cathode accelerate towards the anode. Upon colliding with the tungsten anode the accelerated electrons lose energy as bremsstrahlung × radiation. For example, an electron accelerated in an x-ray tube to an energy of 40 keV, which loses all of its energy upon impact with a tungsten nucleus would produce a single x-ray photon of wavelength calculated as

λ=hchv=12.4 keVAo40 keV=0.31Ao=0.031nm

Ionization and electron excitation were previously described as predominant mechanisms by which a traveling beta particle may lose its kinetic energy in matter (see Sections II.B and V of this chapter). However, the production of bremsstrahlung may also be another significant mechanism for the dissipation of beta-particle energy, particularly as the beta-particle energy and the atomic number of the absorber increase (Kudo, 1995). A more thorough treatment is found in Section V of this chapter, which includes examples of calculations involved to determine the degree of bremsstrahlung production as a function of beta-particle energy and absorber atomic number. In general terms we can state that for a high-energy beta particle such as the “strongest” beta particle emitted from 32P (Emax = 1.7 MeV) in a high-atomic-number material such as lead (Pb = 82), bremsstrahlung production is significant. In a substance of low atomic number such as aluminum (Al = 13) bremsstrahlung occurs at a low and often insignificant level.

In view of the wide spectrum of beta-particle energies emitted from radionuclides and the wide variations of degree of beta-particle interactions with atomic particles, the production of a broad spectrum, or smear, of photon energies of bremsstrahlung is characteristic. This contrasts with x-radiation, which is emitted in atomic electron deexcitation processes as discrete lines of energy. We have excluded bremsstrahlung production by charged particles other than beta particles or electrons, because other charged particles are of much greater mass than the beta particle or electron, and consequently they do not undergo such a rapid deceleration and energy loss as they travel through absorber material.

Bremsstrahlung of very low intensity also results from the transforming nucleus in electron capture decay processes (see Section II.C.2). This is referred to as internal or inner bremsstrahlung. Because a neutrino is emitted in these decay processes, the quantum of energy not carried away by the neutrino is emitted as internal bremsstrahlung. Thus, in electron capture decay, internal bremsstrahlung may possess energies between zero and the maximum, or transition energy of a radionuclide. When gamma radiation is also emitted, the internal bremsstrahlung may be masked by the more intense gamma rays and go undetected. In such cases, internal bremsstrahlung may be of insufficient intensity to lend itself to radionuclide detection. However, in the absence of gamma radiation, the upper limit of the internal bremsstrahlung can be used to determine the transition energy of a nuclide in electron capture decay. Some examples of radionuclides that decay by electron capture without the emission of gamma radiation are as follows:

(1.100) 2355Fe→2355Mn+ν+hν(0.23MeV)

(1.101)1837Ar→1737Cl+ν+hν(0.81MeV)

and

(1.102)2349V→2249Ti+ν+hν(0.60MeV)

where hv is the internal bremsstrahlung, the upper energy limits of which are expressed in MeV.

3 Bremsstrahlung radiation imaging

Bremsstrahlung is a very well-known physical phenomenon, used, for example, in any type of radiology equipment. When an electron or a beta particle passes through matter, it slows down, and a fraction of its energy is directly converted into X-rays. The spectrum of X-ray emission is continuous, and its maximum energy is the initial energy of the electron. For example, a beta emitter such as 14C can emit X-rays of up to 156 keV in any given sample. The same phenomenon is used to produce X-rays in most X-ray sources. The Bremsstrahlung yield is actually proportional to the atomic number of the media and “roughly” proportional to the square of the energy (Evans, 1955). In the case of a biological tissue, the atomic number is low (between 7 and 8), and the yield stays very low. For 90Y (Emax = 2.2 MeV), only 1% of the energy is converted into X-rays, i.e., 20 keV per beta particle, spread over a spectrum, the maximum energy of which is 2.2 MeV. In terms of probability, less than 20% of beta particles give an X-ray that can contribute to form an image. As usual collimators used for scintigraphy have an efficiency of 100 cps/MBq, even for high-energy beta-emitting isotopes, the total efficiency of Bremsstrahlung imaging is never more than 20 cps/MBq. For a lower-energy tracer, such as 14C, the yield is at least 100-fold weaker and therefore not suitable. Bremsstrahlung radiation imaging is therefore mainly used in clinical imaging, where it is combined with high-energy tracers requiring visualization that could not be seen otherwise. A good example is 90Y, a tracer widely used for radiotherapy. Bremsstrahlung scintigraphy allows imaging of the specific localization of the tracer to target tumor sites (Kim, 2011).

2 Reduction in bremsstrahlung emission from binary ionic mixture plasma

The bremsstrahlung emission coefficient E(ω)dω (energy emitted per time, volume, solid-angle and polarization) for binary ionic mixture plasma is given by3

(1)E(ω)dω=G(ω) dω∑α∑βZαZβ (nαnβ)1/2∫dqF(q) Sαβ(q)Pα(q)Pβ(q)/ q

(2)F(q)=1n[1+exp{μ/ T−h2(q/2-2πmeω/hq)2/8π2meT}1+exp{μ/T−h2 (q/2+2πmeω/hq)2/8π2meT}]

where Sαβ (q) is ion structure factor, while Pα(q) is electron shielding factor3.

We estimate reduction of bremsstrahlung emission coefficients as a function of the frequency in a binary ionic mixture plasma, Z1=6, Z2=1, n1:n2=1:1, Γeff=0.553, Zeff=3.97, T=lkeV, by using pair distribution functions obtained by simulation with quantum diffraction and symmetry effects. Here Γeff=Zeff2e2/aT,a=(3/4π(n1+n2))1/3,Zeff2=<Z5/3 ><Z>1/3<Z>1/3 In Fig. 1, the dashed line represents bremsstrahlung emission coefficients included only ion-ion correlation effects, the solid-dashed line represents ion-ion correlation and free electron shielding effects, and solid line represents ion-ion correlation and total electron shielding effects. Bound electron shielding effects are dominant for reduction in bremsstrahlung emission.

We perform the simulation in a fictitious plasma, Z=3.97, Γ=0.553, T=1keV, to investigate the effective ionization state for bremsstrahlung emission4. Fig. 2 shows the reduction factor in the fictitious plasma. The three type of lines represent the same as mentioned above. We conclude if plasma is free ionized, the effective ionization state for bremsstrahlung emission can approximated by the plasma with Γeff and Zeff, for two component plasma.

V.B.2 Angular Distribution of Bremsstrahlung

The angular distribution of bremsstrahlung is generally quite anisotropic and varies with the incident electron energy. Bremsstrahlung induced by low-energy electrons (≲100 keV) is emitted over a relatively broad range of directions around the direction of the incident electron. As the electron energy increases, the direction of the peak intensity shifts increasingly toward the forward direction, until for electrons above a few million electron volts, the bremsstrahlung is confined to a very narrow forward beam. The angular distribution of radiation leaving a target is very difficult to compute since it depends on the target size and orientation. For thin targets the anisotropy of the bremsstrahlung resembles that for a single electron–nucleus interaction, while for thick targets multiple electron interactions and photon absorption in the target must be considered.

Recombination radiation

In addition to Bremsstrahlung radiation, a hot plasma also emits recombination radiation. This radiation is emitted when a free electron is captured in a bound state of an ion. If E is the kinetic energy of a free electron and χn is the ionization potential of the energy level in which the electron is captured, the radiation is emitted with a photon energy of hv=E+χn (Figure 9). As the free electron has a continuous energy distribution, the emitted radiation spectrum is also continuous for hv≥χn. Further, since the recombination can occur in different energy levels of the ion, the overall spectrum is quasi-continuous showing discontinuities at energies equal to the ionization potential energies of various levels. The overall shape of the spectrum is similar to that of plasma Bremsstrahlung radiation shown in Figure 8.

Interestingly, whereas in an X-ray tube, the radiation is on the longer wavelength side of the Duane–Hunt limit, here the spectrum is on the shorter wavelength side of the ionization potential.

7.4.4 Positron annihilation

Positrons interact with matter through ionization, excitation, emission of bremsstrahlung, and Čerenkov radiation in the same manner as negative electrons. As the kinetic energy of the positron decreases in the absorber, there is an increase in probability of direct interaction between the positron and an electron (Fig. 7.8(d)) in which both the positron and electron are annihilated. The energy of the two electron masses is converted into electromagnetic radiation. This process, known as positron annihilation, is a characteristic means of identification of positron emission. Since an electron mass is equivalent to 0.51 MeV, and the kinetic energy of the particles of annihilation is essentially zero, the total energy for the annihilation process is 1.02 MeV. In order to conserve momentum the photons must be emitted with equal energy and in exactly opposite direction in case of only two photons (the dominating case). These photons of 0.51 MeV each are referred to as annihilation radiation. The presence of γ-rays at 0.51 MeV in the electromagnetic spectrum of a radionuclide is strong evidence for the presence of positron emission by that nuclide. In rare cases three γ-rays of correspondingly lower energy are omitted.

Electron Accelerators

The disadvantages of isotope sources mentioned above can be circumvented by using bremsstrahlung for photoactivation. Accelerator-produced high-energy electrons are directed on to a heavy-metal target, preferably tantalum, tungsten, gold, or platinum. In this target, high-energy bremsstrahlung is produced as the electrons are decelerated in the Coulomb fields of the target nuclei.

The achievable photon flux densities usually exceed those of radionuclide sources by orders of magnitude. Moreover, the effective cross-section is significantly enlarged since the bremsstrahlung is continuous with electron energy (see Fig. 1). Finally, much higher photon energies are produced than are obtainable with any isotope source. Hence, photonuclear reactions can be induced with bremsstrahlung, whereas γ-rays, with a few exceptions, can achieve only isomeric-state excitation.

One has to distinguish between linear and circular electron accelerators according to the geometry of the particle trajectories. The different accelerators are further defined by their operation mode, namely static and cyclic devices. In static accelerators electrons are accelerated by a constant high-voltage potential. The maximum achievable particle energy is directly dependent upon the maximum high voltage of the individual machine. Among static machines, only van de Graaff accelerators sometimes have been used for photon activation.

In cyclic accelerators (linacs, betatrons, microtrons) electron energies are achieved by multiple application of comparatively low voltage to the electrons. The maximum achievable energy is dependent on various parameters. Practical experience suggests that accelerators producing energies higher than, say, 50 MeV are unnecessary. Moreover, as explained above, these energies lead to frequent interfering reactions. Analytical requirements are best met by machines that provide ∼ 30 MeV bremsstrahlung at an average electron beam current of at least 100 μA. The output energy should be freely selectable so that interfering higher-order reactions can be discarded by adjustment of the incident energy below the respective threshold energy.

Of these accelerators, two types have mostly been used for photon activation analysis, namely the linear accelerator (also called linac) and the microtron. These and other accelerators will not be described in detail here since normally the analyst is engaged in the sample handling, activity measurement, and data processing rather than in the operation of the radiation sources, which is usually done by separate operating personnel.