The rate of radionuclide production is dependent on a number of factors, including the magnitude of the reaction cross section (i.e., probability of capture) as a function of energy; the incident particle energy; the thickness of the target in atoms per cm², which will determine the exit particle energy; and the flux of incoming particles. In the simplest case, where the cross section is assumed to be constant, the rate of production is given by the equation:
where:

The cross section is always a function of energy, and hence Eq. (6.1) becomes modified as:

As the charged particles passes through the target material, energy is lost due to interactions with the target electrons which is represented in the above equation by the term dE/dx (also called the “stopping power”).Returning to the expression for the cross section, it is evident that n _T is given by the following expression:
where:
If the target material is a compound rather than a pure element, then the number of nuclei per unit area is given by the following expression:
where:

The above equations illustrate that it is not always possible to eliminate the radionuclidic impurities in the product during radionuclide production using cyclotrons. This occurs even when using the highest isotopic target enrichment and the most precise energy selection, resulting from incident particle energy depletion with initiation of secondary nuclear reactions which is increased with higher-energy incident particles.

Radionuclide product decay begins as soon as they have formed, which leads to the following expression, where the overall rate of production becomes:
where:
The term dE/dx in the above expression is often referred to as the total stopping power. At a particular energy E, it can be represented as S _T (E) in units of MeV · cm² · g⁻¹ and is given by the following expression:
where:

The loss of energy, dE, in MeV of the particle is then given by:
where ρ is the density of the material in units of g/cm³, and the thickness of the target? ρdx (in g/cm²) can be expressed as a function of dE:
If this equation is integrated to include the stopping power to account for energy loss during the transit of the particle through the target material and assuming that the beam current is the same as the particle flux (which is true only for particles with a charge of +1), then the yield of a nuclear reaction is given by:
The radionuclide production rate is of course affected by the radioactive decay of the resulting radionuclide product. For short-lived nuclides, the competing reaction rates, production, and decay will achieve equilibrium at sufficiently long bombardment times since the rate of decay is proportional to the number of radionuclide present. The (1 – e ^–λt ) term is often referred to as the saturation factor and accounts for the competition of the production of nuclei due to the particle reaction and the radioactive decay of the nuclei that have been produced. For an infinitely long irradiation, the saturation factor (1 – e ^–λt ) tends to the value 1.

The accelerator production route which involves irradiation of natural ²³²Th targets with medium-energy protons (Fig. 6.3) appears to be an attractive route in terms of yield and cost-effectiveness.

Actinium-225 is of great interest for therapy as well as a generator parent for the availability of ²¹³Bi (Apostolidis et al 2005; Miederer et al 2008; Scheinberg and McDevitt 2011). The scope of availing ²²⁵Ac as well as ²¹³Bi for ²²⁹Th is schematically depicted in Fig. 6.4.

Chemical isolation of Ra from irradiated metallic Th was performed by a gas-chemical method (Zhuikov et al. 2011). For ²²⁵Ac and ²²³Ra processing following irradiation of ^natTh targets using 800 MeV protons, solvent extraction with ethyl acetate has been used (Weidner et al. 2012). A method for purification of ²²⁵Ac from irradiated ²²⁶Ra-targets consisting of a first extraction chromatography for separating ²²⁵Ac from ²²⁶Ra and other Ra-isotopes and a second extraction chromatography for separating ²²⁵Ac from ²¹⁰Po and ²¹⁰Pb has been reported. The finally purified ²²⁵Ac can be used in the preparation of radiopharmaceuticals (Turlera et al. 2013). This separation scheme is shown in Figs. 6.5 and 6.6.

Radium-223 has recently emerged as a key agent for bone pain palliation in castration-resistant metastatic cancer from prostate cancer and is discussed in detail in Chap.​ 12. An ²²⁷Ac/²²³Ra extraction generator based on selective extraction of ²²³Ra from a solution of chlorinated cobalt dicarbollide and polyethylene glycol in a polar diluent from a solution of a mineral acid and a complexing agent has been proposed. Radium is stripped to any appropriate aqueous solution on adding TBP into the extractant (Weidner et al. 2012). A number of additional radiochemical separations approaches for the isolation of ²²³Ra from ²²⁷Th have been reported (Henricksen et al. 2001; Horowitz and Bond 2003; Boll et al. 2005; Kirby 1969). While the isolation of high purity ²²³Ra and ²²⁷Th from ²²⁷Ac chemically appears to be straightforward, it is mechanically complex due to intense alpha and gamma radiation which produces reactive species (solvated electrons, hydroperoxide ions, atomic hydrogen, and free hydroxyl) that can cause the radiation damage to the ion exchangers and solvents and interfere with radiochemical separations.

The radiotherapeutic potential of α-emitting ²¹¹As (T _1/2 = 7.21 h) (see Chap.​ 3) has been recognized for over 30 years (Smit et al. 1973). Astatine in a halogen and the branched pathway for ²¹¹As decay is illustrated in Fig. 6.7. The 7.2 h half-life is sufficient to permit multistep synthetic procedures and is also sufficiently long to accommodate for the pharmacokinetics of a wide variety of potential cell-specific targeting agents. The halogen chemistry of astatine is diverse and permits radiolabeling of a wide range of molecules. It is possible to exploit both its metallic characteristics (Milesz et al. 1989; Yordanov et al. 2000) and its halogen properties for the synthesis of ²¹¹At-labeled molecules. Astatine-211 decays either directly by α-decay to ²⁰⁷Bi (42 %), followed by EC decay to stable ²⁰⁷Pb, or by EC decay to ²¹¹Po (58 %), followed by α-emission to stable ²⁰⁷Pb. The α particles have a range of only 55–80 μm in biological soft tissue, which represents only a few cell diameters. The high mean LET value of about 100 keV/μm is close to the optimum value for a high RBE to maximize the lethal damage (Zalutsky and Bigner 1996). The ²¹¹Po daughter emits 77–92-keV X-rays that provide a valuable means for tissue tracking ²¹¹At by SPECT imaging (Johnson et al. 1995). With regard to radiation protection issues, ²¹¹As is easy to handle, since α particles represent more than 99 % of the radiation energy (Larsen et al. 1999).

Spallation reactions can be useful for ²¹¹At production either directly or indirectly through the decay of ²¹¹Rn, but the required high particle energies between 160 and 660 MeV and limited beam intensity, in addition to the extensive required separation procedures, emerged as major impediments for the use of this strategy for routine production required to meet expected clinical demands (Kirby 1985). Currently, the most commonly used method for producing ²¹¹At is the bombardment of natural bismuth, usually in metallic form, with α particles (Zalutsky and Pruszynski 2011). Although the use of natural bismuth constitutes an ideal target material in terms of cost-effectiveness and precludes the need for chemical recovery for its subsequent use, its poor thermal conductivity (7.97 W · K⁻¹ · m⁻¹) and low melting point (272 °C) necessitates adequate target cooling at high current production runs.

The purity of ²¹¹At required for research and clinical studies is influenced by the radiochemical procedures adapted for the recovery of ²¹¹At from the bismuth cyclotron target. Although a variety of methods have been reported for ²¹¹At recovery (Eberle 1985), the most common method involves dry distillation or acid treatment of the target followed by solvent extraction. The most commonly utilized approach for separating ²¹¹At from bismuth cyclotron targets is dry distillation at a temperature range of 650–800 °C for 30 min using a flow of carrier gas such as nitrogen (Lidegren 2001) or argon (Zalutsky 1996) in a quartz vessel. After volatilization from the cyclotron target, ²¹¹At can be trapped using silica columns (Friedman et al. 1977), bubbler traps (Lindgren 2001), and capillary tubing cryotraps (Lambrecht and Mirzadeh 1985). The solvent extraction procedure consists of dissolution of target using concentrated HNO₃ followed by extraction of ²¹¹At into either butyl or isopropyl ether (Yordanov et al. 2004). Another approach reported is based on dissolution of the Bi₂O₃ target in concentrated perchloric acid followed by solid–liquid extraction employing thiosemicarbazide incorporated onto Amberlite IRC-50 resin (Roy et al. 2004).