Presentation on theme: "Radiopharmaceutical Production"— Presentation transcript:
1Radiopharmaceutical Production Nuclear ReactionsTarget PhysicsSTOP
2Target Physics Contents Nuclear Reaction Q- values Reaction Cross SectionStopping PowerParticle RangeEnergy StragglingMultiple ScatteringSaturation YieldsLiteratureThe physics which govern the nuclear reaction between the incident particle and the target material determine the how much of a radionuclide will be produced and how the target must be constructed.STOP
3Major Nuclear Reaction Types Reactions with charged particles are often different than reactions of the nucleus with a neutron. In the neutron reaction, a gamma is often given off whereas in the charged particle reaction, several nucleons may be emittedγNeutron reaction with the nucleusTargetNucleusProton reaction with the nucleus with several nucleons emitted
4Nuclear Reaction Classic Model Barrier to reaction As the positively charged particle approaches the nucleus, there is an electrostatic repulsive force between the particle and the nucleus. This is often referred to as the Coulomb barrier and is given by the relation:B=Zze2/Rwhere:Z and z = the atomic numbers of the two speciese2 = the electric charge, squaredR = the separation of the two species in cm.
5Projectile/Target Processes As we have seen before, the following types of reactions which may occur when the two particles approach each other and collide.Electron excitation and ionizationNuclear elastic scatteringNuclear inelastic scattering with or without nucleon emissionProjectile absorption with or without nucleon emissionThere are certain probabilities for each of these pathways. The probability can be expressed as follows:σi = σcom(Pi/ ΣPi)where,σi = cross-section for a particular product Iσcom = cross-section for the formation of the compound nucleusPi = probability of process iΣPi = the sum of the probabilities of all processes
6Total Excitation Energy When the incident particle combines with the target nucleus it forms a compound nucleus which will then decay along several channels as outlined previously. The total amount of energy in the compound nucleus will influence the probabilities of any particular channel. The total excitation energy of the compound nucleus is given by the relationship:U = [MA / (MA + Ma)] .Ta + Sawhere:U = excitation energyMA = mass of the target nucleusMa = mass of the incident particleTa = kinetic energy of the incident particleSa = binding energy of the incident particle in the compound nucleus
7Q values >0 mass to energy (exothermic) The probability of any particular reaction will depend on whether the reaction is exothermic or endothermicthe 'Q' value of a nuclear reaction is defined as the difference between the rest energies of the products and the reactants, ( Q = Δmc2 )Negative Q values are endothermic and positive Q values are exothermic>0 mass to energy (exothermic)Q-value<0 energy to mass (endothermic)The Q value will determine the lowest energy at which a nuclear reaction may occur. If the reaction is endothermic, the excitation must be at least high enough to overcome this activation barrier (This is not completely accurate since quantum mechanical tunneling may allow the reaction to occur at lower energies). Some examples of some potential channels for the deuteron reaction with nitrogen-14 are shown on the following slide.
9Reaction Cross-section The rate of any particular reaction is given by the following expression with the variables as defined below.where:R is the number of nuclei formed per secondn is the target thickness in nuclei per cm2I is the incident particle flux per second and is related to beam currentλ is the decay constant and is equal to ln2/t1/2t is the irradiation time in secondsσ is the reaction cross-section, or probability of interaction, expressed in cm2 and is a function of energyE is the energy of the incident particles, andx is the distance traveled by the particleʃ is the integral from the initial to final energy of the incident particle along its path
10Reaction YieldsThe rate of a particular reaction can also be written in the following equation.Where:dn = number of reactions occurring in one secondI0 = number of particles incident on the target in one secondNA = number of target nuclei per gramds = thickness of the material in grams per cm2σab = cross-section expressed in units of cm2This equation can be simplified and rearranged by incorporating the constants in the equation and solving for the nuclear reaction cross section. This simplified equation is given on the next slide.
11Simplified Equation where, σi = cross-section for a process in millibarns for the interval in questionA = the atomic mass of the target material (AMU)Ni = number of nuclei created during the irradiationt = time of irradiation in secondsρ = density of the target in g/cm3x = thickness of the target in cm.I = beam current in microamperes
12Reaction Cross-Section The probability of a particular reaction as a function of energy is the nuclear reaction cross section. The example is for the production of fluorine-18.
13Bragg PeakAs the incident particle enters the target material, the particle starts to slow down due to collisions with electrons and nuclei. The loss of energy as the particle slows is given off in several forms including light and heat. This heat has to be removed by cooling the target material during bombardmentParticle Path with more scattering as the particle slowsEnergy DepositionPenetration into the target materialBragg Peak
14Stopping PowerThe rate at which the energy of the incident particle is lost is called the stopping power of the target material. The stopping power is just the energy lost per unit distance.Stopping power S(E) = - dE/dx-whereE is the particle energy (MeV)x is the distance traveled (cm)The stopping power depends on the characteristics of the incident particle, the target material, the energy and the chemical form of the target.
15Stopping PowerThe expression for the loss in energy can be given by the expressionwhere:z = particle atomic number (amu)Z = absorber atomic number (amu)e = electronic charge (esu)mo = rest mass of the electron (MeV)A = atomic mass number of the absorber (amu)V = particle velocity (cm/sec)N = Avogadro's numberI = ionization potential of the absorber (eV)
16Stopping PowerThis expression can be simplified to the following equation by substitution the values of the physical constants into the equationwhere:z is the particle z (amu)Z is the absorber Z (amu)A is the atomic mass of the absorber (amu)E is the energy (MeV)I is the absorber effective ionization potential (eV)
17Range of charged Particles The range of the particle in the target material is just the inverse of the stopping power as a function of the energy. It can be given by the following expression.z is the particle z (amu)Z is the absorber Z (amu)A is the atomic mass of the absorber (amu)E is the energy (MeV)I is the absorber effective ionization potential (eV)As an example we can use protons on aluminum with z=1, Z=13, A=27 and I = 169 eV. The results of this calculation done on an Excel spreadsheet using 0.1 MeV intervals are shown on the next page labeled as Range (Simple).
18Simple Range Calculations This simplified equation can be used to calculate an approximate particle range. This can be compared to more sophisticated calculations as in the following table for protons on aluminumEnergy Range Range Range Range(MeV) (Simple) SRIM Janni WG&J
19Energy StragglingAs the particle slows down, the distribution in energy also increases. The following graph shows the energy distribution of a 15 MeV proton beam after it has been degraded in energy from 200, 70 and 30 MeV. It can be seen that the beam slowed from 200 MeV has a very broad energy distribution while the beam slowed from 30 MeV still has a relatively narrow energy distribution.
20Energy StragglingThe standard deviation of the energy distribution can be given by a relatively simple expression which is dependent only on the atomic number and atomic weight of the target material, the atomic number of the particle and the distance the particle has traveled through the target in terms of the grams per square centimeterwherez = projectile atomic number (amu)Z = absorber atomic number (amu)A = absorber atomic mass number (amu)x = particle path length (g/cm2)
21Multiple Scattering in Gas Targets As the particle passes through the target material, the beam starts to spread out. This phenomenon is referred to as small angle multiple scattering.The magnitude of the scattering is dependent on the atomic number of the target material and the atomic number of the particleMultiple scattering in the front foil causes the beam shape to enlargeThe Multiple Scattering in the target can be approximated by a simple model
22Multiple Scattering in Gas Targets The scattering angle is dependent on the fraction of the energy lost in the foil and the particular particleZ, z particle and absorber Zx distance traveledE energy of the particleA atomic weight of the absorber
23Beam Profile Alteration An example of this phenomenon is shown in these plots where the calculated beam profile is compared to the measured beam profile with reasonable agreement.Thicker stripper foils were placed in the cyclotron. The original foils were 180 ug/cm² polycrystaline graphite. An assortment of foils from 400 to ug/cm² were purchasedBeam spot shape was measured by irradiating a copper foil and imaging it with a phosphor plate imaging system.Calculated beam profileMeasured beam profile
24Saturation YieldsAs a nuclear reaction occurs in the cyclotron beam, the radionuclides produced start to decay. The overall rate of formation is given by the following equation. The term in parentheses is known as the saturation factor. As the time of irradiation gets longer, the rate starts to slow until at infinite time, the rate is zero.where,R - is the number of nuclei formed per secondn - is the target thickness in nuclei per cm2I - is the incident particle flux per second and is related to beam currentλ - is the decay constant and is equal to ln2/t1/2t - is the irradiation time in secondsσ(E) - is the reaction cross-section, or probability of interaction, expressed in cm2 and is a function of energyE - is the energy of the incident particles, andx - is the distance traveled by the particle
25Saturation Factors(1 - e –λt)Fraction of saturation activity
26LiteratureMore Information on these ideas can be found in the IAEA Publication “Cyclotron Produced Radionuclides: Principles and Practice” and the references in that book. “Cyclotron Produced Radionuclides: Principles and Practice” TRS 465Another IAEA publication which may be of interest is “Cyclotron Produced Radionuclides: Physical Characteristics and Production Methods” TRS 468There is also a publication on the cross sections for a variety of radionuclides which are useful for nuclear medicine called “Charged particle cross-section database for medical radioisotope production: diagnostic radioisotopes and monitor reactions” TECDOC 1211