Useful Things to Memorize (Midterm) Flashcards
What is the mass of a proton, relative to an electron?
1836x
What’s the maximum angle of scattering for a large projectile relative to small target?
0.03 degrees
Maximum angle of scattering for two equal masses?
90 degrees
Maximum angle of scattering for a projectile much smaller than target.
180 degrees
What is the maximum energy lost to an electron by a proton
0.22% (4/1836)
Is the energy deposit of an electron with a large target big or small?
Very small
What make up the vast majority of interactions? Hard or Soft?
Soft
Angle between scatterings of two equal masses?
90 degrees
When is the only time that a charged particle has a magnetic field strength comparable to its electric field strength?
At relativistic speeds
Maximum kinetic energy of a photoelectron
hf - W
Total energy of a particle in special relativity
(gamma)mc^2 E = T + RestEnergy
Approximate rest energy of an Electron, Proton and Neutron
Electron - 0.511 MeV Proton - 938.3 MeV (say 1000) Neutron - 939.6 MeV (say 1000)
What is binding energy proportional to
Proportional to Z^2 Inversely proportional to n^2
How does an Auger electron form
A vacancy exists in a low shell An electron from an upper shell drops down to fill vacancy This releases energy, which excites an upper shell electron and ejects it
Low Z atoms fill K-shell vacancies primarily by ________ High Z atoms fill K-shell vacancies primarily by ___________
Auger Electron Emission Characteristic Radiation
What is the fluorescent yield for vacacnies higher than the L-Shell
Practically zero
Relation between hard angle of a sphere to area
= dA/r^2
For a flat faced detector, the hard angle is equal to what?
Area of detector/r^2
Equation for beam fluence of parallel beam
N/A where N is average number of particles
Fluence relation by the inverse square law
F1/F2 = r2^2/r1^2
What is the interaction cross section of the coulomb force
Infinite
What does the Probability of an interaction depend on?
number of tar/cc Interaction cross section dx or, (cross section)(N)/dA or Nint/N
What does the number of interactions rely on?
(n_targets/cc)(cross section)(Fluence)(dA)(dx)
What are the 3 types of interactions of a charged particle with an atomic electron?
Inelastic Scattering Inelastic Radiative scattering Electron capture
What is the approximate radius of an atom?
Bohr radius, 0.53 * 10^-8 cm
What is the differential cross section proportional to?
Z1^2 and Z2^2
What is the approximate total cross section for elastic p-p scattering
10^-19 cm^2
What is the approximate magnitude of the proton scattering by a heavy nucleus?
10^-19 cm^2
What is the primary mechanism by which projectile charged particles lose radiative energy?
Brensstrahlung Radiation
What approximation is made when a fast moving charged particle interacts with a charged target
Straight trajectory approximation
What is the classical interaction cross section with an electron proportional to?
Proportional to Z1^2 Inversley proportional to (beta)^2
At relativistic speeds, what is the approximate cross section of interactions with an electron? What about at non relativistic speeds?
10^-19 cm^2/e for relativistic 10^-16 cm^2/e for non relativistic
Why are small energy losses much more dominant?
Because they occur for large impact parameters. Large impact parameters have correspondingly large cross sections.
About how much smaller is collision stopping power with a nucleus relative than with an electron?
About 1000x smaller. So normally it is negligible, especially for heavy projectiles
True or false. For all charged particles, nuclei collision stopping power should be taken into account.
False. It’s negligible for all charged particles. Of course for a more accurate result, use it anyway if u have a table. But otherwise don’t bother.
What are the impact parameters for Hard and Soft collisions.
Hard - small parameters Soft - larger parameters (This is why the VAST majority of interactions are soft)
True or false. A proton will lose a substantial amount of its energy to an electron in a hard collision.
False. At most, it’s still only 0.22%. That FAR exceeds the BE of the electron usually, but its still nothing substantial to the proton.
True or false. In a soft collision, energy transferring to electron is so small that BE and Excitations can’t be ignored.
True
True or false. Atomic electrons can still be considered free is a soft collision.
False. These interactions are inelastic
What is collision stopping power proportional to?
Proportional to Z1^2 Inversely proportional to (beta)^2
Remember these graphs
Why do projectiles usually not experience full interactions with the nucleus?
Due to shielding around the nucleus. You need to approach a distance between nucleus and K-shall orbital to not experience shielding.
What is radiation yield defined as
(average energy lost to radiation)/(total beginning energy)
ONLY when projectile is brought to rest
What is the general rule of thumb for electrons in water.
Above 0.5 MeV, you can approximate that electrons lose about 2 MeV/cm in water
Remember this image of stopping powers for electrons in Water
True or false. Heavy particles have much less range straggling than electrons because they deviate from a straight line significantly less.
True
Just remember:
Energy is lost ONLY to electrons. These interactions determine the path length
Energy is NOT lost to the nucleus, BUT interactions with nucleus change directions, and therefore the range
Difference between Rcsda and Rmax
Rcsda = Path length = range assuming NO nuclear scattering
Rmax = range with FEWEST nuclear scattering
Ratio between Rmax/Rcsda for high Z atoms
0.5
Units of dose
Gray = J/kg
If the medium is thin, how much energy on average is lost to electrons?
SceP = Scet
What method must be used to calculate energy lost in a thick medium
Residual Range Method
Difference between slow and fast primary/secondary electrons
Slow - set in motion from soft collisions. Have almost no range. Get absorbef on site locally
Fast - Delta-rays. Energetic enough to leave interaction site. May possibly escape medium
True or False, Brems radiation is absorbed in mass.
FALSE! It escapes. When calculating Eabs for dose, you do NOT include radiation energy
What types of energy contribute to dose in dm
ONLY COLLISION ENERGY! Nothing else!
At what depth that CPE-delta begin at for heavy particle beams?
At a depth greater than Rcsda for the most energetic possible secondary electrons
For electron beams, it’s impossible to predict.
Dose of a beam to a material
D = (ScedxNparticles)/(mass traversed through)
TEmax = Delta = energy of electrons that have an Rcsda less than the thickness of a material. Those will NOT leave
Then use that number and restrictive stopping power into dose equation
Dose around some point for a thin medium
(fluence)(Sce/rho)
Dose at any point
(fluence)(Sce/rho)for T at x
(this only applies for heavy particles due to very small straggling)
Roughly where does the bragg peak occur
At a depth = Rcsda
Roughly how much larger is dose at bragg peak than at surface?
5-10x larger
Why is fluence of a heavy beam even for the most part then drop very heavily at the end?
Due to electron capture
What is the naming convention for primary and secondary electrons
Primary electron is ALWAYS the higher of the two energies. By this sense Tlost mas = T/2
Remember these diagrams of electron beams
Dose at any point x can be calculated by using ___________. This is ALWAYS valid
(fluence)(restrictive stopping power)
In general,
σcp int ____ σphoton int
>>
Compton found that a scattered wave generally has ______ wavelength
longer
Classical wave theory says that scattered waves are formed from
Charged particles oscillating due to Electric field from incoming EMR. The scattered wave has f = original wave
For compton scattering
Low hf lose _____ % of their E
High hf lose ______ % of their E
small
CAN LOSE large
When can electrons be considered free?
When Etr >> BE
For a low hf, electron can’t be considered free. Instead we get two other interactions which are,
Rayleigh Scattering
PE effect
Rayleigh scattering mechanism
Atomic electrons vibrate with same frequency as incoming wave
They radiate a scattered wave with that energy
Then they relax
There’s no excitation or ionization
TtrR = 0
Mechanism of PE Effect
Absorption interaction
Atom absorbs photon, photoelectron is ejected
Vacancy exists in atom and needs to be filled
(nucleus also recoils, but very slightly, energy is negligible)
Vacancy is filled either through Auger electrons or characteristic x-rays
Energy of a photo electron
Tpe = hf - BE
Energy transferred to atom in PE Effect
Ttr = Tpe + TAuger e
Approximately how many electrons/g are there for
Hydrogen
2 <= Z <= 20
Z > 20
NA
NA/2
<= NA/2
Approximately what percent of e-e interactions have very small energy loss?
90%
How come SC/rho for high Z is < low Z
Because as Z increases, I also increases and so does the delta correction factor. In addition, ne/g decreases
Why do heavy charged particles lose essentially no energy to Bremmstrahlung radiation? (and thus SR = 0) for heavy charged particles.
Because the energy loss depends 1/m2
This is why electrons lose energy, but not charged particles.
What is radiative stopping power proportional to?
Ztar2 and Eprof
What is orbital velocity dependent on?
Zeff/n
What is orbital radius dependent on?
a0n2/Zeff
Radius of an approximated nucleus sphere
(1.2E-13)A1/3
Quick approach to find mean free path length?
Recall: MFPL is the dx at which Pint = 1. Solve from there.
Hard angle of a sphere
4π
Regardless of photon energy, a photon scattered in a compton scatter has energy of approximately ____ for 90 degree scatters, and ____ for back scatters.
- 5 MeV
- 25 MeV
