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Dose. Particles lose energy in matter. Eventually energy loss is due to ionization. An important measure is the amount of energy gained by the material as a particle passes or stops. Energy Gained. Energy transferred describes the kinetic energy gained by charged particles.

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Presentation Transcript
energy gained
Particles lose energy in matter.

Eventually energy loss is due to ionization.

An important measure is the amount of energy gained by the material as a particle passes or stops.

Energy Gained
energy transferred
Energy transferred describes the kinetic energy gained by charged particles.

Energy imparted is the energy lost by charged particles.

Energy Transferred

1.1

2.8

4.2

5.4

10 MeV

particle energy

3.6

2.0

0.1

9.0

energy transferred

2.8

3.3

2.8

1.1

energy imparted

energy imparted
Energy transferred

Radiant energy into a volume from uncharged particles

Radiant energy out tpo uncharged particles (not brem or annihilation)

Energy change from mass

Energy imparted

Start with energy transferred

Energy in from charged particles

Energy out from charged particles

Energy Imparted
kerma
Kerma is the energy transferred per unit mass.

Kinetic Energy Released per unit MAss

Radiative kerma is the energy loss per mass due to brem and annihilation.

Collision kerma subtracts the reradiated photons.

Net energy transferred per mass

Kerma
absorbed dose
Absorbed dose or dose is the energy imparted per unit mass.

Like kerma dose is based on mean changes in energy.

Two units are used.

1 gray (Gy) = 1 J / kg

1 rad = 100 erg / g (older)

Absorbed Dose
lethality
Dose can be compared to physical effects.

Lethality refers to the likelihood that a dose will be fatal.

Cell death

Whole body death (see graph at right)

Lethality

Lethality %

Dose (cGy)

Federation of American Scientists

equilibrium
Measuring the relationship between energy transferred and imparted requires equilibrium conditions.

Radiation equilibrium

Charged particle equilibrium

Looser requirement

Equilibrium
exposure
Exposure is defined by the ionization produced by photons.

Gammas and X-rays

Charge per unit mass in air

The original unit is 1 esu / cm3 of dry air at STP (1928).

Roentgen (R)

R = 2.58 x 10-4 C / kg (1962)

Useful Conversion

Show that the original roentgen is equivalent to the modern one.

Look up constants:

Density of air at STP is 0.001293 g / cm-3

1 esu = 3.34 x 10-10 C

3.34 x 10-10 C / 1.293 x 10-6 kg = 2.58 x 10-4 C / kg

Exposure
gamma rate
Assume a point source of gammas.

Activity C

Average photon energy E

Consider a sphere or radius r.

Fluence through sphere F

Mass energy absorption men/r = 2.7 x 10-3 m2/kg

Find the dose and exposure rate.

1 R = 0.0088 Gy

Rate of energy release:

Fluence rate:

Dose rate:

Exposure rate:

Gamma Rate
radiation factor
The effect of radiation on tissue depends on the LET as well as the dose.

Higher LET is more damaging.

Radiation has a weighting factor based on particle.

Factor WR or Q

Updated in 1991

In terms of LET

LET L (keV / mm in water)

< 10; WR = 1

10 – 100; WR = 0.32L – 2.2

> 100;

In terms of particle

e, g, m; WR = 1

n; WR = 5 – 20

p; WR = 5

a; WR = 20

Radiation Factor
restricted stopping power
Secondary electrons ejected from atoms are delta rays.

Deltas deliver most of the dose

Energy less effective if it’s too high

Restricted stopping power measures the energy lost up to a limit D.

Typical Problem

Estimate a cutoff value for irradiating 300 Å viruses.

Answer

Most energetic delta range should not exceed 300 Å.

Find range limit 3 x 10-6 cm

Range in water

500 eV is 2 x 10-6 g/cm2

1 keV is 5 x 10-6 g/cm2

Estimate cutoff at 700 eV.

Restricted Stopping Power
equivalent dose
The equivalent dose is a measure that combines the type of radiation and dose.

Unit is Sievert (Sv)

1 Gy equivalent

Older unit is rem

Roentgen equivalent man

1 rad equivalent

100 rem = 1 Sv

Natural doses

Cosmics: 0.3 mSv / yr

Soil: 0.2 mSv / yr

Radon: 2 mSv / yr

Total natural: 3 mSv / yr

Environmental hazards

Flying at 12 km: 7 mSv / hr

Chest x-ray: 0.1 mSv

Mammogram: 1 mSv

CT scan: 20 mSv

Equivalent Dose
neutron interactions
Neutron Interactions
  • Neutrons present a unique situation for dose determination.
    • No interaction with atomic electrons
    • Cross sections vary with target nucleus
neutron scattering
Elastic scattering from nuclei is the most important process for neutron energy loss.

Assume classical collision

Set M = 1 and compare for nuclei

Nucleus Qmax/En

1H 1.000

2H 0.889

4He 0.640

9Be 0.360

12C 0.284

16O 0.221

56Fe 0.069

118Sn 0.033

238U 0.017

Neutron Scattering
neutron dose equivalent
Neutron weighting factors were variable.

WR = 5-20.

The factors can be determined from assumed elastic scattering.

Example

Find WR for 2-MeV neutrons.

Average recoil p is 1 MeV

Stopping power for 1 MeV p in water is 270 MeV/cm

Equal to 27 keV/mm

Neutron Dose Equivalent
neutron threshold
Inelastic collisions result in a nuclear reaction.

Many are endothermic

Requires extra energy

For example 32S(n,p)32P:

Eth = 0.957 MeV

32P 32S + b-

Ebmax = 1.71 MeV

T = 14.3 days

Used to detect exposure

Change in rest energy

Conservation of energy and momentum

Neutron Threshold
neutron activation
Time dependence of activity from neutron capture is based on exposure and decay.

Constant rate of fluence F

Minimal loss of target NT

Typical Problem

A 3-g sample of 32S is irradiated with fast neutrons at 155 cm-2s-1. The cross section is 0.200 barn. What is the maximum activity?

Answer

The number of target nuclei,

The maximum is for large t.

Neutron Activation