PHYS1008 Nuclear Physics Applications

Three-dimensional Reconstruction from MRI data using DeltaViewer" by Masaaki Wada

Objectives: by the end of this you should understand how fission and fusion reactors work understand how radiation causes damage understand MRI

Fission Reactors

• A typical fission reaction is\color{red}{{}_{92}^{235} U \Rightarrow {}_{53}^{129} I + {}_{39}^{106} Y} .
• This would provide about 100 MeV of energy per fission.
• However, only some nuclei will fission easily: ²³⁵U will undergo a fission reaction with slow neutrons
  \color{red}{ {}_{92}^{235} U + {}_{}^1 N \Rightarrow {}_{92}^{236} U\mathop \Rightarrow \limits_{e.g} {}_{}^{90} Br + {}_{}^{142} La + 4n}
• No control over breakup process, usually fissions into one lighter and one heavier nucleus + some neutrons.

• Release of n's allow chain reaction:

• Hence need enough fissile material so that average n does not escape...

• Critical mass for ²³⁵U is ~ 2.5 kg.
• Nuclear reactions give out millions of eV/nucleus, and fission reactions take ~ 10^-7s to occur.
• Catches:
  1. How do we get fissile material
  2. How do we assemble enough material to reach a critical mass?
  3. How do we slow down the neutrons
  4. How do we control a reaction once it has gone critical?
  5. How do we handle radioactive wastes?

How do we get fissile material?

• Natural Uranium is about 1% ²³⁵U (fissile), 99% ²³⁸U (not fissile), but absorbs neutrons.
• Can separate ²³⁵U from ²³⁸U by forming UF₆ (Uranium hexafluoride: only gaseous compound of uranium).
• Two isotopes have molecular mass 349 and 352, so lighter isotope will diffuse faster.
• What is ratio of velocities?

How do we assemble enough material to reach a critical mass?

• In bomb, start off with 2 subcritical lumps, "assemble" them to make supercritical lump by imploding with conventional explosives.

• In reactor, start with supercritical assembly and absorb excess neutrons.
• How do we slow down the neutrons?
• only slow neutrons cause fission
• Need moderator: ²³⁵U only fissions with n's with energies of ~ few eV. Need a light nucleus, so that elastic collisions will remove energy from n's: e.g. ⁹Be.

• How do we control a reaction once it has gone critical? In reactor, have

  Fuel: usually U enriched with 235U Moderator to slow down neutrons: Absorber: to allow process to be controlled by absorbing neutrons. usually cadmium

• Moving rods in and out allow reaction to be controlled. Helped by the fact that about 1% of neutrons are delayed by up to 1 min.

How do we handle radioactive wastes?

• e.g. ⁹⁰Br ⇒ ⁹⁰Sr very quickly, but this is long-lived, gets incorporated into bones (chemically similar to Ca), and will decay there, damaging the bone-marrow.
• Similarly ¹³¹I damages thyroid.
• Keep high level wastes above ground until most active components have decayed, then encapsulate in glass and bury. Long-lived wastes have t_1/2 ~ 1000 to 10⁸ yrs.
• CANDU (Canadian Deuterium Uranium) reactor uses heavy water (D₂O) as very efficient moderator, allows natural (i.e. non-enriched) U to be used.
• Disadvantage is that

  n + 238U  ⇒ 239Np ⇒ 239Pu
  

• and ²³⁹Pu (plutonium) is very fissile and can be separated chemically from U, giving perfect bomb material....

Controlled Fusion

• Problem: there is a very large repulsive force between nuclei, until distances become very small (~ 10-15 m or 1 femtometre, 1 fm)

• Fusion won’t happen until we can get over the barrier

• Stars: use lots of pressure -> high temp (15*10⁶ ºC) Average energy of protons ~ 100 KeV, so some will fuse.
• Hydrogen bomb: heat small amount of gas up to ~10⁹ °C for a very short time, by imploding layer.

• Tokomak: Confinement by twisted magnetic fields

• Laser implosion: essentially b) with lasers used to replace explosive.

• None work so far:

Radiation Damage:

Ionization of an atom typically requires 10 eV (13.6 for H).

• Hence a 1 MeV charged particle (proton or electron) would cause ~10⁵ ionizations.
• Neutral particles can also cause ionization: γ's via Compton effect, n's via collisions with nucleus.
• Hence absorption of radioactive materials will also cause damage. To make this quantitative:
• Units; 1 becquerel = 1 Bq = 1 disintegration/s.
• Old unit is Curie" 1 Ci = 3.7*10¹⁰ disintegration/s.
• What also matters is the deposited energy or dose: 1 Gray = 100 rad = 1 J/kg of material.
• However, this is not the most important quantity for biological system: α-particles interact much more often than (e.g.) γ's.
• Hence "Quality Factor" (QF) ~ 1 for X-rays, γ's, electrons, fast protons, ~ 3 for slow neutrons, ~ 10 for fast neutrons and 20 for heavy nuclei.
• Then
  • effective dose = dose x QF
  • 1 rem = Rad x QF
  • 1 Sievert = Gy x QF

• Half-life is 12.6 yrs (~ 4x10⁸s).
• How many kg would one need to have a 1 Ci source?
• Need 2.1x10¹⁹ atoms ~ 107 ng.

• Some limits

  .4 rem/year	Background : e.g. 40K, 222Rn
  .04 rem/year	Medical X-rays, etc
  5 rem/year	Usual limits for workers in radiation areas
  400 rem	limit of survivability, if spread over several months
  1000 rem	Fatal Dose

• Note there are some exceptions to this: e.g pilots have a dosage of ~5 rem/annum, since airliners fly at 10000m, where the cosmic ray exposure is much higher.

• Trick is to avoid damage to healthy tissue while destroying tumour. Hence design treatment so that radiation comes from many directions

Medical Imaging

Can be done in many ways

• Ultra-sound: very short λ sound waves (discussed earlier)
• X-rays: respond to electron density, so image bones as dark, flesh as light
• Auto-radiography: add radio-isotope to chemical, (e.g. ¹³¹I) which then travels round body and gets deposited in certain area,
• Positron-emission tomography (PET): some isotopes decay emitting positron, which immediately undergoes annihilation

  e+ e- ⇒ γ + γ

  and γ's come out back-to back with energy of 511 keV (why?)

• e.g. this shows a resting brain

• Here the brain is being stimulated by colour and patterns: the stimulated area is the visual cortex. i.e.l we are watching someone thinking!

  ©1994-2000 Crump Institute for Molecular Imaging UCLA School of Medicine

NMR

• Magnet in mag field has energy depending on orientation.

  .

• Protons act as tiny magnets. Due to quantum mechanics, only two possible orientations of spin, up and down, (Mag field is making a measurement of the proton spin) hence only two possible energy levels.

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• Difference between these energy levels corresponds to a particular photon energy/frequency.

• For B = 1T, f ~ 42.6 MHz. Slightly different for H in water: H₂O produces own mag field.
• Hence signal fed into matter will be strongly absorbed at one particular frequency of water is present.
• This allows chemical binding effects to be determined with great accuracy.

MRI

• To turn this into a image, use a varying mag field

• , so resonance frequency varies across object. Note bone appears as white (no water!). Picks out difference between fat, blood-vessels etc because of very slightly varying frequencies.

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SO that concludes the content of PHYS1008: have a nice life (and a good exam!).

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