1. Nuclear Physics

2. Isotopes and Nuclides the jargon

3. Binding energy per nucleon

4. Models of the nucleus
Liquid drop model

5. Alpha particle model Strong Points: Weak Points:
Explains why only alpha
type nucleons leave
May explain peaks in binding
energy curve
Weak Points:
Can’t explain why radioactivity
Can’t explain g,b radiation
In trouble with N not divisible
by four
Not much about spin etc.
Whoof!

6. Non-central force Spectroscopic model Strong Points: Weak Points:
g, BE, spin etc.
well & radioact.
fuzzy size
Weak Points:
Radioactivity a, b
fission, fusion
Which potential?
Problem: which potential ??

7. Decay Law: Half life
Blue Stable elements;   Green   Radioactive elements with very long-lived isotopes. Their half-live of over four million years confers them very small, if not negligible radioactivities;     
Yellow Radioactive elements that may present low health hazards. Their most stable isotopes have half-lives between 800 and years. Because of this, they usually have some commercial applications;      
Orange Radioactive elements that are known to pose high safety risks. Their most stable isotopes have half-lifes between one day and 103 years. Their radioactivities confers them little potential for commercial uses;      
Red Highly radioactive elements. Their most stable isotopes have half-lives between one day and several minutes. They pose severe health risks. Few of them receive uses outside basic research;     
Purple  Extremely radioactive elements. Very little is known about these elements due to their extreme instability and radioactivity.

8. Radioactivity a, b, g decay
The number of radioactive nuclei of an isotope varies in radioactive decay according to
where N is the number of nuclei at t=0, N0 the remaining number at t, and l is the decay constant.
T1/2 is the half-life, the time from t=0 when half the original nuclei remain.
a, b, g decay
Units Gray [Gy] absorbed dose: energy deposited per unit mass
of medium [J/kg]
Sievert [Sv] risk from ionizing radiation
rad radiation absorbed dose
rem roentgen eq. mammal (to gauge bio effects)
Becquerel [Bq] the activity for which one nucleus decays per s
Curie (today) decays per s ~ moles * t1/2 [yrs]
Isotope
Half life
Mass of 1 curie
Specific activity (Ci/g)
137Cs
30.17 years
12 mg 83
60Co
1925 days
883 μg
1,132

9. What does [kBq/kg] mean? … moles, etc.
Weighting factors WR for equivalent dose: how dangerous are types of radiation?
Radiation Energy wR
x-ray, g-ray, e-, e+, m 1
n < 10 keV 5
< 100 keV 10
< 2 MeV 20
higher < 20
P > 2 MeV 2
a, fission fragments, heavy nuclei 20
What does [kBq/kg] mean?
… moles, etc.

10. Safety After low to moderate radiation poisoning [1-6 Gy]
within hours nausea and vomiting
diarrhea
possibly headache and fever
With increasing dose cognitive impairment
Mortality 5-100%; above 6 Gy > 50%
Primary dangers: (whole body exposure)
immunodeficiency
destruction of bone marrow
shortage of white blood cells

13. .
Penetration Depth
The energy of radiation is typically measured in MeV, mega electronvolt:
If a beam of photons with intensity I0 traverses a layer of material of thickness x, the intensity emerging from the layer is
where m is called the linear absorption coefficient. It is related to the cross section s for photon absorption by
where NA is Avogadro’s constant and r is the density of the material.

15. Alpha, Beta, and Gamma radiation
Criterion for a radiation
more readily fulfilled for excited states
Coulomb barrier keeps a particles from leaving - tunneling
Probability of penetration of
the barrier
Probability to leave the nucleus s-1

17. radiation expression via multipole-expansion of the radiation field
wavelength must be large compared to size of emitter
Transition P for spontaneous emission from
b decay
emission probability n/b ‘the neutrino hypothesis
This is a crude summary of the final ideas. Reality is more complicated as spin, selection rules, etc. play a role.

18. Gamma Experiment, preliminaries
When radiation interacts with matter cross sections represent the area of the scatterer
projected onto the plane normal to the incoming ray.
n dx scatterers will appear per unit area in thickness dx of the material and the probability
of scattering is dP = s n dx.
Nuclear cross sections are
Similarly, the differential cross section is
depends on all energies

19. From this we get to the absorption coefficient m that appears in the basic
law for penetration of radiation into matter:
The P for scattering within depth x
k is called the absorption coefficient

20. A Spherical Gamma Emitter:
w/o attenuation
flux rate = no. g’s from
dV s-1 per steradian
Per area element dS = fluence rate.
with attenuation
fluence rate at surface of sphere:
And for a detector at some distance D:
which can be extended to a spectrum of
g energies by a S
{ }

21. for photons in matter
Photoelectric effect contribution:
Thomson cross section from
Plane polarized EM wave cross section

22. Compton Effect contribution
Pair Production contribution

23. Decay schemes: 137Cs

24. Decay schemes: 60Co

26. 60Co spectrum

27. The Compton Effect

28. Classically, the differential cross section is given by the Thomson cross section:
Averaged over all directions of polarization
Integrated over the angles
With quantum mechanical corrections

30. Half- Life Measurement
Source: Pasco manual

31. Background Radiation