Nuclear Physics

Isotopes and Nuclides the jargon http://en.wikipedia.org/wiki/Isotope_table_(complete)

Binding energy per nucleon

Models of the nucleus Liquid drop model

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!

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 ??

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 34.000 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.

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) 3.7 1010 decays per s ~ 2.7972 10-6 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 https://en.wikipedia.org/wiki/Category:Units_of_radioactivity

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.

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

. 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.

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

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.

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

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

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 { }

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

Compton Effect contribution Pair Production contribution

Decay schemes: 137Cs http://www.nucleonica.net/wiki/index.php?title=Decay_Schemes#55_Cs_137_.28Z.3D55.2C_N.3D82.29

Decay schemes: 60Co http://www.nucleonica.net/wiki/index.php?title=Decay_Schemes#27_Co_60_.28Z.3D27.2C_N.3D33.29

60Co spectrum

The Compton Effect

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

Half- Life Measurement Source: Pasco manual

Background Radiation