Total probability for reaction Yield If target has thickness d, and target material has # nuclei/volume: n 0 [part./cm 3 ] Y=σ n 0 d The yield gives the intensity of the characteristic signal from the reaction process per incoming particle with the cross section σ! It also gives the number of reaction products per incoming particle! N # incident particles/time [part/s] Y tot =σ n 0 d N gives total yield per unit time
Another Example Estimate the number of 14 C atoms produced in the mummy of Ramses II by 3290 years of cosmic ray bombardment! Cosmic ray flux at ground level of ~1 10 4 particles/m 2 s. Adopt a cross section of σ = 0.1 barn for 14 N(n,p) 14 C. The living Ramses contained 2 10 25 14 N particles and 1.6 10 15 14 C particles.
Estimate of 14 C production & 14 C content Production: use standard production equation! 14 14 2 Y( C) = σ [ barn] N( N) I [ particles m s] t 14 24 2 25 4 2 Y( C) = 01. 10 [ cm ] 2 10 10 [ particles m s] 3290[ y] 14 24 2 25 2 7 Y( C) = 01. 10 [ cm ] 2 10 1[ particles cm s] 3290 315. 10 [ s] Y( C) = 207. 10 14 11 cosmic particles are produced in the mummy. Content: use standard decay equation! N ( t ) = N N are (3290 (3290 N 0 y ) y ) e contained λ t = 1.6 10 = 1.075 in the 15 10 e 15 ln 2 3290 5730 y 14 mummy! C y particles
Absorption and Transmission I 0 I(d) Absorption and transmission of the initial beam with intensity I 0 depends on the target thickness d and total interaction cross section σ tot = σ i for all possible reactions between projectiles and target material of cross section σ i: d Id ( ) = I e 0 µ = n σ 0 i µ d i
Cosmic Ray Absorption in Atmosphere µ Id ( ) = I e d ; µ = n σ 0 0 i How many of the 2.15 10 3 /cm 2 neutrons produced at 12 km height will reach the surface of the earth assuming an average nitrogen density of 5 10 19 part/cm 3 and an interaction cross section of 0.1 barn? i 2 I ( 12km) = 215. 10 [n / cm s] e I n n 2 ( 12km) = 53. [n / cm s] 19 14 3 24 2 6 3 510 [ N/ cm ] 0. 110 [ cm ] 1. 2 10 [ cm]
Interaction processes between projectile and target material atomic excitation processes X-ray-visible light (Coulomb Interaction between projectile and atomic electrons): elastic scattering processes (mechanical momentum without energy transfer): σ i [kbarn] char. particle energies inelastic scattering processes char. γ-radiation (mechanical momentum and energy transfer): radiative capture reactions char. γ-radiation (Coulomb Interaction between projectile and atomic nucleus): nuclear reaction processes (Strong Interaction between projectile and atomic nucleus): σ i [barn] σ i [barn] σ i [µbarn] char. particle radiation σ i [mbarn]
Radiation Detectors Radiation detectors are based on material which shows a high probability (cross section) for interacting with a particular kind of radiation (in a particular energy range)! The interaction process initiates an excitation or ionisation event in the material (e.g. atomic excitation, or solid state excitation) which results in light or particle emission which in turn can be used for generating an electrical pulse for analyzing and interpreting the event in the data acquisition electronics. There are three kind of detector materials: Scintillator Solid State Detector Ionisation Chamber X-ray, γ-ray, and neutron radiation particle- and γ-ray radiation particle radiation
Example: NaI scintillator Photons in the visible light range are created by excitation of NaI material with radiation photons are absorbed on photo cathode and generate free electrons by photo-effect electrons are multiplied in photo multiplier and converted to an electrical signal
Ionization chamber and semiconductor detectors Detectors are based on the principle of ionization along the track of energetic charged particle, production of ionelectron pairs, which are accelerated by attached electrical fields to anode or cathode pole of detector, charge pulse is converted in electrical pulse, pulse height corresponds to energy loss of initial energetic particle.
Summary Tools are needed to instigate the characteristic excitation processes by energy transfer The determination of the energy transfer in the excitation process requires the knowledge of the interaction probability cross section Tools are needed to analyze the characteristic light or radiation signatures High detection efficiency requires high absorption probability of radiation in detector high interaction cross section!