Transcript atomicstr

Photons: X-rays, γ- rays; electrons, positrons
Shell structure of the atoms.
Notion of the cross section of the interaction
Lecture 2
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The electromagnetic spectrum
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Each photon has a wavelength λ inversely
proportional to its energy E,
h is the Planck’s constant and c is the speed of light.
X-ray:
Particle-wave duality. For interaction with
aperiodic systems X-rays behave mostly like
particles.
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Electronic structure of atoms
Energy levels of the atom consisting of a nucleus of charge Z and a single
electron:
Here ℏ=h/2π, n principle quantum number. For given n angular
momentum quantum number, l, could be between 0 and n-1. “The
rotation axis” can be oriented in 2l+1 ways:
The electron states are labeled by n and l. l=0,1,2,3,4,5,6 corresponds to
s,p,d,f,g,h. Principal number is written as a number
5d state is n=5, l=2 state.
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Energy levels for multielectron atoms
Prime effect: Spin statistics - electrons have spin 1/2 - fermions.
Cannot be in identical states. For given space
wave function - 2 states - electron with spin
oriented in two opposite directions: S=+1/2 and S=1/2.
If we neglect the electron-electron interaction - effectively
screening of the Coulomb field of the nucleus by the cloud of
the electrons, we have the hydrogen type QM problem with
condition that two electrons should not be in the same
quantum state. Account of the interaction: electronic levels
are functions of both n and l, though the difference is slight.
However it leads to reordering of the filling of the electron
states.
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Schematic diagram showing
electron structure for hydrogen,
helium, lithium, carbon and neon.
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Ground state atoms: all electrons are in the lowest state
Excited atom, one or more electrons are in excited state
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Takes 10 s to drop to a vacant state.
Emission of photons - fluorescence or X-rays.
Shell structure : Electrons with same n have approximately the
same energy. Shells characterized by the value of the principle
number n.
n=1,2,3,4,5, ----> K,L,M,N,..
K-shell 2 electrons, L -shell =2(1+3)=8 electrons.
Subshell - the same l,n.
It (sub)shell is filled - closed (sub)shell. - Important in chemistry
of atom interaction.
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The electron configuration
for, say, iron indicates an
argon electronic core (see
argon) plus six 3d electrons
and two 4s electrons. The
ionization energy is the least
energy necessary to remove
to infinity one electron from
an atom of the element.
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Characteristic X-rays of Tungsten
Charact. X-ray
K
L
L
57.4
M
66.7
9.3
N
M
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68.9
O
69.4
P
69.5
11.5
12.0
12.1
2.2
2.7
2.8
Basic interactions between X-rays
and atoms.
• Coherent scattering
• Photoelectric effect
• Compton scattering
• Pair production
• Photodisintegration
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Attenuation is statistical in nature. Atoms are
randomly distributed in the media. Quantum
mechanics - the uncertainty principle does not allow
too accurate transverse localization of the beam.
Need probabilistic language.
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Let us first consider propagation of a particle through a
homogeneous media.
Number of particles which entered is N. Number which
survived when going the distance L: N(L); N(0)=N.
Interactions in different points are independent. Hence
probability to interact between points x and x+dx for any of
the particles which reached x should be independent of x.
Hence N(x)-N(x+dx)=N(x)μdx.
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Physical meaning of μ, attenuation coefficient
Half-value layer: reduces initial flux by a factor of 2.
L= ln 2 / μ
Average path <L> before the interaction?
Probability to reach point x, P(x) ~ exp(-μ x).
λ=1/μ - mean free path
Exponential decrease → doubling the thickness from L to 2L
reduces flux by a factor of 4. However this refers to only
incident particles. Photons produce electrons, photons, ...
cascade propagates further than initial beam - will discuss
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Graphs of linear attenuation coefficient 
The linear attenuation coefficient  can be obtained from tables, or from automated databases such as
the NIST database:
http://physics.nist.gov/PhysRefData/XrayMassCoef/tab3.html
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How μ depends on the properties of media? Incoming particle
interacts independently with individual atoms. Probability of
interaction depends on number of atoms (mass per unit area) along
the path.
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Since μ,λ are determined by local properties of the media
dependence on the density, ρ , should linear:
where σ is the absorption cross section of
interaction ( I will come back to discussion of2 this
quantity next week). It has dimension of length = area
Dimension of σ
⇒
n=2
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Measurement of σ requires a thin target, narrow beam and detector far away at
zero angle. Nice for particle & nuclear physics - unrealistic for medical applications.
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⇒
Convenient to tabulate μ/ρ
It has the meaning of absorption per unit mass (1
g) of the material in the unit transverse area. To
get μ from it, you have to multiply by ρ.
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The tables and plots of the X-ray mass coefficients are
available from the NIST web page
http://physics.nist.gov/PhysRefData/XrayMassCoef/tab3.h
tml
denotes energy loss
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Per gram of material Hydrogen is less effective
absorber than oxygen for low energies.
However at higher energies situation is
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reversed.
Beam of photons with max energies 400 KeV when going through lead
filters out say 50 KeV photons. If the beam max energy is 20 MeV, a
lead filter would shift the spectrum to 2-3 MeV. A filter made of light
elements will enhance hard component of the spectrum.
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Photon total cross sections as a
function of energy for scattering off
carbon and lead showing
contributions of different
processes:
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σ depends on the composition of the target, on the energy
of the beam.
Absorber removes from the beam the
component which interacts stronger with the
media.
Deviations
from the exponential
dependence on the distance.
It is easy to include dependence of ρ on longitudinal coordinate z:
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