Particle Detectors and Quantum Physics (2) Stefan Westerhoff Columbia University NYSPT Summer Institute 2002
More Quantum Physics We know now how to detect light (or photons) One possibility to detect charged particles is to have them produce light Charged particles produce light when exiting atoms or molecules (for example fluorescence light) So we need to learn more about atoms and how they can be excited
Positron or Electron? Discovery of the positron (Andersen, 1931) Magnetic field B is perpendicular to the paper plane, particles pass through a lead plane Positive charge going up, or negative charge going down? Particle loses energy in the lead (absorber)!
Lab Classes related to this lecture: Scintillators (this afternoon)
Towards a Model for the Hydrogen Atom (the rest is details )
There s a reason physicists are so successful with what they do, and that is they study the hydrogen atom and the helium ion and then they stop. Richard Feynman
Early Model of the Atom (Wrong) Discovery of the electron in 1897 in cathode rays Electrons are part of the atom First model: atom is a homogeneous sphere with electrons in it (plumpudding model)
Rutherford s Experiment Beam of α-particles (He nuclei with charge +2e) is directed at a thin gold foil Expectation: only small deflection (electrons are lighter than α particles, and the positive charge in the atom is spread out and can t do anything either)
Results Most α particles pass through the foil as if it was empty space Some of the α particles are deflected at very large angles, some even backward! Rutherford: α particles must be repelled by a massive positive charge concentrated in a tiny space
New Model (Still Wrong) Atomic model: electrons orbit a tiny positive nucleus of radius 10 15 m The electron moves in orbits around the nucleus like the Earth around the sun Movement is necessary so the electron does not fall into the nucleus (Coulomb!)
Why is it Wrong? From Maxwell s electrodynamics: electrons moving in a circular orbit radiate electromagnetic waves they gradually lose energy. In Rutherford s model, the electron would lose energy and get closer and closer to the nucleus until it falls into the nucleus. This would take about 10 11 s. The fact that you are still sitting here shows that either Rutherford or Maxwell are wrong. Don t argue with Maxwell.
The Bohr Model Bohr believed in Rutherford s model and tried to fix it From Planck and Einstein he knew that energy is quantized so maybe the same is true in atoms, and they can not lose energy continuously, but only in quantum jumps Hydrogen is the simplest atom: just a proton and one electron
Energy Levels Electrons move about the nucleus, but only certain orbits are allowed An electron in one of these orbits has a definite energy and moves on the orbit without energy loss E = 13.6 ev with n = 2 n 1,2,3,...
Energy Levels Notice the minus sign! This is a convention, but a good one: it means that if the electron and the nucleus are very far apart, the energy is zero (they are free particles ) The orbit closest to the nucleus, n = 1, has the lowest energy E = -13.6 ev The next highest state is n = 2, with a higher (!) energy of E = -3.4 ev The state with the lowest energy is the ground state, the states with higher energy are excited states
Photon Emission Electrons can jump from one level to another If they jump into a state of lower energy, a photon is emitted, with a frequency corresponding to the energy difference h f = E E u l
Photon Absorption The opposite is also true you can push an electron into a state of higher energy if you send a photon in that has exactly the right energy The electron is typically in the ground state If it is in an excited state, it will emit photons until it is back in the ground state Systems in physics always try to get into the state of lowest energy (examples?)
Transitions The different transitions from one level to another have different names Photons of the Balmer series have wavelengths in the visible
Ionization If you provide 13.6 ev, you remove the electron from the atom and set it free This is called ionization, and the energy required to remove the electron from the ground state is called binding energy
Line Spectra Bohr s model explains a phenomenon that could not be explained otherwise an excited gas does not emit a continuous spectrum, but a line spectrum Gas at low pressure in a tube with high voltage Excited gas emits light but only certain wavelengths!!
Line Spectra Examples: emission spectrum of hydrogen and helium hydrogen helium Emission spectra look different for different gases and can be used to identify them like fingerprints! The emission spectra indicate what the energy levels are!
Balmer Series The Balmer series marks the transitions from n=2 to n=3,4,5,6, These transitions are in the optical range
Absorption Spectra Of course gases can absorb at the same wavelengths at which they emit If light that contains all wavelengths passes through a gas, we get a spectrum where certain lines are missing! Photons of these wavelengths have been used to move electrons from one level to another and are therefore no longer there! These absorption spectra can help to identify gases for example in the sun!
Absorption Spectrum of the Sun In the light that reaches us from the sun, certain wavelengths are missing - these photons have been absorbed in the sun s atmosphere hydrogen helium sun
Why are the Energy Levels Quantized? (if you really need to know )
Why Quantized? De Broglie s bold hypothesis (1927): if light is a wave and a particle why isn t every particle also a wave? This is outrageous if this was correct, then electrons should show interference and diffraction just like light! Well, did we ever check??
Double Slit for Electrons Beam of electrons is send through a two-slit interference experiment just like Young s experiment with light wave Electrons should go either through the first or the second slit shouldn t they??
Interference 7, 100, 3000, 20000, 70000 electrons
Diffraction
Trapped Waves Consider a wave confined to a limited region of space, for example a wave trapped between two walls Compare this to a string of some length, which is fixed at both ends
Discrete Frequencies Only certain standing waves are allowed, since the string can only be in a state where the two ends are fixed If an electron in an atom is trapped, and electrons are waves, than only certain modes of oscillation are allowed, and each corresponds to a different energy
Electrons in Atoms The electron in the atom is trapped in the Coulomb potential An electron is a wave confined to a limited region of space Consequently, the electron s energy is quantized U = F r = e ( e) r = e r 2
Detectors for Charged Particles
Scintillation Detectors Certain materials emit a small flash of light (a scintillation) when they are struck by a particle Effect is used since 1903, and early experiments used the human eye to detect the light flash (Geiger) tedious! Only with the invention of the photomultiplier tube did the scintillation detector become popular again Scintillator/photomultiplier devices have become one of the most widely used detectors in particle physics
Emission of Photons A charged particle traveling through scintillator leaves excited molecules behind, and the energy is released in part as light Wavelength depends on material If light is released immediately, this is fluorescence If re-emission is delayed, this is called phosphorescence
Scintillation Detectors Different types of scintillator organic, liquid, plastic inorganic crystal (sodium iodide) Wavelength can be shifted by other molecules incorporated in the scintillator (UV to blue)
Scintillation Detectors Scintillators come in different shapes, depending on application Different applications require different scintillator materials Scintillation wavelength and photomultiplier sensitivity must match
A Particle Detector Scintillating material optically coupled to a photomultiplier (either directly or with a light guide) A particle passes through the scintillator and causes a light flash Photons reach the photomultiplier and are converted into a current
Mounting a Scintillation Detector We need to wrap the scintillator with a reflective material (aluminum foil) so the light gets reflected back into the scintillator until it hits the photomultiplier with black tape so no ambient light gets in
Reflection and Refraction When light hits the boundary between two materials with different index of refraction n, there is a refracted and a reflected ray n is a material constant The ray in the denser material is bent towards the normal Light in the medium travels with speed c/n (so light is slower in water than in air) n n vacuum n air water = 1 = 1.00029 = 1.33
Angle of Refraction The reflected ray has an angle to the normal equal to the angle of incidence The refracted ray has an angle to the normal given by sinθ = n1 sinθ 2 1 n2 Refraction bends the light ray toward the normal
Total Internal Reflection There is no solution for the refraction law if the right-hand side is larger than 1 n > This happens if than the critical angle 1 n 2 sinθ = n1 sinθ 2 1 n2 and the incident angle is larger
Total Internal Reflection Above the critical angle, there is no refracted ray and all the light is reflected (total internal reflection) When mounting the scintillator, we want the light to stay in the scintillator until it hits the photomultiplier, so we want a layer of air between aluminum and scintillator Index of refraction of plastic scintillator is typically 1.58, so critical angle is about 40 degrees
Optical Coupling The photomultiplier has to be coupled to the scintillator, and in this case, we don t want total internal reflection Use optical grease with index of refraction of scintillator
Literature W.R. Leo, Techniques for Nuclear and Particle Physics Experiments, Springer (1987) D.C. Giancoli, Physics, Vol. 2, 5 th Edition, Prentice Hall (1998) D. Halliday, R. Resnick, J. Walker, Fundamentals of Physics, Vol. 2, 6 th Edition, J. Wiley (2001)