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INVASIONSIN

PARTICLE PHYSICS

Compton Lectures Autumn 2001Lecture 2

Oct. 13 2001

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LECTURE 2 LECTURE 2 From atoms to quarksFrom atoms to quarks

The atom model- Rutherford Scattering - Nucleus

outline

Previous Lecture

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Bohr’s atom and de Broglie’s electron waves

The atoms can exist onlyin discrete quantum statesseparated by finite energydifferences; when in thesequantum states the atomsdo not radiate ! set ofallowed orbits for theelectrons around thenucleous.

WHEN AN ELECTRONMAKES A TRANSITIONFROM ONE ORBIT TO THEOTHER IT EMITS LIGHT

The atoms can exist onlyin discrete quantum statesseparated by finite energydifferences; when in thesequantum states the atomsdo not radiate ! set ofallowed orbits for theelectrons around thenucleous.

WHEN AN ELECTRONWHEN AN ELECTRONMAKES A TRANSITIONMAKES A TRANSITIONFROM ONE ORBIT TO THEFROM ONE ORBIT TO THEOTHER IT EMITS LIGHTOTHER IT EMITS LIGHT

The wavelength of a particle wave is inverselyproportional to its momentum, the constant ofproportionality being Planck’s contant (h):Allowed orbits are explained as containing anintegral number of the de Broglie’s wavelengths.

The wavelength of a particle wave is inverselyproportional to its momentum, the constant ofproportionality being Planck’s contant (h):Allowed orbits are explained as containing anintegral number of the de Broglie’s wavelengths.

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Hydrogen

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The fingerprints of atoms

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Neon

Helium

Nitrogen

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The intervening gas clouds are mostly made up of hydrogen (themost abundant element in the universe) but also contain ionizedtraces of heavier atoms such as Magnesium (Mg), Aluminium (Al),Silicon (Si), Chromium (Cr), Iron (Fe), Nickel (Ni) and Zinc (Zn) -metallic atoms familiar to us here on Earth

10-10 m

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There is no real classical analog of the spin

It is quantized and comes in multiples of a basic unit of spin which is 1/2*Planck’s constant (has units of angular momentum)

Particles with odd multiples of the spin unit are called fermions

Particles with zero or even multiples of the spin unit are called bosons

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The bizarreness of spin

Take a spin 1/2 particle (fermion, e.g electron)

Rotate the spin state through 360 degrees:it arrives at a quantum state which is measurably different from

the initial state!

Rotate it another 360 degrees (total 720) and you willget it back to the beginning.

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Different components of electron spin are separated in energy bythe presence of a magnetic field

e-

sz=+1/2

e-

sz=-1/2

Spin Particle

s=1/2 e-

N

>>

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The orientation of a spinning quantum particleis quantized ; e.g. the electron can be found in either of exactly two states: spin up or spin downfor each energy level available to it in an atom.

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ABOUT FERMIONS AND BOSONS

The wavefunction of a fermion system is antisymmetricNot two fermions can coexist in identical quantum states.The wavefunction of a boson system is symmetricBosons can coexist in identical quantum states

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BOSE-EINSTEIN CONDENSATION

http://cua.mit.edu/ketterle_group/http://jilawww.colorado.edu/bec/

http://www.nobel.se/physics/laureates/2001/press.html

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Eric A. Cornell, Carl E. Wieman, Wolfgang Ketterle

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From atoms to quarks

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(ELASTIC) COLLISIONS

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A. Atoms to nucleus: Rutherford scattering

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"It was quite the most incredible event that everhappened to me in my life.It was almost as incredible as if you had fired a 15-inchshell at a piece of tissue paper and it came back and hityou."

Rutherford

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Geiger and Marsden found that 1 in 20,000 alpha particleswas turned through 90o thin gold foil -- the soft model predicted 1 in 103500.

cosφ

Data points are fromthe Geiger-Marsdenpaper (1913). The curveis the Rutherfordprediction

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200 eVElectronson Helium(Frank-Hetrz typeexperiment)

Inelastic scattering

The atomic structure seemed to be well described by the quantum mechanics of point-like electrons interacting with each otherand with a point-like nucleus via Coulomb forces

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The Franck-Hertz display for mercury shown here was formed by sweeping the accelerating voltage and recording current vs voltage on an oscilloscope in x-y mode. The measured separation of the peaks corresponds to the excitation energy of the involved mercury transition.

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B. Nuclei to nucleon (Is the nucleus really pointlike?)

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Rutherford assumed that both his alphaparticles and the nucleous were point-like. Accelerators progressed and withhigher momentum (higher resolvingpower of the beam, λ=h/p)deviations from the simple formulastarted being observed.

126 MeV electron beam ongold target (SLAC ’50s)

Curve: point-like nucleus predictionPoints: data

Curve (theory) does not predict thesituation in the data.

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Two factors: *** point-like target scattering (Rutherford, with corrections for relativistic kinematic,spin, target recoil, etc)*** spatial extension of the target’s charged density-- index of this is the ‘form factor’

Charge densityof 612C fromelectronscattering data:this nucleushas a charge radiusof 1-2 fm (10-15 m)(in heavier nucleiit goes as A1/3 fm)

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INELASTIC SCATTERING

150 MeV electrons scatteredat 90o from carbon

WHAT DO WE OBSERVE?

Elastic at 150 MeV

Three inelastic at 4.4, 7.7, 9.6 MeV(after recoil corrections)

The nucleus is excited intoa sequence of quantized states!

Charge density + inelastic peaks nuclei contain constituents distributed over a size of a few fermis

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We have then protons and neutrons in the nuclei--generically called nucleons.The “uncertainty” momentum of the nucleons ina 1 fm space is about 200 MeV.Since neutrons are neutral there has to be a new force operating at the 1 fm range in order to bind thenucleons into nuclei. It has to counterbalance the 200 MeV and therefore it has to be stronger that the electromagnetic energy which for two protons at 1 fm is about 2 MeV.

Energies that excite the atom do not excite the nucleus;the nucleus appears as a small inert core; the nuclear degrees of freedom are frozen on the scale of atomic physics.

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Nucleons to quarks Are nucleons really pointlike?