The Art of Estimation Physics

also known as Ph 2239

II. Forces, etc.

Patrick Diamond, George M. Fuller, Tom Murphy Department of Physics, University of California, San Diego

Handy Facts: Solar System

radius of earth’s orbit around sun Handy Facts: the Universe

Electromagnetism (see handout on comparison of S.I. & c.g.s. units/dimensions)

Thompson Cross Section: (photon energies >> electron binding) (energy-independent photon-electron scattering cross section)

Klein-Nishina (relativistic electron targets; very high energy photons)

Rayleigh Scattering: (when photon energies lower than atomic electron binding) fine structure constant

SI

cgs

Eddington Luminosity Photon scattering-induced momentum transfer rate to electrons/protons must be less than gravitational force on proton

Electrons tied to protons via Coulomb force proton At radius r where interior mass is M( r ) and photon energy luminosity -1 (e.g., in ergs s ) is Lγ( r ) the forces are equal when Sir Arthur Eddington electron www.sil.si.edu

Flux of photon Gravitational force on proton with mass mp momentum The Weak Interaction changes neutrons to protons and vice versa strength of the Weak Interaction:

typically some 20 orders of magnitude weaker than electricity (e.g., Thompson cross section)

Gravitation

Newton’s constant The Strong Interaction

Low Momentum Transfer (i.e., where quark/gluon degrees of freedom can be ignored) The nucleon-nucleon potential is strong, short ranged (~ 1 fm) – if they touch, they interact! --- “sizes” = geometric cross sectional area

--- but for charged ions must convolve with Coulomb barrier penetration probability

Examples neutron capture Examples

lab proton energy 460 keV

lab proton energy 100 keV

The Strong Interaction

High Momentum Transfer (i.e., where degrees of freedom are quarks/gluons) the interaction between quarks and gluons is weak, Coulomb-like

------asymptotic freedom implies zero interaction at very high energy/short distance – a “gas” of free quarks & gluons

Quark-gluon plasma in the very early universe, the deep interior of neutron stars, or the central (low rapidity) regime in relativistic heavy ion collisions Mean Free Path/Time

diffusion constant

Random Walk

time to random walk a distance R