Fundamental Forces

Force Relative Range Carrier Observed? Strength

Gravity 10-39 Infinite Graviton No

Weak 10-6 Nuclear W+ W- Z Yes (1983)

Electromagnetic 10-2 Infinite Photon Yes (1923)

Strong 1 Nuclear Gluon Yes (1978) (Indirect) Units and Dimensions

Size: the order of magnitude is 1fm = 10-15m (a femtometer or fermi) 1/3 Radius (assuming nucleus = sphere): R = R0.A with R0 = 1.2 fm

Nuclear Density: 1017 kg/m3  100 million tons per cm3 !!! density found in the core of a star Nuclear is uncompressible (properties of the strong force)

Energy: units: 1eV = 1.602 x 10-19 J  energy gained by a single unit of electronic charge when accelerated through a potential of one volt

Units and Dimensions

Binding energy: mass of the constituents – mass of the product

Atom Nucleus

Force Coulomb Strong Binding Energy The hydrogen 2H: 2.2 x 106 eV : 13.6 eV  2.2 MeV

Atoms and Nuclei emit photons. What does the binding energy imply about the photons? How might you distinguish Alpha, Beta and Gamma radiation experimentally?

Example of a particle physics experiment (BNL E766) 27 GeV/c interactions in liquid hydrogen

proton 27 GeV/c Conservation laws

• Conservation of Energy

• Conservation of linear momentum

• Conservation of angular momentum

• Conservation of electric charge

•Conservation of baryon number (proton is a stable particle)

• Conservation of A  e.g. total number of is conserved, but Z and N can change Example of a particle physics experiment (BNL E766) 27 GeV/c proton interactions in liquid hydrogen

proton 27 GeV/c Radioactivity ?

Emission of energy stored in the material by the mean of “mysterious” rays

~1900: The structure of the atom is not yet known... But Chemistry is ! (Mendeleiv 1834 – 1907)

The radiation emitted by Radium is identified to be the element Helium

1911: Discovery of the by

The first experiment with a beam of particles: The α-particles are most of the time not deflected, but sometimes they are scattered, even in the backward hemisphere.  the foil is almost “transparent” to the α’s But when interaction occurs, it is on a heavy partner in the foil (the nucleus)  full analysis: size of the nucleus, mass, etc…

Niels Bohr: The model of the atom (1913)

- in discrete orbits

+ Positively charged nucleus

α-radiation is positively charged and too energetic to be emitted by the cloud  α’s are emitted from the atomic nucleus. NUCLEAR PHYSICS Rutherford (1919): transmutation of one element into another by α-radiation α + N  O + p Helium Nitrogen Oxygen Hydrogen  The nucleus has to have exchangeable constituents Elementary Constituents of the Nucleus

All the nuclei can be made with: p proton positively charge (+q) n neutron neutral (, 1932)

Z number of in the nucleus N number of in the nucleus A atomic number = Z + N

The are neutral: Charge of the nucleus: + Z.q Electron cloud is made of Z electrons of charge (–q) The electrons determine the chemical behavior  Z defines the Element

Two nuclei with a same Z but different N (or A) are (of the same element) nucleons A Z X N Notations protons neutrons 1 Ex: Hydrogen 1 H 0 Isotopes of the same element 2 Deuterium 1 H 1

Other examples: 12 12 Carbon 6 C 6 C Simplified: 235 235 Uranium 92 U 143 U

In practice, the Z number is redundant with the element symbol & the N number is obsolete The chart of Nuclei

Stable Isotopes ~300 Unstable >2000+ Law

The activity of a certain sample (e.g. source) depends on the number N of radioactive nuclei and on the probability λ for each nucleus to decay:

A = λ . N

[1/s] [1/s] Evolution with time: dN = -A.dt dN: number of nuclei that decayed during dt

 dN = -λ.N.dt, which gives: dN/dt = -λ.N

Solving the differential equation: -λ.t N(t) = N0.e

N(t=0) Half-life

Similarly, we find that the activity of a source change with time: A(t) = A .e-λ.t 0 From λ = decay constant, one can define τ = 1/λ, the mean lifetime

It is usual to define t1/2, the half-life, the time after which half of the initial nuclei have decayed:

t1/2 = ln 2 / λ = τ ln 2

The half-life is characteristic to the decay of a given nucleus. This number (when known) is usually tabulated.

Question • The atom and the nucleus are both composed of many components. Their structures and states can be studied through spectroscopy.

• Which do you think is more complicated. – Nuclear spectroscopy or – Atomic Spectroscopy?

• Why?

The Nuclear (Strong) Force  Short Range, only a few fm is uncompressible ; repulsive at very short range (< 1 fm) Attractive over a range of a few fm a given only interacts with its next neighbors in the nucleus

 Negligible at long distances

 Same force for protons and neutrons A (simplified) model of the nucleus

U Coulomb Barrier (for the charged particles)

α Unbound levels Tunnel effect (α-decay) (U>0)

Distance from the center of the nucleus

Bound levels Square well potential (approx.) (U<0)

neutrons protons Filled levels – Quantified energy, Pauli principle (Quantum Mechanics, Shell Model) If all nucleons are in U<0, no nucleon can tunnel to the outside  Stable nucleus If unbound levels are filled (U>0), tunneling is possible through the Coulomb barrier  Radioactive nucleus

This picture shows tracks made by alpha particles in a cloud chamber. What physics conclusions can you reach based on this picture? Two isotopes. Alpha particles from a particular decay are mono-energetic α-decay α-particle = 4He: cluster in the nucleus – α: very tightly bound system U 2

r

A A-4 4 Z X N  Z-2 YN -2 + 2 He 2 + Q Nuclei that emit higher energy alphas, have shorter half lives? True or False? Nuclei that emit higher energy alphas, have shorter half lives? True or False?

U

r U

r Nuclei that emit higher energy alphas, have shorter half lives? True or False (other way around)

U

Shorter half life (less tunneling)

Higher Kinetic Energy

r β-decay

Weak interaction can transform a proton into a neutron or a neutron into a proton (It’s actually happening at the level)

β- decay: n  p + e- + anti neutrino e-: electron β+ decay: p  n + e+ + neutrino e+: positron

β- decay

Proton u d u e-

W-

νe Neutron u d d of 3He Sample

Electron energy spectrum of emitted electrons e- e- ν

3 + 3He+ He e- ν

3He+ ν e- Electron energy spectrum

3He+ β- decay

Elementary process: n  p + e- + ν

A A - Decay of the nucleus: Z X N  Z+1Y N -1 + e + ν

β+ decay U

Elementary process: p  n + e+ + ν (only happening inside the nucleus) A A + Decay of the nucleus: Z X N  Z-1 YN+1 + e + ν neutrons protons

Alternative process: (from atomic orbit) p + e-  n + ν

A A - Z X N + e  Z-1 YN+1 + ν

of 238U # of neutrons protons+

# of protons Question:

For a given nuclear transition, which type(s) of emitted radiation are monoenergetic?

1: beta only 2: alpha,gamma 3: gamma,beta 4: alpha only Question:

For a given nuclear transition, which type(s) of emitted radiation are monoenergetic?

1: beta only 2: alpha,gamma 3: gamma,beta 4: alpha only

Beta shares energy with a neutrino that you can’t measure (in ph326) END