applied nuclear physics

minimum set of information to specify a nucleus

X & A

SEMF

model to predict BE of a nucleus. coefficients are determined empirically.

results of the photoelectric experiment

the energy of the ejected electrons was proportional to the frequency of the illuminating light. it remained constant regardless of intensity of the light. as the power increased, the number of ejected electrons increased. this showed that whatever was knocking the electrons out had an energy proportional to light frequency. red light will not cause the ejection of electrons, no matter what the intensity. a weak violet light will eject only a few electrons, but their maximum kinetic energies are greater than those for intense light of longer wavelengths. the fact that the ejection energy was independent of the total energy of illumination showed that the interaction must be like that of a particle which gave all of its energy to the electron (the photon).

intensity of light (I)

# photons/second

power (P) of light

(E) * (I) [J/s]

neutron separation energy

(binding E of X) - (binding E of X: A-1, N-1)

proton separation energy

(binding E of X) - (binding E of X: A-1, Z-1)

energy (E) of an ejected electron

(energy of photon) - (electron binding energy/work function)

average lifetime of a nuclide

1 / decay constant

properties of the nuclear (strong) force

1. strong attractive component that decreases with distance 2. interaction between nucleons is strongly spin dependant. 3. tensor potential 4. charge symmetric- the n-n & p-p interactions are almost identical, accounting for the p-p coulomb interactions. 5. charge independent- no difference between p-p, n-p, or n-p interactions. 6. repulsive at very short range 7. velocity dependent

average beta energy

1/3 (Q)

surface term

a correction to the volume term. binding energy is inversely proportional to the surface area. [nucleons on the surface have fewer neighbors to interact with vs nucleons in the middle. they don't get squished- nucleons/unit volume is constant]

alpha particle

a helium-4 nucleus. very large. very short range, less than 0.1 mm inside the body. extremely stable due to doubly magic nucleus.

quantum tunneling

a particle tunnels through a barrier that it classically could not surmount. the wavefunction associated with a free particle must be continuous at the barrier and will show an exponential decay inside the barrier. The wavefunction must also be continuous on the far side of the barrier, so there is a finite probability that the particle will tunnel through the barrier.

color/color force

a property of quarks labeled color is an essential part of the quark model. the force between quarks is called the color force. when 2 quarks are close together, they exchange gluons, creating a color force field which holds the quarks together. color is conserved. introduced to label a property of the quarks which allowed apparently identical quarks to reside in the same particle, for example, two "up" quarks in the proton. To allow three particles to coexist and satisfy the Pauli exclusion principle, a property with three values was needed

baryon

a type of hadron: 3 quarks together. examples: proton (uud) & neutron (udd)

meson

a type of hadron: a quark & an anti quark. example: pion

black body

an object that absorbs all radiation falling on it, at all wavelengths. when a black body is at a uniform temperature, its emission has a characteristic frequency distribution that depends on the temperature.

double slit experiment

beam of electrons fired at barrier with 2 slits. a pattern is created on an optical screen behind the barrier. one or the other slit open yields patterns P1 and P2. both slits open yields pattern P12.

3 modes of beta decay

beta minus, positron, electron capture

coulomb term

binding energy of the nucleus is reduced with increasing coulomb forces creating decreased stability. [more protons = more repulsions = less tightly bound = lower BE]

weak force

changes one flavor of quark into another. force exchange particles are the bosons: W+, W- & Z (huge mass). the interaction involved in many decays of nuclear particles which require a change of a quark from one flavor to another. responsible for the decay of heavier quarks & leptons into the lighter ones; this explains why all stable matter in the universe appears to be made up of the lightest quarks & neutrinos.

hadron

composite particle of quarks. integral electrical charge, no color charge [color neutral]

standard model of the universe

comprehensive theory of the universe. all predicted particles have been found, but does not explain every interaction (gravity). all known matter is composed of quarks & leptons. all known particles have an anti-particle. use of force exchange particles.

exchange force model

conceptual model for nuclear force. nucleons interact with each other through the exchange of virtual particles which carry the nuclear force. nucleons are held together by a short range interaction [~ the range of the radius of a nucleon] model underlying the liquid drop/collective model.

potential well model

conceptual model for the nuclear force. visualization of the nuclear force underlying the nuclear shell model. an imaginary external force holds all the nuclei together. used to model the deuteron. becomes complicated quickly, not useful for explaining the basic structure of the nucleus.

quantum mechanics

description of the motion and interaction of subatomic particles.

mass defect

difference between predicted and measured atomic/nuclear masses.

photoelectric effect

ejection of electrons from the surface of a metal in response to incident light.

4 fundamental forces

electromagnetic, strong, weak, gravity

atomic spectroscopy

electrons exist in discrete energy levels within an atom. electrons may move between orbitals, but in doing so they must absorb or emit energy equal to the energy difference between their atom's specific quantized orbital energy levels: h*f = (E of original level) - (E of new level). energy absorbed to move an electron to a higher energy level or the energy emitted as the electron moves to a lower energy level is absorbed or emitted in the form of photons because each element will absorb/emit photons in a unique pattern.

de broglie hypothesis

electrons have both wave & particle properties.

quark

elementary particle, fundamental constituent of matter. 6 flavors: up, down, top, bottom, charm, strange. each carries a fractional electrical charge & a color charge. never found alone.

lepton

elementary particle, no internal structure. 3 charged & 3 neutral. no color. 6 flavors: electron and electron neutrino, the muon and muon neutrino, tau and the tau neutrino. always found in their family pairs.

beta minus decay

emission of a negative electron/antineutrino pair. neutron -> proton.

positron decay

emission of a positron/neutrino pair. proton --> neutron.

separation energy

energy required to remove a particle from the nucleus. analogous to ionization energy for electrons.

gluon

exchange particles for the color force between quarks [analogous to photons & EM] the fundamental exchange particle underlying the strong interaction between protons and neutrons in a nucleus. carry a color & anti-color.

neutrino

fermion that only interacts through the weak force & gravity. very small mass.

gravity

force between 2 masses; weakest of the 4 fundamental forces. not explained by the standard model, but it can be neglected as it is not very relevant at the subnuclear level.

chart of the nuclides

graph in which one axis represents the number of neutrons and the other represents the number of protons in an atomic nucleus. each point plotted on the graph represents the nuclide of a real or hypothetical chemical element.

energy (E) of a photon

h * f

strong nuclear force

holds the nucleus together, against the repulsion of the protons. strongest force out of the 4. very short range. the force exchange particle is the gluon [the gluon acts between quarks, which are what makes up the nucleons, using the color force exchange particles]

electroweak theory

in the standard model, the weak & EM forces have been combined.

decay constant

ln (2) / half life

symmetry term

most stable nuclei are symmetrical. reduction in binding energy/stability for non-symmetrical nuclei. [less important for heavy nuclei]

pauli exclusion principle

no two particles in a system can have identical quantum numbers.

parity term

nuclei with unpaired nucleons are less stable.

photonuclear

nucleus captures a photon, E > Q. much smaller cross sections & occur at high energy.

electron capture

nucleus captures an atomic electron. neutrino emitted. competes with positron emission for proton rich nuclei.

neutron number (N)

number of neutrons (A) - (Z)

mass number (A)

number of nucleons

atomic number (Z)

number of protons

fermion

particles which have half-integer spin and therefore are constrained by the Pauli exclusion principle. include electrons, protons, neutrons.

boson

particles which have integer spin and which therefore are not constrained by the Pauli exclusion principle like the half-integer spin fermions.

compton scattering

photon collides with an atomic electron. photon scatters with decreased wavelength & ejects the electron. energy & momentum are conserved.

pair production

photon converts into a positron & electron pair. it must have at least 2X (mass of an electron) or the reaction will have -Q value. E > 1.022 MeV.

wave-particle duality

possession by physical entities (light, matter, etc) of both wave & particle characteristics.

born probability wave

probability of finding a particle within a space at a given point. given by the probability density, equal to the square of the probability amplitude function.

annihilation

process occurs from a particle-antiparticle interaction. complete conversion to energy.

antiparticle

same mass and opposite charge as the corresponding particle.

conceptual models of the nucleus

shell model, liquid drop model, nilsson model, fermi gas model for excited nuclei.

geiger-nuttall rule

short-lived isotopes emit more energetic alpha particles than long-lived ones. log (half-life) is inversely proportional to Q.

alpha decay

spontaneous emission of a helium-4 nucleus. no electrons emitted with it. most common for higher A nuclei. KE released is carried by both daughter & alpha particle.

binding energy

the (E) required to completely break the nucleus down into individual nucleons.

electronvolt (eV)

the energy given to an electron by accelerating it through 1 volt of electric potential difference.

planck's hypothesis

the energy of radiation with a frequency (f) exists only as multiples of a fixed quanta of energy, h*f

force exchange particle

the force between particles. can only be absorbed or produced by particles that can be affected by that force. ex: neutrons cannot exchange electromagnetic force particles.

electromagnetic force

the forces between charges & magnetic force. holds atoms and molecules together. the forces of electric attraction and repulsion of electric charges are dominant over the other three fundamental forces as determiners of atomic and molecular structure. force exchange particle = photon. infinite range.

heisenberg uncertainty principle

the position and momentum of a particle cannot be simultaneously measured with arbitrarily high precision. there is a minimum for the product of the uncertainties of these two measurements.

planck's constant (h)

the quantum of action: 6.62e-34 J⋅s.

potential well

the region surrounding a local minimum of potential energy.

(I) total angular momentum

total angular momentum of a nucleus; also called nuclear spin. nuclei often act as if they are a single entity with intrinsic angular momentum I. the nuclear spins for individual protons and neutrons parallels the treatment of electron spin, with spin 1/2. a nucleus of odd mass number A will have a half-integer spin and a nucleus of even A will have integer spin. angular momenta of nucleons tend to form pairs. all nuclei with even Z and even N have nuclear spin I=0+

volume term

total binding energy of the nucleus is proportional to the number of nucleons in the nucleus. [nucleons can only interact via the strong nuclear force with adjacent nucleons, so the number of pairs interacting is proportional to A]

(E) of an alpha particle

~ 98% (Q)