Dictionary of Material Science and High Energy Physics Part 9 pptx

mode degeneracy Refers to the possibilitythat modes in a resonator or cavity can havethe same energy, i.e., resonant frequency... The frequency distance ν f = c/2L between adjacent long

It is also of great technical importance, since

the flatness of surfaces relative to some reference

surface can be tested by observing the structure

of the interference fringes They give a very

sensitive contour diagram with a resolution of

approximately λ/2.

The Michelson interferometer.

microcanonical distribution For an isolated

system in equilibrium, all of the states within a

small energy band are equally probable and all

of the other states have zero probability An

equilibrium distribution of this type is known as

a microcanonical distribution.

micro-local analysis Let A be an operator in

Hilbert space which represents a physical

var-iable In coordinate representation, its matrix

element is < x|A|x >, where xand x

rep-resent the coordinates of a particle or a

parti-cle assembly In the latter case, x stands for a

Fourier transformation for a set of coordinates

{x1 , x2, , x n } In the micro-local analysis we

which resembles a classical variable The

micro-local analysis is appropriate for semi-classical

analysis

micromaser A maser based on a microwave

cavity with an extremely high Q-factor, i.e.,

pho-ton lifetime, and an extremely small flux of

atoms The parameters are chosen such that

typ-ically only one atom at a time interacts with the

radiation field

Atoms are excited to a Rydberg state beforeentering the cavity Transition frequencies be-tween two of these Rydberg states are in the mi-crowave region, and due to the long lifetime ofRydberg states, the interaction of a single atomwith a single mode of the radiation field can bestudied In order to determine the interactiontime of atoms and photons precisely, only atomswith a certain velocity are excited into the Ryd-berg states This is facilitated using a Fizeau ve-locity selection or by making use of the Dopplereffect in the excitation process In order to in-crease the coupling between cavity modes andatoms, the storage time of the microwave pho-tons within the cavity must be maximized Thecavities are therefore made from niobium, which

is kept at cryogenic temperatures and becomessuperconducting This also reduces the back-ground of thermal photons

Atom–photon interactions are the basis forthe Jaynes–Cummings model Experimentally,many predictions of the Jaynes–Cummings

model could be demonstrated with the maser Examples are revival, photon trapping

micro-states, non-classical light, the maser threshold,power broadening, the Mollow triplet, etc Thefirst entanglement between atoms was also gen-

erated using a micromaser setup.

microstate For a given set of constraints(parameters of the thermodynamic system thatcan be held fixed or varied by some observer),the thermodynamic system still has access to a

very large number of microscopic states or crostates For example, for a gas of constant

mi-volume, the starting conditions (position and locity) of the individual molecules could havemany different values

ve-microsystem When evaluating state tions for large systems it is usually advantageous

func-to divide the system conceptually infunc-to

indepdent microsystems, each with its own set of

en-ergy states For example, when considering themagnetic energy of a paramagnetic salt, the in-dividual ions are considered as an independent

microsystem in order to obtain the state function

of the large system

microturbulence Fluctuations with

wave-lengths much smaller than plasma macroscopic

dimensions

Miller indices A plane in direct lattice is

specified by three numbers, known as Miller

indices, in the following way: Choose a set

of three convenient axes to describe the crystal

with unit lengths a1, a2, and a3 along them Let

the plane intercept these axes at x1a1, x2a2, and

x3a3 The Miller indices of the plane are the

three integers h, k, and l which have no

com-mon factor and are inversely proportional to the

intercepts of the plane on the axes, namely

h : k : l = 1/x1 : 1/x2 : 1/x3 , Miller indices are enclosed by parentheses (hkl)

and negative intercepts are denoted by a

mi-nus above the integer such as (¯13¯1) Equivalent

planes which are obtained by applying

symme-try operations to the crystal are denoted by{hkl}.

The direction of a vector r = n1 a1 + n2 a2 +

n3a3 in direct lattice is denoted by [n1 n2n3] A

set of equivalent (by symmetry) directions are

denoted by < n1n2n3 >.

The vector G = hb1 +kb2 +lb3in reciprocal

space is perpendicular to the plane (hkl) in a

direct lattice The spacing of the set of planes

(hkl) is inversely proportional to 1/ |G| See

Laue’s condition method

In cubic crystals, the crystal axes are three

cube edges (forming a right-handed system)

with a cube edge as a unit length

minimal coupling A method of creating an

interaction (a coupling) between matter

parti-cles and gauge fields which involves replacing

the ordinary derivative in the Lagrange density

via the covariant derivative For example, a

massless Dirac particle has a Lagrange density

of ψ (i
γ µ ∂ µ )ψ If the ordinary derivative is

replaced by the covariant derivative for

electro-magnetism (i.e., ∂ µ −→ ∂ µ + ieA µ , where e is

the magnitude of the electron’s charge and A µis

the electromagnetic four-vector potential or the

gauge field), this introduces a new term into the

Lagrange density (ψ (i.e.,A µ )ψ) which couples

the Dirac matter particle with the gauge field

minimum uncertainty The smallest

possi-ble uncertainty in the measurement of two

con-jugate variables in quantum mechanics It isgiven by Heisenberg’s uncertainty relation.Generally one finds

AB ≥ ¯h/2 ,

where A and B are two conjugate observables,

i.e., observables which do not commute:[A, B]

= A B − A B = 0.

Mirnov oscillations Magnetic perturbationsdetected around the edge of toroidal magneticconfinement devices such as tokamaks

mirror matter A hypothetical form of ter where every known particle (electron, pro-ton, photon, etc.) has a mirror partner (mirror-electron, mirror-proton, mirror-photon, etc.),which has the same mass, but which interacts viaforces which are mirrors of the standard modelinteractions (e.g., ordinary matter will interactvia the electromagnetic interaction, while mirrormatter interacts via mirror-electromagnetism).Only the gravitational force operates the same

mat-on both matter and mirror-matter As a result,matter interacts very weakly with mirror-matter

mirror ratio Ratio of maximum to minimummagnetic field strength along a field line in amagnetically confined plasma

MIT bag model A phenomenological modelfor hadrons, where the quarks which constitutethe hadron are assumed to be confined within acavity or bag Usually, this region in which thequarks are free to move is spherical in shape.The bag model is motivated by an analogy to theMeissner effect in superconductivity: the QCDvacuum outside of the bag is said to expel thecolor electric field in a manner analogous to theway superconductors expel magnetic fields Be-cause of this hypothesized expulsion of the colorelectric field, the quarks remain confined withinthe bag

mixed state Or statistical states States inwhich pure states are superposed with a prob-ability distribution The simplest pure state ordefinite quantum states can be written as a su-perposition

|(θ) =
c n (θ ) |ψ n .

The wave function for a mixed state can then

be written as the superposition of different pure

states

|mix =



p(θ ) |(θ) dθ ,

where p(θ ) is the probability distribution For

mixed states, the average values O for an

ob-servable ˆOare given by

A completely mixed state is represented in the

density matrix picture by off-diagonal elements

with the value zero

mixing angle, Weinberg In the SU (2)×

U (1) standard model, an angle, denoted by θ W,

which parameterizes the particular admixtures

of the third component of the original SU (2)

gauge boson, W µ3, and the weak hypercharge

gauge boson, B µ, which make up the

electro-magnetic field (A µ = cos θ W B µ + sin θ W W µ3)

and the field of the Z-boson (Zµ = − sin θ W

Bµ + cos θ W W µ3)

mixing length In a turbulent flow, the

dis-tance traveled by a fluid parcel before losing its

momentum Generally used as a simple analysis

in turbulence

mixing length estimate Estimate for

non-linear saturation of micro-instabilities in which

the density perturbation becomes comparable to

the background density gradient times the

wave-length

mobility Drift mobility is |qτ/m|, where q is

the electric charge on the particle, m is its mass

(or effective mass), and τ is the average time

(re-laxation time) between collisions An isotropic

medium is assumed It is also the ratio of the

magnitude of the drift velocity to the magnitude

of the electric field (for weak fields)

mobility edge In disordered systems,

elec-tron states can be localized or free A

mobil-ity edge Ec is an energy value below which a

state is localized and above which a state is free

(conducting) If the Fermi level lies below E c,

conduction takes place by hopping and the

con-ductivity is low, and if it lies above E c, we haveordinary conduction A manipulation of the lo-cation of the Fermi level, if possible by externalmeans, can bring about a metal-insulator transi-tion

mode An eigenstate of the electromagnetic

field in a resonator or wave guide The mode

is characterized by a wavelength and the tial distribution of the light In a resonator, the

spa-transverse modes are given by the condition that

an integer number of half-waves will fit in theresonator (standing wave) or an integer num-ber of wavelengths will fit in the resonator (ring

resonator) The lowest order spatial mode for

a resonator is a Gaussian beam, in which thetransverse intensity distribution falls off like aGaussian function Parameters characterizing a

Gaussian beam are the smallest beam waist ω0

and the radius of curvature of the wave front In

a wave guide, the lowest order spatial modes are

Hermite functions

mode competition In a laser, the mechanismwhich determines the longitudinal mode char-acteristics of a laser When many longitudinalmodes are within the gain profile of the lasermodes, modes which are populated by spon-taneous emission first start to oscillate, receivemore of the gain by means of stimulated emis-sion, and grow stronger at the expense of othermodes which either never start to oscillate orstop oscillating In pulsed lasers, this behaviorcan be used to produce single longitudinal modeoutput This technique is referred to as injec-tion seeding One single longitudinal mode isprepopulated by a weak continuous wave seed-ing laser Upon Q-switching the cavity, this onemode will immediately start to oscillate whileothers would have to build up from the vacuum

fluctuations Due to this mode competition, the

single mode will be the only one to oscillate.One requirement for this technique to work isthat the seed laser is resonant with the pulsedslave laser cavity Several schemes are reported

in the literature to achieve this resonance

mode degeneracy Refers to the possibilitythat modes in a resonator or cavity can havethe same energy, i.e., resonant frequency This

includes the degeneracy in polarization or the

transverse distribution of the intensity In a

spherical resonator, the frequencies of the modes

can be found via the condition that the phase of

the waves must change by an integer multiple of

πfor one round trip This results in the

follow-ing frequencies for the modes in standfollow-ing wave

cavities with spherical mirrors with radius R1

terizing the longitudinal modes with a separation

of c/2d, and m and l characterize the Gaussian–

Hermite transverse eigenmodes of the cavity

The factorcos−1±√g1 g2

π is called the Guoy phaseand takes on the following values for the most

important cavity configurations:

One sees that in the case of the confocal etalon,

modes characterized by the integers (n,m,l) are

partly degenerate: modes (n, m, l) are

degener-ate for the same k = m + l Furthermore, those

modes for which m + l is an even integer are

degenerate with the modes (n+m+l,0,0), while

modes (n, m, l), for which l+ m = odd

in-teger, fall exactly halfway between the modes

with (n + m+ l− 1) and (n + m+ l)

caus-ing a mode spaccaus-ing of c/4d Due to this mode

degeneracy an exact mode matching of laser

ra-diation to a confocal Fabry–Perot etalon is not

necessary This has the disadvantage, however,

that the free spectral range is reduced to c/4d.

mode locking A technique to produce

light pulses in the picosecond and

femtosec-ond regime Phase locking of different

longi-tudinal modes can be regarded as the time

ex-pansion of a Fourier series, which, in the time

domain, results in light pulses The frequency

distance ν f = c/2L between adjacent

longi-tudinal modes phase-locked together, where c

is the speed of light and L is the length of the

resonator, leads to a pulse train with separation

2L/c and where individual pulses have a width

of

1

Mν f , where M is the number of modes which are

phase-locked

Experimentally, this phase locking can beachieved by placing an acousto-optic or electro-optic modulator inside the cavity, which is mod-

ulated at the free spectral range c/2L of the

cavity Other techniques include placing a urable absorber inside the cavity The collidingpulse modulation or CPM is based on the lattermethod

sat-mode mismatch The mismatch in spatialprofile or frequency of a light beam with respect

to the eigenmodes of a resonator or wave guide.Mode matching of laser beams is important inmany applications, for instance laser resonators,laser design, build-up cavity for the enhance-ment of non-linear processes, and coupling tooptical fibers

mode pulling The frequency shift of a lasermode due to a mismatch between the maximum

of the gain profile and the longitudinal cavitymodes The sharper the resonator modes, the

less severe the mode pulling, and the sharper the

gain profile, the stronger the frequency pulling

Mode pulling also occurs for pulsed injection

seeded laser systems in the nanosecond regime

If the slave cavity of the pulsed laser is not fectly in resonance with the seed laser, a fre-quency chirp on the pulsed output will be mea-sured that will pull the laser frequency towardsthe output frequency of the slave cavity

per-mode rational surface Magnetic surface in atoroidal magnetic confinement device on whichmagnetic field lines close on themselves withthe same topology as a helical mode of plasmaoscillation

modulation The controlled change of a rameter of the electromagnetic field for the pur-pose of communication One distinguishes fre-

pa-quency (FM) and amplitude (AM) modulation.

In the former, the frequency of a signal is

mod-ulated around the carrier frequency ν0 In the

latter case, the frequency stays constant and the

amplitude of the signal is modulated

molasses The arrangement of six laser beams

in a three-dimensional arrangement similar to

the setup of a magneto-optical trap However, a

magnetic field is not present The arrangement

of the laser beams leads to a velocity-dependent

force on the atoms and, consequently, to

diffu-sive motion of the atoms

mole The amount of substance containing

the number of ions, atoms, or molecules, etc

to equal the number of atoms in 12 grams of

Carbon 12; SI unit is mol

molecular beam Generally consists of a

di-rected beam of non-ionized atoms or molecules

emerging from a source whose momentum

de-pends solely upon their thermal energy For a

beam of ideal gas atoms at thermal equilibrium,

the flux of particles is given by 14n

nis the number density of gas atoms and

is the mean velocity of the beam assuming a

Maxwell–Boltzmann distribution of velocities

molecular crystals Crystals made from

at-oms such as Ar, Kr, Ne, and Xe or molecules

such as H2, and N2, where the atoms or

molecules are weakly affected by the formation

of the crystal The binding forces are weak

molecular dynamics Field which studies

the energy flow in molecules after excitation

with short light pulses According to the Born–

Oppenheimer approximation which separates

the different motions, i.e., rotations, vibrational

and electronic, no perturbations with dark states

should be allowed Dark states are defined as

background states which are not optically active,

formed by rovibrational states in the same or

dif-ferent electronic states In real molecules, the

interaction between bright and dark states does

occur This leads to a flow of energy deposited

in molecules into these background states The

possible mechanisms are intramolecular

vibra-tional relaxation (IVR), intersystem crossing

(ISC), or internal conversion (IC) One can

dis-tinguish three cases: the small, large, and

in-termediate molecule For small molecules, the

density of states is small and no perturbationsare observed; the fluorescence yield, i.e., the ra-tio of radiative decays to total decays, is one

In the case of the large molecule, which is alsocalled the statistical case, the density of states

is so large that the mean separation of states ε

is larger than their decay rates  d, such that thestates form a quasi-continuum This leads, af-ter excitation of the Born–Oppenheimer states,

to an irreversible energy flow (dissipation) intothe background states The non-radiative decayleads to a reduction in the fluorescence yield and

to exponential decays on a much smaller scale than observed for the small molecule case.Quantum mechanically, this decay can be ex-plained by the dephasing of the different states

time-A recurrence cannot be observed, due to the versible energy flow into the background states.Finally, in the intermediate case, coupling el-ements are of the same order of magnitude as theenergy separations The recurrence can be ob-served as deviations from an exponential decay

irre-In the case of coherent excitations it becomespossible to observe phenomena such as quantumbeats and biexponential decays The intermedi-ate case is particularly interesting since it can beinvestigated using quantum beat spectroscopy,which is a quasi Doppler-free technique withvery high relative frequency resolution

Typical tools for the investigation of lar dynamics are high resolution, quantum beat

molecu-and pump-probe femtosecond spectroscopes

molecular dynamics method In the ular dynamics computational method, the dis-

molec-tribution of molecular configurations is lated directly The molecules are given someinitial configuration and each has some defi-nite speed and trajectory Using an assumedforce law (based on the assumed intermolecularpotentials), the subsequent trajectory of everymolecule is then calculated A record of themolecular trajectories is kept, and by averagingthese over time, it is possible to calculate theequation of state Using this method it is alsopossible to calculate non-equilibrium propertiessuch as viscosity or thermal conductivity

calcu-molecular field P Weiss proposed the idea of

a molecular field (or a mean field) which acts on

the magnetic moments of a ferromagnet in

ad-dition to the external field B a The mean field is

assumed to be proportional to the magnetization

M The effective field is thus B a + λM, where

λ is a constant This hypothesis explains the

spontaneous magnetization (when the applied

field is zero) at low temperature It also gives

the Curie–Weiss law, χ = C/(T − T c ), where

χis the paramagnetic susceptibility well above

the Curie temperature Tc , C is a constant, and

T is the temperature Heisenberg replaced the

mean field by the exchange interaction to align

the spins

molecular heat capacity The heat capacity

of a molecule that arises from all of the

individ-ual contributions to its internal energy For a free

diatomic molecule, this energy typically

com-prises contributions from the translational,

rota-tional, and vibrational energies of the molecule

For example, CO at room temperature has a

molecular heat capacity of 5/2 kB, which arises

from a translational energy contribution of 3/2

kB and an unquenched rotational energy

con-tribution of k B At room temperature, the

vi-brational contribution to the molecular heat

ca-pacity is quenched and only becomes significant

for temperatures above 1000 K, whereupon the

molecular heat capacity approaches 7/2 k B

Moller scattering The process in which two

initial electrons scatter from one another into

a final state of two electrons This process is

written as e−+ e−−→ e−+ e−.

Mollow spectrum The three-peaked

emis-sion spectrum of a coherently driven two-level

atom in the strong field limit The occurrence

of the Mollow spectrum can be explained in the

dressed state picture The spectrum consists of

three peaks, formed by four contributions

As-suming resonant excitation of the laser, the

flu-orescence intensity as a function of frequency ω

scatter-tion (  ), but negligible for a strong

excita-tion The other three terms are due to incoherentscattering Two smaller peaks surround a largercentral peak located at the atomic resonance fre-quency The frequency separation between thecentral and the outer peaks is given by the Rabifrequency For resonant excitation, the area ra-tios of the lines is given by 1:2:1, whereas thepeak ratio is given by 1:3:1 For non-resonantexcitation one still finds a three-peaked spec-trum around the laser frequency However, theratio of the main peak to the sideband becomessmaller

Illustration of the Mollow triplet in the resonance orescence of a two-level atom with the help of the dressed atom picture for excitation at the frequency

flu-ω 0.

moment equations Fluid equations derived

by multiplying a plasma kinetic equation bypowers of particle velocity and integrating overall velocities

momentum equation See Navier–Stokes

equations

momentum integral In a boundary layer, the

integral defining a length scale based upon the

loss of momentum due to the boundary layer

The momentum thickness is given by

momentum representation Choose

eigen-functions of momentum as an orthonormal set

of vectors in Hilbert space to represent quantum

states and quantum variables Such

represen-tation is called the momentum represenrepresen-tation.

The momentum eigenfunctions are simply plane

waves

monochromatic radiation Radiation that

contains only the light of one frequency It can

be described by the function E(t) = E0 e ıωt,

where ω is the frequency of the light and E0is

the field amplitude

monoclinic lattice A Bravais lattice

gener-ated by the primitive translations a1, a2, and a3

(whose lengths are a, b, and c respectively) a3

is perpendicular to a1and a2, but a1is not

per-pendicular to a2and a = b = c.

monte-carlo method This computational

method generates a sequence of configurations

of the thermodynamic system (typically a set

of atoms or molecules arranged in space) over

which equilibrium properties can be averaged

The molecules are started in some initial

con-figuration and are then moved sequentially

ac-cording to the following rule If the calculated

change in potential energy (E) of the system

is negative, then the configurational change of

the system is allowed to occur automatically If

the associated potential energy change is

posi-tive, however, then the computer is programmed

to allow the molecule to move with a

probabil-ity of exp ( −E/k B T ) Thus, the system will

reach statistical equilibrium when the

probabil-ity of each configuration is the required

Boltz-mann probability The advantage of this

tech-nique over a molecular dynamics simulation is

that it reaches equilibrium faster, but it cannot be

used to calculate non-equilibrium system erties

prop-Moody chart Plot of the Colebrook pipe tion formula for various surface roughnesses as

fric-a function of the Reynolds number for turbulentflow in a pipe

MOSFET Metal oxide semiconductor fieldeffect transistor

Mössbauer effect (1) Also called recoil-free

gamma-ray resonance absorption Nuclearprocess permitting the resonance absorption ofgamma rays It is made possible by fixing atom-

ic nuclei in the lattice of solids so that energy isnot lost in recoil during the emission and absorp-tion of radiation The process, discovered by theGerman-born physicist Rudolf L Mössbauer in

1957, constitutes a useful tool for studying verse scientific phenomena

di-In order to understand the basis of the bauer effect, it is necessary to understand sev-

Möss-eral fundamental principles The first of these isthe Doppler shift When a locomotive whistles,the frequency, or pitch, of the sound waves in-creases as the whistle approaches a listener anddecreases as the whistle recedes The Dopplerformula expresses this change, or shift in fre-quency, of the waves as a linear function of thevelocity of the locomotive Similarly, when thenucleus of an atom radiates electromagnetic en-ergy in the form of a wave packet known as

a gamma-ray photon, it is also subject to theDoppler shift The frequency change, which isperceived as an energy change, depends on howfast the nucleus is moving with respect to theobserver

Finally, it is necessary to understand the ciples governing the absorption of gamma rays

prin-by nuclei Nuclei can exist only in certain inite energy states For a gamma ray to be ab-sorbed, its energy must be exactly equal to thedifference between two of these states Such

def-an absorption is called resondef-ance absorption Agamma ray that is ejected from a nucleus in a freeatom cannot be resonantly absorbed by a simi-lar nucleus in another atom because its energy

is less than the resonance energy by an amountequal to the kinetic energy given to the recoilingsource nucleus

(2) The phenomenon where a nucleus within

a crystal lattice undergoes a transition between

energy states and emits a high energy photon

(usually a γ -ray photon) without significantly

recoiling This nearly recoilless emission by

the nucleus is possible because the entire

lat-tice takes up the recoil momentum, so that the

nucleus that emits the photon only recoils an

in-finitesimal amount The photons which occur

in the Mössbauer effect are extremely sharply

peaked in energy and frequency

MOT See magneto-optical trap

motor A machine designed to convert

en-ergy into the mechanical form from some other

form For example, an electrical motor converts

electrical energy to mechanical energy, whereas

a chemical motor converts stored chemical

en-ergy into mechanical enen-ergy

motor generator A device for converting

electrical energy at one particular voltage and

frequency (or number of phases) to another

volt-age and frequency (or number of phases)

Con-sists of an electrical motor and generator that are

mechanically coupled

Mott scattering The electromagnetic

scat-tering of electrons from heavy nuclei The

nu-clei are treated as point positive charges, and

are assumed to be heavy enough that their recoil

from the collision with the electron can be

ig-nored In the limit in which the electron is

mov-ing at non-relativistic speeds, Mott scattermov-ing

becomes Rutherford scattering See Rutherford

scattering

Mott scattering formula The formula for the

differential scattering cross-section for identical

charged particles due to a Coulomb force, and

the formula for the scattering cross-section for

a relativistic electron by a Coulomb potential

field

MS renormalization The minimal

subtrac-tion renormalizasubtrac-tion scheme is a specific method

for dealing with the infinities that occur in higher

order radiative corrections to physical processes

In this scheme, one only subtracts the infinite

terms that arise in the calculation of the tive corrections

radia-Mueller matrix A 4×4 matrix which fully

describes the attenuation and polarizing ties of a medium such as polarizers or scatteringmedia The polarization state of the incominglight is described with the help of the Stokesvector, which is a vector with four componentshaving the following meaning The first compo-nent gives the intensity of the light; the secondcomponent is the difference between intensities

proper-of the horizontal and vertical polarizations proper-ofthe beam; the third is the difference of the in-tensities as measured after polarizers oriented at

±45◦; the last component is the intensity

dif-ferences with respect to left and right circularpolarizations of the beam

In general, the components of the Stokes tor are normalized with respect to the total inten-sity, such that the first component has the value

vec-of one For certain polarization states, the lowing Stokes vectors can be found:







left circular polarized







100-1







Any polarizer or scattering medium can now

be described as a Mueller matrix M such that

incident light described by a Stokes vector S

will be transformed to a state S = MS after

passage through the medium Examples of such

Mueller matrices are:

ideal horizontal polarizer 1

muffin tin potential The crystal potential

which an electron sees is often approximated by

nonoverlapping potentials centered at the

equi-librium positions of the ions

multi-photon transition Transition caused

by a multi-photon process, i.e., by

absorp-tion or emission of two or more photons

Multi-photon processes can occur through

vir-tual levels Selection rules for these transitions

are different from one-photon transitions The

transition probability for two-photon transitions

from state |i to state |f can be found, by

sec-ond order perturbation theory, to be proportional

where the sum extends over all real levels |k

In the case of a near resonance transition, an ditional damping term must be included, whichprevents the sum from blowing up

ad-There are three basic types of multi-photon transitions: In a case where the initial level is

higher in energy than the final level, one speaks

of multi-photon emission In the opposite case,one speaks of multi-photon absorption In eithercase, the energy of the photons adds up to result

in the energy difference of the atomic final andinitial levels

In the third process type, the Raman process,emission and absorption events are combined.Most common are two-photon Raman processeswhere one photon at one frequency is annihi-lated and another one is created

multiplet (1) A collection of relatively

closely spaced energy levels, their splitting from

a single energy level caused by a weak

interac-tion Examples are spin-orbit multiplets in the electronic states in atoms and isospin multiplets

in nuclear level structures

(2) A collection of hadrons grouped into

some representation of a mathematical group.For example, the SU(3) flavor quark model con-tains the up, down, and strange quarks in the

fundamental representation, 3 =(u, d, s) A

baryon is formed from various combinations ofthree of these quarks, which mathematically can

be represented via the tensor product 3 ⊗ 3 ⊗ 3.

This tensor product can be decomposed into the

direct product as 10 ⊕ 8 ⊕ 8 ⊕ 1, where 10 is the

decuplet representation of SU(3), 8 is the octet representation of SU(3), and 1 is the singlet rep-

resentation of SU(3) Each of these tions contains a number of particles equivalent

representa-to the number of the representation See octet;nonets

multipole expansion The expansion of theinteraction Hamiltonian of an atom with light tohigher order terms These higher order termsrepresent changes of the electromagnetic fieldacross the dimension of the atom The relevantexpansion yields

e ı  k r = 1 + ıkr +1

2



ı  k r 2+ · · ·

to a higher order than the zeroth order The latter

is called the dipole approximation The higher

order terms correspond to magnetic dipole,

elec-tric quadrupole, etc transitions and have much

lower probabilities than electric dipole-allowed

transitions

multipole selection rules Govern the higher

order transitions possible due to higher order

terms in the operator governing the interaction

of an electromagnetic wave and an atom Most

prominent are the magnetic dipole and electric

quadrupole transitions Their selection rules are

muon An apparently fundamental particle

which carries an electric charge equal to that of

the electron and has a spin of 1/2, making it afermion Except for its mass, which is roughly

200 times that of the electron, the muon appears

to be similar to the electron The muon decays

with a lifetime of approximately 2.2×10−6

sec-onds, and it decays predominantly into an

elec-tron, an anti-electron neutrino, and a muon

neu-trino

muonium A system consisting of a positively

charged antimuon bound to an electron Thissystem is similar to the hydrogen atom exceptthe proton is replaced by the antimuon Thissystem is a good test system for the accuracy

of QED since the electron and antimuon do notinteract via the strong interaction

muon neutrino A neutral spin 1/2 particlewhich, together with the charged muon, formsthe second family or second generation of lep-tonic matter particles See neutrino