Dictionary of Material Science and High Energy Physics Part 12 docx

self-energy The self-energy of a charged particle charge q results from its interaction with the field it produces.. semiclassical theory Type of theory thatdeals with the interaction of

χ = χ (1) + χ (2) E + χ (3) E2 The factor χ (2)

is referred to as the second order susceptibility,

as it results in a term in the polarization second

order in the applied field This factor is only

nonzero for materials with no inversion

sym-metry For a material that is not isotropic, the

second order susceptibility is a tensor.

second quantization Ordinary Schrödinger

equation of one particle or more particles are

described within a Hilbert space of a single

par-ticle or a fixed parpar-ticle numbers The single

electron Schrödinger equation written by the

po-sition representation can be interpreted as the

equation for the classical field of electrons: we

need to quantize the field Then the field

vari-able or, in short, the wave function is regarded as

a set of an infinite number of operators on which

commutation rules are imposed This produces

a formalism in which particles may be created

and annihilated We have to extend the Hilbert

space of fixed particle numbers to that of

arbi-trary number particles

Seebeck effect The existence of a

temper-ature gradient in a solid causes a current flow

as carriers migrate along or against the gradient

to minimize their energy This effect is known

as the Seebeck effect The thermal gradient is

thus equivalent to an electric field that causes

a drift current Using this analogy, one can

de-fine an electric field caused by a thermal gradient

(called a thermoelectric field) This electric field

is related to the thermal gradient according to

E = Q∇T

whereE is the electric field, ∇T is the thermal

gradient, and Q is the thermopower.

seiche Standing wave in a lake For a lake of

length L and depth H , allowed wavelengths are

given by

λ= 2L

2n+ 1

where n = 0, 1, 2,

selection rules (1) Not all possible transitions

between energy levels are allowed with a given

interaction Selection rules describe which

tran-sitions are allowed, typically described in terms

of possible changes in various quantum bers Others are forbidden by that interaction,but perhaps not by others For a hydrogen atom

num-in the electric dipole approximation, the

selec-tion rules are l = ±1, where l is related to

eigenstates of the square of the angular tum operator via ˆL2ψ l = l(l + 1)¯h2ψ l Therules result from the vanishing of the transitionmatrix element for forbidden transitions

momen-(2) Symmetry rules expressing possible

dif-ferences of quantum numbers between an initialand a final state when a transition occurs withappreciable probability; transitions that do not

follow the selection rules have a considerably

lower probability and are called forbidden

selection rules for Fermi-type β− decay

Allowed Fermi β−decay changes a neutron into

a proton (or vice versa in β+decay) There is nochange in space or spin part of the wave function

J = 0 no change of parity (J total

mo-ment);

I (isospin), I f = Ii

isospin zero states are forbidden);

I zf = Izi µ 1I z = 1 (third component of

isospin);

π = 0 (there is no parity change)

In this kind of transition, leptons do not takeany orbital or spin moment

Allowed Gamow–Teller transitions:

J = 0, 1 but Ji = 0; Jf = 0 are forbidden

T = 0, 1 but Ti = 0; Tf = 0 are forbidden

I zf = Izi µ 1I z= 1

π = 0 (no change of parity)

s-electron An atomic electron whose wavefunction has an orbital angular momentum quan-

tum number  = 0 in an independent particle

theory

self-assembly Any physical or chemicalprocess that results in the spontaneous formation(assembly) of regimented structures on a sur-

face In self-assembly, the thermodynamic

evo-lution of a system driving it towards its minimumenergy configuration, automatically results inthe formation of well-defined structures (usuallywell-ordered in space) on a surface without out-side intervention The figure shows the atomicforce micrograph of a self-assembled pattern onthe surface of aluminum foil This well-ordered

pattern consists of a hexagonal

close-packed array of 50 nm pores surrounded

by alumina It was produced by anodizing

alu-minum foil in oxalic acid with a DC current

den-sity of 40 mA/cm2 This pattern was formed by

a non-linear field-assisted oxidation process

A raw atomic force micrograph of a self-assembled

ar-ray of pores in an alumina film produced by the

an-odization of aluminum in an acid.

self-charge A contribution to a particle’s

electric charge arising from the vacuum

polar-ization in the neighborhood of the bare charge

self-coherence function The

cross-correlation function
(
r1 ,
r2 ; t1 , t2 ) =

V∗(
r1 , t1 )V (
r2 , t2 )  reduces to the

self-coherence function for
r1 =
r2 It contains

information about the temporal coherence of

V (
r, t), essentially a measure of how well we

can predict the value of the field at t1 if we

know its value at t2 Common choices for V

are the electric field amplitude and the intensity

of a light field

self-consistent field See Hartree, Hartree–

Fock method

self-energy The self-energy of a charged

particle (charge q) results from its interaction

with the field it produces It is expressed

in terms of the divergent integral Eself =

nonuni-an intensity-dependent index of refraction, n=

n0+ n2I To achieve self-focusing, n2must be

positive The self-focusing increases the

inten-sity of the beam inside the material and can lead

to damage of the material, particularly if it is acrystal

self-induced transparency When a pulse of

a particular shape and duration interacts with

a non-linear optical material, it may form anoptical soliton, which would propagate in ashape preserving fashion For a gas of two-level

atoms, this can be accomplished by a 2π pulse

with a hyperbolic secant envelope

self-similarity Flow whose state dependsupon local flow quantities such that the flow may

be non-dimensionalized across spatial or poral variations Self-similar solutions occur inflows such as boundary layers and jets

tem-Sellmeier’s equation An equation foranomalous dispersion of light passing through amedium and being absorbed at frequencies cor-responding to the natural frequencies of vibra-tion of particles in the medium The equation isgiven by

n2= 1 + Ak l2/(l2− l2

k ) + · · · + · · · Here n is the refractive index of the medium, l is

the wavelength of the light passing through the

medium where the kth particle vibrates at the

natural frequency corresponding to the

wave-length of lk , and Akis constant

semiclassical theory Type of theory thatdeals with the interaction of atoms with light,treating the electromagnetic field as a classicalvariable (c-number) and the atom quantum me-chanically

semiconductor (1) A solid with a filled

va-lence band, an empty conduction band, and asmall energy gap between the two bands Here,

small means approximately one electron volt (1

eV) In contrast, for a conductor, the conduction

band is partially populated with electrons, and

an insulator has a band gap significantly larger

than 1 eV

(2) Materials are classified into four classes

according to their electrical conductivity The

first are conductors, which have the largest

con-ductivity (e.g., gold, copper, etc., these are

mostly metals) In conductors, the conduction

band and valence bands overlap in energy The

second are semi-metals (e.g., HgTe) which have

slightly less conductivity than metals (here the

conduction band and valence band do not

over-lap in energy, but the energy difference between

the bottom of the conduction band and top of the

valence band (the so-called “bandgap”) is zero

or close to it The third are semiconductors,

which have less conductivity than semi-metals

and the bandgap is relatively large (examples are

silicon, germanium, and GaAs) The last are

in-sulators which conduct very little They have

very large bandgaps An example is NaCl

The energy band diagram of metals, semi-metals,

semiconductors, and insulators.

semiconductor detectors Use the formation

of electron-hole pairs in semiconductors

(ger-manium or silicon) to detect ionizing particles

The energy of formation of a pair is only about

3eV, which means that they can provide largesignals for very small deposit energy in the de-tection medium These devices were first used inhigh-resolution energy measurements and mea-surements of stopping power of nuclear frag-ments Now they are used for the precise mea-surement of the position of charged particles.Very thin wafers of semiconductors are used fordetection (200 − 300µ m thick) These detec-

tors are quite linear Two silicon detectors tioned in series can measure the kinetic energyand velocity of any low-energy particle and itsrest mass

posi-semileptonic processes Decays with

hadrons and leptons involved Two types ofthese processes exist In the first type there

is no change in strangeness of hadrons, in thesecond type there is change in strangeness ofhadrons

In the first type, strangeness |S| = 0

(strangeness preserving decay), Isospin I =

1, and Z projection of isospin |Iz| = 1 For

example, n → p + e−+ ¯νe (S n = 0; Iz,n =

semi-metal Elements in the Periodic Tablethat can be classified as poor conductors, i.e., in-between conductors and non-conductors Ex-amples are arsenic, antimony, bismuth, etc See

separation In viscous flows under certainconditions, the flow in the boundary layer maynot have sufficient momentum to overcome alarge pressure gradient, particularly if the gra-dient is adverse The boundary layer approxi-mation results in the momentum equation at thewall taking the form

As dp/dx changes sign from negative to

posi-tive, the flow decelerates and eventually results

in a region of reverse flow This causes a

separa-tion of the flow from the surface and the creasepara-tion

of a separation bubble

Separated flow in a transition region.

separatrix In a tokamak with a divertor (and

in some other plasma configurations), the last

closed flux surface is formed not by inserting

an object (limiter) but by manipulating the

mag-netic field, so that some field lines are split off

into the divertor rather than simply traveling

around the central plasma The boundary

be-tween the two types of field lines is called the

separatrix, and it defines the last closed flux

sur-face in these configurations

sequential resonant tunneling In a

struc-ture with alternating ultrathin layers of

materi-als (called a superlattice), an electron can tunnel

from one layer to the next by emitting or

ab-sorbing a phonon, then tunnel to the next layer

by doing the same, and so on The phonon

en-ergy must equal the enen-ergy difference between

the quantized electronic energy states in

succes-sive layers This type of tunneling is called

in-coherent tunneling because the electron’s wave

function loses global coherence because of its

interaction with the phonon

The current voltage characteristic of a

struc-ture that exhibits sequential resonant tunneling

has a non-monotonicity and hence exhibits

neg-ative differential resistance This has been

uti-lized to make very high frequency oscillators

and rectifiers

Serpukhov Institute for Nuclear Physics

Located 60 miles south of Moscow It has a

The process of sequential resonant tunneling through

a superlattice under the influence of an electric field The conduction band profile of the superlattice is shown along with the quantized sub-band states’ en- ergy levels (in heavy dark lines).

76 GeV proton synchrotron that was the mostpowerful accelerator in the world for several

years The Serpukhov Institute collaborated on

the UNK project (accelerated protons up to 400GeV within one booster synchrotron and theninjected in the next synchrotron with energies

up to 3 TeV — 3 TeV ring with tors magnets Magnets have been developed incollaboration with Saclay Paris

superconduc-Sezawa wave A type of surface acoustic

wave with a specific dispersion relation quency vs wave vector relation)

(fre-shadow matter Unseen matter in the

uni-verse (see supersymmetric theories) This ter is visible only through gravitational interac-tion in the modern theory of superstrings

mat-shadow scattering Quantum scattering that

results from the interference of the incident waveand scattered waves

shallow water theory See surface gravity

shape vibrations of nuclei Vibrational

mod-el of nuclei which describes shape vibrations ofnuclei This type of vibration considers oscilla-tions in the shape of the nucleus without chang-ing its density It is similar to vibrations of a sus-pended drop of water that was gently disturbed

Departures from spherical form are described by



 ,

where R(θ, ϕ, t) is the distance between the

sur-face of the nucleus and its center at the angles

(θ, ϕ) at the time t , and R0 is the equilibrium

radius

Because of properties of spherical

harmon-ics (Y∗

λµ (θ, ϕ) = (−1) µ · Yλ, −µ (θ, ϕ)), and in

order to keep the distance R(θ, ϕ, t ) real, the

requirement for shape parameters α λµ (t ) is

α λµ (t ) = (−1) µ · αλ, −µ (t )

For each λ value there are 2λ +1 values of µ(µ =

−λ, −λ + 1, , λ).

For λ = 1, vibrations are called monopole

and dipole oscillations (the size of the nucleus

is changed, but the shape is not changed for the

monopole oscillations, and for the dipole

oscil-lations the nucleus as a whole is moved), λ= 2

describes quadrupole oscillations of the nucleus

(the nucleus changes its shape from spherical

→ prolate → spherical → oblate → spherical

The value λ = 3 describes more complex shape

vibrations which are named as octupole

vibra-tions

Shapiro steps When a DC voltage is applied

across a Josephson junction (which is a thin

in-sulator sandwiched between two

superconduc-tors), the resulting DC current will be essentially

zero (except for a small leakage current caused

by few normal carriers) But when a small AC

voltage is superimposed on the DC voltage, the

DC component of the current becomes large if

the frequency of the AC signal ω satisfies the

The values of the DC voltage V0 that satisfy

the above equation are called Shapiro steps after

S Shapiro who first predicted this effect

shear A dimensionless quantity measured by

the ratio of the transverse displacement to the

thickness over which it occurs A shear

defor-mation is one that displaces successive layers of

a material transversely with respect to one other, like a crooked stack of cards

an-sheared fields As used in plasma physics,

this refers to magnetic fields having a rotationaltransform (or, alternatively, a safety factor) thatchanges with radius For example, in the stel-

larator concept, sheared fields consist of

mag-netic field lines that increase in pitch with tance from the magnetic axis

dis-shear rate Rate of fluid deformation given by

the velocity gradient du/dy Also called strain

rate and deformation rate

shear strain rate The rate at which a fluid

element is deformed in addition to rotation and

translation The shear strain rate tensor is given

The tensor is symmetric

shear stress See stress and stress tensor

sheath See Debye sheath

shell model A model of the atomic nucleus inwhich the nucleons fill a preassigned set of sin-gle particle energy levels which exhibit a shellstructure, i.e., gaps between groups of energylevels Shells are characterized by quantumnumbers and result from the Pauli principle

shell model (structures) A model based onthe analogous orbital electron structure of atomsfor heavier nuclei Each nucleus is an averagefield of interactions of that nucleon to other nu-clei This average field predicts formation ofshells in which several nuclei can reside Ba-sically, nucleons move in some average nuclearpotential The coulomb potential is binding foratom, the exact form of nuclear potential is un-known, but the central form satisfies initial con-sideration

Experimental evidence shows the following:Atomic shell structure explains chemical peri-

odicity of elements After 1932,

experimen-tal data revealed that there is a series of magic

numbers for protons and neutrons that gives

sta-bility to nuclei with such numbers Z and N

Z = 2, 8, 20, 28, (40)50, 82, and 126 are

sta-ble These numbers are called magic numbers

of nuclei

The spectrum of energies of nuclei forms

shells with big energy gaps between them The

shell model can be calculated on a spherical

or deformed basis, but mathematical convince

makes viable spherical approach In a spherical

model, each particle (nucleon) has an intrinsic

spin s and occupies a state with a finite angular

moment l For many nucleon systems, nucleons

are bonded in states with total angular moment J

and total isospin I There are two ways to

com-pute angular moment coupling One method is

LS coupling and the other is j –j coupling.

In an LS scheme, first the total orbital

mo-mentum for all nucleons (total L) is calculated,

followed by the isospin for all nucleons (S)

Fi-nally, the total momentum (J) is computed as a

vector sum of L and S:

J= L + S

Alternately the j –j model computes orbital and

intrinsic moments coupled for each nucleon and

later sums over all total nucleon moments In a

deformed base the above procedure can be

fol-lowed:

First, nucleons are divided in two groups:

core and valence nucleons The single particle

states are separated into three categories: core

states, active states, and empty states

The low lying states make an inert core The

Hamiltonian can be separated into two parts: the

constant energy term made from single particle

energies and the interaction between them and

the binding energy of active nucleons in the core

This second part is made from the kinetic energy

of nucleons and their average interaction energy

with other nucleons, including nucleons in the

inert core

Magic numbers are configurations that

corre-spond to stable configurations of nuclei These

to the core Interactions between the atoms aretherefore represented by three shell–shell inter-actions: cs–cs, cs–vs, and vs–vs

Shockley–Read–Hall recombination trons and holes in a semiconductor recom-bine, thereby annihilating each other They

Elec-do so radiatively (emitting a photon) or radiatively (typically emitting one or more

non-phonons) Shockley–Read–Hall is a mechanism

for non-radiative recombination The nation rate (which is the temporal rate of change

recombi-of electron or hole concentration) is given by

τp (n + ni ) + τn (p + ni )

where n and p are the electron and hole trations respectively, and n i is the intrinsic car-rier concentration in the semiconductor whichdepends on the semiconductor and the temper-

concen-ature The quantities τ p and τ n are the times of holes and electrons respectively Theydepend on the density of recombination cen-ters (traps facilitate recombination), their cap-ture rates, and the temperature

life-shock tube (1) Device used to study unsteady

shock and expansion wave motion A cavity isseparated with a diaphragm into a high pres-sure section and a low pressure section Uponrupture, a shock wave forms and moves fromthe high pressure region to the low pressure re-gion, and an expansion wave moves from thelow pressure region to the high pressure region.The interface between the two gases moves inthe same direction as the shock wave albeit with

a lower velocity A space-time (phase-space)diagram is used to examine the motion of thevarious structures

(2) A gas-filled tube used in plasma physics to

quickly ionize a gas A capacitor bank charged

Shock tube with phase-space diagram.

to a high voltage is discharged into the gas at one

tube end to ionize and heat the gas, producing

a shock wave that may be studied as it travels

down the tube

shock wave (1) A buildup of infinitesimal

waves in a gas can create a wave with a finite

amplitude, that is, a wave where the changes in

thermodynamic quantities are no longer small

and are, in fact, possibly very large

Analo-gous to a hydraulic jump, this jump is called a

shock wave Shocks are generally assumed to

be spatial discontinuities in the fluid properties

This makes it simpler from a mathematical

per-spective, but physically, shocks have a definite

physical structure where thermodynamic

vari-ables change their values over some spatial

di-mension This distance, however, is extremely

small In general, shocks are curved However,

there will be many cases where the shock waves

in a flow are either entirely straight (such as in

a shock tube) or can be assumed straight in

cer-tain sections (such as ahead of a blunt body) In

these cases, the shock is normal if the incoming

flow is at a right angle to the shock and oblique

for all other cases The figure idealizes a shock

wave as a discontinuity The variations from the

upstream side of the shock to the downstream

side are often called the jump conditions

(2) A wave produced in any medium (plasma,

gas, liquid, or solid) as a result of a sudden

vio-lent disturbance To produce a shock wave in a

given region, the disturbance must take place in

a shorter time than the time required for sound

waves to traverse the region The physics of

shocks is a fundamental topic in modern

sci-ence; two important cases are astrophysics

(su-Shock wave.

pernovae) and hydrodynamics (supersonicflight)

short range order Refers to the probability

of occurrence of some orderly arrangements incertain types of atoms as neighbors and is given

by the following:

s = (b − brandom )/(bmaximum− brandom )

where b is the fraction of bonds between closest neighbors of unlike atoms, brandomis the value of

b when the arrangement is random and bmaximum

is the maximum value that b may assume.

shot noise A laser beam of constant mean tensity incident on a detector creates a photocur-rent, whose mean is proportional to the beam’sintensity There are fluctuations in the photocur-rent as there are quantum fluctuations in the laserbeam For a laser well above threshold produc-ing a coherent state, these beam intensity fluctu-ations are Poissonian The resulting photocur-

in-rent noise is referred to as shot noise Light fields that are squeezed exhibit sub-shot noise

for one quadrature, typically over some range

of frequencies

Shubnikov–DeHaas effect The electricalconductance of a material placed in a mag-netic field oscillates periodically as a function

of the inverse magnetic flux density This

is the Shubnikov–DeHaas effect, and the

cor-responding oscillations are called Shubnikov–DeHaas oscillations The period of the oscil-

lation (1/B) is related to an extremal

cross-sectional area of the Fermi surface in a plane

normal to the magnetic field A according to

If a magnetic field is applied perpendicular to

a two-dimensional electron gas, then

remember-ing that the Fermi surface area is 2π2/n s where

n s is the two-dimensional carrier density, one

Thus, Shubnikov–DeHaas oscillations are

routinely used to measure carrier concentrations

in two-dimensional electron and hole gases

In systems that contain two parallel layers of

two-dimensional electron gases, the oscillations

will show a beating effect if the concentrations in

the two layers are somewhat different The

beat-ing frequency depends on the difference of the

carrier concentrations Beating may also occur

if the spin degeneracy is lifted by the magnetic

field or some other effect

 baryon There are three sigma (triplet)

baryons (+ plus sigma baryon (uus), −

mi-nus sigma baryon (dds), and 0 neutral (uds),

according SU (3) (flavor) symmetry) Wave

6· {|dus > +|uds > +|dsu >

+ |usd > +||sdu > +|sud >}

signal-to-noise ratio The ratio of the useful

signal amplitude to the noise amplitude in

elec-trical circuits, the noise is not used anywhere in

the circuit

silsbee effect The process of destroying or

quenching the superconductivity of a current

carried by a wire or a film at a critical value

similarity See dynamic similarity and

self-similarity

similarity transformation The relationship

between two matrices such that one matrix

be-comes the transform of the second

simplex A system of communication that

op-erates uni-directional at one time

sine operator There is no phase operator inquantum mechanics In a complex represen-

tation, the classical field E = E0 e iθ is

quan-tized such that E0and e iθare separate operators

The imaginary part of the operator e iθ is sin(θ ) There is no operator for θ itself.

single electronics A recently popular field ofelectronics where the granularity of charge (i.e.,electric charge comes in quanta of the singleelectron’s charge of 1.61×10−19 Coulombs) is

exploited to make functional signal processing,memory, or logic devices

Single electronic devices operate on the basis

of a phenomena known as a Coulomb blockadewhich is a consequence of, among other things,the granularity of charge When a single elec-tron is added to a nanostructure, the change inthe electrostatic energy is

E= (Q − e)2

2C = −Q − e/2

C

where e is the magnitude of the charge of the

electron (1.61×10−19 Coulombs), C is the

ca-pacitance of the nanostructure, and Q is the

ini-tial charge on the nanostructure Since this event

is permitted only if the change in energy E is negative (the system lowers its energy), Q must

be positive Furthermore, since Q = e |V | (V is

the potential applied over the capacitor), it lows that tunneling is not permitted (or currentcannot flow) if

fol-−e/2C ≤ V ≤ e/2C

The existence of this range of voltage at whichcurrent is blocked by Coulomb repulsion isknown as the Coulomb blockade

The Coulomb blockade can be manifested

only if the thermal energy kT is much less the electrostatic potential barrier e2/ 2C Otherwise,

electrons can be thermally emitted over the rier and the blockade may be removed In nanos-

bar-tructures, C may be 10−18farads and hence theelectrostatic potential barrier is ∼ 100 meV,

which is four times the room-temperature

ther-mal energy kT Thus, the Coulomb blockade

can be appreciable and discernible at reasonabletemperatures

The phenomenon of the Coulomb blockade

is often encountered in electron tunneling across

a nanojunction (a junction of two materials with

nanometer scale dimensions) with small

capac-itance The tunnel resistance must exceed the

quantum of resistance h/e2 so that single

elec-tron tunneling events may be viewed as discrete

events in time

single electron transistor Consists of a small

nanostructure (called a quantum dot, which is

a solid island of nanometer scale dimension)

interposed between two contacts called source

and drain When the charge on the quantum

dot is nq (n is an integer and q is the electron

charge), current cannot flow through the

quan-tum dot because of a Coulomb blockade

How-ever, if the charge is changed to (n + 0 5)q by a

third terminal attached to the quantum dot, then

the Coulomb blockade is removed and current

can flow Since the current between two

termi-nals (source and drain) is being controlled by

a third terminal (called gate in common device

parlance), transistor action is realized If it is

bothersome to understand why the charge on

the quantum dot can ever be a fraction of the

single electron charge, one should realize that

this charge is transferred charge corresponding

to a shift of the electrons from their equilibrium

positions This shift need not be quantized

Schematic of a single electron transistor.

single electron turnstile A single electron

device consisting of two double nanojunctions

connected by a common nanometer sized island.The island is driven by a gate voltage When an

AC potential of appropriate amplitude is applied

to this circuit, a DC current results which obeysthe relation

I = ef

where e is the single electron charge and f isthe frequency of the applied AC signal Thisdevice, and others like it, have been proposed

to develop a current standard with metrologicalaccuracy

single-mode field A single-mode field is an

electromagnetic field with excitation of only onetransverse and one longitudinal mode

singlet An energy level with no other nearby

levels Nearby is a relative term, and the erational definition is that the energy difference

op-between the singlet and other nearby states is

comparable to the excitation energy See alsodoublet; triplet states

singlet state An electronic state of a molecule

in which all spins are paired

singlet-triplet splitting The process of aration of the singlet state and triplet state in theelectronic configuration of atom or molecule

sep-Sisyphus cooling A method of laser cooling

of atoms It utilizes position-dependent lightshifts caused by polarization gradients of thecooling field It takes its name from the Greekmyth, as atoms climb potential hills, tend tospontaneously emit and lose energy, and thenclimb the hills again

six-j symbols A set of coefficients ing the transformation between different ways

affect-of coupling eigenfunctions affect-of three angular

mo-menta Six-j symbols are closely related to the

Racah coefficients but exhibit greater symmetry

skin depth The depth at which the currentdensity drops by 1 Neper smaller than the sur-face value, due to the interaction with electro-magnetic waves at the surface of the conductor

skin friction Shear stress at the wall which

may be expressed as

τ w = µ ∂u

∂y|y=0

where the velocity gradient is taken at the wall

skin friction coefficient Dimensionless

rep-resentation of the skin friction

For a Blasius boundary layer solution (laminar

flat plate), the skin friction is

C f =√0.664

Rex .For a turbulent flate plate boundary layer,

cf = 0.0576

Re−1/5

x

Also referred to as the wall shear stress

coeffi-cient

Slater determinant A wave function for n

fermions in the form of a single n × n

deter-minant, the elements of which are n-different

one-particle wave functions (also called orbitals)

depending successively on the coordinates of

each of the particles in the system The

ma-trix form incorporates the exchange symmetry

of fermions automatically

Slater–Koster interaction potential Using

a Green’s function model, one can express the

binding energy of an electron to an impurity

(e.g., N in GaP) In this case, one needs to

ex-press the impurity potential V If one chooses to

express V as a delta function in space via the

ma-trix elements of Wannier functions, the potential

is called the Slater–Koster interaction potential.

slip A deformation in a crystal lattice

where-by one crystallographic plane slides over

an-other, causing a break in the periodic

arrange-ment of atoms (see the figure accompanying the

slowly varying envelope approximation

For a time-varying electromagnetic field that is

not purely monochromatic but has a well defined

carrier frequency, we may write E(x, t) = A(x,

t ) cos(kx − ωt + φ), where ω is the carrier

fre-quency and k is the center wave number A(x, t)

is referred to as the envelope function, and in theslowly varying envelope approximation, we as-sume that the envelope does not change much

over one optical period, dA(x, t)/ dt  ωA(x,

t ) A similar approximation can be made in the

spatial domain, dA(x, t)/ dx  kA(x, t)

slow neutron capture This capture reaction

captures thermal neutrons (with few eV energy).This kind of reaction is responsible for most mat-ter in our world (see supernova) An example ofthis reaction is16O(n, γ )17O At higher tem-peratures, capture of protons and alpha particles

is possible

Elements beyond A∼ 80 up to uranium are

mostly produced by slow and rapid neutron ture Knowledge of these kinds of reactions isvery important for synthesis of new elements.The capture of neutrons in uranium can raisethe energy of nuclei to start the fission process

cap-sluice gate Gate in open channel flow inwhich the fluid flows beneath the gate rather thanover it Used to control the flow rate

small signal gain For a laser with weak tation, the output power is linearly proportional

exci-to the pump rate The ratio of output power exci-toinput power in that operating regime is referred

to as small signal gain

S-matrix The matrix that maps the wavefunction at a long time in the past to the wavefunction in the distant future Also referred to

as the scattering, or S-operator, it is defined as

|ψ(t = ∞) = ˆS|ψ(t = −∞) It is typically

calculated in a power expansion in a couplingconstant, such as the fine structure constant forquantum electrodynamics

S-matrix theory A theory of collision nomena as well as of elementary particles based

phe-on symmetries and properties of the scatteringmatrix such as unitarity and analyticity

Snell’s law When light in one medium counters an interface with another medium, the

en-light ray in the other medium traveling in a

dif-ferent direction can be determined from Snell’s

Law, n i sin θ i = n0 sin θ0 Here, the angles are

measured with respect to the normal to the

in-terface, n i is the index of refraction of the initial

medium, and n0 is the index of refraction of the

medium on the other side of the interface For a

given initial angle, there may be no possible ray

that enters the other medium This condition is

known as total internal reflection, and it occurs

when n i /n0 < tan·θ.

SO(10) symmetry (E6 ) A symmetry present

in grand unified theory (gravity not included)

SO(3) group A group of symmetry of spatial

rotations This group is represent by a set of

3×3 real orthogonal matrices with a determinant

equal to one

SO(32) Group symmetry (32 internal

dimen-sional generalization of space-time symmetry)

In chiral theory SO(32) describes Yang-Mills

forces

These forces can be described with E6XE8

sym-metry groups product two continuous groups

discovered by French mathematician Elie

Car-tan

sodium chloride structure See rock salt

soft X-ray X-rays of longer wavelengths, the

term “soft” being used to denote the relatively

low penetrating power

solar (stellar) energy In the sun, 41012 g/s

mass is converted in energy There are two main

type of reactions inside the sun First is the

car-bon cycle (proposed by Bethe in 1938):

In this process, carbon is a catalyst (number

of C stays the same).

The total balance of this process is

Sun (temperature T = 1.5107K) Each proton

in the reaction contributes 6.7 MeV, which iseight times greater than the contribution of onenucleus in235U fission

solar cell A solar cell is a semiconductor p–n junction diode When a photon with energy hν

larger than the bandgap of the semiconductor

is absorbed from the sun’s rays, an electron–hole pair is created The electron–hole pairscreated in the depletion region of the diode travel

in opposite directions due to the electric fieldthat exists in the depletion region This travelingelectron–hole pair contributes to current Thus,

the solar cell converts solar energy to electrical

energy

Solar cells are among the best and

clean-est (environmentally friendly) energy ers They are also inexpensive The cheap-est cells made out of amorphous silicon exhibitabout 4% conversion efficiency

convert-solar corona The solar corona is a very hot,

relatively low density plasma forming the outerlayer of the sun’s atmosphere Coronal temper-atures are typically about one million K, andhave densities of approximately 108–1010 par-ticles per cubic centimeter The corona is muchhotter than the underlying chromosphere andphotosphere layers The mechanism for coronalheating is still poorly understood but appears to

be magnetic reconnection Plasma blowing out

from the corona forms the solar wind See also

solar filament A solar surface structure

vis-ible in Hα light as a dark (absorption)

filamen-tary feature The same structures are referred to

as solar prominences when viewed side-on and

seen extending off the limb

solar flare A rapid brightening in localized

regions on the sun’s photosphere that is

usu-ally observed in the ultraviolet and X-ray ranges

of the spectrum and is often accompanied by

gamma ray and radio bursts Solar flares can

form in a few minutes and last from tens of

min-utes to several hours in long-duration events

Flares also produce fast particles in the solar

wind, which arrive at the earth over the days

following the flare The energy dumped into

the earth’s magnetosphere and ionosphere from

flares is a major cause of space weather

solar neutrinos (physics) Neutrinos

pro-duced in nuclear reactions in the sun are detected

on the earth through neutrino capture reactions

An example of that reaction is the capture of a

neutrino by chloral nuclei:

ν+37Cl→37Ar + e− Q = −0.814 MeV

This Ar isotope is unstable and beta decays into

37Clwith a half-life of 35 days We observe half

as many neutrinos from the sun as are predicted

from a nuclear fusion mechanism There are

several possibilities: the nuclear reaction rates

may be wrong; the temperature of the center

of the sun predicted by the standard solar model

may be too high; something may happen to

neu-trinos on the way from the center of the sun to

the detectors; or electron–muon neutrino

oscil-lations may occur if the neutrino has a rest mass

different than zero

The kamiokande II detector shows that

neu-trinos cannot decay during flight from the sun

solar prominence A large structure visible

off the solar limb, extending into the

chromo-sphere or the corona, with a typical density much

higher (and temperatures much colder) than the

ambient corona When seen against the solar

disk, these prominences manifest as dark

ab-sorption features referred to as solar filaments

solar wind A predominantly hydrogenplasma with embedded magnetic fields whichblows out of the solar corona above escape ve-

locity and fills the heliosphere The solar wind

velocities are approximately 100–1000 km/s

The solar wind’s density is typically around 10

particles per cubic centimeter, and its ture is about 100,000 K as it crosses the earth’s

tempera-orbit The solar wind causes comet tails to point mainly away from the sun Storms in the solar

wind are caused by solar flares.

sol-gel process A chemical process for thesizing a material with definite chemical com-position The constituent elements of the mate-rial are first mixed in a solution and then a gellingcompound is added Residues are evaporated toleave behind the desired material

syn-solid solubility The dissolution of one solidinto another is the process of solid dissolution

Solid solubility refers to the solubility (the

pos-sibility of dissolving) of one solid into another.Diffusion of impurities into a semiconductor(employed as the most common method of dop-

ing an n- or p-type semiconductor) is a process

of solid dissolution Solid solubility is limited

by the solid solubility limit, which is the

max-imum concentration in which one solid can bedissolved in another

soliton (1) Stable, shape-preserving, and

lo-calized solutions of non-linear classical fieldequations, where the non-linearity opposes thenatural tendency of the solution to disperse.Solitons were first discovered in water waves,and there are several hydrodynamic examples,

including tidal waves Solitons also occur in plasmas One example is the ion-acoustic soli-

ton, which is like a plasma sound wave;

an-other is the Langmuir soliton, describing a type

of large amplitude (non-linear) electron

oscil-lation Solitons are of interest for optical fiber

communications, where the use of optical

enve-lope solitons as information carriers in fiber

op-tic networks has been proposed, since the naturalnon-linearity of the optical fiber may balance thedispersion and enable the soliton to maintain itsshape over large distances

(2) A wave packet that maintains its shape as

it propagates Typically, a wave packet spreads