Physical Chemistry
19. Luminescence

Ruifeng ZHOU

Faculty of Science &Institute for the Advancement of Higher Education
Hokkaido University2

1. Photoluminescence
2. Laser3

1. Photoluminescence• In a 2-level quantum system, the transition between
states are accompted by the absorption oremission of photons .
• The energy of absorption, stimulated emission andspontaneous emission is equal to the energy
difference between the 2 levels.

absorption

stimulated emission

spontaneous emission

4

1. Photoluminescence• According to Born-Oppenheimer approximation,the motions of electrons and nuclei can be treatedseparately.
• The molecular states are the combinations of its
electronic states and nuclear states• The nuclear states can be further divided intotranslational, rotational and vibrational states.
∆𝐸𝐸 eV

Radiation typeTranslation

Rotation

Vibration

Electron~0< 0.010.05~0.5>2

N/A

Microwave

IR

Visible to UV• ∆𝐸𝐸: typical energy difference between the groundstates and the first excited states.

51. Photoluminescence• The electronic groundstate is usually asinglet state (𝒮𝒮 = 0),
denoted as 𝑆𝑆0 .
• The next singlet
electronic state isdenoted as 𝑆𝑆1 .
• Each vibrational stateadds a vibrationalenergy to the overallenergy.

𝑆𝑆1𝑆𝑆0

𝑤𝑤 = 4

𝑤𝑤 = 3

𝑤𝑤 = 2

𝑤𝑤 = 1

𝑤𝑤 = 0𝑣𝑣 = 4
𝑣𝑣 = 3
𝑣𝑣 = 2
𝑣𝑣 = 1
𝑣𝑣 = 06

1. Photoluminescence• For example, the 𝑆𝑆0 and 𝑆𝑆1 of N2.
3𝜎𝜎𝑢𝑢

↓

1𝜋𝜋𝑔𝑔

↑↓

↑↓
3𝜎𝜎𝑔𝑔

1𝜋𝜋𝑢𝑢

1 +Σ𝑔𝑔

↑↓

↑↓

3𝜎𝜎𝑢𝑢

1𝜋𝜋𝑔𝑔
↑
3𝜎𝜎𝑔𝑔

1𝜋𝜋𝑢𝑢
1Π𝑔𝑔

↑↓

1. Photoluminescence• The transitions between
states involving EM
radiation (photons) arecalled radiative transitions,otherwise, nonradiativetransitions.
Radiativetransition• Radiative transitions from (absorption)
low energy states to highenergy states are called
the absorption of light(photons).

7

Nonradiative transition

Radiativetransition

1. Photoluminescence8• Nonradiative transitions from low energy to highenergy state can be achieved by several energizing
processes such as heating (flame test), anddischarge.

NaH

1. Photoluminescence9• A lower energy state is morestable than a higher energy state.
Relaxation• The transition from a high energy
state to a low energy state iscalled relaxation.
• Radiative relaxation not in Absorption
luminescencethermal equilibrium is called
luminescence.
• Especially, a luminescence
following absorption is called
Photoluminescencephotoluminescence.

1. Photoluminescence• Chemiluminescence

10

11

1. Photoluminescence• In vibrational relaxation, the vibrational energy isreleased in emission (in the case of IR activemodes), contacts (e.g., to solvent molecules insolution) or collisions (very slow in gas phase).
⋮⋮⋮

𝑣𝑣 = 3

𝑣𝑣 = 2

𝑣𝑣 = 1

𝑣𝑣 = 0

Other molecules

12

1. Photoluminescence• According to theconservation of spin
multiplicity, the systemtransits between thesame spin states byelectric dipoletransitions.
• Luminescence between
the same spin states(e.g., from 𝑆𝑆1 to 𝑆𝑆0 ) is
called fluorescence.

𝑆𝑆1

Absorption

𝑆𝑆0

Vibrational relaxation

Fluorescence13

1. Photoluminescence• In fluorescence, fluorescentfluorophores fluoresce.
• Fluorescence is usually a result or
photoluminescence or
chemiluminescence.

Aragonite (CaCO3)

Biofluorescence1. Photoluminescence14• Quenching refers to any process which decreases
the fluorescent intensity of a given substance.
• For example, quinine dissolved in water fluoresces
a light blue light with a violet laser illuminating.
• Chloride ions, the quencher, quench quinine’sfluorescence.

1. Photoluminescence15• In static quenching, molecules in the ground state
form complexes.
• In dynamic quenching, molecules in the excitedstate transfer energy or electrons to quenchers.
• The quantum yield of fluorescence is𝑁𝑁e<1
Φ=𝑁𝑁a• 𝑁𝑁a and 𝑁𝑁e are the numbers of photon absorbed andfluoresced.
• A good fluorophore has Φ > 0.1.

161. Photoluminescence
Tb:LaPO4

Ce:LaPO4

Eu:Y2O3

A typical fluorescence
spectrum of fluorescentlamp fluorophores.
Hg vapour emits light
predominantly withwavelengths of 185nm
and 253.7nm.

17

1. Photoluminescence• Depending on the energyof absorbed photons, themolecules at vibrational
ground state of 𝑆𝑆0 are
excited to different
vibrational states of 𝑆𝑆1 .
• The molecules at excited
vibrational states of 𝑆𝑆1
quickly vibrationally relax
to vibrational ground stateof 𝑆𝑆1 before fluorescing.

𝑆𝑆1𝑆𝑆01. Photoluminescence• They could fluoresce to thevibrational excited states of 𝑆𝑆1
𝑆𝑆0 and then vibrationally relax
to the ground state of 𝑆𝑆0 .
• The transitions involving thechanges of both electronic
and vibrational states arecalled vibronic transitions.
 The photoluminescence𝑆𝑆0energy is always lower than
the absorption energy.

18

19

1. Photoluminescence• Franck-Condon principle:
during a vibronictransition, the transition
from one vibrational state
to another vibrational
state has higher
probability (intensity) if
their vibrational
wavefunctions havehigher overlap.

𝑆𝑆1𝑆𝑆0201. Photoluminescence• In the time-dependent perturbation theory, thetransition dipole moment between Φ𝛼𝛼 and Φ𝛽𝛽 is⃑ 𝛼𝛼𝕡𝕡 = Φ𝛽𝛽 𝓅𝓅Φ• 𝓅𝓅⃑ is the electric dipole moment of the molecule.
𝓅𝓅⃑ = −e � 𝑟𝑟⃑𝑖𝑖 + e � 𝑍𝑍𝑗𝑗 𝑅𝑅𝑗𝑗 = 𝓅𝓅⃑e + 𝓅𝓅⃑n𝑖𝑖𝑗𝑗• Under Born-Oppenheimer approximation, the total
wavefunction is the product of the electronic andnuclear wavefunctions.
Φ = 𝜑𝜑 𝑅𝑅𝑗𝑗 𝜓𝜓 𝑟𝑟⃑𝑖𝑖 , 𝑅𝑅𝑗𝑗
nuclearelectronic

1. Photoluminescence• Consider the vibronic translation of a diatomicmolecule.
• For simplicity, use 𝒓𝒓 and 𝑹𝑹 for the positions of allelectrons and nuclei.
• The electronic states are 𝜓𝜓0 𝒓𝒓, 𝑹𝑹 and 𝜓𝜓1 𝒓𝒓, 𝑹𝑹 .
• The nuclear states are 𝜑𝜑0,𝑣𝑣 𝑹𝑹 and 𝜑𝜑1,𝑤𝑤 𝑹𝑹 .
• The transition dipole moment is𝕡𝕡 = � 𝜑𝜑0,𝑣𝑣 ∗ 𝜓𝜓0 ∗ 𝓅𝓅⃑e + 𝓅𝓅⃑n 𝜑𝜑1,𝑤𝑤 𝜓𝜓1 𝑑𝑑𝒓𝒓𝑑𝑑𝑹𝑹21

2211. Photoluminescence• the integral can be done wrt 𝒓𝒓 first and then 𝑹𝑹.
𝕡𝕡= � 𝜑𝜑0,𝑣𝑣 ∗ 𝜑𝜑1,𝑤𝑤 � 𝜓𝜓0 ∗ 𝓅𝓅⃑e 𝜓𝜓1 𝑑𝑑𝒓𝒓 𝑑𝑑𝑹𝑹+ � 𝜑𝜑0,𝑣𝑣 ∗ 𝓅𝓅⃑n 𝜑𝜑1,𝑤𝑤� 𝜓𝜓0 ∗ 𝜓𝜓1 𝑑𝑑𝒓𝒓

𝑑𝑑𝑹𝑹

• Note, the nuclear wavefunctions, 𝜑𝜑, areindependent of 𝒓𝒓,• Note, 𝜓𝜓0 and 𝜓𝜓1 are orthogonal.

1. Photoluminescence23• Furthermore, when integrating wrt 𝒓𝒓, 𝑹𝑹 are treatedas the equilibrium positions, 𝑹𝑹0 .

𝕡𝕡 ≈ � 𝜓𝜓0 ∗ 𝒓𝒓, 𝑹𝑹0 𝓅𝓅⃑e 𝒓𝒓 𝜓𝜓1 𝒓𝒓, 𝑹𝑹0 𝑑𝑑𝒓𝒓 � 𝜑𝜑0,𝑣𝑣 ∗ 𝑹𝑹 𝜑𝜑1,𝑤𝑤 𝑹𝑹 𝑑𝑑𝑹𝑹

• ∫ 𝜓𝜓0 𝒓𝒓, 𝑹𝑹0 ∗ 𝓅𝓅⃑e 𝒓𝒓 𝜓𝜓1 𝒓𝒓, 𝑹𝑹0 𝑑𝑑𝒓𝒓 is the orbital selectionrule.
• 𝑓𝑓𝑣𝑣,𝑤𝑤 = ∫ 𝜑𝜑0,𝑣𝑣 𝑹𝑹 ∗ 𝜑𝜑1,𝑤𝑤 𝑹𝑹 𝑑𝑑𝑹𝑹 is the Franck-Condon
factor, which is the degree of overlap between
nuclear states. It modulates the vibronic transition
probability.

1. Photoluminescence24• Suppose the potential energies from 𝑆𝑆0 and 𝑆𝑆1 haveidentical shape, but different equilibrium distances.
𝜑𝜑0,𝑣𝑣 𝑹𝑹 ∝ 𝜑𝜑𝑣𝑣 𝑅𝑅 − 𝑅𝑅0
𝜑𝜑1,𝑤𝑤 𝑹𝑹 ∝ 𝜑𝜑𝑤𝑤 𝑅𝑅 − 𝑅𝑅1• 𝜑𝜑𝑣𝑣 and 𝜑𝜑𝑤𝑤 are the wavefunctions of 1D harmonic
oscillation of vibrational quantum number 𝑣𝑣 and 𝑤𝑤.
• The translational and rotational wavefunctions arenot considered because they do not influence
vibronic transitions.
𝑓𝑓𝑣𝑣,𝑤𝑤 = � 𝜑𝜑𝑣𝑣 𝑅𝑅 − 𝑅𝑅0 𝜑𝜑𝑤𝑤 𝑅𝑅 − 𝑅𝑅1 𝑑𝑑𝑑𝑑

1. Photoluminescence• Substitute 𝑥𝑥 = 𝑅𝑅 − 𝑅𝑅0 .

𝑓𝑓𝑣𝑣,𝑤𝑤 = � 𝜑𝜑𝑣𝑣 𝑥𝑥 𝜑𝜑𝑤𝑤 𝑥𝑥 + 𝑅𝑅0 − 𝑅𝑅1 𝑑𝑑𝑑𝑑

• Consider another transition.

𝑓𝑓𝑤𝑤,𝑣𝑣 = � 𝜑𝜑𝑤𝑤 𝑅𝑅 − 𝑅𝑅0 𝜑𝜑𝑣𝑣 𝑅𝑅 − 𝑅𝑅1 𝑑𝑑𝑅𝑅

• Substitute 𝑥𝑥 = 𝑅𝑅1 − 𝑅𝑅.

𝑓𝑓𝑤𝑤,𝑣𝑣 = − � 𝜑𝜑𝑤𝑤 𝑅𝑅1 − 𝑥𝑥 − 𝑅𝑅0 𝜑𝜑𝑣𝑣 −𝑥𝑥 𝑑𝑑𝑑𝑑

25

26

1. Photoluminescence• Note that 𝜑𝜑𝑣𝑣 are either
odd or even functions.
𝑓𝑓𝑣𝑣,𝑤𝑤2= 𝑓𝑓𝑤𝑤,𝑣𝑣

w=3
w=2

2

• Therefore, the transition
probabilities are𝑃𝑃0,𝑣𝑣 1,𝑤𝑤 = 𝑃𝑃0,𝑤𝑤 1,𝑣𝑣
• The difference inminimum energies of 𝑆𝑆0
and 𝑆𝑆1 is denoted as 𝑇𝑇e .

w=1

𝑆𝑆1

w=0

v=3
v=2
v=1
v=0𝑆𝑆0𝑇𝑇e27

1. Photoluminescence• Mirror image
rule: thefluorescence
spectrum isa mirrorimage of theabsorption
spectrum wrt
𝑇𝑇e .

𝑇𝑇e

ℏ𝜔𝜔

1. Photoluminescence28

1. Photoluminescence• A molecule can also
convert nonradiatively
from 𝑆𝑆1 to 𝑆𝑆0 by several
mechanisms.
• In internal conversion, theelectronic energy converts
to the vibrational energy of𝑆𝑆0 (with high 𝑣𝑣).
absorbs UV• It then vibrationally relaxes Melaninlight and coverts its
to the vibrational ground energy to heat
(photoprotection).
state of 𝑆𝑆0 .

29

30

1. Photoluminescence• Higher electronic states
are closer to each other. 𝑆𝑆2• There is a higher
chance for internalconversion to occur
between higher
electronic states.
• Fluorescence is more
likely to occur between
lower electronic states, 𝑆𝑆0
especially 𝑆𝑆1 → 𝑆𝑆0 .

𝑆𝑆1

31

1. Photoluminescence• Intersystem crossing is a nonradiative process
involving a transition between 2 spin isomers(same orbital, different spins), e.g., between singlet(𝒮𝒮 = 0) and triplet (𝒮𝒮 = 1) states.
• A triplet state is denoted as 𝑇𝑇.
• Change in spin requires strong spin-orbit coupling.

𝑆𝑆𝐿𝐿

𝑆𝑆⃑

Intersystem crossing

𝑇𝑇

32

1. Photoluminescence• As fermions, the total
states of electrons areantisymmetric.
• The orbital with singlet
spin (antisymmetric)
must be symmetric.
• The orbital with triplet
spin (symmetric) must
be antisymmetric.
• Symmetric orbital has
higher energy.

𝑆𝑆1𝑇𝑇1• For a certain electronic
configuration, thetriplet state has lower
energy than the singletstate.

33

1. Photoluminescence• The 𝑆𝑆1 and 𝑇𝑇1 of N2.
↓

↑↓

3𝜎𝜎𝑢𝑢

↑

1𝜋𝜋𝑔𝑔
↑
3𝜎𝜎𝑔𝑔

1𝜋𝜋𝑢𝑢
1Π𝑔𝑔

↑↓

↑↓

3𝜎𝜎𝑢𝑢

1𝜋𝜋𝑔𝑔
↑
3𝜎𝜎𝑔𝑔

1𝜋𝜋𝑢𝑢
3Π𝑔𝑔

↑↓

34

1. Photoluminescence• After intersystemcrossing, themolecule vibrationallyrelaxes to 𝑇𝑇1 ’s
vibrational groundstate.
• Then, it is trappedwith only “forbidden”
transitions available
to return to the lower
energy 𝑆𝑆0 .

𝑆𝑆1𝑆𝑆0𝑇𝑇1×35

1. Photoluminescence• The molecule at
𝑇𝑇1 will finally relax
to 𝑆𝑆0 .
• The luminescence
between spinisomers isphosphorescence.
• Phosphorescenceis much slower
than fluorescence.

Cu:ZnS Eu:SrAl2O4
𝑇𝑇1Phosphorescence
In visible light (top),in darkness (middle),
and after 4 minutes
in the darkness(bottom).

𝑆𝑆0

1. Photoluminescence

Jablonski Diagram36

2. Laser

37• Usually, light from a single source has weakintensity (e.g., LED) and/or wide wavelength
distribution (blackbody radiation).
• In scientific research, lights with very strong
intensity and very narrow wavelength distribution(monochromatic, coherent) are needed forspectroscopies, etc.
• The mechanism to produce such light is Light
Amplification by Stimulated Emission of Radiation(laser).

2. Laser• Consider a 2-level system (𝐸𝐸2 > 𝐸𝐸1 ) underillumination,
𝑑𝑑𝑁𝑁2= 𝑊𝑊𝑁𝑁1 − 𝑊𝑊𝑁𝑁2 − 𝐴𝐴𝑁𝑁2
𝑑𝑑𝑑𝑑• 𝑊𝑊𝑁𝑁1 is the rate of absorption.
• 𝑊𝑊𝑁𝑁2 is the rate of stimulated emission.
• 𝐴𝐴𝑁𝑁2 is the rate of spontaneous emission.
• When the system is in equilibrium,
𝑊𝑊𝑁𝑁1 − 𝐴𝐴𝑁𝑁2 − 𝑊𝑊𝑁𝑁2 = 0𝑁𝑁2𝑊𝑊<1=
𝑁𝑁1 𝐴𝐴 + 𝑊𝑊

38

2. Laser

39• In a 2-level system, 𝑁𝑁2 is always smaller than 𝑁𝑁1 .
• The stimulated emission is always weaker thanabsorption.
• Amplification is the phenomenon that, thestimulated emission is stronger than the absorption.
• To achieve amplification, the system must have
population inversion, i.e., 𝑁𝑁2 > 𝑁𝑁1 .
• 2-level system cannot achieve population inversion
by illumination.

2. Laser

40• Consider a 3-level system (𝐸𝐸3 > 𝐸𝐸2 > 𝐸𝐸1 ).
• Suppose the absorption and stimulatedemission between 𝐸𝐸2 and 𝐸𝐸3 are weak.
𝑁𝑁3𝐸𝐸
3𝑑𝑑𝑁𝑁2= 𝑊𝑊2 𝑁𝑁1 + 𝐴𝐴𝐴𝑁𝑁3 − 𝐴𝐴2 𝑁𝑁2 − 𝑊𝑊2 𝑁𝑁2𝐴𝐴′𝑁𝑁2𝑑𝑑𝑑𝑑
𝐸𝐸2𝑑𝑑𝑁𝑁3𝑊𝑊3 𝐴𝐴3= 𝑊𝑊3 𝑁𝑁1 − 𝐴𝐴3 𝑁𝑁3 − 𝐴𝐴𝐴𝑁𝑁3 − 𝑊𝑊3 𝑁𝑁3𝑑𝑑𝑑𝑑
𝑊𝑊2 𝐴𝐴2• 𝑁𝑁1 , 𝑁𝑁2 and 𝑁𝑁3 are number densities.
𝑁𝑁1𝐸𝐸1• At equilibrium,𝑑𝑑𝑁𝑁2 𝑑𝑑𝑁𝑁3=0=𝑑𝑑𝑑𝑑
𝑑𝑑𝑑𝑑

2. Laser

41

𝐴𝐴𝐴𝑊𝑊3
𝑁𝑁2 𝑊𝑊2 + 𝐴𝐴3 + 𝑊𝑊3 + 𝐴𝐴𝐴=
𝑊𝑊2 + 𝐴𝐴2
𝑁𝑁1
• With a strong incident light with ℎ𝜈𝜈 = 𝐸𝐸3 − 𝐸𝐸1 ,𝑁𝑁2 𝑊𝑊2 + 𝐴𝐴𝐴lim=𝑊𝑊3 →∞ 𝑁𝑁1
𝑊𝑊2 + 𝐴𝐴2
• It is possible to establish such a system in which
𝐴𝐴′ > 𝐴𝐴2 , so that 𝑁𝑁2 > 𝑁𝑁1 .
 Population inversion can be achieved in 3 or morelevel systems by illumination.

2. Laser• If a light with ℎ𝜈𝜈 = 𝐸𝐸2 − 𝐸𝐸1
propagates through a material inx direction, the change in photon
flux (Φ) is proportional to 𝑁𝑁2 − 𝑁𝑁1
and the distance it propagates.
𝑑𝑑Φ
= 𝜎𝜎 𝑁𝑁2 − 𝑁𝑁1 𝑑𝑑𝑑𝑑
Φ• 𝜎𝜎 is the effective cross section.
• The physical meaning of 𝜎𝜎 is theprobability of a photon to interactwith a photoactive site.

42

43

2. Laser• Define the gain: 𝐺𝐺 ≡ 𝑁𝑁2 − 𝑁𝑁1 𝜎𝜎.
Φ = Φ0 𝑒𝑒 𝐺𝐺𝐺𝐺
• Without population inversion, 𝑁𝑁2 < 𝑁𝑁1 , 𝐺𝐺 < 0.
• The exponential decay is equivalent to the BeerLambert law.
• With population inversion, 𝑁𝑁2 > 𝑁𝑁1 , 𝐺𝐺 > 0. Light isamplified.
ΦΦ

44

2. Laser• 3 components are essential to achieve laser.
• A gain medium (active laser medium) is a material
which provides the energy levels.
• A pump is the act of energy transfer from anexternal source into the gain medium.
• An optical cavity is the space where light reflexes
Pumpback and forth. High reflector
Output coupler

Gain medium

Laser beam

2. Laser

45• One pass through the gain medium is not enoughto achieve very high intensity.
• One end of the cavity is a highly reflective mirror.
• The other end is an output coupler, which reflexes
most of the light and allows a small fraction of thelight to exit.

2. Laser46• Light confined in the cavity forms standing waves.
• Only certain wavelengths are sustained, while theothers are suppressed by destructive interference.
• The relationship between the length of cavity (𝐿𝐿)
and the frequency of the standing wave (𝜈𝜈) is𝑞𝑞𝑞𝑞 𝑐𝑐
𝐿𝐿 = 𝜆𝜆 =22 𝜈𝜈𝜈𝜈
• 𝑞𝑞 is an integer.
• 𝑛𝑛 is the refractive index of the gain medium.
𝑞𝑞𝑞𝑞
𝜈𝜈 =2𝐿𝐿𝐿𝐿

2. Laser

47• The frequency different between 2 neighbouring
standing waves is free spectral range (FSR).
𝑐𝑐∆𝜈𝜈 =2𝐿𝐿𝐿𝐿• For example, the linewidth of HeNe laser (𝑛𝑛 ≈ 1) isabout 1.2GHz due to Doppler effect.
• If 𝐿𝐿 = 0.15m.
∆𝜈𝜈 = 1000MHz• Standing waves of 2 wavelengths can besustained.

2. Laser• If 𝐿𝐿 = 0.75m.

∆𝜈𝜈 = 200MHz• Standing waves of about 6 wavelengths can besustained.

48

2. Laser

49• Examples of lasers.
• Ruby laser is a typical solid-state pulse laser.
• The gain medium is a ruby rod: synthetic Al2O3 withtypically 0.05% of Al3+ replaced by Cr3+ (dopant).
• Pump: Xe helical flashlamp.

2. Laser• Ruby is a typical “3-level”
gain medium.
• Ruby has very broad andpowerful absorption
bands near 400nm and550nm.
• After absorption, it
relaxes to a metastablestate.
• Then it lases at 694.3nm.
• Pulse duration is 10ps.

50

2. Laser

•••
•

51

HeNe laser is a typical gas continuous laser.
Gain medium: 75% He, 25% Ne.
Pump: electrical discharge.
During discharge, Ne glows visible light (as in neonlamp), but with He the population inversion is mucheasier.

• The ground state of He is 1S0.

2. Laser52• During discharge, it ionizes to plasma.
He → He+ + e−
• Some He+ and e− recombine to form excited Heatoms.
He+ + e− → He∗ 1𝑠𝑠1 2𝑠𝑠1
• There are 2 spin isomers of He∗ 1𝑠𝑠1 2𝑠𝑠1 , 21S0(parahelium) and 23S1 (orthohelium).
• In the term symbol, “2” denotes that one electron isin the L (𝑛𝑛 = 2) shell.
• 23S1 has a lower energy than 21S0 because it has
antisymmetric orbital (symmetric spin).

53

2. Laser• But 21S0 cannot transit to
23S1 because of theconservation of spin
multiplicity (∆𝑆𝑆 ≠ 0).
• For the same reason, 23S1cannot transit to 1S0.
• 21S0 cannot transit to 1S0because of theconservation of angularmomentum (∆𝐿𝐿 ≠ ±1).

21S0× ∆𝐿𝐿 = 01S0××∆𝑆𝑆 = 1

∆𝑆𝑆 = −123S1

2. Laser

54• Therefore, 21S0 and 23S1 are long-lived metastablestates.
• Collisions between He* and Ne atoms leads toselective and efficient energy transfer from He* toNe.
He∗ 2 3𝑆𝑆1 + Ne 1𝑆𝑆0 → He 1𝑆𝑆0 + Ne∗ 2𝑝𝑝5 4𝑠𝑠1
He∗ 2 1𝑆𝑆0 + Ne 1𝑆𝑆0 → He 1𝑆𝑆0 + Ne∗ 2𝑝𝑝5 5𝑠𝑠1
• The energy changes of these reactions are sosmall (0.05eV) that they can be compensated bykinetic energy.

55

3. Excited states of atoms

1s2s
He∗ 2 3𝑆𝑆1

2p3s1s2sHe∗ 2 1𝑆𝑆1

3p4s
Ne∗ 2𝑝𝑝5 4𝑠𝑠1

2. Laser

56• The excited Ne then luminates.
Ne∗ 2𝑝𝑝5 4𝑠𝑠1 → Ne∗ 2𝑝𝑝5 3𝑝𝑝1
Ne∗ 2𝑝𝑝5 5𝑠𝑠1 → Ne∗ 2𝑝𝑝5 4𝑝𝑝1
Ne∗ 2𝑝𝑝5 5𝑠𝑠1 → Ne∗ 2𝑝𝑝5 3𝑝𝑝1
• Note that both Ne*(2p53p1) and Ne*(2p54p1) have
10 angular momentum states: 1S0, 3S1, 1P1, 3P0,
3P , 3P , 1D , 3D , 3D and 3D .
123123• Both Ne*(2p54s1) and Ne*(2p55s1) have 4 angularmomentum states: 1P1, 3P0, 3P1 and 3P2.

2. Laser

57• There are multiple lines for each transition, but only
one from each transition is dominant.
Ne∗ 4 1𝑃𝑃1 → Ne∗ 3 3𝑃𝑃2 : 1152.3nm
Ne∗ 5 1𝑃𝑃1 → Ne∗ 4 3𝑃𝑃2 : 3391.3nm
Ne∗ 5 1𝑃𝑃1 → Ne∗ 3 3𝑃𝑃2 : 632.8nm• The products are efficiently emptied by fastradiative decay to Ne*(2p53s1).
• Ne*(2p53s1) eventually reaches the ground state bytransferring energy to the wall (cooling).

3. Excited states of atoms
12 𝑆𝑆0Energy

2 3𝑆𝑆0Atomic
collision

58
2𝑝𝑝5 5𝑠𝑠1 Lasing
2𝑝𝑝5 4𝑠𝑠1

2𝑝𝑝5 3𝑠𝑠1

Electroncollision

Radiative
relaxation

Diffusion
He

1 1𝑆𝑆0Ne

2𝑠𝑠 2 2𝑝𝑝6

2𝑝𝑝5 4𝑝𝑝1
2𝑝𝑝5 3𝑝𝑝1