Charlton M., Humberston J.W. Positron Physics
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Index
absorption coefficient, 18
absorption potential, 146
accelerators
cyclotron, 26
electron linear, 26, 249, 324
microtron, 26
adiabatic approximation, 83, 100,
107, 269
adiabatic potential, 100, 101, 111
Anderson-localized states, 295
angular acceptance, 24, 181, 235
angular correlation of annihilation
radiation (ACAR), 11, 16, 271–3,
297–9, 338, 339, 342–7, 350, 351
angular discrimination, 51, 53, 54,
61–6, 71, 77, 182
annihilation, 4, 5, 264–306
cross section and rate for, 5, 6, 12,
37, 38, 40, 122, 264–6, 271, 283,
363
into four or more gamma-rays, 5, 7
into three gamma-rays, 4, 5, 8
into two gamma-rays, 4, 5, 8
radiationless, 4, 6
rate and lifetime of
positronium, 8–10, 307–17
single quantum, 4, 6
antihydrogen, 2, 11, 372–4, 386, 387
formation of, 330, 331, 362, 372,
373, 376–86
antiproton, 362, 372–87
capture in a trap, 374, 375, 379,
382–6
collisions, 240, 244–6, 379–82
confinement times, 376
electron cooling of, 375
antiproton decelerator, 374, 386
antiprotonic helium atom, 376, 385
Arrhenius plot, 30
autoionization, 10, 363
backscattering, 223
beams, see positron beams and
positronium beams
Beer–Lambert law, 40
binary peak, 230
Born approximation, 6, 38, 45, 47,
124, 132, 157, 159–64, 167–70,
174, 189, 192, 216, 219, 230, 234,
246, 251, 260, 266, 336
Born–Oppenheimer
approximation, 126–7
Born series, 45, 46
Bose–Einstein condensate, 368, 371,
372
bound states involving positrons and
positronium, 10, 36, 39, 128,
287, 291, 329, 348–53
break-up of energetic
positronium, 208, 354, 359
449
450 Index
channel coupling, 130, 149, 163, 217,
227
charge conjugation, 4, 10, 36, 330,
362
charge transfer, 200
chemical quenching, see also
quenching of
ortho-positronium, 328, 351
close-coupling approximation, see
coupled-state approximation
clusters, 293–6
convergence
of phase shifts, 101, 103, 107, 108,
113, 117–9, 155
of scattering length, 111
of K-matrix elements, 155
convergent close-coupling metho
d
(CCC) 44, 104, 113, 233, 234
correlations, 103, 105, 112, 113, 116,
120, 128, 153, 228, 230, 240, 249,
252
Coulomb-dipole theory of ionization,
229; see also ionization
coupled-state approximation, 44, 76,
77, 101–4, 113, 124–6, 130–2,
157–9, 162, 165, 166, 170, 172,
185, 191–4, 217, 218, 220, 334–6
coupled-static approximation, 103,
110, 124, 130, 159, 160, 167, 172,
174, 185, 188, 334
CP invariance, 7
CPT invariance, 3, 4, 11, 373, 387
crossed beams, 141–4
cusps, 133, 137, 139, 253
decay rate, see annihilation
differential cross sections
elastic scattering, 50, 94, 96, 122,
123, 131, 132, 139, 141–9
excitation, 215, 225
ionization, 252–9
positronium formation, 151, 161,
162, 168, 169, 174, 176, 201–7,
354, 356
diffusion, 16, 18, 126
diffusion equation, 269, 270, 278,
283, 285, 293
discrimination angle, see angular
discrimination
dispersion relation, 46, 122
dissociative ionization, 243
distorted-wave approximation, 91,
170, 174, 189, 192, 216, 219, 221,
230
distorted-wave Born
approximation, 69, 71, 92, 163
Doppler broadening of annihilation
radiation, 2, 11, 14, 15, 31, 271,
274, 281, 297–300, 365
double differential cross
sections, 252–8
double ionization, 199, 206, 207, 234,
244, 248–51
E × B plates, 179, 188, 237, 238
effective range formula, 334
eikonal Born series, 45, 69, 132
elastic positron scattering, 40–7, 50,
94–149
by alkali atoms, 122–6
by atomic hydrogen, 95–113, 130,
131, 138
by H
2
, 127, 128
by helium, 113–23, 138, 140
by other noble gases, 126, 140,
142–8
by other molecules, 126–9
electric fields
positron annihilation in, 269, 271,
272, 293–7, 304, 305
positron drift in, 269, 271, 304, 305
electron–atom scattering: 41, 42, 75,
77, 90
elastic scattering, 145
excitation, 224, 225
ionization, 227, 228, 230, 237, 252,
257
total cross sections, 41, 68, 72–6,
80–7
electron capture to the continuum
(ECC), 231, 233, 253, 255
Index 451
electron scavengers, 213
end effects, 58, 60
equilibrium region of positron
lifetime spectrum, 271, 276, 278,
281, 286
exchange quenching, see also
quenching of
ortho-positronium, 328, 330,
337, 339, 351
excitation cross sections, 37, 43, 91,
92, 127, 214–27
excited states of positronium, 314,
332, 334, 335
Fadeev equations, 158, 331
Feshbach projection operators, 97
Feshbach resonance, 11, 109, 157,
163, 349, 364
Feynman diagrams, 5, 372
final-state interaction, 228
first Born approximation, see Born
approximation
fixed-nuclei approximation, 83, 126
Fock–Tani field-theoretic
approach, 192
forbidden decay modes of
positronium, 326
forward scattering, see small-angle
scattering
forward scattering amplitude, 45–7,
69
Frank–Condon principle, 82
gamma-rays
energy spectrum, 8, 9, 15
three-gamma-ray annihilation, 9,
176
two-gamma-ray annihilation, 176,
183
Harris variational method, 109, 113,
120
hidden crossing theory, 156
Hylleraas functions, 105, 107, 109,
127, 363, 364, 370
hyperfine structure of positronium,
see positronium hyperfine
structure
implantation depth, 18
inelastic conversion, 339
inelastic scattering, see excitation
cross sections, positronium
formation, ionization
inner shell ionization, 251, 259–63
ionization
by antiproton impact, 245, 246
by electron impact, 93, 227–31,
256, 257, 261, 262
by positron impact, 93, 179, 180,
214, 215, 227–63
by proton impact, 240, 245
double, see double ionization
of atomic hydrogen, 229–34
of positronium, 334
Jackson–Schiff approximation, 175,
189
K-matrix, 152–7
Kohn variational method
as applied to elastic
scattering, 104–13, 124, 127, 333
as applied to positronium
formation, 153–6, 167
lifetime spectra, 13, 122, 269, 274,
275
Liouville’s theorem, 25
Lotz formula, 251
Low Energy Antiproton Ring
(LEAR), 245, 374–8, 386
Lyman-α radiation, 195, 197, 322–4,
387
magnetic-gradient traps, 383
magnetic guiding fields, 48, 51, 58, 59
magnetic mirror, 51, 61
many-body phenomena, 286, 290–3,
341, 351
Massey criterion, 381
452 Index
merging of positron and electron
collision cross sections, 45, 67,
68, 75, 92, 93, 261
partial cross sections, 67, 68, 81
total cross sections, 45, 67, 68, 75,
79, 81, 131
method of models, 114–6, 127, 166
mobility edge, 295
model potentials, 71, 74, 128, 129,
171
moderators, 16, 19
boron, 51, 53
copper, 54
MgO, 3, 48
solid rare gases, 21
tungsten, 22, 48, 133, 142, 177, 221
momentum transfer cross sections
for positrons, 122, 270, 283, 284,
303
for positronium, 342, 344, 346, 359
Monte Carlo methods, 200, 201, 253,
258, 283, 295, 312, 380, 382
multiple ionization, 248–51; see also
double ionization
multiple scattering, 223, 224, 290
Onsager radius, 209
optical model, 71, 73, 146
optical potential, 69, 70, 96–8, 103,
109, 132
optical theorem, 44–6, 69, 96, 157
Ore gap, 38, 151, 157, 160, 167–9
Ore model of positronium
formation, 207–12, 347
ortho-positronium, see positronium
pair production, 1
para-positronium, see positronium
partitioning of the total cross
section, 40, 89–93, 133
Penning trap, 274, 374, 375, 382–4
photodetachment of Ps
−
, 331, 363–5
pick-off quenching, see also quenching
of ortho-positronium, 212, 298,
312, 327, 329, 336, 339–43
pitch angle, 59, 61
polarizability, 39, 100, 117, 171, 266,
330
polarization interaction, 35, 36, 39,
69, 88, 100, 110–3, 119, 128, 129,
171, 243
polarized-orbital approximation, 47,
69, 71, 74, 86, 92, 98–101, 120,
126, 130, 138, 142, 146, 185, 192
positron
annihilation, see annihilation
impact ionization, see ionization
lifetime spectra, see lifetime
spectra
moderation, 17–21; see also
moderators
positron beams, 3, 16, 19–26, 313
brightness enhanced, 25, 26, 34,
369
electrostatically guided, 24–6, 51,
54, 60, 142, 180
magnetically confined, 21–3, 48,
51, 52, 58, 59, 133, 141, 221, 235,
356, 364
positron collisions with atoms and
molecules
alkali atoms, 35, 44, 54, 55, 76–9,
122–6, 218, 219, 218, 219
atomic hydrogen, 43, 44, 56, 57,
79–81, 95–113, 131, 132, 137,
138, 152–66, 217, 231–41, 253,
258
helium, 35, 41, 47, 54, 59, 63–5,
68, 69, 89, 91, 113–23, 134, 138,
218–24, 233, 234, 241, 246, 248,
250
molecules, 81–8, 126–9, 243–5, 258
noble gases, 42, 47, 70–4, 141,
241–3, 252, 255, 258
positron diffusion, see diffusion,
diffusion equation
positron drift, 209, 301–6
positron lifetimes, 126, 214; see also
annihilation
positron mobility, 305, 306
positron plasmas, 368, 383, 384
Index 453
positron trap, 278–81, 285–99, 379,
382–4
POSITRONFIT computer
program, 276
positronium, 2, 6–10, 38, 101–3,
307–61
annihilation rates and
lifetimes, 307–17, 327
Bose–Einstein condensate, see
Bose–Einstein condensate
energy levels, 321–5
hyperfine structure, 314, 317–20
in bubbles, 340, 341
ortho-positronium, 2, 7, 13, 308–15
para-positronium, 7, 308, 314
quenching, see quenching of
ortho-positronium
work function, see work function
positronium beams, 32–4, 161, 202,
353–61
positronium diffraction, 353
positronium formation, 27–34, 37–9,
44, 75, 124, 135–9, 150–213
beam–foil technique, 32
in positron–alkali collisions, 171–4,
182, 192–5
in positron–helium collisions,
166–70, 185–7
in positron–hydrogen collisions,
152–66, 180–2, 190–2
into excited states, 27, 78, 150,
165, 166, 169–75, 185, 192,
195–9, 202, 311, 354, 358
into the ground state, 27, 78, 150,
172; see also specific targets,
models of, see Ore model, spur
model, resonant model
positronium formation fraction, 30,
31, 207–13, 277, 281, 336
positronium hydride, PsH, 11, 39,
333, 349–53, 370
positronium molecule, Ps
2
, 348, 349,
362, 368–70
positronium negative ion, Ps
−
, 2, 10,
36, 348, 362–8, 370
positronium scattering, 38, 138,
328–36, 358–61
prompt peak, 211, 276, 277
proton–atom scattering, 150, 200,
201, 240
comparisons with positron
scattering, 200, 201
pseudostates, 103, 124, 195, 233, 334
pulsed electric fields, 295–7
quenching of ortho-positronium, 212,
298, 312, 313, 316, 327–32,
336–43, 351
radiationless annihilation, see
annihilation
Ramsauer minimum, 36, 37, 42, 65,
67, 71, 81, 122
reactive scattering method, 157
random-phase approximation, 121,
220
recoil peak, 230
remoderator, 25, 313, 356
resonance, 10, 11, 36, 86, 125, 130,
157, 162, 267, 334, 363
see also Feshbach resonance,
shape resonance
resonant excitation, 77, 216–21, 325
resonant model of positronium
formation, 210
R-matrix method, 44, 84, 103, 113,
127, 128, 135, 138, 158, 159, 191
Rost–Pattard parameterization, 251
scattering length, 47, 110, 118, 121,
122, 331–4
Schumann–Runge continuum, 225
Schwartz singularities, 108, 109
second Born approximation, see also
Born approximation, 216, 219
shape resonance, 86
shoulder region in positron lifetime
spectrum, 276, 277, 283, 284,
294
silica aerogel, 312, 337, 342–5
454 Index
small-angle scattering, 44, 50, 51, 54,
59, 61–72, 74, 80, 146, 161, 182,
216, 223, 225, 257
Soa gun, 24, 254, 255
sources of positrons, 13, 17, 18, 22,
26, 48, 51, 249, 259, 301
spiralling, 58, 59, 62
spur model of positronium
formation, 209, 210
S-matrix, 136, 152, 157
slowing down equation, 285
slowing down of positronium, 337,
342–7
static approximation, 38, 98, 103,
120
static-exchange approximation, 328,
329, 332–6
static interaction, 35, 39, 67, 97, 98,
110, 128, 129, 243
surfaces, 19–22, 27, 30, 34, 353
thermalization
of positronium, 342–7
of positrons, 16, 18, 209, 271, 276,
281–7, 299, 301, 304
Thomas mechanism, 166, 202, 207
Thomas peak, 166
threshold effects, 67, 129, 130–40,
158, 183, 189, 228, 229, 246–8
time of flight (TOF), 48, 50, 51, 59,
62, 142, 221–5, 234, 235, 249, 253
time-resolved Doppler broadening
studies (TRDBS), 342, 343, 346,
347
T-matrix, 45, 110, 130, 152, 157, 215,
216, 231
total cross sections, 40–93
total ion yield, 179–83, 188
touch-down energy
distribution, 207–9
trap, see positron traps
triple differential cross sections, 227,
230–3, 258
triple ionization, 251
unitarity of S-matrix, 136
van der Waals interaction, 39, 321,
328, 332, 335, 345
variational methods, see Kohn,
Harris variational methods
Wannier theory of ionization
for electrons, 228, 229, 246–8
for positrons, 228, 229, 246–8
weak equivalence principle
(WEP), 373, 374, 387
work function, 19, 27, 28, 323
Z
eff
, 265–72, 278, 281–91, 294, 303
1
Z
eff
, 277, 327, 335–7, 340