Frank A., Jolie J., Van Isacker P. Symmetries in Atomic Nuclei: From Isospin to Supersymmetry
Подождите немного. Документ загружается.
Index
A
Algebra
definition of, 2–4
dynamical, 5, 8, 20, 22, 24–27, 65,
66, 82, 84, 85, 87, 98–104, 112,
133–136
generator of, 3–5, 8, 22–26, 43–44,
47, 52, 56, 65, 82–84, 87, 88, 99,
109, 112, 117, 118, 134, 135, 137,
155, 158–159, 165–167, 169
graded, 26, 88, 150, 156, 158–159
isomorphic, 82–83
nested, 8, 20–21, 27, 64, 65, 99,
109, 113
spectrum generating, 8, 54
symmetry, 18–32
Algebras
SO(2), 3, 11, 12, 15, 17, 22, 23, 33, 55
SO(3), 3, 47, 48, 54–55, 64–69, 83,
86, 109, 115, 116, 139
SO(5), 54–56, 64–69, 74, 86, 96, 102,
107, 109, 110, 114, 126, 139, 140
SO(6), 54–60, 63–69, 73–74, 78,
84–86, 89–91, 96, 97, 99, 100, 102,
108–110, 113–114, 122, 124–127,
130, 136, 139, 141, 150
SO(8), 24, 108–110, 112, 114
Sp(3,R), 50
SU(1,1), 58
SU(2), 10–12, 14, 15, 17, 22, 24,
31–38, 51, 83, 99, 105–107, 118,
137, 139, 140, 158, 172
SU(3), 21–23, 39, 41, 47–51, 54–55,
57–60, 62–64, 66–68, 85, 116, 122,
124, 158, 172
SU(4), 42–49, 84, 109, 112–113,
115, 172
U(5), 54–60, 62–64, 72–75, 78, 85,
99–100, 102, 114, 122, 124, 126,
130, 138
U(6), 47, 52, 54–55, 64, 66, 67, 84,
86, 96, 99, 102, 105, 112–118,
121, 122
U(6/4), 136
U(6/12), 88–91, 95–97, 99–103, 136
U(15), 57
B
Bethe ansatz, 34, 36–37
Binding energy, 13, 37, 39, 45, 52–54,
86, 89, 120
C
Casimir operator, 4, 7–8, 21, 27, 33, 47,
54–56, 64, 66, 85, 86, 89, 99, 101,
109, 112–113, 135
Coherent state, 58, 59
Collective model, 39–41, 71
Consistent-Q formalism, 103
Cooper pairs, 52, 105, 111
Core excitation, 69–71
Coupling coefficient, 11–13, 16–17
D
Degeneracy, 6–7, 15, 30, 38, 47, 49,
55, 89
F
F spin
multiplet, 119–121
mass equation (FMME), 120
symmetry, 118–121
G
Gell-Mann-Okubo mass formula, 21, 23
183
184 Index
Group
continuous, 3
definition of, 2–4
finite, 2–4
order of, 2–3
I
IBFM (Interacting Boson-Fermion
Model), 79, 80–85, 87, 89, 96, 99,
103, 133, 135, 138
IBM-2, neutron-proton interacting
boson model, 119–125
IBM-3, 111, 113, 116–118
IBM-4, 106, 111–117
IBM (Interacting boson model), 29,
51–69, 72, 79, 105, 117–121,
133–136, 138, 172
IMME (Isobaric-multiplet mass
equation), 13–15
Interaction
exchange, 82, 167
isoscalar, 13, 108
isovector, 11, 108, 110, 113
long-range nucleon-nucleon, 164–167
pairing, 31–34, 36, 57, 105, 107–108,
110–111
quadrupole, 29, 31, 47, 48, 58,
71, 82
residual, 30–31, 44, 46, 50, 51–52
Intruder state, 71–74, 76
Isoscalar factor, 11, 12, 16, 17, 67,
85, 86
Isospin
multiplet, 13
symmetry, 8–11, 16, 17, 118
I spin
multiplet, 70–71, 119
symmetry, 70, 76, 118–119
J
Jacobi identity, 3, 5
L
Landau theory, 60–63
Lie
algebra, 3–7, 23–25, 42, 47, 52, 82–84,
88, 150, 155, 156, 158–159, 171
group, 3
Lipkin-Meshkov-Glick(LMG) model,
38, 50
Liquid drop model, 39, 48, 58
N
Nuclei
As, 18
Au, 85, 134, 136, 139, 140, 141–153
Cd, 70–78
Dy, 120
Er, 120
Ga, 18
Ge, 18
Hf, 120
Hg, 120
Mo, 123–131
Ne, 48
Os, 120
Pb, 32
Pt, 56, 64, 68, 69, 89–97, 120, 134,
136, 139, 140, 143, 147, 153
Rh, 101, 102
Ru, 76, 100
Sn, 69–70, 130
W, 120
Yb, 120
P
Pairing, 106–112
Pauli principle, 19, 43, 79, 80, 106, 169
Phase diagram
of IBFM, 103
of IBM, 62
Phase transition, 62–63, 103
Pseudo-SU(3) model, 49
R
Reduced isospin, 107, 109
Representation
irreducible, 6, 7, 13, 16, 26, 42, 43,
99, 135, 137
reducible, 23, 43, 47, 48, 54, 84–86,
88, 96, 118, 137
Richardson model, 34–37
S
Scattering, 17, 74, 75, 77, 123–124,
128–130, 162–164, 170
Second quantization, 18–19, 32, 46
Index 185
Selection rule, 17, 56, 69, 140
Self-conjugate nuclei, 16
Seniority, 33, 51, 74, 106, 107, 109, 110,
114, 117, 138
Separation energy, 37, 38
Shell model, 29–57, 81, 96, 105, 108,
110, 111, 114–116, 118, 125,
131, 138
SO(8) model, 109, 110–112, 114
Spin-orbit interaction, 30, 31, 44, 49
Spin
singlet, 106, 108
triplet, 108
Standard model, 155–158
Strings, 156–158
Structure constants, 3–5, 26
SU(3) model, 39, 48–49, 172
SU(3) octet, 22, 23
SU(4) model, 39, 41–48, 108–116
Superalgebra, 24–26, 65, 88,
133–135, 159
Super
conductivity, 34
fluidity, 33–34, 38, 79, 110
multiplet, 47, 87–89, 109, 113, 115,
116, 134–138, 147–150
model, 39, 41, 44, 46
string, 87, 155–158, 171
Supersymmetry
extended, 136–141
with neutrons and protons, 105–125
nuclear, 87–89
quantum mechanics, 158–159
without dynamical symmetry, 98–104
Symmetry
algebra, 5, 8, 20–21, 27, 65,
98–99, 150
Bose-Fermi, 82–86, 90, 98, 103
breaking, 7–8, 12, 16, 20, 22, 47, 169,
171–172
definition of, 2–3, 5–6
dynamical, 7–8, 18–22, 54–57, 64–69,
98–104
mixed, 43, 76, 86, 122, 123–131
with neutrons and protons, 105–125
parameter, 57, 83, 112
partial dynamical, 64–69, 103
permutation, 42–43
pseudo-spin, 49, 83, 86, 89, 116, 137
quasi-spin, 24, 32, 33, 38, 105
transformation, 4–5, 8–9, 164, 171
T
Transfer
one-nucleon, 138–141
two-nucleon, 138, 150–153
V
Valence shell, 30, 31, 38, 46, 52, 69–70,
105, 111, 117, 119
W
Wigner-Eckart theorem, 11–13,
16–17, 67
Wigner’s
mass anomaly, 44–45
principle, 7
Y
Young
diagram, 42–44
pattern, 43
tableau, 43, 118