pulsed synchrotron source (Figs. 9.17 and 9.18), which starts the “clock” for the
experiment. The incoming beam direction defines the quantization axis, and the
decay back to the ground state is typically monitored by one or more detectors
perpendicular to this axis. The basic physics is thus the same for both radioisotope
and synchrotron experiments—a time-dependent angular correlation results from the
nucleus precessing in the local chemical and magnetic environment. Alternatively,
one can view the results as quantum beats between two or more nuclear states
excited by the synchrotron beam.
As derived by Sergueev in the case of M 1 magnetic dipole transitions, SRPAC for
a powder sample with only a quadrupole splitting can be described by [454]:
I t, θ
ð Þ ¼ I 0 e
Àt=τ 0 1 À 2 Á A
exp
22 Á P 2 cos θ
ð
ÞÁG 22 t
ð Þ
Â
Ã
ð9:25Þ
with “anisotropy coefficient A 22 ,” “perturbation factor G 22 (t),” excited-state lifetime
τ 0 , and θ as the angle between the direction of the magnetic polarization h
!
1 of the
incoming photon and the direction of scattering for outgoing photon k
!
2 . Theoretical
anisotropy coefficients are given in Table 9.2. The experimental anisotropy coefficient will be reduced from the theoretical value because of the finite solid angle
covered by the scattered photon detector.
Table 9.1. Popular TDPAC isotopes [453]
Isotope
Half-life
Decay
Isomer
Half-life (ns)
E (γ 1 ) (keV)
E (γ 2 ) (keV)
62
Zn
9.2 h
EC /β
+
6 2
Cu
4.57
597
41
99
Mo
66 h
β
À
99
Tc
3.61
739
181
111m
Cd
49 months
IT
111 Cd
85.0
151
245
111
In
2.8 days
EC
111 Cd
85.0
171
245
111
Ag
7.5 days
β
À
111 Cd
85.0
97
245
133
Ba
10.5 years
EC
133 Cs
6.27
356
81
160
Tb
72 days
β
À
160 Dy
2.02
197
87
181
Hf
42 days
β
À
181 Ta
10.8
133
482
199m
Hg
43 months
IT
199 Hg
2.45
374
158
204m
Pb
67 months
IT
204 Pb
265
912
374
EC electron capture, β
+ positron emission β decay, β
À electron emission β decay, IT isomeric
transition
Fig. 9.17 Left: geometry of a TDPAC experiment. Right: geometry of the SRPAC experiment
9.6 Perturbed Angular Correlation
249
experiment. The incoming beam direction defines the quantization axis, and the
decay back to the ground state is typically monitored by one or more detectors
perpendicular to this axis. The basic physics is thus the same for both radioisotope
and synchrotron experiments—a time-dependent angular correlation results from the
nucleus precessing in the local chemical and magnetic environment. Alternatively,
one can view the results as quantum beats between two or more nuclear states
excited by the synchrotron beam.
As derived by Sergueev in the case of M 1 magnetic dipole transitions, SRPAC for
a powder sample with only a quadrupole splitting can be described by [454]:
I t, θ
ð Þ ¼ I 0 e
Àt=τ 0 1 À 2 Á A
exp
22 Á P 2 cos θ
ð
ÞÁG 22 t
ð Þ
Â
Ã
ð9:25Þ
with “anisotropy coefficient A 22 ,” “perturbation factor G 22 (t),” excited-state lifetime
τ 0 , and θ as the angle between the direction of the magnetic polarization h
!
1 of the
incoming photon and the direction of scattering for outgoing photon k
!
2 . Theoretical
anisotropy coefficients are given in Table 9.2. The experimental anisotropy coefficient will be reduced from the theoretical value because of the finite solid angle
covered by the scattered photon detector.
Table 9.1. Popular TDPAC isotopes [453]
Isotope
Half-life
Decay
Isomer
Half-life (ns)
E (γ 1 ) (keV)
E (γ 2 ) (keV)
62
Zn
9.2 h
EC /β
+
6 2
Cu
4.57
597
41
99
Mo
66 h
β
À
99
Tc
3.61
739
181
111m
Cd
49 months
IT
111 Cd
85.0
151
245
111
In
2.8 days
EC
111 Cd
85.0
171
245
111
Ag
7.5 days
β
À
111 Cd
85.0
97
245
133
Ba
10.5 years
EC
133 Cs
6.27
356
81
160
Tb
72 days
β
À
160 Dy
2.02
197
87
181
Hf
42 days
β
À
181 Ta
10.8
133
482
199m
Hg
43 months
IT
199 Hg
2.45
374
158
204m
Pb
67 months
IT
204 Pb
265
912
374
EC electron capture, β
+ positron emission β decay, β
À electron emission β decay, IT isomeric
transition
Fig. 9.17 Left: geometry of a TDPAC experiment. Right: geometry of the SRPAC experiment
9.6 Perturbed Angular Correlation
249