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CHAPTER 3 / PHOTOELECTRON SPECTROSCOPY
␥ ⫽ (1 ⫺ v
2
/c
2
)
⫺1/2
⫽ ratio of electron mass to its rest mass (m/m
o
),
and
o
the orbital angular frequency.
E
XAMPLE.
Consider the 7-GeV Advanced Photon Source at Ar-
gonne National Laboratory. In a curved section of this synchrotron
with local radius equal to 30 m, calculate the energy range of the
synchrotron radiation.
S
OLUTION.
The 7-GeV designation means that the electron energy
is equal to 7 GeV. Therefore,
␥
is equal to 7000/0.5 ⫽ 14,000, since
the electron rest mass is equal to 0.5 MeV. At these energies, the speed
of electrons is effectively the speed of light (⫽ 3 ⫻ 10
8
m/s). For a
local radius of 30 m, the angular frequency
o
⫽ 3 ⫻ 10
8
/30⫽ 10
7
/
sec. The energy range of synchrotron radiation is then equal to
␥
3
ប
o
⫽ (14000)
3.
(1.05 ⫻ 10
⫺34
) (10
7
) / 1.6 ⫻ 10
⫺19
eV ⫽ 18 keV.
Q
UESTION FOR
D
ISCUSSION.
What are the major advantages and
disadvantages of using synchrotron radiation?
3.3 DETECTORS
Most photoelectron spectrometers are of the band-pass type. With labo-
ratory photon sources, typical photoelectron signals are on the order
of a few hundred to a few hundred thousand electrons per second
(10
⫺17
to 10
⫺14
A). Such small signals are normally detected by electron
counting: The photoelectrons impinge on an electron multiplier that is
set to give a gain on the order of 10
5
, that is, for each electron entering
the multiplier, a charge pulse containing 10
5
electrons will emerge at
the output end of the multiplier. The electron pulse is amplified further
and counted by standard counting electronics
1
. In some cases, parallel
detection using an electron multiplier array is used to increase the
effective data rate. Also, electron optics are sometimes used to collect
photoelectron signals from areas as small as 1–10 microns.
1
At a multiplier gain of 10
5
, the total charge is 1.6 ⫻ 10
⫺14
C. When this charge
falls on a capacitor (as in the case of a field effect transistor), one obtains a stepwise
increase in voltage dV. For capacitance ⫽ 1pF,dV ⫽ 0.016 V. This voltage signal
can be readily conditioned and amplified for further processing. Counting electronics
can be set to discriminate against signals that are too low (background noise) or too
high (occasional glitches). Most counting electronics can handle signals up to ⬃1 ⫻
10
6
per second.