ls3_unit_6 - THE INTERACTION OF RADIATION AND MATTER...

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T HE I NTERACTION OF R ADIATION AND M ATTER : Q UANTUM T HEORY P AGE 62 R. Victor Jones, April 28, 2000 VI. P HOTOELECTRIC D ETECTION AND P HOTON C OUNTING To introduce the subject let us quote Glauber in Photon Statistics 34 “Photon counters function by absorbing photons from the field. What they count are, strictly speaking, not photons but atomic photoabsorption processes rendered individuall detectable by an amplification mechanism of some sort. In most of the devices used experimental the fundamental absorption process is the photoemission of an electron. The amplifying mechanism for the photoelectrons is usually a cascade multiplier. The precise way in which amplification is achieved need not concern us here however, since it plays no direct role in determining what the counter detects. “An ideal photon counter would be one which is quite small in size and has a sensitivity independent of photon frequencies (at least over the spectral of the incident field). Both requirements can be met rather well, in fact, by the simplest possible model of a counter, a single atom which we observe to see whether and when it emits a photoelectron . Since the atom is quite small compared with the wave length of visible light most of the transitions it can undergo may be treated by means of the electric dipole approximation. in this approximation the atom is coupled to the field through the interaction Hamiltonian H = e r q γ γ r E r r , t ( ) in which r q γ is the spatial coordinate of the γ th electron of the atom relative to its nucleus which is located at r r . 34 From Fundamental Problems in Statistical Mechanics II (edited by E. G. D. Cohen), North-Holland Publishing (1968), pp. 140-187.
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T HE I NTERACTION OF R ADIATION AND M ATTER : Q UANTUM T HEORY P AGE 63 R. Victor Jones, April 28, 2000 “The intensity of a field is proportional to the rate at which a counter records photons, or in the case of our single-atom counter to the probability per unit time of our observing a photoabsorption process. …” With careful designed, high gain photomultipliers, it is possible to register the atomic ionization caused by individual, isolated photons. Following Glauber then we will take the photoelectric interaction Hamiltonian as H PE = e r r n n r E r R , t ( ) [ VI-1 ] where the r r n 's are the relative spatial coordinates of the electrons bound to a nucleus located at r R . First-order perturbation theory informs us that the transition amplitudes associated with the process of photoelectric absorption are proportial to the matrix elements
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T HE I NTERACTION OF R ADIATION AND M ATTER : Q UANTUM T HEORY P AGE 64 R. Victor Jones, April 28, 2000 f H PE i = e f
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