A Career In Theoretical Physics by P. W. Anderson

By P. W. Anderson

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Molecule (1), so that T' and Tf axe. still essentially This integration is legitimate because of our assumption diagonal in molecule (2) because they are so in molecule that dr can be chosen long compared to the duration (1) (this is the interesting case corresponding to resonant of one collision. We call the resulting T matrix T{da); interactions). In either case, a reduces to the following then the average in (41) gives the following equation simple form: for?. p(da in dr) = nvdadr. W) 1 1 . J (42) aa%= (PB)«2 (43) r X It is obvious that the shift in frequency and the linebreadth follow from the real and imaginary parts of the number a, precisely according to (28).

Mod. Phys. 20, 668 (1948)) and it is to be hoped that the observation of one or two of these lines will definitely settle the question. C. Foreign Gas Broadening: Van der Waals Interactions Broadening of microwave lines by pressures of foreign gases has been the subject of some experimental investigations. 20,24 The theoretical approach to the problem of foreign gas broadening has generally been that of computing the Van der Waals interactions between the molecules concerned and using these to obtain broadening cross sections.

However, several simple models and some general reasoning have led us to conclude that a definite upper limit for the real part of a, and a probable lower limit, can be assigned on the basis of two rather arbitrary choices of S{b), while a third choice gives a good working approximation. Figure 1 illustrates the various possibilities. Our three approximate "ideas" for curves are labeled "approximation # 1 , 2 , 3 . " # 1 is essentially the S(b) curve used in the phase-shift theory. 5#i(6) = l-cos(25 2 (6))».

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