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we actually had a certain range Aœ, then we may not have the resolving power
needed to see a narrow curve. Ofhand, we cannot say whether the width in
--- Trang 420 ---
°
40 45 50 55 60 65 70
Wavelength in microns (10~4 cm)
Fig. 23-7. Transmission of infrared radiation through a thin (0.17 u})
sodium chloride film. [After R. B. Barnes, Z. Phys¡ik 75, 723 (1932).
Kittel, Introduction to Solid State Physics, Wiley, 1956.]
Fig. 23-7 is natural, or whether it is due to inhomogeneities in the crystal or the
ñnite width of the slit of the spectrometer.
Now we turn to a more esoteric example, and that is the swinging of a magnet.
Tf we have a magnet, with north and south poles, in a constant magnetic field,
the N end of the magnet will be pulled one way and the S5 end the other way, and
there will in general be a torque on it, so ít will vibrate about its equilibrium
position, like a compass needle. However, the magnets we are talking about are
a‡oms. 'These atoms have an angular momentum, the torque does not produee a
simple motion in the direction of the field, but instead, of course, a precession.
Now, looked at from the side, any one component is “swinging,” and we can
disturb or drive that swinging and measure an absorption. The curve in Fig. 23-8
represents a typical such resonance curve. What has been done here is slightly
diferent technically. "The frequency of the lateral feld that is used to drive
this swinging is always kept the same, while we would have expected that the
investigators would vary that and plot the curve. They could have done it that
way, but technically it was easier for them to leave the frequency œ fñxed, and
change the strength of the constant magnetic field, which corresponds to changing
œg in our formula. 'They have plotted the resonance curve against œ0. Anyway,
this is a typical resonance with a certain œọ and +.
Now we go still further. Our next example has to do with atomiec nuclei. "The
motions of protons and neutrons in nuclei are oscillatory in certain ways, and we
--- Trang 421 ---
2.0
1.8
SIŠ 1.4
S812
GÌE 42
la OERSTEDS
»J2 1.0 ~
S5 0ø
SE 0.6
0.2
8100 8200 8300 8400 8500 8600 8700 8800
STATIC MAGNETIC FIELD IN OERSTEDS
Fig. 23-8. Magnetic energy loss in paramagnetic organic compound
as function of applied magnetic field intensity. [Holden et al., Phys.
Rev. 75, 1614 (1949)]
can demonstrate this by the following experiment. We bombard a lithium atom
with protons, and we discover that a certain reaction, producing +-rays, actually
has a very sharp maximum typical of resonance. We note in Eig. 23-9, however,
one difference from other cases: the horizontal scale is not a frequency, it is an
energ! The reason is that in quantum mechanics what we think of classically as
the energy will turn out to be really related to a frequency of a wave amplitude.
'When we analyze something which in simple large-scale physics has to do with a
frequency, we fnd that when we do quantum-mechanical experiments with atomic
matter, we get the corresponding curve as a function of energy. In fact, this
curve is a demonstration of this relationship, in a sense. It shows that frequency
and energy have some deep interrelationship, which of course they do.
Now we turn to another example which also involves a nuclear energy level,
but now a mụch, much narrower one. The œ in Fig. 23-10 corresponds to an
energy of 100,000 electron volts, while the width + is approximately 105 electron
--- Trang 422 ---
: L]| HN L | |
s 4 Í í b : N
2 Z5 l : }TEm==m —?
BEPE/PRIrienman
300 400 500 600
PROTON ENERGY IN KEV
Fig. 23-9. The intensity of gamma-radiation from lithium as a func-
tion of the energy of the bombarding protons. The dashed curve Is a
theoretical one calculated for protons with an angular momentum £ = 0.
[Bonner and Evans, Phys. Rev. 73, 666 (1948)]
AI —5 —5 —5
m= 0 2-10 410 56V, A
0 -4 0 +4 +8 cm/sec vV
~—0.8%
Fig. 23-10. [Courtesy of Dr. R. Mössbauer]
--- Trang 423 ---
volt; in other words, this has a Q of 101! When this curve was measured it was
the largest @Q of any oscillator that had ever been measured. It was measured by
Dr. Mössbauer, and it was the basis of his Nobel prize. The horizontal scale here
1s velocity, because the technique for obtaining the slightly diferent requencies
was to use the Doppler efect, by moving the source relative to the absorber. Ône
can see how delicate the experiment is when we realize that the speed involved is
a few centimeters per secondl Ơn the actual scale of the figure, zero frequency
would correspond to a point about 1010 em to the left—slightly of the paperl
c 2 \ 7
Đ 3 Z
= NN 4
ĐS TH %
li G:
° SN
200 300 400 500
P‹ (MeV/c)
Fig. 23-11. Momentum dependence of the cross section for the
reactions (a) K” +p + A+ xử +7 and (b) K” +p > K?+n.
The lower curves in (a) and (b) represent the presumed nonresonant
backgrounds, while the upper curves contain in addition the superposed
resonance. [Ferro-Luzzi et al., Phys. Rev. Lett. 8, 28 (1962)]
Jinally, ifƒ we look in an issue oŸ the Phsical Reuieu, say that of January 1,
1962, will we fñnd a resonance curve? Every issue has a resonance curve, and