Chapter 10
Nuclear Resonaynce Vibrational
Spectroscopy
We learned in Chap. 9 that Mössbauer spectroscopy and nuclear forward scattering
rely on the zero-phonon, recoil-free fraction, as determined by the Lamb-Mössbauer
factor—f LM . In the Mössbauer experiment, the intensity is reduced by this factor, so
that the observed cross section is reduced from the total cross section according to
σ(0) ~ (π/2) σ N f LM . However, there is a “sum rule” that states that the integrated
cross section for a nuclear transition remains the same [478]. So, where does this
missing intensity go?
The missing intensity is in the “recoil fraction,” 1 À f LM , in which nuclear
transitions couple to vibrations, resulting in the creation or destruction of phonons
(Fig. 10.1). It turns out that this fraction contains useful and detailed information
about the vibrational properties of a sample. Before the advent of synchrotron
radiation sources, most experiments probed the recoil fraction indirectly, by observing the loss of Mössbauer intensity. (There were also a few heroic experiments with
radioactive sources spinning around in ultracentrifuges to achieve the requisite
Doppler shifts.) With high brightness third-generation sources, we can now probe
the recoil fraction directly by the technique known as “Nuclear Resonance Vibrational Spectroscopy” (“NRVS”) or sometimes called “Nuclear Resonant Inelastic
X-Ray Scattering” (“NRIXS”).
Why is NRVS of interest to chemists, biologists, geologists, and materials
scientists? Among other things, it is an exciting tool because:
• NRVS yields a vibrational spectrum for a specific isotope of a specific element.
• The resulting vibrational spectrum is easily calculated and interpreted.
• The isotopic sensitivity allows labeling experiments, say of surfaces or of specific
sites in metalloenzymes.
• NRVS provides quantities such as the speed of sound and average kinetic energy.
Before going further, we present a pair of examples to show what all the
excitement is about (Fig. 10.2). At one extreme is the spectrum of Fe metal, in
which the vibrations are described as propagating phonons with a continuous density
© Springer Nature Switzerland AG 2020
S. P. Cramer, X-Ray Spectroscopy with Synchrotron Radiation, Biological and Medical
Physics, Biomedical Engineering, https://doi.org/10.1007/978-3-030-28551-7_10
257
Nuclear Resonaynce Vibrational
Spectroscopy
We learned in Chap. 9 that Mössbauer spectroscopy and nuclear forward scattering
rely on the zero-phonon, recoil-free fraction, as determined by the Lamb-Mössbauer
factor—f LM . In the Mössbauer experiment, the intensity is reduced by this factor, so
that the observed cross section is reduced from the total cross section according to
σ(0) ~ (π/2) σ N f LM . However, there is a “sum rule” that states that the integrated
cross section for a nuclear transition remains the same [478]. So, where does this
missing intensity go?
The missing intensity is in the “recoil fraction,” 1 À f LM , in which nuclear
transitions couple to vibrations, resulting in the creation or destruction of phonons
(Fig. 10.1). It turns out that this fraction contains useful and detailed information
about the vibrational properties of a sample. Before the advent of synchrotron
radiation sources, most experiments probed the recoil fraction indirectly, by observing the loss of Mössbauer intensity. (There were also a few heroic experiments with
radioactive sources spinning around in ultracentrifuges to achieve the requisite
Doppler shifts.) With high brightness third-generation sources, we can now probe
the recoil fraction directly by the technique known as “Nuclear Resonance Vibrational Spectroscopy” (“NRVS”) or sometimes called “Nuclear Resonant Inelastic
X-Ray Scattering” (“NRIXS”).
Why is NRVS of interest to chemists, biologists, geologists, and materials
scientists? Among other things, it is an exciting tool because:
• NRVS yields a vibrational spectrum for a specific isotope of a specific element.
• The resulting vibrational spectrum is easily calculated and interpreted.
• The isotopic sensitivity allows labeling experiments, say of surfaces or of specific
sites in metalloenzymes.
• NRVS provides quantities such as the speed of sound and average kinetic energy.
Before going further, we present a pair of examples to show what all the
excitement is about (Fig. 10.2). At one extreme is the spectrum of Fe metal, in
which the vibrations are described as propagating phonons with a continuous density
© Springer Nature Switzerland AG 2020
S. P. Cramer, X-Ray Spectroscopy with Synchrotron Radiation, Biological and Medical
Physics, Biomedical Engineering, https://doi.org/10.1007/978-3-030-28551-7_10
257