10.7 Prognosis
Shenoy and collaborators have speculated on the future of nuclear spectroscopies at
synchrotron sources [503]. A recent workshop report on the potential of XFELO
sources predicted enormous gains in sensitivity and range of isotopes (see Chap. 12)
[504]. Improved sources will clearly provide more flux, allowing for better data,
study of more dilute samples, weaker modes, and so on. These sources will also
provide more high-energy flux and shorter pulses, perhaps quite a few resonances in
the 40–100 keV region for NRVS experiments (Fig. 10.4). It remains to be seen if
future monochromator developments with novel materials will allow meV resolution
above 40 keV [117]. It would also be valuable to have more detectors with time
resolution on the 100 ps scale, as recently demonstrated by Masuda and coworkers
[189]. The combination of these three improvements could open up at least another
dozen resonances, including important elements such as W and Ni. Stay tuned.
10.8 Suggested Exercises
1. Estimate the temperature of the sample in Fig. 10.5 from the ratio of (a) peaks at
~Æ3 meV and (b) peaks at Æ17 cm
À1 . (A more accurate calculation would use the
areas.)
2. Calculate the overall one-, two-, and three-phonon excitation probabilities, P 1 , P 2 ,
and P 3 , assuming a Lamb-Mössbauer factor f LM of (a) 0.85 and (b) 0.5.
3. Calculate the average number (over the whole spectrum) of phonons excited,
, assuming a Lamb-Mössbauer factor f LM of (a) 0.85 and (b) 0.5.
4. Compare the relative cross sections for an
57 Fe vs. a
119 Sn nucleus in a
powder sample, assuming T ¼ 50 K and in both cases a mode frequency
150 cm
À1 , e
2
Fe ¼ e
2
Sn ¼0.2, and f LM ¼ 0.5.
5. Suppose you have an
57 Fe system with fundamental frequency 150 cm
À1 ,
e
2
Fe ¼ 0.2, and f LM ¼ 0.9. What is the ratio of two-phonon intensity (ϕ αα ) to
one-phonon intensity (ϕ αα ) in the low-temperature limit of T ~ 0 K?
10.9 Reference Books and Review Articles
1. Ralf Röhlsberger, Nuclear Condensed Matter Physics with Synchrotron Radiation - Basic Principles, Methodology and Applications, Springer, Berlin/Heidelberg, 2004. ISBN 3-540-23244-3.
2. E. E. Alp, W. Sturhahn, T. S. Toellner, J. Zhoa, M.Hu, D. E. Brown. “Vibrational
Dynamics Studies by Nuclear Resonant Inelastic X-ray Scattering”, Hyp. Int.
144/145: 3–20, 2002.
10.9 Reference Books and Review Articles
277
Shenoy and collaborators have speculated on the future of nuclear spectroscopies at
synchrotron sources [503]. A recent workshop report on the potential of XFELO
sources predicted enormous gains in sensitivity and range of isotopes (see Chap. 12)
[504]. Improved sources will clearly provide more flux, allowing for better data,
study of more dilute samples, weaker modes, and so on. These sources will also
provide more high-energy flux and shorter pulses, perhaps quite a few resonances in
the 40–100 keV region for NRVS experiments (Fig. 10.4). It remains to be seen if
future monochromator developments with novel materials will allow meV resolution
above 40 keV [117]. It would also be valuable to have more detectors with time
resolution on the 100 ps scale, as recently demonstrated by Masuda and coworkers
[189]. The combination of these three improvements could open up at least another
dozen resonances, including important elements such as W and Ni. Stay tuned.
10.8 Suggested Exercises
1. Estimate the temperature of the sample in Fig. 10.5 from the ratio of (a) peaks at
~Æ3 meV and (b) peaks at Æ17 cm
À1 . (A more accurate calculation would use the
areas.)
2. Calculate the overall one-, two-, and three-phonon excitation probabilities, P 1 , P 2 ,
and P 3 , assuming a Lamb-Mössbauer factor f LM of (a) 0.85 and (b) 0.5.
3. Calculate the average number (over the whole spectrum) of phonons excited,
4. Compare the relative cross sections for an
57 Fe vs. a
119 Sn nucleus in a
powder sample, assuming T ¼ 50 K and in both cases a mode frequency
150 cm
À1 , e
2
Fe ¼ e
2
Sn ¼0.2, and f LM ¼ 0.5.
5. Suppose you have an
57 Fe system with fundamental frequency 150 cm
À1 ,
e
2
Fe ¼ 0.2, and f LM ¼ 0.9. What is the ratio of two-phonon intensity (ϕ αα ) to
one-phonon intensity (ϕ αα ) in the low-temperature limit of T ~ 0 K?
10.9 Reference Books and Review Articles
1. Ralf Röhlsberger, Nuclear Condensed Matter Physics with Synchrotron Radiation - Basic Principles, Methodology and Applications, Springer, Berlin/Heidelberg, 2004. ISBN 3-540-23244-3.
2. E. E. Alp, W. Sturhahn, T. S. Toellner, J. Zhoa, M.Hu, D. E. Brown. “Vibrational
Dynamics Studies by Nuclear Resonant Inelastic X-ray Scattering”, Hyp. Int.
144/145: 3–20, 2002.
10.9 Reference Books and Review Articles
277