Abstract
The literature on effects of time-dependent hyperfine interactions on perturbed angular correlation (PAC) spectra is dominated by analyses based on models of stochastically fluctuating interactions. The Floquet formalism offers a convenient alternative analysis when interactions have a harmonic time dependence. This is demonstrated in the present work through simulation of PAC spectra due to uniformly rotating electric field gradients (EFGs). Physically, this situation would arise when PAC tracers are embedded in molecules with inertial rotation velocities much larger than molecular collision rates, in which case reorientation of rotation axes would be negligible on the characteristic PAC timescale. The prospect for using PAC to study inertial properties of molecules is explored through simulations with molecules modeled as symmetric, rigid bodies.
Similar content being viewed by others
References
Andrade, P.D.R., Vasquez, A., Rogers, J.D., Fraga, E.R.: Nuclear relaxation in (NH4)3HfF7 studied by gamma-gamma angular correlation. Physical Review B 1(7), 2912 (1953)
Shirley, D.A.: Estimates of correlation times of dissolved complexes from rotational tracer experiments. Journal of Chemical Physics 53, 465 (1970)
Wagner, H.F., Popp, M., Forker, M.: Determination of nuclear multipole relaxation times by measurements of statistically perturbed angular correlations. Z. Physik 248, 195 (1971)
Gerdau, E., Birke, J., Winkler, H., Braunsfurth, J.: Time-dependent electric quadrupole interactions in (NH4)3HfF7. Z. Physik 263, 5 (1973)
Baudry, A., Boyer, P., Vulliet, P.: PAC study of molecular reorientations in liquids. Hyperfine Interactions 2, 279 (1976)
Baudry, A., Boyer, P., Fabris, J.D., Vulliet, P.: PAC study of molecular rotational motions in dilute solutions. Hyperfine Interactions 10, 1057 (1981)
Danielsen, E., Bauer, R.: Analysis of perturbed angular correlation spectra of metal ions bound to proteins with rotational correlation times in the intermediate region. Hyperfine Interactions 62, 311 (1990)
Danielsen, E., Bauer, R., Schneider, D.: Rotational correlation times of peptides determined by perturbed angular correlations of γ-rays. European Biophysics Journal 20, 193 (1991)
Hemmingsen, L., Sas, K.N., Danielsen, E.: Biological applications of pertrubed angular correlations of γ-ray spectroscopy. Chemical Reviews 104, 4027 (2004)
Chakraborty, S., Pallada, S., Pedersen, J.T., Jansco, A., Correia, J.G.: Nanosecond dynamics at protein metal sites: An application of perturbed angular correlation (PAC) of γ-rays spectroscopy. Accounts of Chemical Research 50, 2225 (2017)
Haas, H., Röder, J., Correia, J.G., Schell, J., Fenta, A.S., Vianden, R., Larsen, E.M.H., Aggelund, P.A., Fromseger, R., Hemmingsen, L.B.S., Sauer, S.P.A., Lupascu, D.C., Amaral, V.S.: Free molecule studies by perturbed γ-γ angular correlations: A new path to accurate nuclear quadrupole moments. Physical Review Letters 126, 103001 (2021)
Abragam, A., Pound, R.V.: Influence of electric and magnetic fields on angular correlations. Physical Review 92, 943 (1953)
Marshall, A.G., Werbelow, L.G., Meares, C.F.: Effect of molecular shape and flexibility on gamma-ray directional correlations. The Journal of Chemical Physics 57(1), 364 (1972)
Winkler, H.: γγ angular correlations perturbed by randomly reorienting hyperfine fields. Z Physik A 276, 225 (1976)
Scherer, C.: Gamma-gamma angular correlations: A model for statistical perturbation with any correlation time. Nuclear Physics A 157, 81 (1970)
Blume, M.: Perturbed angular correlations: Perturbation factor for arbitrary correlation time. Nuclear Physics A 167, 81 (1971)
Fetter, A.L., Walecka, J.D.: Theoretical Mechanics of Particles and Continua. McGraw-Hill Publishing Company, New York (1980)
Thornton, S.T., Marion, J.B.: Classical Dynamics of Particles and Systems, 5th edn. Brooks/Cole—Thompson Learning, Pacific Grove (2004)
Shirley, J.H.: Solution of the Schrödinger equation with a hamiltonian periodic in time. Physical Review 138(4B), 979 (1965)
Chu, S.I., Telnov, D.A.: Beyond the floquet theorem: generalized floquet formalisms and quasienergy methods for atomic and molecular multiphoton processes in intense laser fields. Physics Reports 390, 1 (2004)
Hubbard, P.S.: Angular velocity of a nonspherical body undergoing rotational brownian motion. Physical Review A 15(1), 329 (1977)
Samoson, A., Tuherm, T., Reinhold, A., Heinmaa, I.: In: Klinowski, J. (ed.) New Techniques in Solid-State NMR, Topics in Current Chemistry, vol. 294, pp. 15–31. Springer (2005)
Nishiyama, Y.: In: Experimental Approaches of NMR Spectroscopy, ed. by T.N.M.R.S. of Japan, pp. 171–195. Springer (2018)
Kühne, D., Klappenberger, F., Krenner, W., Klyatskaya, S., Ruben, M., Barth, J.V.: Rotational and constitutional dynamics of caged supramolecules. Proceedings of the National Academy of Sciences 107(50), 21332 (2010)
Palma, C.A., Björk, J., Rao, F., Kühne, D., Klappenberger, F., Barth, J.V.: Topological dynamis in supramolecular rotors. Nano Letters 14, 4461 (2014)
Ito, M., Ebata, T., Mikami, N.: Laser spectroscopy of large polyatomic molecules in supersonic jets. Annual Review of Physical Chemistry 39, 123 (1988)
Acknowledgements
This work was supported in part by the Sabbatical Leave Program and the College of Arts and Sciences Professional Development Award at Northern Kentucky University.
Author information
Authors and Affiliations
Corresponding author
Additional information
This article is part of the Topical Collection on Proceedings of the International Conference on Hyperfine Interactions (HYPERFINE 2021), 5-10 September 2021, Brasov, Romania
Edited by Ovidiu Crisan
Rights and permissions
About this article
Cite this article
Zacate, M.O., Hemmingsen, L. Perturbed angular correlation spectra due to rotating electric field gradients. Hyperfine Interact 242, 56 (2021). https://doi.org/10.1007/s10751-021-01783-x
Accepted:
Published:
DOI: https://doi.org/10.1007/s10751-021-01783-x