ISSN 10628738, Bulletin of the Russian Academy of Sciences: Physics, 2010, Vol. 74, No. 3, pp. 310–314. © Allerton Press, Inc., 2010. Original Russian Text © F.G. Vagizov, E.K. Sadykov, O.A. Kocharovskaya, 2010, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2010, Vol. 74, No. 3, pp. 338–343. 310 INTRODUCTION The probability of the recoilless absorption f (emis sion) of nuclei, also known as the Lamb–Mössbauer (LM) factor, is closely associated with the dynamics of a crystal lattice and is an important and informative parameter of Mössbauer spectroscopy. The probability of recoilless transitions of Mössbauer nuclei, , provides information on the root meansquare displacements of these atoms in the direction of the propagation of γradiation. It is extremely sensitive to various changes in the solid state under the effects of temperature, pressure, phase tran sitions, and other processes that lead to changes in the phonon spectrum of a crystal. Such information can be obtained from the elastic neutron scattering and Xray radiation data. Since these methods are based on the interference of radia tion, they are sensitive to the degree of crystallinity of the objects under study, and their informative capabil ities decline considerably when they are used to study amorphous matter and nanocrystalline substances. In determining the rootmeansquare displacements of resonant atoms, the Mössbauer effect has certain advantages since its results depend only weakly on the structural order, and the method can be used equally well for both crystal substances and amorphous com pounds. In Mössbauer spectroscopy, several methods for determining the Lamb–Mössbauer factor [1–11] are known. Most of them are based on the dependence of the width [3–5], intensity [6–8], and areas of the Mössbauer lines [9–11] on the effective absorber thickness , where n is the number of resonant nuclei per area unit, and σ 0 is the crosssection of the resonant absorption. In the geometry most used in Mössbauer experiments (transmission), the ratio = (N(∞) – N(υ s ))/(N(∞) – N b ), where ( ) = -  / 2 2 exp f x 2 x β= σ 0 fn υ ε ( ) s υ ( ) s N and are the count rate of γquanta at the reso nance far from it, respectively, is the background intensity in the energy range of the Mössbauer radia tion (14.4 keV for 57 Co). The main components of the background radiation in this range are the Xray(6– 7 keV) radiation in the source due to βdecay and internal conversion, and the scattered radiation result ing from the Compton effect and the electron absorp tion of highenergy γquanta (122, 136.4 keV). The background radiation leads to a systematic error in the determination of the Lamb–Mössbauer factor when using the dependence of the intensity and the area of the resonant line on the effective absorber thickness [2, 12]. The situation improves somewhat when using detectors with good energy resolution. The applica tion of softradiation filters and semiconductor detec tors allows us to reduce considerably the contribution of the wings from Xray peaks in the energy range of the Mössbauer transitions. However, this approach works only in the softradiation range. Further progress can be expected from the application of delayed coincidence technique. Already in the first Mössbauer experiments, it was noticed that in delayed coincidence spectra the absorption line intensity increases considerably and the energy resolution is even improved when the spec trum is recorded in certain time intervals after the decay of the excited state [13, 14]. In particular, one is due to diminishing of the background radiation in the region of the resonant peak upon time gating, and fur thermore a part of the scattered radiation is delayed in time. The delayed coincidence spectra are very sensi tive to the effective absorber thickness, and can hence be effectively used to obtain information on the prob ability of recoilless transitions in crystals. In this work, the experimental results on determin ing the Lamb–Mössbauer factor by the delayed coin cidence technique are given. ∞ ( ) N b N Determination of the Lamb–Mössbauer Factor by the Delayed Coincidence Technique F. G. Vagizov a, b , E. K. Sadykov a *, and O. A. Kocharovskaya b a Kazan State University, Kazan, 420008 Russia b Texas A and M University, College Station, 77843 Texas, USA *email: esad@ksu.ru Abstract—A method for determining the Lamb–Mössbauer factor by means of the delayed coincidence technique is proposed. The effective thickness of a series of K 4 Fe(CN) 6 ⋅ 3H 2 O samples was measured and recoilless fraction f = 0.339 ± 0.004 was determined. DOI: 10.3103/S1062873810030056