In this work, the path-integral effective potential (PIEP) method has been applied to re-study the temperature dependence of extended X-ray absorption fine structure (EXAFS) cumulants of materials. Using the trial density matrix and effective potential expression, we derived the analytical expressions of the first three EXAFS cumulants in the first shell of materials. The cumulant relation is also calculated to determine the temperature range in which the PIEP method could be applied. Our results are compared with available experimental data as well as with those calculated by the first-order perturbation approach in anharmonic Einstein model and the reasonable agreements are achieved. | Communications in Physics, Vol. 24, No. 3S1 (2014), pp. 40-44 DOI: APPLICATION OF PATH-INTEGRAL FOR STUDYING EXAFS CUMULANTS HO KHAC HIEU Duy Tan University, Da Nang, Viet Nam NGUYEN MANH HAI Hanoi University of Science, Vietnam National University, Hanoi E-mail: hieuhk@ Received 04 April 2014 Accepted for publication 24 May 2014 Abstract. In this work, the path-integral effective potential (PIEP) method has been applied to re-study the temperature dependence of extended X-ray absorption fine structure (EXAFS) cumulants of materials. Using the trial density matrix and effective potential expression, we derived the analytical expressions of the first three EXAFS cumulants in the first shell of materials. The cumulant relation is also calculated to determine the temperature range in which the PIEP method could be applied. Our results are compared with available experimental data as well as with those calculated by the first-order perturbation approach in anharmonic Einstein model and the reasonable agreements are achieved. Keywords: EXAFS cumulants, path-integral, effective potential. I. INTRODUCTION On the determination of the local structures of materials, the extended X-ray Absorption Fine Structure (EXAFS) spectroscopy is one of powerful techniques. The EXAFS data can be theoretically analyzed by means of the cumulant expansion method [1]. There are several approaches used to study the temperature dependence of anharmonic EXAFS cumulants such as perturbation approach in Einstein model [2] and Debye model [3], and statistical moment method [4]. However, most of these methods still can not be valid at very high temperature due to the strong anharmonic contributions. Recently, the path-integral effective potential (PIEP) method has been efficiently used to theoretically study thermodynamic properties of materials [5–8]. This method has included the anharmonic contributions as well as the quantum effects. In present .
