Maximum‐entropy analysis of atomic compton profiles

Abstract

rnThe maximum-entropy formalism is used to obtain approximations to the atomic Compton profile, Its), in terms of the first few radial expectation values ( p " > of the momentum density y(p). This method leads to the least-biased results by the information not used. In particular, analytical and numerical approximations to the kinetic energy T and to the height of the peak J (0) structural properties of the variables p(r) and y(p> play a relevant role in the description of manybody systems. However, it is not easy to experimentally access these kinds of properties. Probably, the main way of obtaining experimental data on such one-particle densities is the measurement of isotropic Compton profiles [5-71: lntraduction One of the most important theories of matter, namely, the density functional theory, has the one-body density in position space p(r) as a basic variable [ 1, 21. An alternative formulation of this theory in terms of the one-body density in momentum space y(p> has been also carried out [3, 41.In the modern density functional theory, the

Compton profile and charge density reconstruction by the maximum entropy method

“…A formal derivation of the maximum entropy distribution is easily achieved using Lagrange multipliers λ t , which requires solving the differential equation subject to the prescribed values of the t moments. Details of the conditions, properties, applications and solutions for the existence of maximum entropy can be seen in references [24,25] and applications to Compton profile studies in [4,9,21].…”

“…The probability density function, which maximizes maximum entropy distributions, can be derived having specified values for the expectations of certain functions of the random variables [4,21].…”

Maximum-entropy and Padé-like approximations to atomic scattering factors

“…On the other hand, due to the tightness of the ME approximations, this method has been widely used in the literature in a great variety of fields (see e.g. [16][17][18][19][20][21][22][23][24][25][26][27]). It is worthy to remark that analytical ME solutions are only known for the case M = 1, namely…”

Maximum-entropy analysis of one-particle densities in atoms

“…It should be mentioned that this ME method has been also applied in a great variety of fields, including e.g. radioastronomy [45], parameter spectral estimation [46], particle physics [47] or atomic and many-fermion physics [25,[48][49][50]. On the other hand, let us remark that the ME technique provides complementary information to the one obtained from the Stieltjes-Chebyshev method, recently applied to the study of (r) [29], (p) [31] and J(q) [30].…”