Analysis of Compton profile through information theory in H-like atoms inside impenetrable sphere

Abstract

Confinement of atoms inside various cavities has been studied for nearly eight decades. However, the Compton profile for such systems has not yet been investigated. Here we construct the Compton profile (CP) for a H atom radially confined inside a hard spherical enclosure, as well as in free condition. Some exact analytical relations for the CP's of circular or nodeless states of free atom is presented. By means of a scaling idea, this has been further extended to the study of an H-like atom trapped inside an impenetrable cavity. The accuracy of these constructed CP has been confirmed by computing various momentum moments. Apart from that, several information theoretical measures, like Shannon entropy (S) and Onicescu energy (E) have been exploited to characterize these profiles. Exact closed form expressions are derived for S and E using the ground state CP in free H-like atoms. A detailed study reveals that, increase in confinement inhibits the rate of dissipation of kinetic energy. At a fixed ℓ, this rate diminishes with rise in n. However, at a certain n, this rate accelerates with progress in ℓ. A similar analysis on the respective free counterpart displays an exactly opposite trend as that in confined system. However, in both free and confined environments, CP generally gets broadened with rise in Z. Representative calculations are done numerically for low-lying states of the confined systems, taking two forms of position-space wave functions: (a) exact (b) highly accurate eigenfunctions through a generalized pseudospectral method. In essence, CPs are reported for confined H atom (and isoelectronic series) and investigated adopting an information-theoretic framework.

Hydrogen-like ions in plasma environment

“…To calculate energy and spectroscopic properties, the GPS method has been exploited. Over the time, its accuracy and efficiency in calculating various bound-state properties in several central potentials in both free and confined condition have been verified and established (see [59][60][61][62][63] and references therein).…”

Shell-confined atom and plasma: incidental degeneracy, metallic character and information entropy

“…Thus in essence, it combines the simplicity of direct finite-difference or finite element method, with the fast convergence of finite basis set approaches. Over the time, it has been successfully used to estimate various bound-state properties of several central potentials including energy and other properties in CHA and confined many-electron atom [24,25,29,[62][63][64][65][66],…”

“…Information entropic measures are functionals of density and they quantify density in several complimentary ways. They have potential applications in atomic avoided crossing, electron correlation effect, quantum entanglement, orbital-free density functional theory etc [25,29]. S is the arithmetic mean of uncertainty, and expressed as an expectation value of logarithmic density.…”

“…Recently a new virial-like theorem is also formulated for such confinement situation [24]. Moreover, various properties like hyper-fine splitting constant, dipole shielding factor, nuclear magnetic screening constant, static, and dynamic polarizability, information entropy, Compton profiles [25][26][27][28][29][30][31] were examined for CHA. Further, the information theoretic measures are investigated for H-like atoms in Debye plasmas [32].…”

Hellmann–Feynman theorem and internal pressure for atoms, molecules and plasmas under pressure

“…The first situation relates to an irreversible environment, whereas the latter indicates a reversible condition. For the ease of discussion, it may be appropriate to classify several confining conditions, in two broad categories [21][22][23][24]: (a) the impenetrable barrier, where the confining potential (V c ) becomes infinite at a certain finite r value. This characteristic r is termed the confinement radius R. (b) A penetrable barrier with a finite boundary.…”