Computation of ionization and various excited state energies ofhelium and helium‐like quantum dots

Yakar, Yusuf; Çakır, Bekir; Özmen, Ayhan

doi:10.1002/qua.22973

Cited by 40 publications

(54 citation statements)

References 41 publications

(39 reference statements)

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“…As a result, the correlated Hylleraas basis set becomes flexible for a complete range of confining parameters and produces accurate energy levels for helium‐like ions. Although there exists several investigations on the series of

^{1} S^{e}

states of helium‐like systems, limited works are available in literature where precise energy values of

^{3} S^{e}

states of helium‐like ions are reported along with detailed studies on singlet states and most them are on the

1 s 2 s

state of helium only. To be specific, Patil and Varshni first estimated the energy values of

1 s 2 s

(

^{3} S^{e}

) state of helium under the perturbative framework with a simple single‐term uncorrelated wavefunction satisfying proper boundary condition for

R \to \infty

and the electron‐electron interaction was replaced by an effective screening of the nuclear charge.…”

Section: Introductionmentioning

confidence: 99%

Ritz variational calculation for the singly excited states of compressed two‐electron atoms

Saha

Bhattacharyya²,

Mukherjee³

2016

Int J of Quantum Chemistry

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A detailed analysis on the effect of spherical impenetrable confinement on the structural properties of two-electron ions in S2 states has been performed. The energy values of 1sns [n5224] ( 3 S e ) states of helium-like ions (Z5125) are estimated within the framework of Ritz variational method using explicitly correlated Hylleraas-type basis sets. The correlated wave functions used here are consistent with the finite boundary conditions due to spherical confinement. A comparative study between the singlet and triplet states originating from a particular electronic configuration shows incidental degeneracy and the subsequent level-crossing phenomena. The thermodynamic pressure felt by the ion inside the sphere pushes the energy levels toward continuum. Critical pressures for the transition to strong confinement regime (where the singly excited two-electron energy levels cross the corresponding one-electron threshold) as well as for the complete destabilization are also estimated.correlation, pressure confinement, two-electron atom, variational method | I N T R O D U C T I O NStudies on the subject of confined atomic systems have started soon after the advent of quantum mechanics. In recent years, a paradigm shift in the facility for doing controlled experiment on confined atom and modern high-speed computational resources open up a new horizon for this subject. The modifications of the structural and spectral properties of the atom or the molecule depending on the number and degree of confining parameters is the interesting aspect of the problem. Comprehensive reviews [1][2][3] are now available on this topic. Theoretically, different types of confinement models can be realized for different physical situations, for example, atoms under plasma environment, [4,5] endohedrally confined atoms and molecules in fullerene cages, [6] impurities in quantum dots or nano crystals, [7,8] matter under extreme pressure in zeolite sieves, [9] or in the walls of nuclear reactors, [10] and so forth. Moreover, the confined atom models assume contemporary significance in understanding the cores of Jovian planets such as Jupiter and Saturn. [11] Nonspherical confinement models [12][13][14][15] are also assumed to deal with important quantum mechanical problems. Vast applicability of the outcomes from such studies in different branches of science and technology makes the subject a topic of immense interest in the recent times. [16][17][18] Hydrogen atom confined in impenetrable spherical cavity was first studied by Michels et al. [19] to model the effects of pressure on its energy and polarizability. Subsequently, many workers [20][21][22][23][24][25][26] have addressed this problem from different angles to develop a comprehensive understanding about such confined systems. Helium atom confined by such spherical cavity is a much complicated numerical problem as compared to the hydrogen-like ions for obvious reasons. For ions having two or more electrons, the effect of electron correlation plays an important role in the str...

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^{1} S^{e}

states of helium‐like systems, limited works are available in literature where precise energy values of

^{3} S^{e}

states of helium‐like ions are reported along with detailed studies on singlet states and most them are on the

1 s 2 s

state of helium only. To be specific, Patil and Varshni first estimated the energy values of

1 s 2 s

(

^{3} S^{e}

) state of helium under the perturbative framework with a simple single‐term uncorrelated wavefunction satisfying proper boundary condition for

R \to \infty

and the electron‐electron interaction was replaced by an effective screening of the nuclear charge.…”

Section: Introductionmentioning

confidence: 99%

Ritz variational calculation for the singly excited states of compressed two‐electron atoms

Saha

Bhattacharyya²,

Mukherjee³

2016

Int J of Quantum Chemistry

View full text Add to dashboard Cite

show abstract

“…QDs have the atomic properties such as discrete energy levels and shell structures and they are often referred to as artificial atoms [1,2]. Therefore, a great deal of works has been performed on the electronic structure of QDs with one-and twoelectrons by using several calculation methods [1][2][3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Refractive index changes and absorption coefficients in a spherical quantum dot with parabolic potential

Çakır

Yakar

Özmen

2012

Journal of Luminescence

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“…In the work of Ndengué and Motapon [31] was computed the energy levels of the ground and a few excited states of helium and helium-like ions confined in a finite potential well by using configuration interaction method. Flores-Riveros and Rodríguez-Contreras [33] and Yakar et al [35] carried out the ground and excited energy states for the confined helium and helium-like ions spherically enclosed by an impenetrable box. They also calculated the ionization energies and the ionization dot radii of the confined systems.…”

Section: Introductionmentioning

confidence: 99%

“…The Coulomb interaction between electrons effects considerably the physical properties of such structures and must be considered in calculations [29]. Therefore, various properties of the confined helium and helium-like ions have been investigated by many researchers [30][31][32][33][34][35][36][37][38]. In the work of Ndengué and Motapon [31] was computed the energy levels of the ground and a few excited states of helium and helium-like ions confined in a finite potential well by using configuration interaction method.…”

Section: Introductionmentioning

confidence: 99%

Linear and nonlinear absorption coefficients of spherical two-electron quantum dot

Yakar

Çakır

Özmen

2015

Computer Physics Communications

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Computation of ionization and various excited state energies ofhelium and helium‐like quantum dots

Cited by 40 publications

References 41 publications

Ritz variational calculation for the singly excited states of compressed two‐electron atoms

Ritz variational calculation for the singly excited states of compressed two‐electron atoms

Refractive index changes and absorption coefficients in a spherical quantum dot with parabolic potential

Linear and nonlinear absorption coefficients of spherical two-electron quantum dot

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