### Abstract

In this work we report progress in the development and implementation of quantum-mechanical methods for calculating bound ground and excited states of small atomic systems. The work concerns singlet states with the L=1 total orbital angular momentum (P states). The method is based on the finite-nuclear-mass (non-Born-Oppenheimer; non-BO) approach and the use of all-particle explicitly correlated Gaussian functions for expanding the nonrelativistic wave function of the system. The development presented here includes derivation and implementation of algorithms for calculating the leading relativistic corrections for singlet states. The corrections are determined in the framework of the perturbation theory as expectation values of the corresponding effective operators using the non-BO wave functions. The method is tested in the calculations of the ten lowest P1 states of the helium atom and the four lowest P1 states of the beryllium atom.

Original language | English |
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Article number | 012513 |

Journal | Physical Review A |

Volume | 97 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 25 2018 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A*,

*97*(1), [012513]. https://doi.org/10.1103/PhysRevA.97.012513

**Leading relativistic corrections for atomic P states calculated with a finite-nuclear-mass approach and all-electron explicitly correlated Gaussian functions.** / Stanke, Monika; Bralin, Amir; Bubin, Sergiy; Adamowicz, Ludwik.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 97, no. 1, 012513. https://doi.org/10.1103/PhysRevA.97.012513

}

TY - JOUR

T1 - Leading relativistic corrections for atomic P states calculated with a finite-nuclear-mass approach and all-electron explicitly correlated Gaussian functions

AU - Stanke, Monika

AU - Bralin, Amir

AU - Bubin, Sergiy

AU - Adamowicz, Ludwik

PY - 2018/1/25

Y1 - 2018/1/25

N2 - In this work we report progress in the development and implementation of quantum-mechanical methods for calculating bound ground and excited states of small atomic systems. The work concerns singlet states with the L=1 total orbital angular momentum (P states). The method is based on the finite-nuclear-mass (non-Born-Oppenheimer; non-BO) approach and the use of all-particle explicitly correlated Gaussian functions for expanding the nonrelativistic wave function of the system. The development presented here includes derivation and implementation of algorithms for calculating the leading relativistic corrections for singlet states. The corrections are determined in the framework of the perturbation theory as expectation values of the corresponding effective operators using the non-BO wave functions. The method is tested in the calculations of the ten lowest P1 states of the helium atom and the four lowest P1 states of the beryllium atom.

AB - In this work we report progress in the development and implementation of quantum-mechanical methods for calculating bound ground and excited states of small atomic systems. The work concerns singlet states with the L=1 total orbital angular momentum (P states). The method is based on the finite-nuclear-mass (non-Born-Oppenheimer; non-BO) approach and the use of all-particle explicitly correlated Gaussian functions for expanding the nonrelativistic wave function of the system. The development presented here includes derivation and implementation of algorithms for calculating the leading relativistic corrections for singlet states. The corrections are determined in the framework of the perturbation theory as expectation values of the corresponding effective operators using the non-BO wave functions. The method is tested in the calculations of the ten lowest P1 states of the helium atom and the four lowest P1 states of the beryllium atom.

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U2 - 10.1103/PhysRevA.97.012513

DO - 10.1103/PhysRevA.97.012513

M3 - Article

VL - 97

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 1

M1 - 012513

ER -