Excited-state populations in the multiconfiguration time-dependent Hartree–Fock method

<jats:title>Abstract</jats:title> <jats:p> We study time-dependent populations in the excited states of many-electron atoms and molecules with the multiconfiguration time-dependent Hartree–Fock method and reveal the non-stationary behavior of the excited-state populations during field-free propagation originating from the nonlinear character of the equations of motion. We calculate the time-dependent populations of the three lowest singlet <jats:italic>S</jats:italic> states in a helium atom for two different cases of intense laser-atom interaction. In the first case, He is excited by a VUV pulse with the central wavelength of 108 nm, which is two-photon resonant with the <jats:inline-formula> <jats:tex-math> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mi>S</mml:mi> <mml:mspace width="0.25em"/> <mml:mn>1</mml:mn> <mml:mi>s</mml:mi> <mml:mn>3</mml:mn> <mml:mi>s</mml:mi> <mml:mo>←</mml:mo> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mi>S</mml:mi> <mml:mspace width="0.25em"/> <mml:mn>1</mml:mn> <mml:msup> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> </jats:inline-formula> transition. In the second case, He is excited by an off-resonant UV laser pulse with the central wavelength of 200 nm. We obtain the stationary wave functions of the excited states by imaginary time propagation and show that the populations oscillate as a function of time even after the laser pulse has vanished. The time-dependent variations in the populations in the respective eigenstates can be sufficiently suppressed when the number of orbitals adopted in the expansion of the wave function exceeds eight. </jats:p>