Articulation of the measured replication of the rovibrational energy levels of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> onto the energy continuum of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mfenced> <mml:mrow> <mml:msubsup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> <mml:mo>*</mml:mo> </mml:mrow> </mml:msup> </mml:math> leading to <i>H</i> ⁺ + <i>H</i> ⁺ + <i>H</i> ⁻ within the sudden approximation

Abstract We studied the production of discrete <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mfenced close=")" open="(" separators=""> <mml:mrow> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="italic">H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> <mml:mo>*</mml:mo> </mml:mrow> </mml:msup> </mml:math> continuum states following the two-electron excitation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="italic">H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> caused by the impact of He atoms. These states decay in time intervals of approximately <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>15</mml:mn> <mml:mspace width="0.25em"/> </mml:mrow> </mml:msup> <mml:mi mathvariant="bold">s</mml:mi> </mml:math> into the three-body system of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mspace width="0.25em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="italic">H</mml:mi> </mml:mrow> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>+</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant="italic">H</mml:mi> </mml:mrow> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>+</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant="italic">H</mml:mi> </mml:mrow> <mml:mo>−</mml:mo> </mml:msup> <mml:mo>.</mml:mo> </mml:math> We simultaneously measured in triple coincidence the sum of the center-of-mass kinetic energies of all three fragments from a single dissociation event. When plotted on a Cartesian Dalitz plot, the energy dependence of the measured sums matched that of the rovibrational energy levels of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi mathvariant="italic">H</mml:mi> <mml:mn>3</mml:mn> <mml:mo>+</mml:mo> </mml:msubsup> </mml:math> ion before the collision. This work has led to new types of data, and their interpretation has led to new physics. The experimental results were reproduced and further articulated in a non-trivial manner when the sudden approximation was used to describe the excitation from the initial rovibrational states of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mspace width="0.25em"/> <mml:msubsup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> to discrete states within the continuum energy system of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mfenced close=")" open="(" separators=""> <mml:mrow> <mml:msubsup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> <mml:mo>*</mml:mo> </mml:mrow> </mml:msup> </mml:math> . The mapping of the initial energies of the bound rovibrational states onto the discrete continuum energies was discovered by re-analyzing previously published triple coincidence measurements made by our group at the University of Nebraska-Lincoln. An additional process predicted within the sudden approximation formalism is the existence of intermediate states in the continuum with excitation energies that are equal to the ground state rovibrational energy, plus a multiple of the zero-point energy of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> at the instant of two-electron excitation. The experimental data confirmed this prediction. This process dominated the global structure of the triple-event spectrum. The data provided a dynamic zero-point energy of 0.543 ± 0.003 eV for the ground-state vibrational component. This is the first report of an experiment to determine the zero-point energy in this manner.