Strong geometrical-phase effects in the complex reaction <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>μ</mi><mo>+</mo><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><msup><mrow></mrow><mo>+</mo></msup><mo>→</mo><mi mathvariant="normal">H</mi><mo>+</mo><mi>μ</mi><msup><mrow><mi mathvariant="normal">H</mi></mrow><mo>+</mo></msup></mrow></math>

Hailin Zhao; Yin Huang; Jianyi Ma

doi:10.1103/dhwg-gdlr

Strong geometrical-phase effects in the complex reaction $μ + H_{2}^{+} \to H + μ H^{+}$

Hailin Zhao ^1,*, Yin Huang ^2,†, and Jianyi Ma^1,‡

¹Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China
²School of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou, Hubei 434023, China

^*Contact author: zhaohl94@scu.edu.cn
^†Contact author: huangyin@yangtzeu.edu.cn
^‡Contact author: jianyima@scu.edu.cn

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Phys. Rev. A 113, 032806 – Published 3 March, 2026

DOI: https://doi.org/10.1103/dhwg-gdlr

Abstract

A pronounced geometric-phase (GP) effect is observed in the integral cross sections (ICSs) of the $μ + H_{2}^{+}$ reaction and is analyzed using the interaction-asymptotic region decomposition method within the thermal-collision-energy range of 0.17 to 0.4 eV. Based on topological analysis, two distinct reaction pathways are identified, with a significant GP effect arising from strong interference between these pathways. Wave-function analysis indicates that the GP effect originates from an increased nodal structure around the conical-intersection (CI) region. Further investigation reveals that the time delay of the reactive resonance state is closely correlated with the amplitude of the wave function near the CI region. These results enable sensitive probing of the GP effect using the $μ$ atom from the perspective of the ICS.

Physical Review A

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Strong geometrical-phase effects in the complex reaction $μ + H_{2}^{+} \to H + μ H^{+}$

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Strong geometrical-phase effects in the complex reaction μ+H2+→H+μH+

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Strong geometrical-phase effects in the complex reaction $μ + H_{2}^{+} \to H + μ H^{+}$