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Chinese Physics Letters

Existence of Two Higher L = 0 Bound States of the Dipositroniums

Bao Cheng-guang, Ting-Yun Shi

Published Apr 1, 1999• 3 citations
Publisher

Abstract

Symmetry has imposed very strong constraints on the internal structure of quantum mechanical system. In particular, whether a state can access a given outgoing channel is constrained by symmetry. For the dipositroniums, the most important channel is the Ps-Ps channel. However, based on symmetry consideration it was found that only a few excited states are allowed to access the Ps-Ps channel, thereby at least the existence of two higher L = 0 bound states (higher than the Ps-Ps threshold) has been affirmed.

DOI
10.1088/0256-307x/16/4/013

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Symmetry has imposed very strong constraints on the internal structure of quantum mechanical system. In particular, whether a state can access a given outgoing channel is constrained by symmetry. For the dipositroniums, the most important channel is the Ps-Ps channel. However, based on symmetry consideration it was found that only a few excited states are allowed to access the Ps-Ps channel, thereby at least the existence of two higher L = 0 bound states (higher than the Ps-Ps threshold) has been affirmed.
The constraints imposed by symmetry on the open channels of dipositronium has been studied, and the symmetry-adapted lowest open channel of each quantum state has been identified. Based on this study, the existence of two more 0+{0}^{+}0+ bound states has been theoretically confirmed, and a 0+{0}^{+}0+ narrow resonance has been predicted. A variational calculation has been performed to evaluate the critical strength of the repulsive interaction. Two ${0}^{\ensuremath{-}}$ states are found to have their critical strengths very close to 1, they are considered as candidates of new narrow resonances or loosely bound states.
The projection method with explicitly correlated Gaussians is used to demonstrate the existence of two doubly excited states of the positronium molecule (Ps2{\mathrm{Ps}}_{2}Ps2​). One is below the Ps(n=2)+Ps(n=2)\mathrm{Ps}(n=2)\phantom{\rule{4pt}{0ex}}+\phantom{\rule{4pt}{0ex}}\mathrm{Ps}(n=2)Ps(n=2)+Ps(n=2) threshold, with A1{A}_{1}A1​ symmetry, and the other is below the Ps(n=2)+Ps(n=3)\mathrm{Ps}(n=2)+\mathrm{Ps}(n=3)Ps(n=2)+Ps(n=3) threshold, with EEE symmetry. These states exist as resonances in the Ps-Ps continuum. Moreover, the resonance positions and resonance widths of the two states are calculated using the complex rotation method with basis sets obtained via the orthogonalizing pseudoprojector method. The resonance positions obtained using the complex rotation method agree with the results of the orthogonalizing pseudoprojector method. We also investigate the various structural properties of these states as well as the decay probabilities of $2\ensuremath{\gamma}$ emission due to electron-positron annihilation.
't Hooft anomalies impose fundamental constraints on quantum matter and often lead to emergent symmetry structures upon gauging. We analyze a lattice model with four global symmetries realizing a mixed anomaly described by ∼a1∧a2∧a3∧a4\sim a_1\wedge a_2\wedge a_3\wedge a_4∼a1​∧a2​∧a3​∧a4​, where the aia_iai​ denote background gauge fields for the global symmetries. Through explicit lattice gauging, we demonstrate the emergence of higher symmetry structures, including 2-group, non-invertible, and higher fusion categorical symmetries. We also provide a field-theoretical understanding of these results. Applying this framework to systems with Lieb-Schultz-Mattis anomalies, obtained by promoting part of the internal symmetries to translational symmetries, we demonstrate that modulated (dipole) symmetries arise as direct counterparts of those in systems with purely internal typeIV anomalies. Importantly, we uncover a qualitatively new feature absent in previously studied modulated symmetries: their realization can become intrinsically defect-dependent. In particular, the emergent symmetry structure changes depending on whether symmetry defects are present. This work establishes a concrete lattice realization of mixed anomalies and reveals a rich structure of emergent symmetries, thereby clarifying their role in constraining quantum phases of matter.
Recent productions of large numbers of cold antiprotons as well as the formation of antihydrogens at CERN and Fermilab have raised basic questions about possible coexistence of matter and antimatter in nature. In the present work, previous mathematical considerations are revisited which support the possible coexistence of Antihydrogen with Hydrogen, Deuterium and Tritium atoms. In particular, the main objective of the present work is to present computational treatments which confirm the possible formation of these quasi molecules in laboratory. These treatments are based on a nonadiabatic picture of the system in which generalized basis functions are adjusted within the framework of Rayleigh-Ritz' variational method. Thus, it is ruled out in the present work the Born-Oppenheimer adiabatic picture of the system, which demands the existence of bound states composed of fixed quasi heavy atoms (containing at least two baryons, e.g. protonium (Pn), with mean lifetime 1.0x10^^-6 s) and quasi light atoms (composed of two leptons, e.g. positronium (Ps), with mean lifetime 125x10^^-12 s for para-Ps and 142.05x10^^-9 s for ortho-Ps). Our calculations of the binding energies and internal structure of Antihydrogen-Hydrogen, Antihydrogen-Deuterium and Antihydrogen-Tritium show that these quasi molecules are bound and could be formed in nature. On the other hand, having in mind the adiabatic picture of the systems, our results suggest the possible formation of these molecules as resonant states in Antihydrogen-Atom interaction. Nevertheless, several arguments are accumulated in the conclusion as consequences of the proposed bound states.