### Abstract

A mapping between the quantum few-body problem and its classical mechanics pseudo-system analog is used to study the critical parameters for the helium isoelectronic sequence. The critical point is the critical value of the nuclear charge Z_{c}. for which the energy of a bound state becomes degenerate with a threshold. A finite-size scaling ansatz in the form of a phenomenological renormalization equation is used to obtain very accurate results for the critical point of the ground-state energy, λ_{c}=1/Z_{C}=1.0976±0.0004, as well as for the excited 2p^{2} ^{3}P state, λ_{c}=1.0058±0.0017. The results for the critical exponents α and ν are also included.

Original language | English |
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Pages (from-to) | 2765-2770 |

Number of pages | 6 |

Journal | Journal of Chemical Physics |

Volume | 108 |

Issue number | 7 |

DOIs | |

Publication status | Published - 15 Feb 1998 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*Journal of Chemical Physics*,

*108*(7), 2765-2770. https://doi.org/10.1063/1.475701