Hyperfine structure splitting of the positron-helium ions $e^{+}[^3$He$(2^3S)]$ and $e^{+}[^4$He$(2^3S)]$

TL;DR

This paper calculates the hyperfine structure splittings of positron-helium ions with helium-3 and helium-4 isotopes, providing precise values that can be tested in current experimental setups.

Contribution

The study provides the first detailed calculations of hyperfine splittings for these specific positron-helium ions, including multiple splitting values for helium-3 isotope.

Findings

Hyperfine splitting for $e^{+}[^3$He$(2^3S)]$ includes three distinct values.

For $e^{+}[^4$He$(2^3S)]$, a single hyperfine splitting value is identified.

All calculated splittings are within measurable ranges for modern experiments.

Abstract

The hyperfine structure splittings are determined for the lowest bound state in the positron-helium ion $e^{+}[^3$He$(2^3S)]$ and $e^{+}[^4$He$(2^3S)]$. In particular, we have fond that for the $e^{+}[{}^3$He$(2^3S)]$ ion one can observe the three following hyperfine structure splittinings: 5824.3986 $MHz$, 76466.5308 $MHz$ and 5824.4019 $MHz$. In the $e^{+}[{}^4$He$(2^3S)]$ ion only one hyperfine structure splitting 82963.0427 $MHz$ can be observed. All these values can be measured in modern experiments.