Muonic alchemy: Transmuting elements with the inclusion of negative muons

Abstract

In this Letter we present a theoretical study of atoms in which one electron has been replaced by a negative muon. We have treated these muonic systems with the Any Particle Molecular Orbital (APMO) method. A comparison between the electronic and muonic radial distributions revealed that muons are much more localized than electrons. Therefore, the muonic cloud is screening effectively one positive charge of the nucleus. Our results have revealed that by replacing an electron in an atom by a muon there is a transmutation of the electronic properties of that atom to those of the element with atomic number Z − 1.

Introduction

For centuries chemists have been interested in exploring the properties of atoms, molecules and materials which are composed of electrons, protons and neutrons. In recent decades, there has been a growing interest in studying the so-called exotic atoms and molecules (i.e. systems containing either positrons, muons, among others) due primarily to advances in the generation and manipulation of these subatomic particles.

Among these exotic systems those containing positrons and positive muons have received most of the attention by the chemistry community. This is due in part to advances in the development of positron and positive muon techniques which, for instance, have resulted in methods currently used in medicine and chemistry such as positron emission tomography [1] and muon spin resonance [2]. In contrast, the study of systems containing negative muons (μ in the rest of the document) has mainly attracted the physicists’ community. They have investigated extensively for the last 60 years, both theoretical and experimentally, muonic atoms and molecules. These studies have been inspired primarily by the potential of muonic systems to catalyse nuclear fusion processes. Refs. [2], [3], [4], [5] and references therein present overviews of muon catalysed fusion in the dtμ molecule.

A wide variety of aspects have been investigated experimentally on these negative muonic systems: muon transfer and capture processes [2], [4], [6], [7], nuclear fusion reaction rates [2], [4], [8], quantum electrodynamics effects (e.g. Lamb shifts and vacuum polarization) [9], [10], X-ray spectroscopy [11] among others.

From a theoretical perspective, the investigation of atomic and molecular muonic systems has also been used to study the above-mentioned properties [6], [12], [13], [14], [15], [16], [17] and to determine the accuracy of many-body approximation methods [18], [19], [20], [21], [22], [23], [24], [25].

The chemical properties of μ-many-electron atoms (denoted in the rest of the document by Xμ, where X is the atomic symbol) and molecules were rarely investigated in the last century. There are only a few reports of μ-spin resonance studies on solids [26], [27], [28], [29], [30]. From a theoretical perspective, there are a few Dirac–Fock calculations on many-electron muonic atoms [31], [32]. The lack of reports on these muonic species is in part due to: (1) experimental difficulties in the preparation and manipulation of these short-lived systems; (2) limitations of the theoretical methods implemented so far to study molecular systems containing particles other than electrons and nuclei.

In this regard, in recent years a couple of papers [33], [34], [35] have presented measurements of reaction rates for the collisional process ${}^4\text{He}\mathrm{\mu }+{\text{H}}_2\to {}^4\text{He}\mathrm{\mu }\text{H}+\text{H}$. It has been concluded from these reports that Heμ chemically behaves as a heavy isotope of hydrogen.

Inspired by the findings of these experimental studies, in this Letter we want to study theoretically electronic properties of muonic atoms in which one electron has been replaced by a negative muon. Our goal is to determine how the electronic structure of atom change after substituting one electron for one negative muon. This will be accomplished by analysing muon and electron radial distributions as well as the electronic ionization potentials of neutral muonic atoms.

These muonic systems can be studied considering electrons and muons as quantum particles and invoking the Born–Oppenheimer approximation (BOA) for nuclei. However, because of the large mass of μ (206.8 m_e), which is about 1/9 of that of a proton, the use of the BOA for the nucleus may lead to large errors in the total energy [36]. We have therefore treated these muonic systems with a non-relativistic, non-BOA approach in which nuclei, muons and electrons are considered under the same footing as electrons are treated in conventional quantum chemistry methods. We will refer to this method as the Any-Particle Molecular Orbital approach, APMO. A similar approach has been utilized to study electronic properties of atoms [37] revealing good agreement with experimental and other theoretical results.

This Letter is organized as follows. In Section 2 we summarize the equations of the APMO method. In Section 3 we provide some computational details. In Section 4 we present the calculated electron and muon radial distributions and ionization potentials for muonic atoms and compare these with theoretical and experimental results for regular atoms. Finally, in Section 5 we conclude.