Muonic Ions Research Articles

Negative muon beam generation with muon catalyzed fusion

A new scheme of low energy negative muon source with muon catalyzed fusion (MuCF) is described. In the MuCF reaction process, muonic helium ions (μHe+) are created. By re-accelerating and stripping μHe+ ions, a low emittance negative muon beam is generated.

Properties of the weakly-bound (1,1)-states and rotationally excited (2,0)-states in the muonic molecular and ions

Total energies and other bound state properties of the weakly-bound (1,1)-states and rotationally excited (2,0)-states in the three-body muonic molecular and ions are determined to high numerical accuracy and investigated. Our current numerical accuracy achieved for the total and binding energies of the weakly-bound (1,1)-states in the both and ions significantly exceeds similar accuracy obtained in earlier computations of these weakly-bound states in these two ions. The bound state properties of the weakly-bound (1,1)-states and (2,0)-states in the and muonic ions have never been determined to high accuracy in earlier studies. We also briefly discuss the current status of muon-catalysed nuclear fusion and develop the new universal variational expansion which can be used for extremely accurate bound state calculations of arbitrary three-body systems, including the truly adiabatic H ion and close systems.

Relativistic fine structure of the [formula omitted] ion [formula omitted]-levels

Motivated by the recent experimental measures of the 2p-states fine splitting of the muonic He4 ion (Krauth et al., 2021), we think it may be of interest to present an independent calculation in terms of the two-body relativistic equation for a scalar and a fermion developed in Giachetti and Sorace (2021, 2019) for mesic atoms. This work can thus be considered an addendum to these last papers in a different range for the masses of the two components. It gives theoretical results in good agreement with the recent experimental measures.

Development of negative muonium ion source for muon acceleration

A negative muonium ion (${\mathrm{Mu}}^{\ensuremath{-}}$) source using an aluminum foil target (Al target) was developed as a low-energy muon source. ${\mathrm{Mu}}^{\ensuremath{-}}$ ions are produced by irradiating the Al target with a 3-MeV positive muon (${\ensuremath{\mu}}^{+}$) beam and observed using a microchannel plate. An experiment to produce ${\mathrm{Mu}}^{\ensuremath{-}}$ ions was conducted to evaluate the performance of this ${\mathrm{Mu}}^{\ensuremath{-}}$ ion source. The measured event rate of ${\mathrm{Mu}}^{\ensuremath{-}}$ ions was $(1.7\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\text{ }\text{ }{\mathrm{Mu}}^{\ensuremath{-}}/\mathrm{s}$ when the event rate of the incident ${\ensuremath{\mu}}^{+}$ beam was $1.3\ifmmode\times\else\texttimes\fi{}{10}^{6}/\mathrm{s}$. The experiment was conducted at the Muon Science Establishment, D-line in the Materials and Life Science Experimental Facility within the Japan Proton Accelerator Research Complex. The formation probability, defined as the ratio of the ${\mathrm{Mu}}^{\ensuremath{-}}$ ions to the incident muons on the Al target, was $(1.1\ifmmode\pm\else\textpm\fi{}0.2(\mathrm{stat}{)}_{+0.1}^{\ensuremath{-}0.0}(\mathrm{syst}))\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. This ${\mathrm{Mu}}^{\ensuremath{-}}$ ion source was first adopted in the commissioning of the muon accelerator at the D-line, and the event rate of the accelerated ${\mathrm{Mu}}^{\ensuremath{-}}$ ions was consistent with the expectation. This ${\mathrm{Mu}}^{\ensuremath{-}}$ ion source boosted the development of the muon accelerator, and the practicality of this low-energy muon source obtained using a relatively simple apparatus was demonstrated.

Precision physics of muonic ions of lithium, beryllium and boron

The problem of determining the main parameters of light nuclei from precision atomic spectroscopy is considered. Within the framework of the quasipotential method in quantum electrodynamics, the energy interval [Formula: see text] in muonic ions of lithium, beryllium and boron is calculated. Corrections of orders [Formula: see text], which are determined by relativistic effects, effects of vacuum polarization, nuclear structure and recoil, as well as combined corrections, including the above, are taken into account. Nuclear structure effects are expressed in terms of the nuclear charge radius in the case of one-photon interaction and the electromagnetic form factors of nuclei in the case of two-photon interaction. The obtained numerical values for the [Formula: see text] interval can be used for comparison with future experimental data and for a more accurate determination of the nucleus charge radii.

Measuring the \u03b1-particle charge radius with muonic helium-4 ions

The energy levels of hydrogen-like atomic systems can be calculated with great precision. Starting from their quantum mechanical solution, they have been refined over the years to include the electron spin, the relativistic and quantum field effects, and tiny energy shifts related to the complex structure of the nucleus. These energy shifts caused by the nuclear structure are vastly magnified in hydrogen-like systems formed by a negative muon and a nucleus, so spectroscopy of these muonic ions can be used to investigate the nuclear structure with high precision. Here we present the measurement of two 2S–2P transitions in the muonic helium-4 ion that yields a precise determination of the root-mean-square charge radius of the α particle of 1.67824(83) femtometres. This determination from atomic spectroscopy is in excellent agreement with the value from electron scattering1, but a factor of 4.8 more precise, providing a benchmark for few-nucleon theories, lattice quantum chromodynamics and electron scattering. This agreement also constrains several beyond-standard-model theories proposed to explain the proton-radius puzzle2–5, in line with recent determinations of the proton charge radius6–9, and establishes spectroscopy of light muonic atoms and ions as a precise tool for studies of nuclear properties.

Energy levels of three particle muonic ions (μeLi), (μeBe), (μeB)

We calculate the electron Lamb shift (2P-2S) and the electron energy interval (2S-1S) in muonic Coulomb three particle systems (μeLi), (μeBe), (μeB) on the basis of variational method. Basic relativistic corrections, corrections to the vacuum polarization and nuclear structure are taken into account by the perturbation theory. The obtained numerical results can be used for a comparison with future experimental data.

Energy interval 2S-1S in muonic ions of lithium, beryllium and boron

Within the framework of the quasipotential method in quantum electrodynamics, the energy interval (2S – 1S) in muonic ions of lithium, beryllium and boron is calculated. Corrections of order α 3 – α 6, which are determined by relativistic effects, effects of vacuum polarization, nuclear structure and recoil, as well as combined corrections, including the above, are taken into account. Nuclear structure effects are expressed in terms of the nuclear charge radius in the case of one-photon interaction and the electromagnetic form factors of nuclei in the case of two-photon interaction. The obtained numerical values for the (2S – 1S) energy interval can be used for comparison with future experimental data and for a more accurate determination of the nuclear charge radii.

Nuclear Structure Correction to Hyperfine Splitting in Light Muonic Ions

Within the framework of the quasipotential method in quantum electrodynamics, the corrections for the structure of the nucleus are calculated from two-photon exchange diagrams in the hyperfine splitting of energy levels in muon ions of lithium, beryllium and boron. The particle interaction operator is constructed using the method of projection operators on particle states with certain values of the total atomic momentum F and muon j. Corrections to the structure of the nucleus are presented in integral form containing the electromagnetic form factors of the nuclei. After the decomposition of form factors at small momentum transfers, the studied contribution is expressed in terms of the nuclear charge radii. The corrections obtained must be taken into account in the precision calculation of the transition frequencies between the 2S and 2P levels.

NUCLEAR STRUCTURE CORRECTIONS IN THE HYPERFINE STRUCTURE OF P-STATES IN LIGHT MUONIC IONS

The effects of the nuclear structure from two-photon exchange amplitudes in the hyperfine structure of P-states in muonic ions of lithium, beryllium, and boron are calculated. The operator of particle interaction in momentum space is constructed using the method of projection operators on states with certain total momenta of the atom F and muon J. Corrections to the nucleus structure are expressed in terms of electromagnetic form factors of nuclei and nuclear charge radii.

Non-Born–Oppenheimer study of the muonic molecule ion 4He μ+**Project supported by the National Natural Science Foundation of China (Grant No. 11704399), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB21030300), and the National Key Research and Development Program of China (Grant No. 2017YFA0304402).

Accurate non-Born–Oppenheimer variational calculations of all bound states of the positive muon molecular ion 4Heμ+ have been performed using explicitly correlated Gaussian functions in conjunction with the global vectors. All the energies obtained are accurate in the order of 10−6 Hartree (1 Hartree = 27.2114 eV). Compared with the binding energies obtained from calculations based on the Born–Oppenheimer potential with the mass-weighted adiabatic corrections (Chem. Phys. Lett. 110 487 (1984)), the largest relative deviation is up to 15%. By analyzing the average interparticle distances and possibility distributions of interparticle distances of this system, it is confirmed that the Born–Oppenheimer approximation is reasonable for this system and that 4He μ+ can be regarded as a system of positive muon bound to a slightly distorted helium atom.

On the possibility of observable signatures of μp and (μ4He)+ lines on the spectra of astrophysical sources

We examine the processes of the luminescence in subordinate lines of muonic hydrogen μp and muonic helium ion (μ4He)+ in the presence of background source of x-ray emission. It is supposed that a certain amount of muonic atoms existing in the vicinity of astrophysical source reemits absorbed radiation in the subordinate lines. The intensity of luminescence of such a process is proportional to the quantum yield which was calculated for different pumping channels and different models of spectra. It is shown that the luminescent lines of muonic hydrogen and muonic helium ion can be very noticeable in the spectrum of background source.

Hyperfine structure of P states in muonic ions of lithium, beryllium, and boron

We calculate hyperfine structure intervals $\Delta E^{hfs}(2P_{1/2})$ and $\Delta E^{hfs}(2P_{3/2})$ for P-states in muonic ions of lithium, beryllium and boron. To construct the particle interaction operator in momentum space we use the tensor method of projection operators on states with definite quantum numbers of total atomic momentum F and total muon momentum j. We take into account vacuum polarization, relativistic, quadruple and structure corrections of orders $\alpha^4$, $\alpha^5$ and $\alpha^6$. The obtained numerical values of hyperfine splittings can be used for a comparison with future experimental data of the CREMA collaboration.

Hyperfine structure of S-states in muonic ions of lithium, beryllium and boron

On the basis of quasipotential method in quantum electrodynamics we make precise calculation of hyperfine structure of S-states in muonic ions of lithium, beryllium and boron. Nuclear structure and recoil corrections of orders α1 and α6, vacuum polarization corrections in first and second orders of perturbation theory are taken into account. Total values of hyperfine splittings are obtained which can be used for a comparison with future experimental data.

Nuclear Structure Effects in the Hyperfine Structure of Muonic Lithium, Beryllium, and Boron

Nuclear structure corrections to hyperfine splitting of energy levels in muonic lithium, beryllium, and boron ions are calculated. Account is taken of the contributions from the two-photon exchange amplitudes, including the vacuum polarization effect, and from the one-photon amplitude, which provide corrections to the nuclear structure and recoil of order $${{\alpha }^{5}}$$ and $${{\alpha }^{6}}$$ . Numerical results for different parametrizations of electromagnetic form factors are compared.

On the weakly-bound (1,1)-states in the three-body ddμ and dtμ muonic ions

The both total and binding energies of the (1,1)-states in the weakly-bound three-body muonic ddμ and dtμ ions are determined to high numerical accuracy. The binding energy of the (1,1)-state in the muonic dtμ ion is evaluated as ε(dtμ)=−0.66033003831(30)eV, while for the same state in the muonic ddμ ion we have found that ε(ddμ)=−1.9749806166970(30)eV. These energies are the most accurate numerical values obtained for these systems and they are sufficient for all current and future experimental needs.

Hyperfine splitting of P-states in light muonic ions

We calculate hyperfine structure intervals for P–states in muonic ions of lithium, beryllium and boron. To construct the particle interaction operator in momentum space we use the tensor method ofprojection operators on states with definite quantum numbers of total atomic momentum F and total muonmomentum j. We take into account vacuum polarization, relativistic, quadruple and structure corrections of orders α4, α5 and α6. The obtained numerical values of hyperfine splittings can be used for a comparison with future experimental data.

1S-2S energy shift in muonic hydrogen

We calculate corrections of orders α4, α5, α6 to the (1S – 2S) fine structure interval in muonic hydrogen (μp), muonic tritium (μt) and muonic helium ion $$((\mu _2^3He) + )$$. They are determined by the effects of vacuum polarization, nuclear structure and recoil and relativistic corrections. The nuclear structure effects are taken into account in terms of the charge radii of the nuclei in one-photon interaction and in terms of electromagnetic form-factors in the case of two-photon interaction. The obtained results for the (1S – 2S) splitting can be used for a comparison with future experimental data.

Energy spectra of muonic atoms in quantum electrodynamics

Vacuum polarization, nuclear structure and recoil, radiative corrections to the hyperfine structure of S-states in muonic ions of lithium, beryllium and boron are calculated on the basis of quasipotential method in quantum electrodynamics. We consider contributions in first and second orders of perturbation theory which have the order α5 and α6 in the energy spectrum. Total values of hyperfine splittings are obtained which can be used for a comparison with future experimental data.

Hyperfine structure of S states in muonic ions of lithium, beryllium, and boron

We make precise calculation of hyperfine structure of $S$-states in muonic ions of lithium, beryllium and boron in quantum electrodynamics. Corrections of orders $\alpha^5$ and $\alpha^6$ due to the vacuum polarization, nuclear structure and recoil in first and second orders of perturbation theory are taken into account. We obtain estimates of the total values of hyperfine splittings which can be used for a comparison with future experimental data.