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Register a new userMuonic hydrogen cascade time and lifetime of the short-lived $2S$ state
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Metastable ${2S}$ muonic-hydrogen atoms undergo collisional ${2S}$-quenching, with rates which depend strongly on whether the $mu p$ kinetic energy is above or below the ${2S}to {2P}$ energy threshold. Above threshold, collisional ${2S} to {2P}$ excitation followed by fast radiative ${2P} to {1S}$ deexcitation is allowed. The corresponding short-lived $mu p ({2S})$ component was measured at 0.6 hPa $mathrm{H}_2$ room temperature gas pressure, with lifetime $tau_{2S}^mathrm{short} = 165 ^{+38}_{-29}$ ns (i.e., $lambda_{2S}^mathrm{quench} = 7.9 ^{+1.8}_{-1.6} times 10^{12} mathrm{s}^{-1}$ at liquid-hydrogen density) and population $epsilon_{2S}^mathrm{short} = 1.70^{+0.80}_{-0.56}$ % (per $mu p$ atom). In addition, a value of the $mu p$ cascade time, $T_mathrm{cas}^{mu p} = (37pm5)$ ns, was found.
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Ab initio study of the density-dependent population and lifetime of the long-lived $(mu p)_{2s}$ and the yield of $(mu p)_{1s}$ atoms with kinetic energy 0.9 keV have been performed for the first time. The direct Coulomb $2sto 1s$ deexcitation is proved to be the dominant quenching mechanism of the $2s$ state at kinetic energy below $2p$ threshold and explain the lifetime of the metastable $2s$ state and high-energy 0.9 keV component of $(mu p)_{1S}$ observed at low densities. The cross sections of the elastic, Stark and Coulomb deexcitation processes have been calculated in the close-coupling approach taking into account for the first time both the closed channels and the threshold effects due to vacuum polarization shifts of the $ns$ states. The cross sections are used as the input data in the detailed study of the atomic cascade kinetics. The theoretical predictions are compared with the known experimental data at low densities. The 40% yield of the 0.9 keV$(mu p)_{1s}$ atoms is predicted for liquid hydrogen density.
The atomic cascade in $mu^- p$ and $pi^- p$ atoms has been studied with the improved version of the extended cascade model in which new quantum mechanical calculations of the differential and integral cross sections of the elastic scattering, Stark transitions and Coulomb de-excitation have been included for the principal quantum number values $nle 8$ and the relative energies $E ge 0.01$ eV. The $X$-ray yields and kinetic energy distributions are compared with the experimental data.
As an important step towards an atomic parity violation experiment in one single trapped Ra$^+$ ion, laser spectroscopy experiments were performed with on-line produced short-lived $^{212,213,214}$Ra$^+$ ions. The isotope shift of the $6,^2$D$_{3/2}$,-,$7,^2$P$_{1/2}$ and $6,^2$D$_{3/2}$,-,$7,^2$P$_{3/2}$ transitions and the hyperfine structure constant of the $7,^2$S$_{1/2}$ and $6,^2$D$_{3/2}$ states in $^{213}$Ra$^+$ were measured. These values provide a benchmark for the required atomic theory. A lower limit of $232(4)$ ms for the lifetime of the metastable $6,^2$D$_{5/2}$ state was measured by optical shelving.
The K$beta$ transition in muonic hydrogen was measured with a high-resolution crystal spectrometer. The spectrum is shown to be sensitive to the ground-state hyperfine splitting, the corresponding triplet-to-singlet ratio, and the kinetic energy distribution in the $3p$ state. The hyperfine splitting and triplet-to-singlet ratio are found to be consistent with the values expected from theoretical and experimental investigations and, therefore, were fixed accordingly in order to reduce the uncertainties in the further reconstruction of the kinetic energy distribution. The presence of high-energetic components was established and quantified in both a phenomenological, i.e. cascade-model-free fit, and in a direct deconvolution of the Doppler broadening based on the Bayesian approach.
The interaction of two excited hydrogen atoms in metastable states constitutes a theoretically interesting problem because of the quasi-degenerate 2P_{1/2} levels which are removed from the 2S states only by the Lamb shift. The total Hamiltonian of the system is composed of the van der Waals Hamiltonian, the Lamb shift and the hyperfine effects. The van der Waals shift becomes commensurate with the 2S-2P_{3/2} fine-structure splitting only for close approach (R < 100 a_0, where a_0 is the Bohr radius) and one may thus restrict the discussion to the levels with n=2 and J=1/2 to good approximation. Because each S or P state splits into an F=1 triplet and an F=0 hyperfine singlet (eight states for each atom), the Hamiltonian matrix {em a priori} is of dimension 64. A careful analysis of symmetries the problem allows one to reduce the dimensionality of the most involved irreducible submatrix to 12. We determine the Hamiltonian matrices and the leading-order van der Waals shifts for states which are degenerate under the action of the unperturbed Hamiltonian (Lamb shift plus hyperfine structure). The leading first- and second-order van der Waals shifts lead to interaction energies proportional to 1/R^3 and 1/R^6 and are evaluated within the hyperfine manifolds. When both atoms are metastable 2S states, we find an interaction energy of order E_h chi (a_0/R)^6, where E_h and L are the Hartree and Lamb shift energies, respectively, and chi = E_h/L ~ 6.22 times 10^6 is their ratio.
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