Muonic Spectra Research Articles

Table of experimental nuclear ground state charge radii: An update

The present table contains experimental root-mean-square (rms) nuclear charge radii R obtained by combined analysis of two types of experimental data: (i) radii changes determined from optical and, to a lesser extent, Kα X-ray isotope shifts and (ii) absolute radii measured by muonic spectra and electronic scattering experiments. The table combines the results of two working groups, using respectively two different methods of evaluation, published in ADNDT earlier. It presents an updated set of rms charge radii for 909 isotopes of 92 elements from 1H to 96Cm together, when available, with the radii changes from optical isotope shifts. Compared with the last published tables of R-values from 2004 (799 ground states), many new data are added due to progress recently achieved by laser spectroscopy up to early 2011. The radii changes in isotopic chains for He, Li, Be, Ne, Sc, Mn, Y, Nb, Bi have been first obtained in the last years and several isotopic sequences have been recently extended to regions far off stability, (e.g., Ar, Mo, Sn, Te, Pb, Po).

Pionic and muonic X-ray measurements on light isotopes

New data on strong interaction effects in the pionic atoms of 3He, 16O, 18O and Cl are presented. Energies and lorentzian widths of the 1s and partly of the 2p levels have been determined from the X-ray spectra. For the first time significant isotope effects could be observed in the 1s level width. Absolute and relative intensities are presented for K and L X-ray transitions respectively trom pionic and muonic spectra. Thus by fitting cascade parameters p-state absorption probabilities could be determined even for the lightest isotopes. The results are compared with those of others and with recent theoretical calculations. The nuclear γ-ray of the transition 5 2 + → 3 2 − in 13C was determined to be 169.356 ± 0.020 keV.

Radiationless 3d→1s transition in muonic atoms of 238U

The probability of the radiationless muonic transition 3d→1s in 238U has been determined. This was done by comparing the singles muonic spectrum with the one gated by the 2p→1s transition. The probability was found to be (14±5)%.

Muonic x-ray study of the even Os nuclei

Precision measurements have been made of the muonic x-ray spectra of the transitional nuclei $^{186,188,190,192}\mathrm{Os}$. Equivalent Barrett radii and isotope shifts have been determined, as have isomer shifts of the first excited ${2}^{+}$ states. These results are compared with other experiments and with theoretical calculations. The systematics of isotope shifts in the deformed nuclei are also discussed. Generalized $E2$ moments of the charge distribution have been extracted in a nearly model-independent way and conventional electromagnetic moments have been deduced by assuming a specific transition charge density model. The latter are in good agreement with recent calculations of both the interacting boson approximation and the boson expansion theory. However, a serious discrepancy in the values of the quadrupole moments determined from the muonic and Coulomb excitation experiments is apparent. The model dependence of the muonic results (including the effect of a triaxial model charge distribution) is explored as a possible cause of the discrepancy; however, no effect large enough to explain the discrepancy is found. Furthermore, no feature of the muonic spectra was found which could be used to distinguish between a triaxial and an axially symmetric charge distribution.NUCLEAR STRUCTURE $^{186,188,190,192}\mathrm{Os}$; measured muonic x-ray spectra; deduced monopole and quadrupole charge parameters, isotope and isomer shifts.

Muonic resonance excitation ofOs188andYb172

Anomalous lines of significant intensity have been observed in the muonic spectra of $^{188}\mathrm{Os}$ and $^{172}\mathrm{Yb}$. These anomalous lines are interpreted as $3d\ensuremath{-}2p$ muonic-nuclear resonances involving ${1}^{\ensuremath{-}}$ and ${3}^{\ensuremath{-}}$ nuclear states at about 2-MeV excitation energy. Electric multipole moments and isomer shifts of the resonant nuclear states have been determined. Such accidental resonances, which presumably occur in other heavy muonic atoms, can provide an opportunity to obtain otherwise unavailable nuclear structure information.

Rydberg Values for X- and γ-Rays

An improved connection chain has been established between the hydrogen Rydberg (i.e., H Balmer α) and γ-ray lines to which mesic X-ray transitions are compared. This new γ-ray scale, together with improved comparisons between muonic spectra and the γ-ray lines, appears to have resolved the long-standing problem of vacuum polarization in high Z muonic atoms. It now becomes of interest to turn to high Z electronic spectra Where accurate relativistic calculations are recently available. Direct re-measurement of these spectra is underway; meanwhile, however, there are already some results available. This report describes the H Balmer α to γ-ray comparisons and summarizes the results of initial comparisons between re-evaluated X-ray transition energies and those which follow from recent relaxed-orbital relativistic Hartree-Fock-Slater calculations.

A study of high-energy cosmic-ray interactions at sea level. II. Theory

For pt.I see ibid., vol.3, p.979 (1977). The expected cosmic-ray burst spectrum ( approximately 1 TeV) in a lead target at sea level has been determined using the published hadronic and muonic spectra. The response of the recording scintillator detector is carefully assessed. The muon burst size spectrum is straightforwardly calculated. Two different approaches are used to determine the expected hadronic burst spectrum, one an analytical technique and the other a Monte-Carlo method. Good agreement between the two techniques is found. The Monte-Carlo method has the advantage of taking into account multiple hadron interactions. The results are compared with experimental data derived from the scintillator detector. The muon-initiated burst spectrum shows close agreement, but a discrepancy of at least a factor of three appears between calculated and measured intensities of hadron-induced bursts.

Polarized muonic beam with variable helicity

A special mode of muonic beam with an average momentum of 21 GeV/ c and opposite helicity from 40 GeV/ c π-meson decay (the soft part of muonic spectrum corresponding to backward emission of muons in the pion rest-frame; negative polarization of muonic beam) and from 28 GeV/ c μ-meson decay (the hard part of the muonic spectrum, positive polarization of muonic beam) has been realized at the IHEP muon beam channel with the view of search for parity-nonconservation effects in deep inelastic μN-interactions. The beam channel is automatically retuned from the operational mode with one helicity to that with the opposite one in each five accelerator cycles during the time intervals between the cycles. Muonic polarization was measured with the help of the energy spectrum of electrons from μ→eνν̃ decay in-flight. In the momentum range 19–23 GeV/ c the difference in polarization of two muonic beams was λ = 0.80±0.15.

Muonic x rays in lead isotopes

Results of an experiment to measure muonic transition energies in separated lead isotopes are presented. The main results are as follows: 1. Muonic spectra of the four lead isotopes $^{204}\mathrm{Pb}$, $^{206}\mathrm{Pb}$, $^{207}\mathrm{Pb}$, and $^{208}\mathrm{Pb}$ were studied with high resolution. No anomalous splitting or broadening of the lines was detected. The effect of the natural linewidth could, however, be observed. 2. An anomaly was found in the $3d$ fine structure splitting whose measured value turned out to be larger than the calculated value by nearly 300 eV (or 10 standard deviations) in all four isotopes. 3. Except for this anomaly, the lower levels of muonic lead can be described adequately with the help of a two-parameter Fermi distribution of the nuclear charge. There is no evidence in the x-ray data for a central depression in the nuclear density. 4. We determine the nuclear polarization in the ground state of all four isotopes of lead and find values ranging from -7.3 \ifmmode\pm\else\textpm\fi{} 2.2 to -10.1 \ifmmode\pm\else\textpm\fi{} 1.1 keV, which are somewhat higher than, but not inconsistent with, the best theoretical predictions of -6.8 \ifmmode\pm\else\textpm\fi{} 2.0 keV. This analysis is made possible by our ability to measure the weak transitions involving the $2s$ level. 5. We find a slight and regular increase in nuclear density, going from $^{204}\mathrm{Pb}$ to $^{208}\mathrm{Pb}$. The skin-thickness parameter $t$ appears, however, to be practically the same in all four isotopes measured.RADIOACTIVITY $^{204}\mathrm{Pb}$, $^{206}\mathrm{Pb}$, $^{207}\mathrm{Pb}$, $^{208}\mathrm{Pb}$; muonic atoms, measured transition energies, levels up to $6f$; observed natural linewidth of $L$ lines; observed anomalous $\mathrm{fs}$ splitting of $3d$; deduced Fermi parameters; deduced nuclear polarization of ground state.

Nuclear polarization energy correction for muonic spectra in the lead region

The nuclear polarization energy correction in muonic lead has been calculated, employing a method in which the energy difference of the muonic states relative to the nuclear excitation energy has been considered. To describe the nuclear states of excitation that are expected to contribute most significantly, we have employed the hydrodynamical model and treated the following modes of excitation, isovector and compression modes of multipolarity 0, 1, 2 and shape oscillations of multipolarity 2 and 3.

Hyperfine Effects in Muonic Bi and Pb

We have investigated the $K$ and $L$ transitions in the muonic spectra of ${\mathrm{Bi}}^{209}$ and of the separated isotopes ${\mathrm{Pb}}^{206}$, ${\mathrm{Pb}}^{207}$, and ${\mathrm{Pb}}^{208}$, using a Ge(Li) spectrometer. Our isotope shifts in Pb, in excellent agreement with the optical data, are half those predicted by the ${A}^{\frac{1}{3}}$ law. The agreement between our shifts and the optical shifts strongly suggests the absence of nuclear polarization by the muon. We have studied the $M1$ and $E2$ hyperfine (hf) interactions in ${\mathrm{Bi}}^{209}$. The $M1$ results, although not sensitive enough to distinguish models of nuclear magnetization distributions, rule out a point magnetic dipole. The $E2$ constants, when used in conjunction with the measured isotone shift between ${\mathrm{Bi}}^{209}$ and ${\mathrm{Pb}}^{208}$, suggest a quadrupole distribution produced by an ${h}_{\frac{9}{2}}$ proton and a slightly (\ensuremath{\sim}1%) deformed ${\mathrm{Pb}}^{208}$ core. We have examined the effects of $E3$ mixing of ${\mathrm{Bi}}^{209}$ nuclear levels on the $K$ and $L$ intensity ratios and on the interpretation of the hf constants.

Experimental observations of electric quadrupole effects in the muonic spectra of 235U, 181Ta and 239Pu

The spectra of the 2p → 1s and 3d → 2p transitions in the muonic atoms of 235U, 181Ta and 239Pu were studied using a NaI(Tl) scintillation spectrometer with an anticoincidence annulus of NaI(Tl). The effects caused by the electric quadrupole interaction between the muon and these nuclei were detected and the intrinsic quadrupole moments Q 0 of 181Ta and 235U were measured. The intrinsic quadrupole moment of 239Pu was found to be large and positive.

Measurements on the cosmic radiation intensity in the mont blanc tunnel

Measurements on the muonic vertical intensity at different depths under rock (140; 290; 1325; 4100±100 m w.e.) have been performed in the M. Blanc tunnel. The experimental equipment is described. Our results are compared with the results obtained by other authors. Taking into account the valuesZ2/A of the various types of rock there is a good agreement among all these measurements. The comparison of experimental points with the muonic spectrum at s.l. suggests to use the Weizsacker-Williams instead of Kessler-Kessler virtual photonic spectrum in the calculation of the energy losses due to nuclear interactions.