Nuclear polarization shifts in light muonic atoms

A consistent nonrelativistic expression for the energy shift in muonic atoms due to second-order processes is derived under the assumption that the muon is weakly bound. The transverse contribution is shown to be finite only if the two-photon (“seagull”) amplitude is taken into account as required by gauge invariance. Numerical results are presented for muonic ¹²C using a recently developed model for the nuclear response function. The total transverse contributions to the energy shift are found to be small although dependent to some extent on the detailed high-momentum behaviour of the seagull term.     

Nuclear auger effect in muonic atoms

In a muonic atom electromagnetic transitions proceed via emission of X-rays, electrons from the atomic cloud (Auger electrons), or neutrons from the nucleus (nuclear Auger effect). We calculate the neutron spectrum for muonic ²⁰⁷Pb and ²⁰⁹Bi within a microscopic theory of nuclear reactions. The compound nucleus mechanism is dominant. Most of the neutrons arise from the E2 transition 3d → 1s. Agreement between experiment and calculation is achieved to within a factor of 2.     

Nuclear finite-size effects in light muonic atoms

The finite nuclear size corrections to the s-state energy levels of light muonic (or hydrogenic) atoms are calculated analytically through order (Zα)⁶. In addition to the usual expression of order (Zα)⁴, the (Zα)⁵, (Zα)⁶ and (Zα)⁶ log(Zα) contributions have been determined. These corrections have been separated into terms of nonrelativistic and relativistic orders. The results have been checked by solving perturbatively the exact eigenvalue equations of the Schroedinger and Dirac problems of a particle orbiting in the Coulomb field of a uniform charge distribution of fixed radius. Application is made to the case of the μ-⁴He atom. Finite-size contributions to the hydrogen Lamb shift and the relativistic recoil effect are briefly discussed.     

Nuclear polarization in muonic atoms of deformed nuclei

The treatment of nuclear polarization correction in muonic atoms belonging to deformed nuclei is analyzed. The geometrical factors involved are expanded into a series of multipoles and the exact expansion coefficients are calculated. It is shown that, using reasonable assumptions about the nuclear spectrum, the nuclear polarization correction may be expressed as a shift of all hyperfine components plus a renormalization of the even multipole hyperfine interaction constants. All nuclear excited states contribute to the shift, but the ground-state rotational band gives an over-whelming contribution to the multipole moment renormalization. The effect of the ground-state band is analyzed in detail. The radial coefficients are calculated and an approximate formula, applicable over a broad range of atomic numbers and deformations, is obtained. By comparing our results with exact calculations we conclude that this part of the nuclear polarization correction may be calculated with accuracy better than 10 %.     

Nuclear excitation and prompt fission in muonic238U

A study of muonic²³⁸U has been performed in a combined (μ ^?,γ f) and (μ ^?,γγ) coincidence experiment to investigate the role of non-radiative transitions and their fission probabilities. An augmentation of the outer fission barrier ofΔE _b =(0.6±0.1) MeV due to the presence of the muon is deduced. A significant contribution to the prompt fission yield not only results from the (2p→1s) and (3d→1s) non-radiative transitions, but also from other radiationless transitions. Specifically, the measured fission probabilities of the transitions (2p→1s), (3d→1s), and (3p→1s) are (1.5±0.4)%, (5.7±1.7)%, and (5.3±1.9)%, respectively.     

Critical discussion of the vacuum polarization measurements in muonic atoms

Recent disagreement between theoretical and experimental values of transition energies for outer states in muonic atoms is discussed in the range of 150–440 keV. A brief review of the present status of calculation of the theoretical contributions is given. A rigorous theoretical framework for the electron-muon system is considered. A set of self-consistent equations is derived. Several mechanisms for the explanation of the discrepancy are discussed. No explanation within the frame of standard quantum electrodynamics is found.     

Nuclear signatures in high-order harmonic generation from laser-driven muonic atoms

High-order harmonic generation from muonic atoms exposed to intense laser fields is considered. Our particular interest lies in effects arising from the finite nuclear mass and size. We numerically perform a fully quantum mechanical treatment of the muon-nucleus dynamics by employing modified soft-core and hard-core potentials. It is shown that the position of the high-energy cutoff of the harmonic spectrum depends on the nuclear mass, while the height of the spectral plateau is sensitive to the nuclear radius. We also demonstrate that gamma-ray harmonics can be generated from muonic atoms in ultrastrong VUV fields, which have potential to induce photonuclear reactions.     

Change of nuclear radii due to rotation: Calculation of Mössbauer and muonic isomer shifts

Mössbauer and muonic isomer shifts of 2⁺ rotational states are calculated for rare-earth nuclei in good agreement with experiment using Migdal's effective p-h and p-p interactions. The second-order cranking equations are developed in the framework of the theory of finite Fermi systems. In contrast to the pairing-plus-quadrupole model, the results of this work show a small stretching contribution for most nuclei, but a dominating role for the Coriolis antipairing effect. Shrinking charge radii are found for Dy and Os isotopes and some other nuclei as a consequence of the CAP mechanism. Detailed information is given about the redistribution of protons and neutrons due to rotation. It is seen that only a few levels within the range of the diffuse Fermi edge take part in the redistribution and determine the isomer shifts. Shrinking m.s. proton radii and, at the same time, increasing m.s. neutron radii are obtained for the “back-bending” nuclei ^{158, 160, 162}Dy ^{160, 162}Er and ^{164, 166}Yb.     

Correlation between muonic levels and nuclear structure in muonic atoms

A method that deals with the nucleons and the muon unitedly is employed to investigate the muonic lead, with which the correlation between the muon and nucleus can be studied distinctly. A “kink” appears in the muonic isotope shift at a neutron magic number where the nuclear shell structure plays a key role. This behavior may have very important implications for the experimentally probing the shell structure of the nuclei far away from the β-stable line. We investigate the variations of the nuclear structure due to the interaction with the muon in the muonic atom and find that the nuclear structure remains basically unaltered. Therefore, the muon is a clean and reliable probe for studying the nuclear structure. In addition, a correction that the muon-induced slight change in the proton density distribution in turn shifts the muonic levels is investigated. This correction to muonic level is as important as the Lamb shift and high order vacuum polarization correction, but is larger than anomalous magnetic moment and electron shielding correction.     

Relaxation shifts and plasmon excitation in absorption spectroscopy of adsorbed atoms

The excitation probability for surface plasmons, and the level shift due to the image force, are investigated when an electron is excited from a core level to an unoccupied virtual level of the adatom. The results differ strongly from the corresponding ones in XPS, in a manner depending on the energy variation of the width of the virtual level.     

Polarizability effects in electronic and muonic atoms

Zeitschrift für Physik A Hadrons and nuclei - TheS state polarizability shifts are derived from the virtual forward Compton scattering in the unretarded dipole approximation. In the...     

Nuclear charge radii from X-ray transitions in muonic atoms of carbon,nitrogen and oxygen

Energies of muonic X-rays of the K-series of carbon, nitrogen and oxygen have been measured with an accuracy of about 15 eV. Root mean square radii of the nuclear charge distributions were deduced. The results 2.49±0.05 fm for carbon, 2.55±0.03 fm for nitrogen and 2.71 ±0.02 fm for oxygen are in good agreement at comparable accuracy with recent electron scattering data.     

Nuclear compressibility and its effect on nuclear binding energies from the study of muonic atoms

The variation of nuclear parameter with mass number elicits information about nuclear compressibility. Analysis of muonic x-ray transitions provides an elegant method to investigate the behaviour of the nuclear parameterr ₀. It is observed from the behaviour ofr ₀ that nuclei in the regionA⩽70 are highly compressible while those in the regionA∼210 are almost incompressible. The behaviour ofr ₀ is incorporated into the semi-empirical mass formula through the Coulomb energy term. From the modified mass formula thus obtained binding energies of about 440 spherical nuclei have been calculated. The results suggest that nuclear compressibility imposes certain relationship between excess binding energies (E _exp−E _cal) and neutron. proton number. The present study also points out that shell effects exhibited by nuclear binding energies cannot be accounted for by simply varying the coefficients of the mass formula: on the other hand extra terms are necessary to explain them.     

OBEP and eikonal form factor: (II). Nuclear matter results

Nuclear matter properties are calculated in a first-order Brueckner-Bethe calculation using a one-boson exchange potential recently proposed by the authors, in which the phenomenological cutoff of dipole type used so far has been replaced by a form factor obtained from an eikonal approximation to multiple vector meson exchange processes. We find ?23.5 MeV saturation energy at a Fermi momentum k_F = 1.77 fm^?1, i.e. about 12 MeV more binding than realistic OBEP using dipole-type cutoffs and about 8 MeV overbinding compared to the empirical value of 16 MeV. On the other hand, estimates suggest that, compared to the Reid soft-core potential, this new OBEP predicts about 1.5 MeV more binding in the case of the triton and about 4 MeV more binding in the case of ¹⁶O, i.e. gives nearly the correct empirical result. The additional binding is traced back to the small deuteron D-state probability of 4.32% predicted by this OBEP, which is a consequence of the special structure of the eikonal form factor. However, taking the effect of the Δ-resonance into account recently given by Green and Niskanen, one arrives at ?14 MeV saturation energy for nuclear matter at k_F = 1.36 fm^?1, whereas the results for the triton and ¹⁶O are changed to a negligible extent only.     

Optical-model analysis of exotic atom data: (II). Antiprotonic and sigma atoms

Data for antiprotonic and sigma atoms are fitted using a simple optical model with a potential proportional to the nuclear density. The potential strength can be related to the free hadron-nucleon scattering length using a model due to Deloff. A good overall representation of the data is also obtained with a black-sphere model.     

Photon-electron directional correlation in muonic atoms and weak-interaction models

Measurements of photon-electron directional correlation in muonic atoms may provide useful information on the low-energy neutral-current effective interaction of charged leptons with light quarks, significantly complementing the information obtainable from other low-energy parity-violation experiments. We calculate the expectations for the correlation coefficients in conventional extended gauge models, such as to test for possible deviations with respect to the standard model. We discuss sources of uncertainty in the estimate of such deviations. The physical relevance of this analysis is exhibited in a number of graphs which illustrate how such experiments, at presumably attainable precision, would significantly improve the bounds on the effective lagrangian as obtained from other sets of data (including LEP).     

Pion condensation in neutron star matter: (II). Nuclear forces and stability

This paper presents several stable models of charged-pion condensed neutron star matter. The non-relativistic limit of the chirally symmetric Weinberg Lagrangian is used to describe interactions of the condensed pion field with the nucleons, as well as the pi-pi interactions of the condensed field. In the absence of nucleon-nucleon interactions, matter in this model is unstable, tending to ever-increasing baryon density and condensate wave vector. The connection of this model of condensation with the σ-model is shown.A general framework for including nuclear forces is then laid out. Results are given for a simple model in which the nuclear forces are assumed to produce an interaction energy V(ρ) dependent only on the total baryon density, independent of the degree of pion condensation, and also to produce a constant G-matrix element g in the nucleon-nucleon charge exchange channel. In the absence of condensation the equation of state reduces to that of interacting normal matter. We also consider effects of beta equilibrium and form factors in the p-wave pion-nucleon interaction. The condensed models are stable. Depending on the choice of parameters the models exhibit first- or second-order pion condensation phase transitions, or both.