Including Recoil Effects Research Articles

Atomic electron distribution and recoil effects following beta decay of the halo nucleus helium-6

SynopsisFollowing the β decay of a 6He nucleus to form 6Li, the atomic electrons adjust to the sudden change of nuclear charge from 2 to 3. The probabilities for electron shake-up and shake-off are calculated, including recoil effects, by the use of a Stieltjes imaging representation of the final states. The results will be applied to ongoing angular correlation studies in a search for new physics beyond the Standard Model.

Rare $$B\rightarrow \pi l\bar{l}$$ B → π l l ¯ and $$B\rightarrow \rho l \bar{l}$$ B → ρ l l ¯ decays in the relativistic quark model

The branching fractions of the rare weak $B\to \pi l^+l^-(\nu\bar\nu)$ and $B\to\rho l^+l^-(\nu\bar\nu)$ decays are calculated in the framework of the relativistic quark model based on the quasipotential approach. The form factors parametrizing weak decay matrix elements are explicitly determined in the whole kinematical $q^2$ range without additional assumptions and extrapolations. Relativistic effects are systematically taken into account including recoil effects in meson wave functions and contributions of the intermediate negative-energy states. New experimental data on the differential distributions in the semileptonic heavy-to-light $B\to\pi l\nu_l$ and $B\to\rho l\nu_l$ decays are analyzed in detail. Good agreement of the predictions and data is found. The obtained results for the branching fractions of the rare semileptonic decays are found to be in agreement with other theoretical estimates and recent experimental data available for the $B^+\to\pi^+ \mu^+\mu^-$ decay.

An effective Dirac equation for a binary of two fermions

Effective Dirac equations are, by following the work of Pilkuhn, derived for a binary of two fermions from the original two-fermion Dirac-type Hamiltonian written in a 16-component spinor representation. For spherical interaction potential (like the static Coulomb potential) the spin dynamics in the product spin space and spatial dynamics in the particle–antiparticle state space can be fully decoupled and separated. The case of atomic hydrogen is solved again as an example, and the standard results including recoil effects through the reduced mass and fine structure induced by spin–orbit coupling are recovered for the energy spectrum.

Theory of recoil effects of elastically scattered electrons and of photoelectrons

Quasi-elastic scatterings of high-energy electrons are studied with quantum scattering theory including recoil effects by use of correlation functions. Two different types of recoil processes are investigated; one is free atom recoil and the other is phonon excited recoil processes within harmonic vibration approximation where Mermin’s theorem works. The recoil effects of photoelectrons excited by high-energy X-rays are also studied, where the atomic displacement after the core-hole production also plays some important roles. For practical calculations the Debye approximation is used for phonon spectra, which gives rise to the simple free atom recoil energy shift. The broadenings of the spectra depend on the temperature in contrast to the energy shift, and is quite different from the free atom approximation in particular at low temperature. Numerical calculations are carried out for Be, C (graphite), Si and Ge powders. The energy shifts for solids composed of light elements are comparable with typical chemical shifts.

Energy dependence of two-particle transfer in heavy-ion collisions

The effective form factor describing pair transfer in heavy-ion collisions is generalized to include recoil effects and the energy dependence of the interaction potential. It is based on a microscopic description of the transfer process treated to second order in the single-particle potential. The result is also formulated in terms of the macroscopic description of pair transfer analogous to that associated with the excitation of surface modes. The angular distributions calculated by semiquantal methods are compared to experimental data. With the present prescription, the discrepancy between theory and recently published experimental data is reduced by two orders of magnitude.

Improved estimates for processes b-->sl+l-, B-->Kl+l-, and B-->Kl+l-

We present the complete calculation for the short-distance flavor-changing process $b\ensuremath{\rightarrow}s{l}^{+}{l}^{\ensuremath{-}}$ and discuss the effect of QCD enhancement, and the resulting $e\ensuremath{-}\ensuremath{\mu}$ rate difference. We estimate the exclusive rates for $B\ensuremath{\rightarrow}k{l}^{+}{l}^{\ensuremath{-}}$ and $B\ensuremath{\rightarrow}{k}^{*}{l}^{+}{l}^{\ensuremath{-}}$ using the relativistic constituent-quark model to calculate the different form factors that include recoil effects. The effect of the fourth generation in enhancing the rates is also discussed.

Finite-PT contribution to relativistic Coulomb excitation: A possible explanation for the clean-fission puzzle.

We study the quantum relativistic Coulomb-excitation process including recoil effects in the plane-wave Born approximation. It is shown that there exists an interplay between quantum and relativistic recoil effects in certain kinematical regions which cannot be accounted for in the conventional theories. This specific feature is shown to modify the angular distribution of Coulomb-induced fission fragmentation in an essential manner. In contrast with usual treatments we find that our results compare favorably with recent data.

The interaction between an electron and the polarization modes of a metal-insulator interface

We study the interaction between an electron and the polarization modes of a metal-insulator interface by employing a self-energy approach. The coupling between the metal surface plasmons and the insulator surface excitons is explicitly considered. The surface optical phonons are shown to be screened out by the plasmon field. We derive expressions for the charge-coupling Hamiltonians of the bulk and interface modes and calculate a self-energy profile that includes recoil effects due to the quantum nature of the electron's motion.

The method of virtual quanta applied to pion production in heavy ion collisions

Pion production in nuclear heavy collisions is calculated using the method of virtual quanta. The model makes predictions for exclusive cross sections, where the pion is produced in coincidence with a nucleus excited into an isobar analogue state. We improve our previous work by including recoil effects, properly taking in account the velocity change of the projectile, and extending the calculations to symmetric collisions. We find that the approximation to neglect recoil effects and the projectile velocity change, which is frequently used in the literature, can drastically overestimate the final results.

Effect of atomic electrons on resonant nuclear scattering

A systematic study is made of the theory of inner-shell ionisation which occurs during a resonant nuclear scattering process. Some previous treatments had emphasised the effect of nuclear recoil as an electronic excitation mechanism while others focused on the effect of the direct projectile-electron Coulomb interaction. In the present approach both excitation mechanisms are accounted for. One contribution to the transition amplitude is closely related to the approximation introduced earlier by Briggs and Lane (1981). The other components provide a generalisation of the Blair formula to include recoil effects non-perturbatively. This formula had been suggested as the basis for a determination of nuclear resonance widths. The observation of Briggs and Lane that recoil excitation can lead to a smearing of the resonance profile is extended to apply to the Blair formula. These results may be useful in future resonance studies to determine whether one is observing an intrinsic nuclear width or some average effect of a sequence of closely spaced projectile-atom resonances.

A study of the 26Mg( 12C, 12B) 26Al charge-exchange reaction

The reaction 26Mg( 12C, 12B) 26A1(5 +, 3 +) has been studied using a beam of 102 MeV of 12C. Shell-model, microscopic direct model and finite-range coupled reaction channel (CRC) calculations including recoil effects, have been performed, for comparison with the experimental data. DWBA calculations were performed for the intermediate states of interest in the 11B + 27Al and in the 13C + 25Mg channels and these results were also compared with the experimental ones. The dominant reaction mechanism for 26Mg( 12C, 12B) 26Al(5 +, 3 +) appears to be the sequential mode.

Jdependence in theCr50(Li7,He6)Mn51reaction at 28 MeV

The reaction $^{50}\mathrm{Cr}$($^{7}\mathrm{Li}$,$^{6}\mathrm{He}$)$^{51}\mathrm{Mn}$ was investigated at extreme forward angles, $1.6\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}\ensuremath{\theta}\ensuremath{\le}12\ifmmode^\circ\else\textdegree\fi{}$, in order to study the $j$ dependence for the ($^{7}\mathrm{Li}$,$^{6}\mathrm{He}$) reaction at 28 MeV. The $^{6}\mathrm{He}$ ejectiles were detected with a position-sensitive (helix) counter in the focal plane of an Enge-split-pole spectrograph. A total energy resolution of about 30 keV was obtained. The angular distributions for seven low-lying states in $^{51}\mathrm{Mn}$ show a pronounced $j$ dependence for angles below 7\ifmmode^\circ\else\textdegree\fi{} and the expected $l$ dependence at angles $\ensuremath{\theta}\ensuremath{\ge}9\ifmmode^\circ\else\textdegree\fi{}$. Finite-range distorted-wave Born approximation calculations which include recoil effects reproduce the $j$-dependent angular distributions very well and permit a clear distinction between ${p}_{\frac{3}{2}}$, ${p}_{\frac{1}{2}}$, ${f}_{\frac{7}{2}}$, and ${f}_{\frac{5}{2}}$ final state angular momenta. The relative spectroscopic factors deduced were in reasonable agreement with those obtained in a recent $^{50}\mathrm{Cr}(^{3}\mathrm{He},d)^{51}\mathrm{Mn}$ reaction study.NUCLEAR REACTIONS $^{50}\mathrm{Cr}$($^{7}\mathrm{Li}$,$^{6}\mathrm{He}$)$^{51}\mathrm{Mn}$, ${E}_{\mathrm{Li}}$ MeV; measured ${E}_{^{6}\mathrm{He}}$ and $\ensuremath{\sigma}(\ensuremath{\theta},{E}_{^{6}\mathrm{He}})$ in split pole spectrograph with 30 keV resolution. Finite-range-DWBA analysis, deduced ${j}_{\mathrm{transfer}}$, spectroscopic factors.

New quantum representation for treating recoil effects in non-linear spectroscopy

The problem of saturated absorption by a gas of two-level molecules, including recoil effects, is formulated in a new quantum representation for the molecular motion. The relationship to other representations is clarified in a simple chart. The new formulation requires the solution of simultaneous linear differential equations with mixed boundary conditions, instead of linear difference equations in two variables followed by an integration over velocity. Analytic solutions are presented for one running wave with Doppler line broadening, and for a weak probe beam in the Doppler limit. The latter lineshape is analysed to show when power broadening obscures the recoil splitting.

Transfer reactions induced by 16O on 29, 30Si

Angular distributions for one- and two-nucleon transfer reactions induced by 16O on 29, 30Si and for the elastic scattering of 16O on 28, 29, 30Si have been measured at 73.5 MeV bombarding energy. The results are analyzed with the DWBA code BRUNHILD that includes recoil effects. Spectroscopic factors extracted for all observed transitions in one-nucleon transfer reactions agree well with those derived from light panicle reactions. The effects of recoil on the Spectroscopic factors for transitions to final states with different spins are discussed. The transitions from smooth to oscillating angular distributions are examined. It is found that the shape of the angular distributions depends on both the matching conditions of the reaction and the localization of the S-matrix amplitudes in L-spacef.

IsS32(O16,C12)Ar36α*Transfer?

The differential cross section for $^{32}\mathrm{S}$($^{16}\mathrm{O}$, $^{12}\mathrm{C}$)$^{36}\mathrm{Ar}$ has been analyzed with the finite-range distorted-wave Born-approximation computer code MERCURY (which includes recoil effects exactly). The general features of the data were reproduced only by assuming that the $\ensuremath{\alpha}$ particle was transferred in an excited state. Good fits to the data were found by also including $L$-dependent absorption in the optical potentials.

Does backscattering of 4He ions by nuclei obey the Rutherford cross-section formula?

Implicit in the use of nuclear backscattering as a quantitative analytic tool is the accuracy of calculating cross sections using a classical Coulombic scattering formula (Rutherford cross section) which includes recoil effects, but ignores spin, nuclear size, electron screening, hard-sphere scattering, and any nuclear-force effects. The Rutherford cross section has not previously been verified experimentally for ions of 4He (1–2.5 MeV) for targets of 16O, 27Al, and 28Si. For 14N, agreement has been found with an accuracy of about 5%. Our experimental results show that 27Al and 28Si have the Rutherford formula value (±1%), and 16O is Rutherford from 1.4 to 2.4 MeV. 14N appears to deviate by about 2% at energies from 1.2 to 2.2 MeV and by more beyond this energy band.

Study of optimum Q-value in 16O induced reactions on even Zr isotopes

Angular behaviour and optimum Q-value of 16O induced transfer reactions on the even Zr isotopes have been studied near the Coulomb barrier as a function of various parameters. The results are compared to semiclassical estimates including recoil effects and nuclear distortions of the Coulomb trajectories.

Finite-Range Calculations of thejDependence of (C12,B11) and (O16,N15) onNi62

Full finite-range calculations, including recoil effects exactly, have been performed for single-proton-transfer reactions on $^{62}\mathrm{Ni}$. Projectiles of $^{16}\mathrm{O}$ and $^{12}\mathrm{C}$ are considered. It is found that the ratios of cross sections leading to the ground and first excited states in $^{63}\mathrm{Cu}$ are in good agreement with experiment. This is not true when recoil is neglected.

Recoil Effects in Single-Nucleon—Transfer Heavy-Ion Reactions

Using a distorted-wave Born-approximation treatment which exactly includes recoil for the data from the reaction $^{12}\mathrm{C}$($^{14}\mathrm{N}$,$^{13}\mathrm{C}$)$^{13}\mathrm{N}$ at $E(^{14}\mathrm{N})=78$ MeV, we demonstrate the necessity for including recoil effects in calculations for single-nucleon-transfer reactions with heavy ions.

Relativistic Balmer Formula Including Recoil Effects

It is shown that an approximate summation of the crossed-ladder Feynman diagrams for the scattering of two charged particles leads to the formula $s={{m}_{1}}^{2}+{{m}_{2}}^{2}+2{m}_{1}{m}_{2}{[1+\frac{{Z}^{2}{\ensuremath{\alpha}}^{2}}{{(n\ensuremath{-}{\ensuremath{\epsilon}}_{j})}^{2}}]}^{\ensuremath{-}\frac{1}{2}}$ for the squared mass of bound states. This formula neglects radiative corrections. It includes recoil effects properly, and reduces in the limit of one infinite mass to the corresponding spectrum of a relativistic particle in a static Coulomb potential. In the particular case of positronium, its expansion in powers of $\ensuremath{\alpha}$ coincides up to order ${\ensuremath{\alpha}}^{4}$ with the singlet energy levels. In an appendix we investigate some properties (gauge invariance, static limit) of this series of graphs.