Cross-sections for low-energy πgamma; reactions

We review the cross-sections for low-energy π^-γ reactions in the framework of chiral perturbation theory. Charged-pion Compton scattering, π^-γ → π^-γ , is considered up to one-loop order where the pion's internal structure enters through the difference of the electric and magnetic pion polarizability, α_π - β_π . The ongoing COMPASS experiment aims at measuring this important structure constant with high statistics using the Primakoff effect. In the same way, the reaction π^-γ → π^-π⁰ serves as a test of the QCD chiral anomaly (via the γ3π -coupling constant F _γ3π . Furthermore, we calculate the total cross-sections for neutral and charged pion-pair production, π^-γ → π^-π⁰π⁰ and π^-γ → π^-π⁺π^- , which are governed by the chiral ππ -interaction. Finally, we investigate the radiative (correction) process π^-γ → π^-γγ and calculate the corresponding two-photon mass spectrum. This information will be useful for analyzing the π^- Primakoff scattering events with photons in the final state.     

Alpha decay of the new isotopes 188,189Po

New neutron-deficient isotopes ^188,189Po have been produced in the complete fusion reaction of ⁵²Cr ions with a ¹⁴²Nd target at the velocity filter SHIP. The evaporation residues were separated in-flight and subsequently identified on the basis of α-γ and α-conversion electron coincidence measurements and of α-α position and time correlations. In ¹⁸⁹Po a ground state to ground state α decay with E_α1= 7540(20) keV, T_1/2= 5(1) ms and two fine structure α-decays at E_α2= 7264(15) keV and E_α3= 7316(15) keV have been observed. In ¹⁸⁸Po (T_1/2= 400⁺²⁰⁰ ₋₁₅₀μs) a ground state to ground state α decay at E_α= 7915(25) keV and a fine structure α decay at E_α= 7350(40) keV have been found. Improved data on the α-decay of ¹⁸⁹Bi were obtained. Received: 15 October 1999     

The Primakoff reaction study for pion polarizability measurement at COMPASS

The electromagnetic structure of charged pions can be described by the electric (α_π) and magnetic (β_π) polarizabilities that depend on the rigidity of pion’s internal structure as a composite particle. It is shown that the values of α_π and β_π can be precisely measured via the Primakoff reaction π⁻ + (A, Z) → π⁻ + (A, Z) + γ in the COMPASS experiment at CERN.     

The dependence of the Fe <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="BoldItalic">α</Emphasis></Subscript> yield on the chirp of the femtosecond exciting laser pulse

The hard X-ray yield generated with femtosecond laser pulses is studied for differently chirped irradiating laser pulses. The radiation of a Ti:sapphire CPA laser system (29 fs, 750 μJ, 1 kHz) is focused onto an iron containing solid state target producing incoherent hard X-ray radiation, Bremsstrahlung as well as target-specific K_α and K_β lines. The hard X-ray yield has been optimized by introducing negative and positive group delay dispersion (GDD) and third order dispersion (TOD) to the femtosecond laser pulse. The K_α yield could be enhanced by a factor of 1.7 and reached 1.9×10⁸ Fe K_α photons/s in 4π with the laser pulse positively chirped, and 1.5×10⁸ Fe K_α photons/s with the pulse negatively chirped. When the pulse energy is lowered to about 400 μJ the yield maximum at negative chirp vanishes and only the maximum at positive chirp remains. We explain this behavior with an increased electron temperature caused by the induced GDD and TOD in the pulse. PACS 42.65.Re; 52.38.Ph; 52.50.Jm     

Noise sensitivity of an atomic velocity sensor

We use Bloch oscillations to accelerate coherently rubidium atoms. The variation of the velocity induced by this acceleration is an integer number times the recoil velocity due to the absorption of one photon. The measurement of the velocity variation is achieved using two velocity selective Raman -pulses: the first pulse transfers atoms from the hyperfine state 5S1/2, $" align="middle" border="0"> to 5S1/2, $" align="middle" border="0"> into a narrow velocity class. After the acceleration of this selected atomic slice, we apply the second Raman pulse to bring the resonant atoms back to the initial state 5S1/2, $" align="middle" border="0"> . The populations in (F=1 and F=2) are measured separately by using a one-dimensional time-of-flight technique. To plot the final velocity distribution we repeat this procedure by scanning the Raman beam frequency of the second pulse. This two -pulses system constitutes then a velocity sensor. Any noise in the relative phase shift of the Raman beams induces an error in the measured velocity. In this paper we present a theoretical and an experimental analysis of this velocity sensor, which take into account the phase fluctuations during the Raman pulses.     

Molecular-orbital structure in neutron-rich Be and C isotopes

The structure of Be and C isotopes are investigated based on the molecular-orbit (MO) model. The low-lying states are characterized by several configurations of valence neutrons, which are constructed as combinations of basic orbits. In ¹⁰Be, all of the observed positive-parity bands and the negative-parity bands are described within the model. The second 0⁺ state of ¹⁰Be has a large α-α cluster structure, and this is characterized by a (1/2⁺ _σ)² configuration. An enlargement of the α-α distance due to two-valence neutrons along the α-α axis makes their wave function smooth and reduces the kinetic energy drastically. Furthermore, the contribution of the spin-orbit interaction due to coupling between the S _z = 0 and the S _z = 1 configurations, is important. In the ground state of ¹²Be, the calculated energy exhibits similar characteristics, that the remarkable α clustering and the contribution of the spin-orbit interaction make the binding of the state with (3/2^- _π)²(1/2⁺ _σ)² configuration properly stronger in comparison with the closed p-shell (3/2^- _π)²(1/2^- _π)² configuration. This is related to the breaking of the N = 8 (closed p-shell) neutron magic number. Also, the molecule-like structure of the C isotopes is investigated using a microscopic α+α+α+n+n+ ^{. . .} model. The combination of the valence neutrons in the π- and the σ-orbit is promising to stabilize the linear-chain state against the breathing and bending modes, and it is found that the excited states of ¹⁶C are the most promising candidates for such structure. Received: 1 May 2001 / Accepted: 4 December 2001     

Accurate mass spectrometry of trapped ions

The Penning trap Ion Cyclotron Resonance (ICR) method we use to weigh atomic masses is reviewed, and our plans for future measurements, new methods, and apparatus improvements are discussed. Our ultimate goal is to develop a new technique for measuring atomic masses with an accuracy of a few parts in 10¹². We will do this by comparing the cyclotron frequencies of two simultaneously trapped ions. In order to successfully implement this new method we are developing a quieter, more sensitive DC SQUID-based detector and a new more harmonic trap, and we plan to use our classical squeezing techniques to reduce the effects of thermal noise. With our improved apparatus we will weigh Cs and Rb to help determine the fine structure constant α, weigh ²⁹Si and ³⁰Si as part of the current effort to replace the artifact kilogram standard with a Si crystal containing a known number of atoms, and measure the ³H-³He mass difference to help set a limit on the mass of the electron neutrino. Our higher accuracy will also enable us to ``weigh' the neutron capture gamma rays of <sup>28</sup>Si, <sup>32</sup>S, and <sup>48</sup>Ti to help determine the molar Planck constant N<sub>A</sub>h and the fine structure constant α. Finally, with a mass measurement accuracy \sim 10<sup>-12</sup> we will be able to ``weigh' chemical bonds. This revised version was published online in August 2006 with corrections to the Cover Date.     

0-π oscillations in nanostructured Nb/Fe/Nb Josephson junctions

The physics of the π phase shift in ferromagnetic Josephson junctions may enable a range of applications for spin-electronic devices and quantum computing. We investigate transitions from “0” to “π” states in Nb/Fe/Nb Josephson junctions by varying the Fe barrier thickness from 0.5 nm to 5.5 nm. From magnetic measurements we estimate for Fe a magnetic dead layer of about 1.1 nm. By fitting the characteristic voltage oscillations with existing theoretical models we extrapolate an exchange energy of 256 meV, a Fermi velocity of 1.98 ×10⁵ m/s and an electron mean free path of 6.2 nm, in agreement with other reported values. From the temperature dependence of the I_CR_N product we show that its decay rate exhibits a nonmonotonic oscillatory behavior with the Fe barrier thickness.     

Precise Measurements of the Masses of Cs, Rb and Na – A New Route to the Fine Structure Constant

We report new values for the atomic masses of the alkali ¹³³Cs, ⁸⁷Rb, ⁸⁵Rb, and ²³Na with uncertainties ≤ 0.2 ppb. These results, obtained using Penning trap single ion mass spectrometry, are typically two orders of magnitude more accurate than previously measured values. Combined with values of h/m _atom from atom interferometry measurements and accurate wavelength measurements for different atoms, these values will lead to new ppb-level determinations of the molar Planck constant N _A h and the fine structure constant α. This route to α is based on simple physics. It can potentially achieve the several ppb level of accuracy needed to test the QED determination of α extracted from measurements of the electron g factor. We also demonstrate an electronic cooling technique that cools our detector and ion below the 4 K ambient temperature. This technique improves by about a factor of three our ability to measure the ion's axial motion. This revised version was published online in July 2006 with corrections to the Cover Date.     

Interaction of frequency modulated light pulses with rubidium atoms in a magneto-optical trap

The spatial displacement of the ⁸⁵Rb atoms in a Magneto-Optical Trap (MOT) under the influence of series of frequency modulated light pulse pairs propagating opposite to each other is measured as a function of the time elapsed after the start of the pulse train, and compared with the results of simulations. Adiabatic excitation and consecutive de-excitation take place between the ground 5²S_1/2 (F=3) and the 5²P_3/2 (F'=2, 3, 4) excited levels as the result of the interaction. The displacement of the ⁸⁵Rb atoms is calculated as the solution of simple equation of motion where the expelling force is that arising from the action of the frequency modulated light pulses. The restoring and friction forces of the MOT are taken into account also. The system of Bloch equations for the density matrix elements is solved numerically for transitions between six working hyperfine levels of the atom interacting with the sequence of the frequency modulated laser pulses. According to these simulations, the momentum transferred by one pulse pair is always smaller than the expected 2ħk, (1) where ħ is the Plank constant and k=2π/λ where λ is the wavelength, (2) having a maximum value in a restricted region of variation of the laser pulse peak intensity and the chirp.     

A symmetry relating certain processes in 2-and 4-dimensional space-times and the value α0 = 1/4π of the bare fine structure constant

The symmetry manifests itself in exact relations between the Bogoliubov coefficients for processes induced by an accelerated point mirror in 1 + 1 dimensional space and the current (charge) densities for the processes caused by an accelerated point charge in 3 + 1 dimensional space. The spectra of pairs of Bose (Fermi) massless quanta emitted by the mirror coincide with the spectra of photons (scalar quanta) emitted by the electric (scalar) charge up to the factor e ²/ħc. The integral relation between the propagator of a pair of oppositely directed massless particles in 1 + 1 dimensional space and the propagator of a single particle in 3 + 1 dimensional space leads to the equality of the vacuum-vacuum amplitudes for the charge and the mirror if the mean number of created particles is small and the charge e = √ħc. Due to the symmetry, the mass shifts of electric and scalar charges (the sources of Bose fields with spin 1 and 0 in 3 + 1 dimensional space) for the trajectories with a subluminal relative velocity β₁₂ of the ends and the maximum proper acceleration w ₀ are expressed in terms of the heat capacity (or energy) spectral densities of Bose and Fermi gases of massless particles with the temperature w ₀/2π in 1 + 1 dimensional space. Thus, the acceleration excites 1-dimensional oscillation in the proper field of a charge, and the energy of oscillation is partly deexcited in the form of real quanta and partly remains in the field. As a result, the mass shift of an accelerated electric charge is nonzero and negative, while that of a scalar charge is zero. The symmetry is extended to the mirror and charge interactions with the fields carrying spacelike momenta and defining the Bogoliubov coefficients α^B,F. The traces trα^B,F, which describe the vector and scalar interactions of the accelerated mirror with a uniformly moving detector, were found in analytic form for two mirror trajectories with subluminal velocities of the ends. The symmetry predicts one and the same value e ₀ = √ħc for the electric and scalar charges in 3 + 1 dimensional space. Arguments are adduced in favor of the conclusion that this value and the corresponding value α₀ = 1/4π of the fine structure constant are the bare, nonrenormalized values. The text was submitted by the author in English.     

Scalar mesons in <Emphasis Type="Italic">η</Emphasis>′ → <Emphasis Type="Italic">ηπ</Emphasis><Superscript>0</Superscript><Emphasis Type="Italic">π</Emphasis><Superscript>0</Superscript> decay

The decay η′ → ηπ ⁰ π ⁰ is studied in the framework of isobar model. It is shown, that good agreement with the experiment is achieved if α ₀- and σ-meson contributions are taken into account. The contribution of α ₀-meson is dominant, but σ-meson is necessary to reproduce the form of the Dalitz plot. Instead of the usual Breit-Wigner form of σ-meson propagator we use parametrization of the ππ-amplitude, which satisfies analyticity, crossing, unitarity and chirality constraints. This amplitude has a pole in the complex plane, which corresponds to σ-meson and describe experimental data on ππ-scattering in K _e4 decay.     

A new photon recoil experiment: towards a determination of the fine structure constant

We report on progress towards a measurement of the fine structure constant α to an accuracy of 5×10^-10 or better by measuring the ratio h/m_Cs of the Planck constant h to the mass of the cesium atom m_Cs. Compared to similar experiments, ours is improved in three significant ways: (i) simultaneous conjugate interferometers, (ii) multi-photon Bragg diffraction between same internal states, and (iii) an about 1000-fold reduction of laser phase noise to -138 dBc/Hz. Combining that with a new method to simultaneously stabilize the phases of four frequencies, we achieve 0.2 mrad effective phase noise at the location of the atoms. In addition, we use active stabilization to suppress systematic effects due to beam misalignment. PACS 03.75.Dg; 06.20.Jr; 06.30.Ft; 39.20.+q; 03.65.Ta     

Optical nutation at a Raman-active transition

Optical nutation at the Raman-active transition 6P _1/2−6P _3/2 of thallium atoms (ω _R /2πc=7793 cm ⁻¹) under resonant Raman excitation by a biharmonic picosecond pulsed field, giving rise to substantial motion of the population, is detected. Optical nutation appears as an oscillatory behavior of the energy of the anti-Stokes scattering of probe pulses, which follow with a fixed delay, as a function of the product of the energies of the excitation pulses. As a result of the dynamic Stark effect, which decreases the frequency of the transition under study, resonance excitation conditions are satisfied for negative initial detunings of the Raman excitation frequency from resonance. The Raman scattering cross section for the transition under study is estimated by comparing the experimental data with the calculations. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 1, 7–12 (10 July 1999)     

Nuclear spins, magnetic moments and α-decay spectroscopy of long-lived isomeric states in 185Pb

Alpha-decay properties of the neutron-deficient isotope ¹⁸⁵Pb were studied at the PSB-ISOLDE (CERN) on-line mass separator using the resonance ionisation laser ion source (RILIS). The nuclei of interest were produced in a 1.4 GeV proton-induced spallation reaction of a uranium graphite target. In contrast to previous studies, two α-decaying isomeric states were identified in ¹⁸⁵Pb. The relative production of the isomers, monitored by their α-counting rates, could be significantly changed when a narrow-bandwidth laser at the RILIS setup was used to scan through the atomic hyperfine structure. Based on the atomic hyperfine structure measurements, along with the systematics for heavier odd-mass lead isotopes, the spin and the parity of these states were interpreted as 3/2^- and 13/2⁺ and their nuclear magnetic moments were deduced. The α-decay energy and half-life value for the I ^π = 13/2⁺ isomer are E _α = 6408(5) keV, T _1/2 = 4.3(2) s, respectively; while for the I ^π = 3/2^- isomer ( T _1/2 = 6.3(4) s) two α-decays with E _α1 = 6288(5) keV, I _α1 = 56(2)% and E _α2 = 6486(5) keV, I _α2 = 44(2)% were observed. By observing prompt α-γ coincidences new information on the low-lying states in the daughter isotope ¹⁸¹Hg was obtained. Received: 7 February 2002 / Accepted: 19 February 2002     

Effect of the relative phase between two-colour pump pulses on structure of harmonic spectra

We numerically calculate the high-order harmonic generation (HHG) power spectra from a one-dimensional model atom irradiated by linearly polarised 12 fs two-colour laser pulses composed of a fundamental pulse from Ti:sapphire laser and its second harmonic. It is found that a distinct double plateau structure appears when the relative phase of the two pulses is set as π/8, 2π/8 or 3π/8, and the double plateau structure disappears when the relative phase is set as 4π/8, 5π/8, 6π/8 or 7π/8. The relative-phase-dependent plateau structure is explained by the temporal profile of the synthesised electric fields as well as the semi-classical “three-step” model. Moreover, our numerical result shows that cut-off frequencies of the two-colour pulse HHG spectra can be exactly predicted by use of the semi-classical “three-step” model.     

Radioactive decay of 217Pa

The radioactive decay of ²¹⁷Pa was investigated by means of α-γ-spectroscopy. Fine structure in the ground-state α-decay was established. Ambiguities in the fine structure of the α-decay of the previously known isomeric state could be clarified by α-γ-coincidence measurements. A previously unknown α-transition of E _α = (8306 ± 5) keV was detected and identified by means of delayed α-α- and α-γ-γ-coincidence measurements. A second isomeric state decaying by α-emission was not observed. The quality of the previously reported data of the α-decay fine structure of ²¹⁷Th was improved. Received: 29 April 2002 / Accepted: 17 June 2002 / Published online: 19 November 2002 RID="a" ID="a"e-mail: f.p.hessberger@gsi.de Communicated by J. ?yst?     

Electromagnetic polarizabilities of the nucleon and properties of the σ-meson pole contribution

The t-channel contribution to the difference of electromagnetic polarizabilities of the nucleon, (α - β)^t, can be quantitatively understood in terms of a σ-meson pole in the complex t-plane of the invariant scattering amplitude A ₁(s, t) with properties of the σ-meson as given by the quark-level Nambu-Jona-Lasinio model (NJL). Equivalently, this quantity may be understood in terms of a cut in the complex t-plane where the properties of the σ-meson are taken from the ππ → σ → ππ, γγ → σ → ππ and Nˉ → σ → ππ reactions. This equivalence may be understood as a sum rule where the properties of the σ-meson as predicted by the NJL model are related to the f ₀(600) particle observed in the three reactions. In the following, we describe details of the derivation of (α - β)^t making use of predictions of the quark-level NJL model for the σ-meson mass. An erratum to this article is available at .     

On the existence and detection of Bloch oscillations in superlattices

While many predicted superlattice behaviors depend on the presence of Bloch oscillations, the existence of such oscillations remains problematical. Here, we consider procedures by which their existence within a superlattice could be detected. We first set upper and lower bounds on the necessary fields. We then demonstrate that while a negative differential mobility is expected, no resonant peak occurs in this mobility at the Bloch frequency. However, we provide two ways of directly observing Bloch oscillations. In the first, we note the existence of structures in the dc velocity-field characteristic when an externally applied RF field has a frequency which is harmonically related to the Bloch frequency. The second approach is to measure the velocity fluctuation noise spectra, which should have a peak at the field-tunable Bloch frequency.     

On Minimal Eigenvalues¶of Schrödinger Operators on Manifolds

We consider the problem of minimizing the eigenvalues of the Schr?dinger operator H=−Δ+αF(κ) (α>0) on a compact n-manifold subject to the restriction that κ has a given fixed average κ₀. In the one-dimensional case our results imply in particular that for F(κ)=κ² the constant potential fails to minimize the principal eigenvalue for α>α_c=μ₁/(4κ₀ ²), where μ₁ is the first nonzero eigenvalue of −Δ. This complements a result by Exner, Harrell and Loss, showing that the critical value where the constant potential stops being a minimizer for a class of Schr?dinger operators penalized by curvature is given by α _c . Furthermore, we show that the value of μ₁/4 remains the infimum for all α >α _c . Using these results, we obtain a sharp lower bound for the principal eigenvalue for a general potential. In higher dimensions we prove a (weak) local version of these results for a general class of potentials F(κ), and then show that globally the infimum for the first and also for higher eigenvalues is actually given by the corresponding eigenvalues of the Laplace–Beltrami operator and is never attained. Received: 17 July 2000 / Accepted: 11 October 2000