U. D. Jentschura

Publications (100)65.46 Total impact

• Article: Quantum dynamics in atomic-fountain experiments for measuring the electric dipole moment of the electron with improved sensitivity

  B. J. Wundt, C. T. Munger, U. D. Jentschura
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  ABSTRACT: An improved measurement of the electron electric dipole moment (EDM) appears feasible using ground-state alkali atoms in an atomic fountain in which a strong electric field, which couples to a conceivable electron dipole moment (EDM), is applied perpendicular to the fountain axis. In a practical fountain, the ratio of the atomic tensor Stark shift to the Zeeman shift is a facto mu~100. We expand the complete time evolution operator in inverse powers of this ratio; complete results are presented for atoms of total spin F=3, 4, and 5. For a specific set of entangled hyperfine sublevels (coherent states), potential systematic errors enter only as even powers of 1/mu, making the expansion rapidly convergent. The remaining EDM mimicking effects are further suppressed in a proposed double-differential setup, where the final state is interrogated in a differential laser configuration, and the direction of the strong electric field also is inverted. Estimates of the signal available at existing accelerator facilities indicate that the proposed apparatus offers the potential for a drastic improvement in EDM limits over existing measurements, and for constraining the parameter space of supersymmetric (SUSY) extensions of the Standard Model.
  11/2012;
• Article: Quantum Electrodynamic Corrections to the g Factor of Helium P States

  M. Puchalski, U. D. Jentschura
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  ABSTRACT: The Lande g factor describes the response of an atomic energy level to an external perturbation by a uniform and constant magnetic field. In the case of many-electron systems, the leading term is given by the interaction mu_B*(L+2S.B), where L and S are the orbital and spin angular momentum operators, respectively, summed over all electrons. For helium, a long-standing experimental-theoretical discrepancy for P states motivates a reevaluation of the higher-order terms which follow from relativistic quantum theory and quantum electrodynamics (QED). The tensor structure of relativistic corrections involves scalar, vector, and symmetric and anti-symmetric tensor components. We perform a tensorial reduction of these operators in a Cartesian basis, using an approach which allows us to separate the internal atomic from the external degrees of freedom (magnetic field) right from the start of the calculation. The evaluation proceeds in a Cartesian basis of helium eigenstates, using a weighted sum over the magnetic projections. For the relativistic corrections, this leads to a verification of previous results obtained using the Wigner-Eckhart theorem. The same method, applied to the radiative correction (Bethe logarithm term) leads to a spin-dependent correction which is different for singlet versus triplet P states. Theoretical predictions are given for singlet and triplet 2P and triplet 3P states and compared to experimental results where available.
  09/2012;
• Article: An Infinitesimally Superluminal Neutrino is Left-Handed, Conserves Lepton Number and Solves the Autobahn Paradox (Illustrative Discussion)

  U. D. Jentschura, B. J. Wundt
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  ABSTRACT: Consider a gedanken experiment in which a massive left-handed neutrino, traveling on an autobahn at a speed of v=0.999c is overtaken by a tuned-up Cagiva V-Raptor 1000 traveling at a speed of 0.999999c. The biker, looking back, would see a right-handed neutrino. Unless one invokes exotic mechanisms like a sterile neutrino, this "autobahn paradox" implies that a massive subluminal (tardyonic) neutrino necessarily has to be a Majorana particle, i.e, equal to its own antiparticle. In turn, this would require us to assign the same lepton number to charged leptons and antileptons, essentially voiding the concept of lepton number. By contrast, an infinitesimally superluminal (tachyonic) neutrino is not equal to its own antiparticle and allows us to assign proper lepton number, just as if the neutrino were a Weyl particle. Furthermore, if Lorentz symmetry holds, then an infinitesimally tachyonic neutrino remains superluminal upon Lorentz transformation, which implies that it is impossible to overtake it in a gedanken experiment. Consistently, right-handed neutrino and left-handed antineutrino states have recently been shown to acquire negative norm under the assumption of an ever-so-slightly tachyonic neutrino, and it would thus not be necessary to invoke a seesaw mechanism. An infinitesimally superluminal neutrino does not necessarily violate causality, as has been discussed in the literature. This paper is devoted to an illustrative discussion of related questions. Under certain conditions, an infinitesimally superluminal neutrino could appear to solve at least as many problems as it raises.
  06/2012;
• Article: From Generalized Dirac Equations to a Candidate for Dark Energy

  U. D. Jentschura, B. J. Wundt
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  ABSTRACT: We consider extensions of the Dirac equation with mass terms m1+i*gamma5*m2 and i*m_1+gamma*m2. The corresponding Hamiltonians are Hermitian and pseudo-Hermitian ("gamma5 Hermitian"), respectively. The fundamental spinor solutions for all generalized Dirac equations are found in the helicity basis and brought into concise analytic form. We postulate that the time-ordered product of field operators should yield the Feynman propagator (i*epsilon prescription), and we also postulate that the tardyonic as well as tachyonic Dirac equations should have a smooth massless limit. These postulates lead to sum rules that connect the form of the fundamental field anticommutators with the tensor sums of the fundamental plane-wave eigenspinors and the projectors over positive-energy and negative-energy states. In the massless case, the sum rules are fulfilled by two egregiously simple, distinguished functional forms. The first sum rule remains valid in the case of a tardyonic theory and leads to the canonical massive Dirac field. The second sum rule is valid for a tachyonic mass term and leads to a natural suppression of the right-handed helicity states for tachyonic particles, and left-handed helicity states for tachyonic spin-1/2 antiparticles. When applied to neutrinos, the theory contains a free tachyonic mass parameter. Tachyons are known to be repulsed by gravity. We discuss a possible role of a tachyonic neutrino as a contribution to the accelerated expansion of the Universe ("dark energy").
  05/2012;
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  Available from: www-ap.gsi.de

  Article: Electron capture into few-electron heavy ions: Independent particle model

  A. Surzhykov, U. D. Jentschura, T. Stöhlker, S. Fritzsche
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  ABSTRACT: We apply the density matrix theory to re-investigate the radiative electron capture into heavy ions with one valence electron. Attention has been paid particularly to the magnetic sublevel population of the residual ions, as described in terms of alignment parameters. Simple method, based on an independent particle model, which takes into account the Pauli principle, is proposed for evaluating the alignment of the excited ionic states. By making use of this method, detailed calculations are performed for electron capture into (initially) hydrogen-like and lithium-like europium, gold and uranium ions, and are compared with the results of the multiconfiguration Dirac-Fock approach.As seen from the calculations and from the comparison with available experimental results, the independent particle model provides a good estimate for the alignment parameters of few-electron heavy ions. Therefore, our simple model may help to understand the basic properties of the X-ray emission from heavy, few-electron ions without the need for invoking sophisticated MCDF calculations.
  The European Physical Journal D 04/2012; 46(1):27-36. · 1.48 Impact Factor
• Article: Large contribution of virtual Delbrück scattering to the emission of photons by relativistic nuclei in nucleus–nucleus and electron–nucleus collisions

  I.F. Ginzburg, U.D. Jentschura, V.G. Serbo
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  ABSTRACT: Delbrück scattering is the elastic scattering of a photon in the Coulomb field of a nucleus via a virtual electron loop. The contribution of this virtual subprocess to the emission of a photon in the collision of ultra-relativistic nuclei, Z1Z2→Z1Z2γ, is considered. We identify the incoming virtual photon as being generated by one of the relativistic nuclei involved in the binary collision and the scattered photon as being emitted in the process. The energy and angular distributions of the photons are calculated. The discussed process has no infrared divergence. The total cross section obtained is 14barn for Au–Au collisions at the RHIC collider and 50barn for Pb–Pb collisions at the LHC collider. These cross sections are considerably larger than those for ordinary tree-level nuclear bremsstrahlung in the considered photon energy range, me⪡Eγ⪡meγ, where γ is the Lorentz factor of the nucleus. Finally, photon emission in electron–nucleus collisions, eZ→eZγ, is discussed in the context of the eRHIC option.
  European Physical Journal C 04/2012; 54(2):267-276. · 3.63 Impact Factor
• Article: Bound-free pair production in ultra-relativistic ion collisions at the LHC collider: Analytic approach to the total and differential cross sections

  A. N. Artemyev, U. D. Jentschura, V. G. Serbo, A. Surzhykov
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  ABSTRACT: A theoretical investigation of the bound-free electron-positron pair production in relativistic heavy ion collisions is presented. Special attention is paid to the positrons emitted under large angles with respect to the beam direction. The measurement of these positrons in coincidence with the down--charged ions is in principle feasible by LHC experiments. In order to provide reliable estimates for such measurements, we employ the equivalent photon approximation together with the Sauter approach and derive simple analytic expressions for the differential pair--production cross section, which compare favorably to the results of available numerical calculations. Based on the analytic expressions, detailed calculations are performed for collisions of bare Pb$^{82+}$ ions, taking typical experimental conditions of the LHC experiments into account. We find that the expected count rate strongly depends on the experimental parameters and may be significantly enhanced by increasing the positron-detector acceptance cone.
  04/2012;
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  Available from: ArXiv

  Article: Localizability of Tachyonic Particles and Neutrinoless Double Beta Decay

  U. D. Jentschura, B. J. Wundt
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  ABSTRACT: The quantum field theory of superluminal (tachyonic) particles is plagued with a number of problems, which include the Lorentz non-invariance of the vacuum state, the ambiguous separation of the field operator into creation and annihilation operators under Lorentz transformations, and the necessity of a complex reinterpretation principle for quantum processes. Another unsolved question concerns the treatment of subluminal components of a tachyonic wave packets in the field-theoretical formalism, and the calculation of the time-ordered propagator. After a brief discussion on related problems, we conclude that rather painful choices have to be made in order to incorporate tachyonic spin-1/2 particles into field theory. We argue that the field theory needs to be formulated such as to allow for localizable tachyonic particles, even if that means that a slight unitarity violation is introduced into the S matrix, and we write down field operators with unrestricted momenta. We find that once these choices have been made, the propagator for the neutrino field can be given in a compact form, and the left-handedness of the neutrino as well as the right-handedness of the antineutrino follow naturally. Consequences for neutrinoless double beta decay and superluminal propagation of neutrinos are briefly discussed.
  01/2012;
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  Available from: ArXiv

  Article: Numerical calculation of Bessel, Hankel and Airy functions

  U. D. Jentschura, E. Lötstedt
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  ABSTRACT: The numerical evaluation of an individual Bessel or Hankel function of large order and large argument is a notoriously problematic issue in physics. Recurrence relations are inefficient when an individual function of high order and argument is to be evaluated. The coefficients in the well-known uniform asymptotic expansions have a complex mathematical structure which involves Airy functions. For Bessel and Hankel functions, we present an adapted algorithm which relies on a combination of three methods: (i) numerical evaluation of Debye polynomials, (ii) calculation of Airy functions with special emphasis on their Stokes lines, and (iii) resummation of the entire uniform asymptotic expansion of the Bessel and Hankel functions by nonlinear sequence transformations. In general, for an evaluation of a special function, we advocate the use of nonlinear sequence transformations in order to bridge the gap between the asymptotic expansion for large argument and the Taylor expansion for small argument ("principle of asymptotic overlap"). This general principle needs to be strongly adapted to the current case, taking into account the complex phase of the argument. Combining the indicated techniques, we observe that it possible to extend the range of applicability of existing algorithms. Numerical examples and reference values are given.
  Computer Physics Communications 01/2012; 183:506. · 3.27 Impact Factor
• Article: Thermal correction to the molar polarizability of a Boltzmann gas

  U. D. Jentschura, M. Puchalski, P. J. Mohr
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  ABSTRACT: Metrology in atomic physics has been crucial for a number of advanced determinations of fundamental constants. In addition to very precise frequency measurements, the molar polarizability of an atomic gas has recently also been measured very accurately. Part of the motivation for the measurements is due to ongoing efforts to redefine the International System of Units (SI), for which an accurate value of the Boltzmann constant is needed. Here we calculate the dominant shift of the molar polarizability in an atomic gas due to thermal effects. It is given by the relativistic correction to the dipole interaction, which emerges when the probing electric field is Lorentz transformed into the rest frame of the atoms that undergo thermal motion. While this effect is small when compared to currently available experimental accuracy, the relativistic correction to the dipole interaction is much larger than the thermal shift of the polarizability induced by blackbody radiation.
  Phys. Rev. A. 12/2011; 84(6).
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  Available from: ArXiv

  Article: Semi-Analytic Approach to Higher-Order Corrections in Simple Muonic Bound Systems: Vacuum Polarization, Self-Energy and Radiative-Recoil

  U. D. Jentschura, B. J. Wundt
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  ABSTRACT: The current discrepancy of theory and experiment observed recently in muonic hydrogen necessitates a reinvestigation of all corrections to contribute to the Lamb shift in muonic hydrogen muH, muonic deuterium muD, the muonic 3He ion, as well as in the muonic 4He ion. Here, we choose a semi-analytic approach and evaluate a number of higher-order corrections to vacuum polarization (VP) semi-analytically, while remaining integrals over the spectral density of VP are performed numerically. We obtain semi-analytic results for the second-order correction, and for the relativistic correction to VP. The self-energy correction to VP is calculated, including the perturbations of the Bethe logarithms by vacuum polarization. Subleading logarithmic terms in the radiative-recoil correction to the 2S-2P Lamb shift of order alpha (Zalpha)^5 mu^3 ln(Zalpha)/(m_mu m_N) are also obtained. All calculations are nonperturbative in the mass ratio of orbiting particle and nucleus.
  12/2011;
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  Available from: ArXiv

  Article: Retardation and Coupling to the Sources in Lorenz and Coulomb Gauge

  B. J. Wundt, U. D. Jentschura
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  ABSTRACT: We investigate the coupling of the electromagnetic sources (charge and current densities) to the scalar and vector potentials in classical electrodynamics, using Green function techniques. As is well known, the scalar potential shows an action-at-a-distance behavior in Coulomb gauge. The conundrum generated by the instantaneous interaction has intrigued physicists for a long time. Starting from the differential equations that couple the sources to the potentials, we here show in a concise derivation, using the retarded Green function, how the instantaneous interaction cancels in the calculation of the electric field. The time derivative of a specific additional term in the vector potential, present only in Coulomb gauge, yields a supplementary contribution to the electric field which cancels the gradient of the instantaneous Coulomb gauge scalar potential, as required by gauge invariance. This completely eliminates the contribution of the instantaneous interaction from the electric field. It turns out that a careful formulation of the retarded Green function, inspired by field theory, is required in order to correctly treat boundary terms in partial integrations. Finally, compact integral representations are derived for the Lienard-Wiechert potentials (scalar and vector) in Coulomb gauge which manifestly contain two compensating action-at-a-distance terms.
  10/2011;
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  Available from: ArXiv

  Article: Pseudo-Hermitian Quantum Dynamics of Tachyonic Spin-1/2 Particles

  U. D. Jentschura, B. J. Wundt
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  ABSTRACT: We investigate the spinor solutions, the spectrum and the symmetry properties of a matrix-valued wave equation whose plane-wave solutions satisfy the superluminal (tachyonic) dispersion relation E^2 = p^2 - m^2, where E is the energy, p is the spatial momentum, and m is the mass of the particle. The equation reads (i gamma^mu partial_mu - gamma^5 m) psi = 0, where gamma^5 is the fifth current. The tachyonic equation is shown to be CP invariant, and T invariant. The tachyonic Hamiltonian H_5 = alpha.p + beta gamma^5 m breaks parity and is non-Hermitian but fulfills the pseudo-Hermitian property H_5(r) = P H^+_5(-r) P^{-1} = PP H^+_5(-r) PP^{-1} where P is the parity matrix and PP is the full parity transformation. The energy eigenvalues and eigenvectors describe a continuous spectrum of plane-wave solutions (which correspond to real eigenvalues for |p|>=m and evanescent waves, which constitute resonances and antiresonances with complex-conjugate pairs of resonance eigenvalues (for |p|<=m) . In view of additional algebraic properties of the Hamiltonian which supplement the pseudo-Hermiticity, the existence of a resonance energy eigenvalues E implies that E^*, -E, and -E^* also constitute resonance energies of H_5.
  10/2011;
• Article: Blackbody-radiation correction to the polarizability of helium

  M. Puchalski, U. D. Jentschura, P. J. Mohr
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  ABSTRACT: The correction to the polarizability of helium due to blackbody radiation is calculated near room temperature. A precise theoretical determination of the blackbody radiation correction to the polarizability of helium is essential for dielectric gas thermometry and for the determination of the Boltzmann constant. We find that the correction, for not too high temperature, is roughly proportional to a modified hyperpolarizability (two-color hyperpolarizability), which is different from the ordinary hyperpolarizability of helium. Our explicit calculations provide a definite numerical result for the effect and indicate that the effect of blackbody radiation can be excluded as a limiting factor for dielectric gas thermometry using helium or argon.
  Phys. Rev. A. 04/2011; 83(4).
• Article: Hydrogen-deuterium isotope shift: From the 1S-2S-transition frequency to the proton-deuteron charge-radius difference

  U.D. Jentschura, A. Matveev, C.G. Parthey, J. Alnis, R. Pohl, Th. Udem, N. Kolachevsky, T.W. Hänsch
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  ABSTRACT: We analyze and review the theory of the hydrogen-deuterium isotope shift for the 1S-2S transition, which is one of the most accurately measured isotope shifts in any atomic system, in view of a recently improved experiment. A tabulation of all physical effects that contribute to the isotope shift is given. These include the Dirac binding energy, quantum electrodynamic effects, including recoil corrections, and the nuclear-size effect, including the pertaining relativistic and radiative corrections. From a comparison of the theoretical result Δfth=670 999 566.90(66)(60) kHz (exclusive of the nonrelativistic nuclear-finite-size correction) and the experimental result Δfexpt=670 994 334 605(15) Hz, we infer the deuteron-proton charge-radius difference 〈r2〉d-〈r2〉p=3.820 07(65) fm2 and the deuteron structure radius rstr=1.975 07(78) fm.
  Phys. Rev. A. 04/2011; 83(4).
• Source

  Available from: ArXiv

  Article: Black-Body Radiation Correction to the Polarizability of Helium

  M. Puchalski, U. D. Jentschura, P. J. Mohr
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  ABSTRACT: The correction to the polarizability of helium due to black-body radiation is calculated near room temperature. A precise theoretical determination of the black-body radiation correction to the polarizability of helium is essential for dielectric gas thermometry and for the determination of the Boltzmann constant. We find that the correction, for not too high temperature, is roughly proportional to a modified hyperpolarizability (two-color hyperpolarizability), which is different from the ordinary hyperpolarizability of helium. Our explicit calculations provide a definite numerical result for the effect and indicate that the effect of black-body radiation can be excluded as a limiting factor for dielectric gas thermometry using helium or argon.
  03/2011;
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  Available from: ArXiv

  Article: Self-Energy Correction to the Hyperfine Splitting for Excited States

  B. J. Wundt, U. D. Jentschura
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  ABSTRACT: The self-energy corrections to the hyperfine splitting is evaluated for higher excited states in hydrogenlike ions, using an expansion in the binding parameter Zalpha, where Z is the nuclear charge number, and alpha is the fine-structure constant. We present analytic results for D, F and G states, and for a number of highly excited Rydberg states with principal quantum numbers in the range 13 <= n <= 16, and orbital angular momenta l = n-2 and l = n-1. A closed-form, analytic expression is derived for the contribution of high-energy photons, valid for any state with l <= 2$ and arbitrary n, l and total angular momentum j. The low-energy contributions are written in the form of generalized Bethe logarithms and evaluated for selected states.
  03/2011;
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  Available from: V. G. Serbo

  Article: Compton Upconversion of Twisted Photons: Backscattering of Particles with Non-Planar Wave Functions

  U. D. Jentschura, V. G. Serbo
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  ABSTRACT: Twisted photons are not plane waves, but superpositions of plane waves with a defined projection hbar m of the orbital angular momentum onto the propagation axis (m is integer and may attain values m >> 1). Here, we describe in detail the possibility to produce high-energy twisted photons by backward Compton scattering of twisted laser photons on ultra-relativistic electrons with a Lorentz-factor gamma=E/(m_e c^2) >> 1. When a twisted laser photon with the energy hbar omega ~ 1 eV performs a collision with an electron and scatters backward, the final twisted photon conserves the angular momentum m, but its energy hbar omega' is increased considerably: omega'/omega=4 gamma^2/(1+x), where x=4E hbar omega/(m_e c^2)^2. The S matrix formalism for the description of scattering processes is particularly simple for plane waves with definite 4-momenta. However, in the considered case, this formalism must be enhanced because the quantum state of twisted particles cannot be reduced to plane waves. This implies that the usual notion of a cross section is inapplicable, and we introduce and calculate an averaged cross section for a quantitative description of the process. The energetic upconversion of twisted photons may be of interest for experiments with the excitation and disintegration of atoms and nuclei, and for studying the photo-effect and pair production off nuclei in previously unexplored regimes.
  01/2011;
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  Available from: V. G. Serbo

  Article: Generation of high-energy photons with large orbital angular momentum by compton backscattering.

  U D Jentschura, V G Serbo
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  ABSTRACT: Usually, photons are described by plane waves with a definite 4-momentum. In addition to plane-wave photons, "twisted photons" have recently entered the field of modern laser optics; these are coherent superpositions of plane waves with a defined projection hm of the orbital angular momentum onto the propagation axis, where m is an integer. In this Letter, we show that it is possible to produce high-energy twisted photons by Compton backscattering of twisted laser photons off ultrarelativistic electrons. Such photons may be of interest for experiments related to the excitation and disintegration of atoms and nuclei, and for studying the photoeffect and pair production off nuclei in previously unexplored experimental regimes.
  Physical Review Letters 01/2011; 106(1):013001. · 7.37 Impact Factor
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  Available from: ArXiv

  Article: Imaginary Cubic Perturbation: Numerical and Analytic Study

  J. Zinn-Justin, U. D. Jentschura
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  ABSTRACT: The analytic properties of the ground state resonance energy E(g) of the cubic potential are investigated as a function of the complex coupling parameter g. We explicitly show that it is possible to analytically continue E(g) by means of a resummed strong coupling expansion, to the second sheet of the Riemann surface, and we observe a merging of resonance and antiresonance eigenvalues at a critical point along the line arg(g) = 5 pi/4. In addition, we investigate the convergence of the resummed weak-coupling expansion in the strong coupling regime, by means of various modifications of order-dependent mappings (ODM), that take special properties of the cubic potential into account. The various ODM are adapted to different regimes of the coupling constant. We also determine a large number of terms of the strong coupling expansion by resumming the weak-coupling expansion using the ODM, demonstrating the interpolation between the two regimes made possible by this summation method. Comment: 18 pages; 4 figures; typographical errors corrected
  06/2010;