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  • 1. Belov, Sergey
    et al.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Marletta, Marco
    Msezane, Alfred
    Naboko, Serguei
    On Regge pole trajectories for a rational function approximation of Thomas-Fermi potentials2010In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, Vol. 43, no 36, p. 365301-Article in journal (Refereed)
    Abstract [en]

    The positions of two Regge poles caused by the rational function approximate Thomas-Fermi potential (a screened attractive Coulomb potential) are studied in detail as a function of the scattering energy. The leading pole is traced from the right-hand (physical) complex angular momentum plane K(l) > - 1/2 to the left-hand (unphysical) complex angular momentum plane K(l) < - 1/2 as the scattering energy is increased indefinitely. The second Regge pole is located in the unphysical half-plane at all energies. In this study an exact numerical and an approximate semiclassical WKB methods are discussed in some detail, where the boundary conditions of the regular (physical) Schrodinger solution become important. Transitions in behavior of Regge poles are explained in terms of Stokes lines and turning points evolution. The major change in the direction of Regge trajectories is demonstrated as a transition in the topology of Stokes lines. This phenomenon is caused by switching from one pair of turning points to another pair as the third turning point approaches the Stokes line connecting to the original turning points.

  • 2. Hamzavi, M.
    et al.
    Ikhdair, S. M.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Equivalence of the empirical shifted Deng-Fan oscillator potential for diatomic molecules2013In: Journal of Mathematical Chemistry, ISSN 0259-9791, E-ISSN 1572-8897, Vol. 51, no 1, p. 227-238Article in journal (Refereed)
    Abstract [en]

    We obtain the bound-state solutions of the radial Schrodinger equation with the shifted Deng-Fan oscillator potential in the frame of the Nikiforov-Uvarov method by employing Pekeris-type approximation to deal with the centrifugal term. The analytical expressions for the energy eigenvalues and the corresponding normalized wave functions are obtained in closed form for arbitrary l-state. The ro-vibrational energy levels for a few diatomic molecules are also calculated. They are found to be in good agreement with those ones previously obtained by the Morse potential.

  • 3. Hamzavi, M.
    et al.
    Ikhdair, S. M.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Pseudospin symmetry in the relativistic Killingbeck potential: Quasi-exact solution2012In: Zeitschrift fur Naturforschung A-A Journal of Physical Sciences, ISSN 0932-0784, E-ISSN 1865-7109, Vol. 67, no 10-11, p. 567-571Article in journal (Refereed)
    Abstract [en]

    The Killingbeck potential consisting of the harmonic oscillator plus Cornell potential, ar2 +br-c/r, is of great interest in particle physics. The solution of the Dirac equation with the Killingbeck potential is studied in the presence of the pseudospin (p-spin) symmetry within the context of quasiexact solutions. Two special cases of the harmonic oscillator and Coulomb potential are also discussed.

  • 4. Hamzavi, M.
    et al.
    Ikhdair, S. M.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Spin and pseudospin symmetries in relativistic trigonometric Pöschl-teller potential with centrifugal barrier2012In: International Journal of Modern Physics E, ISSN 0218-3013, Vol. 21, no 12, p. 1250097-Article in journal (Refereed)
    Abstract [en]

    Approximate analytical solutions of the Dirac equation with the trigonometric Pöschl-Teller (tPT) potential are obtained for arbitrary spin-orbit quantum number κ using an approximation scheme to deal with the spin-orbit coupling terms κ(κ±1)r-2. In the presence of exact spin and pseudo-spin (p-spin) symmetric limitation, the bound state energy eigenvalues and the corresponding two-component wave functions of the Dirac particle moving in the field of attractive and repulsive tPT potential are obtained using the parametric generalization of the Nikiforov-Uvarov (NU) method. The case of nonrelativistic limit is studied too.

  • 5. Hamzavi, M.
    et al.
    Ikhdair, S. M.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Spinless particles in the field of unequal scalar-vector Yukawa potentials2013In: Chinese Physics B, ISSN 1009-1963, E-ISSN 1741-4199, Vol. 22, no 4, p. 040301-Article in journal (Refereed)
    Abstract [en]

    We present analytical bound state solutions of the spin-zero Klein-Gordon (KG) particles in the field of unequal mixture of scalar and vector Yukawa potentials within the framework of the approximation scheme to the centrifugal potential term for any arbitrary l-state. The approximate energy eigenvalues and unnormalized wave functions are obtained in closed forms using a simple shortcut of the Nikiforov-Uvarov (NU) method. Further, we solve the KG-Yukawa problem for its exact numerical energy eigenvalues via the amplitude phase (AP) method to test the accuracy of the present solutions found by using the NU method. Our numerical tests using energy calculations demonstrate the existence of inter-dimensional degeneracy amongst the energy states of the KG-Yukawa problem. The dependence of the energy on the dimension D is numerically discussed for spatial dimensions D = 2-6.

  • 6. Hamzavi, M.
    et al.
    Movahedi, M.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Rajabi, A. A.
    Approximate analytical solution of the yukawa potential with arbitrary angular momenta2012In: Chinese Physics Letters, ISSN 0256-307X, E-ISSN 1741-3540, Vol. 29, no 8, p. 080302-Article in journal (Refereed)
    Abstract [en]

    The Yukawa potential is often used to compute bound-state normalizations and energy levels of neutral atoms. By using the generalized parametric Nikiforov-Uvarov method, we obtain approximate analytical solutions of the radial Schrödinger equation for the Yukawa potential. The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented and show that these results are in good agreement with those obtained previously by other methods. Also, we find the energy levels of the familiar pure Coulomb potential energy levels when the screening parameter of the Yukawa potential goes to zero.

  • 7. Hamzavi, M.
    et al.
    Rajabi, A. A.
    Thylwe, Karl -Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    The rotation-vibration spectrum of diatomic molecules with the tietz-hua rotating oscillator2012In: International Journal of Quantum Chemistry, ISSN 0020-7608, E-ISSN 1097-461X, Vol. 112, no 15, p. 2701-2705Article in journal (Refereed)
    Abstract [en]

    The Tietz-Hua (TH) potential is one of the very best analytical model potentials for the vibrational energy of diatomic molecules. By using the Nikiforov-Uvarov method, we have obtained the exact analytical s-wave solutions of the radial Schrodinger equation for the TH potential. The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms. Some numerical results for diatomic molecules are also presented.

  • 8. Hamzavi, M.
    et al.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Rajabi, A. A.
    Approximate Bound States Solution of the Hellmann Potential2013In: Communications in Theoretical Physics, ISSN 0253-6102, E-ISSN 1572-9494, Vol. 60, no 1, p. 1-8Article in journal (Refereed)
    Abstract [en]

    The Hellmann potential, which is a superposition of an attractive Coulomb potential -a/r and a Yukawa potential b e(-delta r)/r, is often used to compute bound-state normalizations and energy levels of neutral atoms. By using the generalized parametric Nikiforov-Uvarov (NU) method, we have obtained the approximate analytical solutions of the radial Schrodinger equation (SE) for the Hellmann potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented, which show good agreement with a numerical amplitude phase method and also those previously obtained by other methods. As a particular case, we find the energy levels of the pure Coulomb potential.

  • 9. Hassanabadi, S.
    et al.
    Ghominejad, M.
    Thylwe, Karl Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Two-body scattering in (1 + 1) dimensions by a semi-relativistic formalism and a Hulthén interaction potential2015In: Communications in Theoretical Physics, ISSN 0253-6102, E-ISSN 1572-9494, Vol. 63, no 4, p. 423-426, article id 423Article in journal (Refereed)
    Abstract [en]

    Scattering solutions of two-body Spinless Salpeter Equation (SSE) are investigated in the center of mass frame with a repulsive, symmetric Hulthén potential in one spatial dimension. Transmission and reflection coefficients are calculated and discussed.

  • 10. Linnaeus, I. Jakusjina
    et al.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Doubly uniform semiclassical quantization formula for resonances2009In: European Physical Journal D: Atomic, Molecular and Optical Physics, ISSN 1434-6060, E-ISSN 1434-6079, Vol. 53, no 3, p. 283-288Article in journal (Refereed)
    Abstract [en]

    The radial Schrodinger equation with an effective potential containing a single well and a single barrier is treated with an improved uniform semiclassical method. The improved quantization formula for complex energies (or resonances) contains a correction term that originates from a uniform treatment of the classically forbidden region near the origin in addition to the more familiar uniform treatment of the barrier region. In the present case the origin has a second-order pole, due to the centrifugal barrier potential term, and/or a Coulomb-type singularity, and these terms dominate the region inside the innermost classical turning point. Numerical results for first-order and third-order approximate complex resonance energies are compared with those of a standard (first- and third-order) barrier-uniform semiclassical method and also with those of 'exact' numerical computations. The improved quantization formula provides results in significantly better agreement with the exact results as the angular momentum quantum number l approaches zero.

  • 11. Oluwadare, O. J.
    et al.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Oyewumi, K. J.
    Non-Relativistic Phase Shifts for Scattering on Generalized Radial Yukawa Potentials2016In: Communications in Theoretical Physics, ISSN 0253-6102, E-ISSN 1572-9494, Vol. 65, no 4, p. 434-440Article in journal (Refereed)
    Abstract [en]

    Non-relativistic phase shifts for a generalized Yukawa potential V(r) = -Vo(e(-alpha r)/r) Vi(e(-2 alpha r)/r(2)) are studied by the amplitude-phase method and by a frequently used analytic method based on a Pekeris-type approximation of power-law potential terms. Small variations of V-1 seem to have marginal effects on the effective potential and on exact phase shifts. However, as pointed out in this study, a Pekeris-type approximation in scattering applications often implies serious distortions of both effective potentials and phase shifts. The Pekeris-type based analytic approximation in this study seems to give low-quality scattering results for this model potential at low energies.

  • 12.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    A new amplitude-phase method for analyzing scattering solutions of the radial Dirac equation2008Article in journal (Refereed)
    Abstract [en]

    A novel amplitude-phase method for analyzing radial Dirac solutions is presented. This approach addresses the original coupled radial Dirac equations without first transforming them to decoupled second-order differential equations. As a reference test, the method is applied to the scattering problem of a Dirac particle (electron) in a long-range Coulomb 4-vector potential with zero space components. Numerical results for the partial-wave S-matrix are compared with those from an exact analytic S-matrix formula.

  • 13.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Amplitude-phase formula for the S-matrix derived from invariants of the reduced first-order radial Dirac equation2008In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 78, no 6Article in journal (Refereed)
    Abstract [en]

    A formula for calculating the Dirac S-matrix for central Lorentz scalar and vector potentials is derived by use of a new amplitude-phase method. The derivation also makes use of certain invariants of the reduced 2-spinor radial Dirac equations.

  • 14.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Amplitude-phase methods for analyzing the radial Dirac equation: calculation of scattering phase shifts2008In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 77, no 6Article in journal (Refereed)
    Abstract [en]

    Approaches inspired by a recent amplitude-phase method for analyzing the radial Dirac equation are presented to calculate phase shifts. Regarding the spin- and pseudo-spin symmetries of relativistic spectra, the coupled first-order and the decoupled second-order differential forms of the radial Dirac equation are investigated by using a novel and the 'classical' amplitude-phase methods, respectively. The quasi non-relativistic limit c --> +infinity of the amplitude- phase formulae is discussed for both positive and negative energies. In the positive (E > mc(2)) low-energy region, the relativistic effects of scattering phase shifts are discussed based on two scattering potential models. Results are compared with those of non-relativistic calculations. In particular, the numerical results obtained from a rational approximation of the Thomas-Fermi potential are discussed in some detail.

  • 15.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Applications of the amplitude-phase method to symmetric double-well potentials2015In: Journal of Mathematical Chemistry, ISSN 0259-9791, E-ISSN 1572-8897, Vol. 53, no 7, p. 1608-1616Article in journal (Refereed)
    Abstract [en]

    An amplitude-phase method is used to derive general quantization conditions for energy levels in smooth double-well potentials. The resulting quantization condition is applied to symmetric double-well potentials, where the two types of symmetry levels are shown to be determined by separate quantization conditions.

  • 16.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Bound Dirac states, different Lorentz-type couplings of central potentials and the non-relativistic limit2009In: European Physical Journal D: Atomic, Molecular and Optical Physics, ISSN 1434-6060, E-ISSN 1434-6079, Vol. 54, no 3, p. 591-596Article in journal (Refereed)
    Abstract [en]

    The analysis of bound radial Dirac states is shown to simplify for problems with an equal mixture of Lorentz vector and Lorentz scalar potentials, thus satisfying a so-called spin symmetry of the energy spectrum. Typical relativistic restrictions on potentials that are singular at the origin then disappear. Such potentials may even be strongly singular at the origin like the well known Lennard-Jones potentials modelling many atom-atom interactions, and they reduce to non-relativistic potentials of identical form. Bound state energies for potentials with equal vector- and scalar couplings are compared with those of a pure vector coupling of the same radial (attractive screened and unscreened Coulomb) shapes, and with non-relativistic results.

  • 17.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Dirac resonance energies for central potentials with different Lorentz-type potential couplings2010In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 81, no 3Article in journal (Refereed)
    Abstract [en]

    The amplitude-phase method is applied to relativistic Dirac-particle resonances related to electron-atom collisions. Complex-energy resonance poles of the S matrix in central potentials of differing Lorentz couplings are studied near the non-relativistic limit. It is confirmed that an equal mixture of a Lorentz vector-type potential (with a single time component) and a Lorentz scalar-type potential of the same radial shape makes the interaction essentially spin independent, as if spin does not couple to orbital angular momentum. Hence, resonance poles of the S matrix depend simply on the orbital angular momentum and the radial quantum number in a similar way as in the Schrodinger limit and in the Klein-Gordon equation. In a Lorentz-vector potential model, there is a splitting of pole positions, but the splitting may be surprisingly small, as demonstrated for one of the potentials considered. The numerical method used automatically assigns a vibrational (radial) quantum number to the resonance state, which is usually a characteristic feature of semiclassical methods.

  • 18.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Discontinuous radial potentials, bound states and Dirac equations2019In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 94, no 6, article id 065201Article in journal (Refereed)
    Abstract [en]

    Discontinuous, radial 'square-well' potentials of scalar and (time-component) vector types require special quantization conditions in Dirac equations transformed to second-order differential equations. Quantization conditions for positive energies are derived from first-order and second-order differential equations using amplitude-phase methods. Analytic condition for no orbital angular momentum of the large spinor component is obtained. Numerical applications relevant to independent-nucleon shell models illustrate level shifts due to shape (square-well/Woods-Saxon) differences.

  • 19.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Generalization of the amplitude-phase S-matrix formula for coupled scattering states2005In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 38, no 46, p. 10007-10013Article in journal (Refereed)
    Abstract [en]

    The amplitude-phase method is generalized to coupled Schrodinger scattering states with a common angular momentum quantum number. A pair of expontentail-type amplitude-phase solutions u(j)((+/-))(r)exp[+/- i phi(j)(r)] for each channel is obtained, containing a common complex scalar phase function phi(j)(r) and two (column) vector amplitudes u(j)((+/-))(r). The amplitude functions satisfy certain nonlinear generalized Milne equations and the scalar product of the two amplitudes determines the derivative of the common phase function. Fundamental amplitude-phase matrix solutions that are proportional to Jost-like Schrodinger matrix solutions are constructed. It is shown how a generalized amplitude-phase S-matrix formula can be derived from Wronskian relations involving the two amplitude-phase matrix solutions and a regular matrix solution.

  • 20.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Heavy-particle resonance phase shifts: an improved amplitude-phase formula2018In: Journal of Mathematical Chemistry, ISSN 0259-9791, E-ISSN 1572-8897, Vol. 56, no 9, p. 2674-2690Article in journal (Refereed)
    Abstract [en]

    An improved amplitude-phase formula suitable for non-relativistic heavy-particle resonance phase shifts is derived. The present formula makes use of two amplitude functions instead of one for a central potential; an inner amplitude which is non-oscillatory in the well region of the effective potential, and an outer amplitude function which is non-oscillatory far away from the origin of the effective potential. The low-energy limit is discussed in connection with Levinson's theorem. Numerical computations at resonance energies and graphical illustrations are presented. Numerical comparisons with an existing single-amplitude formula are made.

  • 21.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Improved amplitude-phase method for complex angular momentum analysis2005In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 38, no 33, p. 7363-7375Article in journal (Refereed)
    Abstract [en]

    An amplitude-phase formula for the S matrix using two Milne solutions and the regular Schrodinger solution is derived. The formula is particularly useful in the analysis of Regge poles located far out in the complex e-plane, particularly for discontinuous scattering potentials. Numerical applications for an attractive square-well potential and an inverse-power potential similar to r(-4) are presented.

  • 22.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Multi-state complex angular momentum residues2006In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 39, no 38, p. 11895-11899Article in journal (Refereed)
    Abstract [en]

    A relation between a multi-state complex angular momentum (CAM) pole residue and the corresponding CAM-state wavefunction is derived for a real symmetric potential matrix. The result generalizes a residue formula available for single-channel atomical collision systems and it is based on a diagonalization of the S matrix together with the use of exact Wronskian relations.

  • 23.
    Thylwe, Karl-Erik
    KTH, Superseded Departments, Mechanics.
    Note on invariants for uncoupled Ermakov systems2002In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 35, no 19, p. 4359-4362Article in journal (Refereed)
    Abstract [en]

    Several invariants for an Ermakov system consisting of a parametric oscillator and a Milne oscillator in one dimension are derived. This system appears in amplitude-phase analysis of parametric oscillator solutions. First- and second-order invariants for such a system are derived using the Wronskian relations of a fundamental pair of parametric oscillator solutions. In this way Wronskian invariants of the parametric oscillator system alone imply Ermakov-Lewis type invariants for the combined Ermakov system, as well as invariants for the Milne oscillator alone.

  • 24.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    On relativistic shifts of negative-ion resonances2012In: European Physical Journal D: Atomic, Molecular and Optical Physics, ISSN 1434-6060, E-ISSN 1434-6079, Vol. 66, no 1Article in journal (Refereed)
    Abstract [en]

    Results from a Dirac approach to electron-(neutral) atom resonance calculations are compared with those from nonrelativistic ones. A recently developed amplitude-phase method for the Dirac equations that is valid also in the non-relativistic limit is applied. The main conclusion is that significant energy differences are expected for long-lived resonances.

  • 25.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Relativistic energy shifts of negative-ion bound states: the rational function Thomas-Fermi potential model2012In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 85, no 6, p. 065009-Article in journal (Refereed)
    Abstract [en]

    The rational function Thomas-Fermi (RTF) potential recently used for describing electron-atom scattering interactions is investigated as to its bound (negative-ion) states. Although the (static) RTF potential may account for some relativistic and many-body corrections, this study focuses on (relativistic) dynamical aspects of the 'extra' electron in the negative-ion bound states. Some exotic states near threshold are shown to exist in the Dirac equations but not in the Schrodinger equation that neglects the spin of the 'extra' electron. Results are presented for the two large atomic charge numbers Z = 54 and Z = 64.

  • 26.
    Thylwe, Karl-Erik
    KTH, Superseded Departments, Mechanics.
    Scattering S-matrix derived from invariants of the Ermakov-Lewis type2004In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 37, no 44, p. L589-L591Article in journal (Refereed)
    Abstract [en]

    An amplitude-phase formula for the S-matrix due to a central potential is derived. The derivation makes use of invariants of the Ermakov-Lewis type.

  • 27.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Semi-Relativistic Two-Body States of Spinless Particles with a Scalar-Type Interaction Potential2018In: Communications in Theoretical Physics, ISSN 0253-6102, E-ISSN 1572-9494, Vol. 69, no 2, p. 127-130Article in journal (Refereed)
    Abstract [en]

    A semi-relativistic quantum approximation for mutual scalar interaction potentials is outlined and discussed. Equations are consistent with two-body Dirac equations for bound states of zero total angular momentum. Two-body effects near the non-relativistic limit for a linear scalar potential is studied in some detail.

  • 28.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    The barrier transmission problem treated by the amplitude-phase method and expressed in terms of an invariant of the Ermakov-Lewis type2005In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 38, no 1, p. 235-243Article in journal (Refereed)
    Abstract [en]

    Transmission and reflection of a quantal particle by a single-hump potential barrier are analysed by means of an amplitude-phase decomposition of the wavefunction on both sides of the barrier. The amplitude-phase analysis of the wavefunction provides a particular invariant of the Ermakov-Lewis type, which originates in the matching process. The transmission and reflection coefficients turn out to be simple functions of this invariant. Numerical calculations of the invariant for an Eckart-Epstein potential barrier provide very accurate results.

  • 29.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Two-Body Local-Momentum Approximation of Spinless Particles Scattered by a (1+1)-D Woods-Saxon Barrier Potential2017In: Communications in Theoretical Physics, ISSN 0253-6102, E-ISSN 1572-9494, Vol. 67, no 6, p. 619-625Article in journal (Refereed)
    Abstract [en]

    A local momentum (LM) approximation applicable to semi-relativistic two-body repulsive interactions is presented. It assumes negligible variations in the (vector-type) potential. A Woods-Saxon barrier with a rectangular-like shape is studied in some detail. The LM-approximation gives exact results within the semi-relativistic framework for rectangular barrier interactions in (1+1) dimensions. Further approximations of the local momentum approach leads to the two-body approximation of Ikhdair & Sever, known since the early 90's as the spinless Salpeter equation approximating the Bethe-Salpeter equation. LM- and GS-results indicate significant two-body effects. Results obtained from the (single-mass) Dirac equation are similar for certain two-body mass combinations.

  • 30.
    Thylwe, Karl-Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Hamzavi, Majid
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Light-heavy quark-type linear potential models with spin- and pseudospin-symmetric states2013In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, no 8, p. 085305-Article in journal (Refereed)
    Abstract [en]

    Possible spin- and pseudospin-symmetric states with positive energies of the Dirac equation with linear scalar and vector potentials are investigated. Two exact relativistic spin symmetries of linear quark-type potential models are shown to exist for positive energies. It is known that positive-energy states which still exist in the non-relativistic limit are always of the spin-symmetric type, like those described in the Schrodinger framework. However, if significant relativistic corrections to the Schrodinger theory are considered and also different possible signs of vector and scalar potentials, there exist two exact spin symmetries: a spin- symmetric energy spectrum that tends to the previously known spectrum obtained by the Schrodinger theory in the non-relativistic limit, and a pseudospin-symmetric energy spectrum that does not. The exact symmetries are perturbed by modifying the strengths of the relativistic linear vector and scalar potentials and introducing a tensor coupling. These perturbations may cancel each other.

  • 31.
    Thylwe, Karl-Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Hamzavi, Majid
    KTH, School of Engineering Sciences (SCI), Mechanics.
    On pseudospin symmetry of Dirac states2013In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 87, no 2, p. 025004-Article in journal (Refereed)
    Abstract [en]

    Some aspects of pseudospin symmetry for bound Dirac particle states of finite potentials vanishing as r -> +infinity are discussed. Energy states showing pseudospin symmetry are of interest in nuclear spectroscopy for states explained by a single nucleon interacting with a heavy nucleus. Such states may be approximated by Dirac theory as Dirac particle states with positive relativistic energies and/or Dirac anti-particles with negative relativistic energies. It is confirmed, in this study of an exponential-shaped potential model of vector, scalar and tensor interactions, that positive-energy pseudospin symmetric Dirac states exist in relativistic quantum mechanics, but not in the Schrodinger theory, and that tensor coupling may play an important role in the pseudospin symmetry.

  • 32.
    Thylwe, Karl-Erik
    et al.
    KTH, Superseded Departments, Mechanics.
    Korsch, H. J.
    Harmonic oscillator subject to parametric pulses: an amplitude (Milne) oscillator approach2001In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 34, no 16, p. 3497-3510Article in journal (Refereed)
    Abstract [en]

    harmonic oscillator subject to a parametric pulse is examined. The aim of the paper is to present a new theory for analysing transitions caused by parametric pulses. The new theoretical notions which are introduced relate the pulse parameters in a direct way with transition matrix elements. The harmonic-oscillator transitions are expressed in terms of the asymptotic properties of a companion oscillator, the Milne (amplitude) oscillator. A traditional phase-amplitude decomposition of the harmonic-oscillator solutions results in the so-called Milne's equation fur the amplitude, and the phase is determined by an exact relation to the amplitude. This approach is extended in the present analysis with new relevant concepts and parameters for pulse dynamics of classical and quantal systems. The amplitude oscillator has a particularly nice numerical behaviour. In the case of strong pulses it does not possess any of the fast oscillations induced by the pulse on the original harmonic oscillator. Furthermore, the new dynamical parameters introduced in this approach are closely related to the relevant characteristics of the pulse. The relevance to quantum mechanical problems such as reflection and transmission from a localized well and the mechanical problem of controlling vibrations is illustrated.

  • 33.
    Thylwe, Karl-Erik
    et al.
    KTH, Superseded Departments, Mechanics.
    Korsch, H. J.
    On pulse-induced transition amplitudes in a two-state quantum system without level crossings2002In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 35, no 34, p. 7507-7523Article in journal (Refereed)
    Abstract [en]

    An exact dynamical parametrization of pulse-induced transition amplitudes in a Rosen-Zener- or Nikitin-type two-level system is constructed. The three dynamical parameters are closely related to the shape of the interaction pulse and are convenient to calculate. The Milne equation with a complex coefficient function is essential for these calculations. Its complex solution is non-oscillatory and makes the computation of transition probabilities efficient. The paper reviews the quantum calculations for the rectangular pulse, which has well-defined duration and strength. By comparing transition matrix elements from a rectangular pulse with those of a general symmetric pulse, we introduce effective strength and effective duration for a general pulse. It is also possible to define an equivalent rectangular pulse, with respect to the transition probabilities, for each general pulse.

  • 34.
    Thylwe, Karl-Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Linnaeus, Staffan
    Semiclassical aspects and supersymmetry of bound Dirac states for central pseudo-scalar potentials2011In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 84, no 2, p. 025006-Article in journal (Refereed)
    Abstract [en]

    Relativistic bound states for a linear, radial pseudo-scalar potential model are discussed. The two radial Dirac components are known to have a close connection to partner states in super-symmetric quantum mechanical theory. The pseudo-scalar potential plays the role of the 'super potential'. Hence, the Dirac components satisfy decoupled Schrodinger-type equations with isospectral, so-called, 'partner potentials' except possibly for a single state; the ground state corresponding to one of the partner potentials. The energy spectrum of a confining linear radial potential is discussed in some detail. Accurate amplitude-phase computations and a novel semiclassical (phase-integral) approach are presented.

  • 35.
    Thylwe, Karl-Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    McCabe, P.
    Amplitude-phase calculations of Regge poles obtained from coupled radial Dirac equations2011In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 44, no 27, p. 275305-Article in journal (Refereed)
    Abstract [en]

    A recently developed amplitude-phase method for spinor-wave solutions is applied to the calculations of Regge pole positions and residues of Dirac particles. At a given energy the Dirac spin causes two sets of Regge poles that tend to coalesce in the non-relativistic limit. For the particular case of equal Lorentz-type vector and scalar potentials there is only one pole string, located very close to the non-relativistic pole string.

  • 36.
    Thylwe, Karl-Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    McCabe, Patrick
    A theoretical study of spin-angular behaviors of potential scattering resonances2014In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 89, no 8, p. 085401-Article in journal (Refereed)
    Abstract [en]

    Resonance scattering of a Dirac particle (electron) in a screened Coulomb potential (of Lorentz vector type) is investigated. The so-called direct and spin-flip differential cross-sections (DCSs) for Dirac particles are analyzed by a partial-wave analysis, as well as the spin-polarization parameters, here denoted S, T and U. This model study of angular as well as energy behaviors shows that DCSs, at forward and backward angles, together with the polarization parameter. seem to be best indicators of energy and orbital angular momentum of sharp, isolated, resonances.

  • 37.
    Thylwe, Karl-Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    McCabe, Patrick
    Bohr-Sommerfeld quantization condition for Dirac states derived from an Ermakov-type invariant2013In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 54, no 5, p. 052301-Article in journal (Refereed)
    Abstract [en]

    It is shown that solutions of the second-order decoupled radial Dirac equations satisfy Ermakov-type invariants. These invariants lead to amplitude-phase-type representations of the radial spinor solutions, with exact relations between their amplitudes and phases. Implications leading to a Bohr-Sommerfeld quantization condition for bound states, and a few particular atomic/ionic and nuclear/hadronic bound-state situations are discussed.

  • 38.
    Thylwe, Karl-Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    McCabe, Patrick
    Coupled radial Schrodinger equations written as Dirac-type equations: application to an amplitude-phase approach2012In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, no 13, p. 135302-Article in journal (Refereed)
    Abstract [en]

    The classical amplitude-phase method due to Milne, Wilson, Young and Wheeler in the 1930s is known to be a powerful computational tool for determining phase shifts and energy eigenvalues in cases where a sufficiently slowly varying amplitude function can be found. The key for the efficient computations is that the original single-state radial Schrodinger equation is transformed to a nonlinear equation, the Milne equation. Such an equation has solutions that may or may not oscillate, depending on boundary conditions, which then requires a robust recipe for locating the (optimal) 'almost constant' solutions for its use in the method. For scattering problems the solutions of the amplitude equations always approach constants as the radial distance r tends to infinity, and there is no problem locating the 'optimal' amplitude functions from a low-order semiclassical approximation. In the present work, the amplitude-phase approach is generalized to two coupled Schrodinger equations similar to an earlier generalization to radial Dirac equations. The original scalar amplitude then becomes a vector quantity, and the original Milne equation is generalized accordingly. Numerical applications to resonant electron-atom scattering are illustrated.

  • 39.
    Thylwe, Karl-Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    McCabe, Patrick
    Note on Resonant and Non-resonant Peaks in Electron-Atom Total Scattering Cross Sections2018In: Communications in Theoretical Physics, ISSN 0253-6102, E-ISSN 1572-9494, Vol. 69, no 1, p. 28-30Article in journal (Refereed)
    Abstract [en]

    Certain broad low-energy peaks caused by a single partial wave in total cross sections are explained in terms of phase shifts. Such peaks have been associated with the real part of a Regge pole trajectory, having a maximum near an integer value of the angular momentum quantum number. At the peak energies, the pertinent partial-wave phase shift was shown to have a local maximum near a value pi/2 modulo pi. This implies no time delay in the semiclassical context. The phenomenon is a quantum effect, lacking a semiclassical interpretation.

  • 40.
    Thylwe, Karl-Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    McCabe, Patrick
    On Calculations of Legendre Functions and Associated Legendre Functions of the First Kind of Complex Degree2015In: Communications in Theoretical Physics, ISSN 0253-6102, E-ISSN 1572-9494, Vol. 64, no 1, p. 9-12Article in journal (Refereed)
    Abstract [en]

    Formulas for calculating Legendre functions and associated Legendre functions of the first kind of complex degree using an Ermakov-Lewis invariant are presented. These formulas are straight-forward to implement numerically and are motivated by the lack of computational routines in standard university tools like those of Mat Lab and Maple. Angular waves propagating in opposite directions are also obtained. The results are particularly useful in complex angular momentum theories and nearside/farside analysis of spin-dependent angular scattering from central potentials.

  • 41.
    Thylwe, Karl-Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    McCabe, Patrick
    Partial-wave analysis of particular peaks in total scattering cross sections caused by a single partial wave2014In: European Physical Journal D: Atomic, Molecular and Optical Physics, ISSN 1434-6060, E-ISSN 1434-6079, Vol. 68, no 10, p. 323-Article in journal (Refereed)
    Abstract [en]

    Certain broad low-energy peaks in the total cross sections relevant for electron-atom scattering are studied and found to be caused by a single partial wave. Such peaks are associated here with complex orbital angular momentum (Regge) pole trajectories. At the peak energies these S-matrix poles are in some neighborhood of an integer value and at the same time near its maximum real part value as a function of energy. Such peaks are found to have no time delays. Results are presented for the Dirac equation using three rational function Thomas-Fermi potential models, all with the same behavior at large and small radial distances.

  • 42.
    Thylwe, Karl-Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Oluwadare, O. J.
    Oyewumi, K. J.
    Semi-Relativistic Reflection and Transmission Coefficients for Two Spinless Particles Separated by a Rectangular-Shaped Potential Barrier2016In: Communications in Theoretical Physics, ISSN 0253-6102, E-ISSN 1572-9494, Vol. 66, no 4, p. 389-395Article in journal (Refereed)
    Abstract [en]

    A generalized Schrodinger approximation, due to Ikhdair & Sever, of the semi-relativistic two -body problem with a rectangular barrier in (1+1) dimensions is compared with exact computations. Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers. The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range vertical bar epsilon - Vo vertical bar < 2 mu c(2), where is the reduced mass, the scattering energy, and V-o the barrier top energy. The approximate wave numbers are less accurate.

  • 43.
    Thylwe, Karl-Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Sokolovski, D.
    An amplitude-phase approach to calculating Regge-pole positions and residues2005In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 38, no 23, p. 5305-5313Article in journal (Refereed)
    Abstract [en]

    New amplitude-phase formulae for Regge-pole positions and residues are derived. The derivation makes use of certain invariants of the En-nakov-Lewis type. The formulas allow calculation to be made on the real r-axis, with an additional flexibility to optimize its numerical aspects.

  • 44.
    Thylwe, Karl-Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Yngve, Staffan
    Froman, Per Olof
    Study of the validity of the phase-integral connection formula for potential barriers of arbitrary thickness2006In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 47, no 7Article in journal (Refereed)
    Abstract [en]

    The validity of the phase-integral connection matrix for potential barriers is discussed in a concrete way for a particular parabolic barrier, for the symmetric Eckart-Epstein barrier, and for the inverted Morse potential, when the first-order phase-integral approximation is used.

1 - 44 of 44
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