Bound states by a pseudoscalar Coulomb potential in one-plus-one dimensions

The Dirac equation is solved for a pseudoscalar Coulomb potential in a two-dimensional world. An infinite sequence of bounded solutions are obtained. These results are in sharp contrast with those ones obtained in 3 + 1 dimensions where no bound-state solutions are found. Next the general two-dimensional problem for pseudoscalar power-law potentials is addressed consenting us to conclude that a nonsingular potential leads to bounded solutions. The behaviour of the upper and lower components of the Dirac spinor for a confining linear potential nonconserving- as well as conserving-parity, even if the potential is unbounded from below, is discussed in some detail. (C) 2003 Elsevier B.V. All rights reserved.

Bound states of the Duffin-Kemmer-Petiau equation with a mixed minimal-nonminimal vector cusp potential

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Bound states of bosons and fermions in a mixed vector-scalar coupling with unequal shapes for the potentials

The Klein - Gordon and the Dirac equations with vector and scalar potentials are investigated under a more general condition, V(v) + V(s) = constant. These intrinsically relativistic and isospectral problems are solved in the case of squared hyperbolic potential functions and bound states for either particles or antiparticles are found. The eigenvalues and eigenfuntions are discussed in some detail and the effective Compton wavelength is revealed to be an important physical quantity. It is revealed that a boson is better localized than a fermion when they have the same mass and are subjected to the same potentials.

Scattering and bound states of spinless particles in a mixed vector-scalar smooth step potential

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Scattering and bound states of spin-0 particles in a nonminimal vector double-step potential

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Insights into metal ion binding in phospholipases A(2): ultra high-resolution crystal structures of an acidic phospholipase A(2) in the Ca2+ free and bound states

The electrophile Ca2+ is an essential multifunctional co-factor in the phospholipase A(2) mediated hydrolysis of phospholipids. Crystal structures of an acidic phospholipase A(2) from the venom of Bothrops jararacussu have been determined both in the Ca2+ free and bound states at 0.97 and 1.60 angstrom resolutions, respectively. In the Ca2+ bound state, the Ca2+ ion is penta-coordinated by a distorted pyramidal cage of oxygen and nitrogen atoms that is significantly different to that observed in structures of other Group I/II phospholipases A(2). In the absence of Ca2+, a water molecule occupies the position of the Ca2+ ion and the side chain of Asp49 and the calcium-binding loop adopts a different conformation. (c) 2005 Elsevier SAS. All rights reserved.

Integrable aspects of the scaling q-state Potts models I: bound states and bootstrap closure

We discuss the q-state Potts models for q less than or equal to 4, in the scaling regimes close to their critical or tricritical points. Starting from the kink S-matrix elements proposed by Chim and Zamolodchikov, the bootstrap is closed for the scaling regions of all critical points, and for the tricritical points when 4 > q greater than or equal to 2. We also note a curious appearance of the extended last line of Freudenthal's magic square in connection with the Potts models. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Quantization rules for bound states in quantum wells

An algebraic reformulation of the Bohr-Sommerfeld (BS) quantization rule is suggested and applied to the study of bound states in one-dimensional quantum wells. The energies obtained with the present quantization rule are compared to those obtained with the usual BS and WKB quantization rules and with the exact solution of the Schrodinger equation. We find that, in diverse cases of physical interest in molecular physics, the present quantization rule not only yields a good approximation to the exact solution of the Schrodinger equation, but yields more precise energies than those obtained with the usual BS and/or WKB quantization rules. Among the examples considered numerically are the Poeschl-Teller potential and several anharmonic oscillator potentials. which simulate molecular vibrational spectra and the problem of an isolated quantum well structure subject to an external electric field.

Bound states of attractive Bose-Einstein condensates in shallow traps in two and three dimensions

Using variational and numerical solutions of the mean-field Gross-Pitaevskii equation for attractive interaction (with cubic or Kerr nonlinearity), we show that a stable bound state can appear in a Bose-Einstein condensate (BEC) in a localized exponentially screened radially symmetric harmonic potential well in two and three dimensions. We also consider an axially symmetric configuration with zero axial trap and a exponentially screened radial trap so that the resulting bound state can freely move along the axial direction like a soliton. The binding of the present states in shallow wells is mostly due to the nonlinear interaction with the trap playing a minor role. Hence, these BEC states are more suitable to study the effect of the nonlinear force on the dynamics. We illustrate the highly nonlinear nature of breathing oscillations of these states. Such bound states could be created in BECs and studied in the laboratory with present knowhow.

Reply to comment on 'Quantization rules for bound states in quantum wells'

In this reply to the comment on 'Quantization rules for bound states in quantum wells' we point out some interesting differences between the supersymmetric Wentzel-Kramers-Brillouin (WKB) quantization rule and a matrix generalization of usual WKB (mWKB) and Bohr-Sommerfeld (mBS) quantization rules suggested by us. There are certain advantages in each of the supersymmetric WKB (SWKB), mWKB and mBS quantization rules. Depending on the quantum well, one of these could be more useful than the other and it is premature to claim unconditional superiority of SWKB over mWKB and mBS quantization rules.

Three- and Four-Nucleon Bound States in Three Dimensions, Without PW Decomposition

A brief review of a three-dimensional (3D) numerical method to solve few-nucleon bound and scattering states, without the standard partial-wave (PW) decomposition, is presented. The approach is applied to three-and four-nucleon bound states, by considering the solutions of the corresponding Faddeev-Yakubovsky (FY) integral equations in momentum space. Realistic spin-isospin dependent 3D and PW formalism are presented for the alpha particle and the triton binding energies, with numerical results given in both schemes for comparison.

Scaling and universality in two dimensions: three-body bound states with short-ranged interactions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Toward the Application of Three-Dimensional Approach to Few-body Atomic Bound States

The first step toward the application of an effective non partial wave (PW) numerical approach to few-body atomic bound states has been taken. The two-body transition amplitude which appears in the kernel of three-dimensional Faddeev-Yakubovsky integral equations is calculated as function of two-body Jacobi momentum vectors, i.e. as a function of the magnitude of initial and final momentum vectors and the angle between them. For numerical calculation the realistic interatomic interactions HFDHE2, HFD-B, LM2M2 and TTY are used. The angular and momentum dependence of the fully off-shell transition amplitude is studied at negative energies. It has been numerically shown that, similar to the nuclear case, the transition amplitude exhibits a characteristic angular behavior in the vicinity of He-4 dimer pole.

J/Psi-nuclear bound states

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Bound states of the barium atom by the hyperspherical approach

We present a nonadiabatic hyperspherical calculation of the highly excited and low lying doubly excited states of the barium atom using effective potentials for the two optically active electrons' interactions. Within the hyperspherical adiabatic approach the investigation of the spectra is performed with potential curves and nonadiabatic couplings of a unique radial variable, which allows clear identification of the states. The convergence of energy is obtained within well established bound limits, and the precision is comparable to accurate configuration interaction calculations. A very good agreement with experimental results is obtained with only few nonadiabatic couplings. (C) 2004 American Institute of Physics.