Tensor coupling and pseudospin symmetry in nuclei

In this work we study the contribution of the isoscalar tensor coupling to the realization of pseudospin symmetry in nuclei. Using realistic values for the tensor coupling strength, we show that this coupling reduces noticeably the pseudospin splittings, especially for single-particle levels near the Fermi surface. By using an energy. decomposition of the pseudospin energy splittings, we show that the changes in these splittings come mainly through the changes induced in the lower radial wave function for the low-lying pseudospin partners and through changes in the expectation value of the pseudospin-orbit coupling term for surface partners. This allows us to confirm the conclusion already reached in previous studies, namely that the pseudospin symmetry in nuclei is of a dynamical nature.

Integral equations of scattering in one dimension

A self-contained discussion of integral equations of scattering is presented in the case of centrally symmetric potentials in one dimension, which will facilitate the understanding of more complex scattering integral equations in two and three dimensions. The present discussion illustrates in a simple fashion the concept of partial-wave decomposition, Green's function, Lippmann-Schwinger integral equations of scattering for wave function and transition operator, optical theorem, and unitarity relation. We illustrate the present approach with a Dirac delta potential. (C) 2001 American Association of Physics Teachers.

Effect of electron correlation on positronium formation in positron-helium scattering

A three-parameter correlated wave function for the helium ground state is used to study the scattering reaction e(+) + He --> He+ + Ps, where Ps stands for positronium atom. An exact analytical expression is constructed for the first Born scattering amplitude for Ps formation from helium. Based on this numerical results are presented for both differential and total cross-sections. It is demonstrated that the inner electronic correlation of the target atom plays a crucial role in explaining the discrepency between theory and experiment.

Tunneling time through a barrier using the local value of a time operator

A time for a quantum particle to traverse a barrier is obtained for stationary states by setting the local value of a time operator equal to a constant. This time operator, called the tempus operator because it is distinct from the time of evolution, is defined as the operator canonically conjugate to the energy operator. The local value of the tempus operator gives a complex time for a particle to traverse a barrier. The method is applied to a particle with a semiclassical wave function, which gives, in the classical limit, the correct classical traversal time. It is also applied to a quantum particle tunneling through a rectangular barrier. The resulting complex tunneling time is compared with complex tunneling times from other methods.

Structure of large two-neutron halos in light exotic nuclei

The structure of three-body halo nuclei formed by two neutrons and a core (nnc) is studied using zero-range interactions. The halo wave function can be completely parameterized only by the s-wave scattering lengths and two-neutron separation energy. The sizes and the neutron-neutron correlation function of Li-11 and Be-14 are calculated and compared to experimental data. A general classification scheme for three-body halos with two identical particles is discussed as well as the critical conditions to allow excited Efimov states.

Gap solitons in a model of a superfluid fermion gas in optical lattices

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

Light Front Boson Model Propagation

The scope and aim of this work is to describe the two-body interaction mediated by a particle (either the scalar or the gauge boson) within the light-front formulation. To do this, first of all we point out the importance of propagators and Green functions in Quantum Mechanics. Then we project the covariant quantum propagator onto the light front time to get the propagator for scalar particles in these coordinates. This operator propagates the wave function from x(+) = 0 to x(+) > 0. It corresponds to the definition of the time ordering operation in the light front time x(+). We calculate the light-front Green's function for 2 interacting bosons propagating forward in x(+). We also show how to write down the light front Green's function from the Feynman propagator and finally make a generalization to N bosons.

Spontaneous symmetry breaking of Bose-Fermi mixtures in double-well potentials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Measurement of the shape of the boson-transverse momentum distribution in p(p)over-bar -> Z/gamma*-> e(+)e(-)+X events produced at root s=1.96 TeV

We present a measurement of the shape of the Z/gamma* boson transverse momentum (q(T)) distribution in p (p) over bar -> Z/gamma(*)-> e(+)e(-)+X events at a center-of-mass energy of 1.96 TeV using 0.98 fb(-1) of data collected with the D0 detector at the Fermilab Tevatron collider. The data are found to be consistent with the resummation prediction at low q(T), but above the perturbative QCD calculation in the region of q(T)> 30 GeV/c. Using events with q(T)< 30 GeV/c, we extract the value of g(2), one of the nonperturbative parameters for the resummation calculation. Data at large boson rapidity y are compared with the prediction of resummation and with alternative models that employ a resummed form factor with modifications in the small Bjorken x region of the proton wave function.

Spin-1 particle in the light-front approach

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

UNUSUALLY STRONG ATTRACTION IN THE PRESENCE OF CONTINUUM BOUND-STATE

The result of few-particle ground-state calculation employing a two-particle nonlocal potential supporting a continuum bound state in addition to a negative-energy bound state has occasionally revealed unusually strong attraction in producing a very strongly bound ground state. In the presence of the continuum bound state the difference of phase shift between zero and infinite energies has an extra jump of pi as in the presence of an additional bound state. The wave function of the continuum bound state is identical with that of a strongly bound negative-energy state, which leads us to postulate a pseudo bound state in the two-particle system in order to explain the unexpected attraction. The role of the Pauli forbidden states is expected to be similar to these pseudo states.

Classes of exact Klein-Gordon equations with spatially dependent masses: Regularizing the one-dimensional inversely linear potential

In this work we consider the effect of a spatially dependent mass over the solution of the Klein-Gordon equation in 1 + 1 dimensions, particularly the case of inversely linear scalar potential, which usually presents problems of divergence of the ground-state wave function at the origin, and possible nonexistence of the even-parity wave functions. Here we study this problem, showing that for a certain dependence of the mass with respect to the coordinate, this problem disappears. (c) 2006 Elsevier B.V. All rights reserved.

COMPLEX KOHN VARIATIONAL PRINCIPLE FOR 2-NUCLEON BOUND-STATE AND SCATTERING WITH THE TENSOR POTENTIAL

Complex Kohn variational principle is applied to the numerical solution of the fully off-shell Lippmann-Schwinger equation for nucleon-nucleon scattering for various partial waves including the coupled S-3(1), D-3(1), channel. Analytic expressions are obtained for all the integrals in the method for a suitable choice of expansion functions. Calculations with the partial waves S-1(0), P-1(1), D-1(2), and S-3(1)-D-3(1) of the Reid soft core potential show that the method converges faster than other solution schemes not only for the phase shift but also for the off-shell t matrix elements. We also show that it is trivial to modify this variational principle in order to make it suitable for bound-state calculation. The bound-state approach is illustrated for the S-3(1)-D-3(1) channel of the Reid soft-core potential for calculating the deuteron binding, wave function, and the D state asymptotic parameters. (c) 1995 Academic Press, Inc.

UNITARY POLE APPROXIMATION FOR THE COULOMB-PLUS-YAMAGUCHI POTENTIAL AND APPLICATION TO A 3-BODY BOUND-STATE CALCULATION

The unitary pole approximation is used to construct a separable representation for a potential U which consists of a Coulomb repulsion plus an attractive potential of the Yamaguchi type. The exact bound-state wave function is employed. U is chosen as the potential which binds the proton in the 1d5/2 single-particle orbit in F-17. Using the separable representation derived for U, and assuming a separable Yamaguchi potential to describe the 1d5/2 neutron in O-17, the energies and wave functions of the ground state (1+) and the lowest 0+ state of F-18 are calculated in the Gore-plus-two-nucleons model solving the Faddeev equations.

A MODEL OF THE DEUTERON BASED ON A BREIT TYPE EQUATION

A relativistic treatment of the deuteron and its observables based on a two-body Dirac (Breit) equation, with phenomenological interactions, associated to one-boson exchanges with cutoff masses, is presented. The 16-component wave function for the deuteron (J(pi) = 1+) solution contains four independent radial functions which obey a system of four coupled differential equations of first order. This radial system is numerically integrated, from infinity to the origin, by fixing the value of the deuteron binding energy and using appropriate boundary conditions at infinity. Specific examples of mixtures containing scalar, pseudoscalar and vector like terms are discussed in some detail and several observables of the deuteron are calculated. Our treatment differs from more conventional ones in that nonrelativistic reductions of the order c-2 are not used.