J. Broeckhove

On the equivalence of time-dependent variational-principles

Abstract We consider the relationship between three variational principles which generate approximate time evolution in a parametrized manifold of wavefunctions. These are: the McLachlan variational principle, the Dirac-Frenkel variational principle and the time-dependent variational principle. We show that if the manifold can be parametrized by pairs of “complementary” parameters, the abovementioned principles are equivalent. The condition of complementarity, which is a sufficient one, is demonstrated to be satisfied in a number of important applications. However, a case of non-equivalence in the recent literature warns against liberal assumptions about the equivalence of the time-dependent variational principles.

The Sp(2, R) model applied to 8Be

Abstract We work out the complete Sp(2, R ) model for the low-lying states of 8 Be. The calculation in the infinite dimensional representation space is performed with the generator coordinate method. The spectrum shows a marked departure from truncated Sp(2, R ) results and compares favourably with experiment.

Quantum time evolution of vibrational states in curve-crossing problems

Abstract The quantum time evolution in a two-state curve-crossing situation can be computed with the split-operator FFT method. We present an improved version of that scheme, based on the analytic exponentiation of two-by-two matrices. We use this approach to investigate the vibrational dynamics of the coupled b′, c′ 1 Σ + u states of the N 2 molecule.

Dynamics of wave packets and the time-dependent variational principle

Abstract The quantal time evolution of a one-dimensional Gaussian wave packet according to the time-dependent variational principle (TDVP) is shown to be formally equivalent to the classical motion of a particle in a two-dimensional potential. The formal and practical advantages of the TDVP approach are indicated.

The algebraic model for scattering in three-s-cluster systems: theoretical background

A framework to calculate two-particle matrix elements for fully antisymmetrized three-cluster configurations is presented. The theory is developed for a scattering situation described in terms of the Algebraic Model. This means that the nuclear many-particle state and its asymptotic behaviour are expanded in terms of oscillator states of the intra-cluster coordinates. The Generating Function technique is used to optimize the calculation of matrix elements. In order to derive the dynamical equations, a multichannel version of the Algebraic Model is presented.

Three-cluster description of properties of light neutron- and proton-rich nuclei in the framework of the algebraic version of the resonating group method

A three-cluster microscopic approach to description of the properties of light atomic nuclei (algebraic version of the resonating group method) is presented. The approach is based on the application of oscillator functions for determination of the wave functions of each cluster and expansion of the function of relative cluster motion. Those applications of the method that are related to the study of the properties of states of the discrete and continuous spectra of neutron- and proton-rich 6He, 8He, 6Be, 5H nuclei and fusion reactions 3H(2H, 2n)4He and 3He(3He, 2p)4He are mainly considered. Technical issues of calculations are discussed to the extent necessary for understanding the presented material. The main attention is concentrated on the presentation of physical results, their comparison with experimental data, and results obtained in other theoretical approaches. Problems associated with the role of the Pauli principle, convergence of numerical results, and approximations made in the course of calculations are also discussed in sufficient detail

The Sp(2,R) nuclear model of 12C

Abstract The dynamics of the oblate deformation in 12C is studied within the framework of the Sp(2, R) nuclear model. We identify the eigenstates with the Sp(2, R ) phorion states. These are vibrationally excited configurations in the deformed-shell model, and are linked to the isoscalar giant quadrupole resonance.

The 5H resonance structure studied with a three-cluster J-matrix model

The resonance structure of 5H is investigated within a three-cluster microscopic model. Hyperspherical harmonics are used to characterize the channels of the three-cluster continuum and to implement the appropriate boundary conditions. The model reveals the energy and width of the 5H resonance states and allows for a detailed channel analysis. These results are verified against the available experimental data and compare qualitatively favorably with some other theoretical calculations.

Algebraic model for scattering in three-s-cluster systems. II. Resonances in the three-cluster continuum of6Heand6Be

The resonance states embedded in the three-cluster continuum of 6He and 6Be are obtained in the Algebraic Version of the Resonating Group Method. The model accounts for a correct treatment of the Pauli principle. It also provides the correct three-cluster continuum boundary conditions by using a Hyperspherical Harmonics basis. The model reproduces the observed resonances well and achieves good agreement with other models. A better understanding for the process of formation and decay of the resonance states in six-nucleon systems is obtained.

The generator coordinate approximation for molecules: A review

The generator coordinate approximation is a non-adiabatic theory of molecular systems. Its fundamental outlines were developed during the 1970s. A further analysis and first applications were published during the 1980s. In this paper, we review the present status of the theory.