P. Van Leuven

Cu-isotopes by the unified model

Abstract The experimental data of the odd-mass Cu-isotopes are interpreted on the basis of the unified model. A value of the 3p1/2−3p3/2 and 3p1/2−4f5/2 single proton level splittings is determined.

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.

Quantum theory and molecular spectra

Abstract The “generator coordinate method” is proposed as a fully quantum mechanical treatment of molecular spectra.

Projected hartree-fock calculation for light nuclei (I). Energies and wave functions

Abstract An approximate projected Hartree-Fock calculation has been carried out for the low-lying levels of nuclei with 4 ≦ A ≦ 8. The two-body interaction used is Volkovs potential no. 1. The calculated binding energies are compared which those from other variational methods. With respect to the shell-model approximation, a considerable increase is obtained, which reaches 15 MeV for 8 Be. The orbitals, resulting from the minimization of the energy, can be looked upon as approximate eigenfunctions of a deformed oscillator potential. The systematics of size and deformation of these orbitals are presented. The deformation is larger for the orbitals of the inner 4 He core than for the orbitals of the outer particles.

A projected Hartree-Fock calculation for 12C

Abstract An approximate projected Hartree-Fock calculation for 12 C is carried out. An increase of 11 MeV in the binding energy can be obtained by admixing 0d and 0f oscillators states to the orbitals. These admixtures enhance the E2 transition from the first excited state to the ground state and bring it in agreement with the experimental value.

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.

A new particle-hole approach to collective states

Abstract The relevance of the particle-hole space is demonstrated by showing that in some commonly used formalisms the first excited state lies entirely within the particle-hole space generated from the correlated ground state. This property is proved for several cases of angularmomentum projection — projected Hartree-Fock method (PHF) — and for the generator coordinate method in the Gaussian overlap approximation, while in other cases it has been verified only numerically. A new method is presented for the approximate calculation of energies and transition amplitudes of particle-hole excited states. Only hermitian one-body operators are used to generate the excited states. The two-body density matrix of a correlated state approximating the ground state is required as input data. The formula is tested on the 2 + and 3 − states of 8 Be and 12 C by using the PHF ground state. Where comparison is possible the method gives better agreement with PHF and experiment than the extended random-phase approximation.

Configuration interaction and rotational structure in 8Be

Abstract A configuration interaction calculation for 8Be is carried out in which 0 h ω, 2 h ω and 4 h ω configurations are taken into account. The results indicate a reordering of levels into new rotational bands and a grouping of bands into “families”.

Projected Hartree-Fock calculations for light nuclei (II). Form factors of 6Li

Abstract The form factors for elastic and inelastic scattering of high-energy electrons from 6 Li have been calculated using the wave functions obtained in paper (I) of this series. Although considerable deviation from the experimental data remains, the improvement with respect to the shell-model approximation is significant.