Gamov states in the generator coordinate method

Starting from the generator coordinate theory, a method is developed for calculating-decay widths within a microscopic dynamical theory. Antisymmetrization is taken into account exactly between all nucleons of the decaying system. For illustration, the method is applied to the-decay of⁸Be and²⁰Ne.     

Gamov states in the generator coordinate method

Starting from the generator coordinate theory, a method is developed for calculatingα-decay widths within a microscopic dynamical theory. Antisymmetrization is taken into account exactly between all nucleons of the decaying system. For illustration, the method is applied to theα-decay of⁸Be and²⁰Ne.     

Pairing vibrational states and the generator coordinate method

The pairing vibrational states and the two-neutron transfer cross sections between these states are calculated in Ni, Sn and Pb isotopes by the generator coordinate method (GCM). The particle number fluctuation of the BCS functions is handled by projecting in a good approximation on sharp particle numbers. The results agree quite well with the experimental data.     

The coulomb problem for scattering states in the generator coordinate method

The proportionality of the Hill-Wheeler amplitude ? and of the scattering wave function g for large separation distance is proved for Coulomb + nuclear scattering. Practical problems are discussed.     

The coordinate coherent states approach revisited

We revisit the coordinate coherent states approach through two different quantization procedures in the quantum field theory on the noncommutative Minkowski plane. The first procedure, which is based on the normal commutation relation between an annihilation and creation operators, deduces that a point mass can be described by a Gaussian function instead of the usual Dirac delta function. However, we argue this specific quantization by adopting the canonical one (based on the canonical commutation relation between a field and its conjugate momentum) and show that a point mass should still be described by the Dirac delta function, which implies that the concept of point particles is still valid when we deal with the noncommutativity by following the coordinate coherent states approach. In order to investigate the dependence on quantization procedures, we apply the two quantization procedures to the Unruh effect and Hawking radiation and find that they give rise to significantly different results. Under the first quantization procedure, the Unruh temperature and Unruh spectrum are not deformed by noncommutativity, but the Hawking temperature is deformed by noncommutativity while the radiation specturm is untack. However, under the second quantization procedure, the Unruh temperature and Hawking temperature are untack but the both spectra are modified by an effective greybody (deformed) factor.     

Correspondence between generalized binomial field states and coherent atomic states

We show that the N-photon generalized binomial states of electromagnetic field may be put in a bijective mapping with the coherent atomic states of N two-level atoms. We exploit this correspondence to simply obtain both known and new properties of the N-photon generalized binomial states. In particular, an over-complete basis of these binomial states and an orthonormal basis are obtained. Finally, the squeezing properties of generalized binomial state are analyzed.     

Towards a macroscopic generator coordinate method

Collective quantities are defined as macroscopic statistical averages over many level crossing points where microscopic densities are redistributed. Accordingly, the generator coordinate method (GCM) is reconsidered. It is concluded that, contrary to earlier arguments, the macroscopically defined inertia parameter which appears in the GCM Hamiltonian has a finite value close to that obtained using traditional theories assuming the existence of the adiabatic BCS ground state.     

The generator coordinate method and the theory of metals

An application is made of the Generator Coordinate Method to a system of permions interacting with bosons. The problem treated in the present work is the collective dynamics of a metal regarded as an electron system interacting dynamically with the phonons of the lattice. A generalization of the Bohn-Staver formula for the sound velocity in metals is obtained.     

Pairing vibrational and isospin rotational states in a particle number and isospin projected generator coordinate method

Pairing vibrational and isospin rotational states are described in different approximations based on particle number and isospin projected, proton-proton, neutron-neutron and proton-neutron pairing wave functions and on the generator coordinate method (GCM). The investigations are performed in models for which an exact group theoretical solution exists. It turns out that a particle number and isospin projection is essential to yield a good approximation to the ground state or isospin yrast state energies. For strong pairing correlations (pairing force constant equal to the single-particle level distance) isospin cranking (-ωT_x) yields with particle number projected pairing wave function also good agreement with the exact energies. GCM wave functions generated by particle number and isospin projected BCS functions with different amounts of pairing correlations yield for the lowest T = 0 and T = 2 states energies which are practically indistinguishable from the exact solutions. But even the second and third lowest energies of charge-symmetric states are still very reliable. Thus we conclude that also in realistic cases isospin rotational and pairing vibrational states may be described in the framework of the GCM method with isospin and particle number projected generating wave functions.     

The connection between the generator coordinate method and Bose expansions

It is shown that the generator coordinate method leads to a Bose expansion which in lowest order agrees with the RPA, and which for infinite order is equivalent to the Marumori expansion.     

Effective nucleus-nucleus potentials derived from the generator coordinate method

The equivalence of the generator coordinate method (GCM) and the resonating group method (RGM) and the formal equivalence of the RGM and the orthogonality condition model (OCM) lead to a relation connecting the effective nucleus-nucleus potentials of the OCM with matrix elements of the GCM. This relation may be used to derive effective nucleus-nucleus potentials directly from GCM matrix elements without explicit reference to the potentials of the RGM. In a first application local and l-independent effective potentials are derived from diagonal GCM matrix elements which represent the energy surfaces of a two-centre shell model. Using these potentials the OCM can reproduce the results of a full RGM calculation very well for the elastic scattering of two α-particles and fairly well for elastic ¹⁶O-¹⁶O scattering.     

Variational principles for scattering in the generator coordinate method

The generator coordinate method (GCM) wave function is used as a trial function in a Kohn type variational principle for scattering phase shifts. It is shown that a GCM trial function is a solution of the variational equations if the Hill-Wheeler integral equation is satisfied subject to an appropriate boundary condition. A new method for introducing the scattering boundary condition is presented. There is a uniqueness theorem for the phase shift.     

Spin squeezing and entanglement via hole-burning in atomic coherent states

We study the generation of spin squeezing via the hole burning of selected Dicke states out of an atomic coherent state prepared for a collection of N two-level atoms or ions. The atoms or ions of the atomic coherent state are not entangled, but the removal of one or more Dicke states generates entanglement, and spin squeezing occurs for some ranges of the relevant parameters. Spin squeezing in a collection of two-level atoms or ions is of importance for precision spectroscopy.     

Derivation of collective potential and mass from the generator coordinate method

The Hill-Wheeler equation of the generator coordinate method is approximated by a local collective Schrödinger equation. General expressions for the potential and the mass parameter are obtained by a symmetrized moment expansion. The validity of the approximation is tested for several examples where the exact solution is known. These include the Gaussian overlap with harmonic and anharmonic interaction, the Lipkin model, and monopole resonances of spherical light nuclei. In all cases, surprisingly close agreement with the exact solution is found. Other possible applications of the formalism are indicated.     

Collective potential and mass parameters derived from the generator coordinate method

The collective hamiltonian for the axial quadrupole vibrations was derived from theQQ+PP model. The generator coordinate method was applied and the results obtained through the symmetric moments expansion and the gaussian overlap approximation were compared. It was found that the collective potential and the average magnitude of the mass parameter obtained in both approximations are close to each other.     

A particle number projection study with the generator coordinate method

The generator coordinate method (GCM) is used in order to describe pairing vibrations. The generating wave functions are particle-number-projected BCS-wave functions. With the conventional pairing Hamiltonian the method is tested in some simple models and applied also to the even Nickel isotopes. The results obtained can be regarded as encouraging ones.     

On calculating scattering phase shifts by the generator coordinate method

The generator coordinate equations for scattering phase shifts are solved for α-α scattering. Calculations are made in the coordinate representation and the results agree well with those obtained by a more laborious procedure which is formulated in the momentum representation. The results disagree with another calculation in the coordinate representation, where the scattering boundary condition is introduced less accurately.     

Teleportation of atomic states with a weak coherent cavity field

A scheme is proposed for the teleportation of an unknown atomic state. The scheme is based on the resonant interaction of atoms with a coherent cavity field. The mean photon-number of the cavity field is much smaller than one and thus the cavity decay can be effectively suppressed. Another advantage of the scheme is that only one cavity is required.