Properties Of Bound States Research Articles

Bound-state properties and muon sticking probabilities for theS(L = 0)-states in non-symmetric muonic molecular ions

The bound-state properties of the non-symmetric muonic molecular ions pdµ, ptµ and dtµ in S(L = 0)-states are determined toa high accuracy. The corresponding variational wavefunctions have beenconstructed by using the two-stage strategy proposed previously(Frolov A M 1998 Phys. Rev. A 57 2436). The two- and three-particle deltafunctions and cusp values have also been determined for these systemsquite accurately. The new multiprecision FORTRAN package developed byD H Bailey from NASA (1995 ACM Trans. Math. Softw. 21 379) hasbeen used extensively to perform our present calculations. The muonsticking probabilities are determined numerically for each of these muonicmolecular ions in their S(L = 0)-states. The obtained values of thetotal sticking probabilities equal 99.800% (pdµ), 98.812% (ptµ), 0.893% (dtµ, ground state) and 0.893% (dtµ,excited state), respectively. The best variational results for all known22 bound states in the muonic molecular ions are also presented.

Impurity bound states in a compensated quantum well

A detailed study of the bound-state properties of an impurity in a compensated semiconductor quantum well is presented using the screened potential of a minority impurity ion in a compensated semiconductor due to Schechter (1981). Accurate eigenenergies for the first 15 states are obtained for this potential as a function of the screening parameter λ by numerical integration of the two-dimensional (2D) Schrödinger equation. The energies are found to decrease with increasing values of the screening parameter λ in all cases. The variation of splitting between adjacent levels for the same value of n with the screening parameter is also studied.

Multibox strategy for constructing highly accurate bound-state wave functions for three-body systems.

Variational, multibox approach is proposed to construct extremely accurate, bound-state wave functions for arbitrary three-body systems. The high efficiency of our present approach is based on an optimal choice of nonlinear parameters in the exponential basis functions. The proposed method is very flexible, since the final wave function can also include a large number of separately optimized cluster fragments. The wave functions obtained are very compact and highly accurate. Such wave functions can be used to compute various bound state properties for different three-body systems. The proposed approach has been successfully tested on a large number of actual systems. It is shown that the present approach can be used to solve various three-body problems with, in principle, arbitrary precision. In particular, the long-standing problem of highly accurate determination of the weakly bound (1,1) states in the ddmu and dtmu muonic molecular ions has finally been solved. The determined binding energies are -1.974 988 088 0+/-5 x 10(-10) eV and -0.660 338 74+/-1 x 10(-8) eV, respectively.

Study of ΛΛ dynamics and ground state structure of low and medium mass double Λ hypernuclei

We critically review the ΛΛ dynamics by examining Λ - Λ and Λ-nucleon phenomenological potentials in the study of the bound state properties of double-Λ hypernuclei ΛΛ6He, ΛΛ10Be, ΛΛ14C, ΛΛ18O, ΛΛ22Ne, ΛΛ26Mg, ΛΛ30Si, ΛΛ34S, ΛΛ38Ar, ΛΛ42Ca, ΛΛ46Ti, ΛΛ50Cr, ΛΛ54Fe, ΛΛ58Ni, ΛΛ62Zn, ΛΛ66Ge, ΛΛ70Se, ΛΛ74Kr, ΛΛ78Sr, ΛΛ82Zr, ΛΛ86Mo, ΛΛ90Ru, ΛΛ94Pd, ΛΛ98Cd, ΛΛ102Sn in the frame work of (core+Λ+Λ) three body model. An effective ΛN potential is obtained by folding the phenomenological ΛN potential into the density distribution of the core nuclei. The former two cases (i.e. ΛΛ6He and ΛΛ10Be) are revisited to justify the correctness of the present potential model. Assuming the same potential model we predicted some of the structural properties of heavier doubly Λ-hypernuclei. The hyperspherical harmonics expansion method, which is an essentially exact method has been employed for the three body system. A convergence in binding energy up to 0.15% for Kmax=20 has been achieved. In our calculation we have made no approximation in restricting the allowed l-values of the interacting pairs.

High-precision, variational, bound-state calculations in coulomb three-body systems

The present study contains high-precision variational results for a number of bound states in various Coulomb three-body systems. In particular, we discuss the bound-state properties for the 2(3)S state of the infinityHe atom, the bound S(L=0) and P(L=1) states in symmetric muonic molecular ions, and ground states in the 3He2+&mgr;(-)e(-) and 4He2+&mgr;(-)e(-) atoms. The accuracy achieved for the total energies in these systems is significantly higher than known from the previous works. These results have been obtained by using a package of FORTRAN programs and a pretranslator written by D. H. Bailey from NASA [D.H. Bailey, ACM Trans. Math. Softw. 21, 379 (1995)]. This multiprecision FORTRAN package can completely eliminate all problems related to numerical instabilities at large dimensions, which are crucial for high-precision, bound-state calculations in few-body systems. In fact, the multiprecision FORTRAN programs open another avenue in the study of bound states in few-body systems.

Properties of the nonlocalNNinteractions required for the correct triton binding energy

In order to investigate their effect on the triton binding energy, a set of nonlocal ${}^{1}{S}_{0}$ and ${}^{3}{\mathrm{SD}}_{1}$ nucleon-nucleon $(\mathrm{NN})$ interactions is constructed in coordinate space. The properties which make possible the reproduction of the triton binding energy without a three-nucleon force are studied. For all of the investigated local and nonlocal interactions the dominant contribution to the triton binding energy comes from the pole terms of the ${}^{1}{S}_{0}$ and ${}^{3}{\mathrm{SD}}_{1}$ states; consequently the singlet virtual bound state and deuteron properties have a dominant role. Low deuteron D-state and substantial S-state short-distance probabilities, which could not be produced by local $\mathrm{NN}$ interactions, are necessary requirements for the correct binding energy.

Bound-state properties of the positronium negative ionPs−

Various geometrical and energetical (bound-state) properties of the positronium negative ion $({\mathrm{Ps}}^{\ensuremath{-}}$ or ${e}^{\ensuremath{-}}{e}^{+}{e}^{\ensuremath{-}})$ are determined by using highly accurate variational wave functions. These wave functions have been constructed by applying the advanced two-stage strategy proposed by Frolov [Phys. Rev. A 57, 2436 (1998)]. The determined total energy of the ground state $E=\ensuremath{-}0.2620050702329757\mathrm{a}.\mathrm{u}.$ is the lowest and most accurate value obtained for this system to date (the corresponding binding energy equals $\ensuremath{-}0.326674721317821\mathrm{eV}).$ The computation of the second-order relativistic corrections $(\ensuremath{\simeq}{\ensuremath{\alpha}}^{2})$ to the total energy is discussed also. The general form of the Breit-Pauli Hamiltonian in the relative coordinates for the ${\mathrm{Ps}}^{\ensuremath{-}}$ ion is presented.

Calculation of relativistic atomic transition and ionization properties for highly-charged ions

Recent years have seen a growing number of large-scale atomic structure calculations using both nonrelativistic and relativistic theories. For investigations of multiple and highly charged ions, of course, a relativistic structure code like the widely known GRASP program is required. In a revised version of this program, namely GRASP92 (F A Parpia, C F Fischer and I P Grant 1996 Comput. Phys. Commun. 94 249), systematic studies of level energies and a few other bound-state properties are now being supported. — Here, we briefly introduce a new package RATIP which extends GRASP92 towards the computation of various Relativistic Atomic Transition and Ionization Properties. A short overview of the capabilities of RATIP along with current developments will be given.

Bound-state properties of negatively charged hydrogenlike ions

The results of high-precision, variational, bound-state calculations for the ground state in the negatively charged hydrogenlike ions ${}^{\ensuremath{\infty}}{\mathrm{H}}^{\mathrm{\ensuremath{-}}}{,\mathrm{}\mathrm{T}}^{\mathrm{\ensuremath{-}}}{,\mathrm{}\mathrm{D}}^{\mathrm{\ensuremath{-}}},$ ${}^{1}{\mathrm{H}}^{\ensuremath{-}},$ and ${\mathrm{Mu}}^{\ensuremath{-}}$ are presented. The mass dependence for various properties is studied. The results are formulated in the form of relatively simple analytical expressions. The probabilities of finding the final He atom in its ground and low-lying excited states (after the nuclear ${\ensuremath{\beta}}^{\ensuremath{-}}$ decay in the ${T}^{\ensuremath{-}}$ ion) have been determined numerically. It is shown that the total ionization probability has a very large value (\ensuremath{\approx}30%). A possible explanation may include the spin conversion between the ${\ensuremath{\beta}}^{\ensuremath{-}}$ particle and remaining ${}^{3}\mathrm{He}$ atom. This means that the final ${}^{3}\mathrm{He}$ atom can be found not only in its singlet states, but also in the triplet states.

Excitation and ionization of molecules by a single-mode laser field using a time-dependent approach

We consider procedures for solving the time-dependent Schrödinger equation for the interaction of a single-mode laser field with a molecule, leading to electronic excitation, vibration, dissociation, and ionization. The temporal propagation occurs through application of Real Space Product Formulae, which scale linearly with the number of states and the number of radial mesh points. We extract basic bound-state properties such as potential energy surfaces and transition dipole matrix elements for configuration interaction calculations. Bound-free matrix elements come from electron—molecule scattering programs. We present several examples, including photodissociation of H 2 + and pump-probe excitation-ionization of K 2.

The three-boson bound state in massive QED 2

We derive the (matrix-valued) Feynman rules of mass perturbation theory of the massive Schwinger model for non-zero vacuum angle theta. Further, we discuss the properties of the three-boson bound state and compute -- by a partial resummation of the mass perturbation series -- its mass and its partial decay widths.

ππ,Kπ, andπNpotential scattering and a prediction of a narrowσmeson resonance

Low energy scattering and bound state properties of the \pi N, \pi\pi and K\pi systems are studied as coupled channel problems using inversion potentials of phase shift data. In a first step we apply the potential model to explain recent measurements of pionic hydrogen shift and width. Secondly, predictions of the model for pionium lifetime and shift confirm a well known and widely used effective range expression. Thirdly, as extension of this confirmation, we predict an unexpected medium effect of the pionium lifetime which shortens by several orders of magnitude. The \sigma meson shows a narrow resonance structure as a function of the medium modified mass with the implication of being essentially energy independent. Similarly, we see this medium resonance effect realized for the K\pi system. To support our findings we present also results for the \rho meson and the \Delta(1232) resonance.

Ground state of positronium hydride

The ground bound state in the positronium hydride molecule (HPs) is determined from extensive variational four-body calculations with the James-Coolidge four-body variational expansion in the relative coordinates r{sub 12},r{sub 13},r{sub 23},r{sub 14},r{sub 24}, and r{sub 34}. For the positronium hydride with the infinitely heavy nucleus ({sup {infinity}}HPs) the total energy found, E={minus}0.7891369 a.u., is one of the lowest variational values published to date. A number of bound-state properties have been calculated also, including the {delta}-function expectation values, two-body cusps, and the two-photon annihilation rate. {copyright} {ital 1997} {ital The American Physical Society}

CESD97 — A revised version to expand jj-coupled symmetry functions into determinants

Recently, a major revision of the widely used relativistic atomic structure program GRASP (cf. F.A. Parpia, C.F. Fischer and I.P. Grant, Comput. Phys. Commun. 92 (1996) 249) has been published. This new version has been designed for systematic investigations of level energies and other bound state properties. It is being extended so as to facilitate accurate predictions of atomic ionization and decay properties. Redistribution of electrons during a decay may have important effects on transition probabilities. Rearrangement effects are known to be important for line transitions, and particularly in the Auger effect and in photoionization processes, and can be accounted for quite simply if the atomic wave functions of the initial and final states involved are optimized independently. However, the resulting one-electron orbital functions are not quite orthogonal. This ‘nonorthogonality’ can easily be included in the computation of the (many-electron) transition matrix if the initial and final state wave functions are each expressed as a linear combination of determinants. In order to expand the symmetry-adapted configuration and/or atomic states from GRASP92, a revised and extended version of the CESD program (S. Fritzsche and I.P. Grant, Comput. Phys. Commin. 92 (1995) 111) is presented. It supports all new features of GRASP92 and extends the range of previous applications.

High-Precision Calculation of the Triton Ground State Within the Hyperspherical-Harmonics Method

The problem of calculating the three-nucleon bound-state properties in the case of realistic nucleon-nucleon potentials is studied by means of the hyperspherical-harmonics approach. Important aspects of the method are the inclusion of all relevant channels in the wave function and the use of large expansion bases. Results are presented for some of the local nucleon-nucleon potentials most frequently used. The conclusion is that, in these cases, the hyperspherical-harmonics approach allows at present for the results of highest precision. Moreover, the extension of the calculation technique to larger systems appears feasible and very promising.

Exact six-dimensional quantum calculations of the rovibrational levels of (HCl)2

Results of comprehensive full-dimensional (6D) quantum calculations of the rovibrational levels of (HCl)2, for total angular momentum J=0,1 are presented. The calculations employed two 6D potential energy surfaces (PES)—the ab initio PES of Bunker and co-workers, and the semiempirical PES of Elrod and Saykally. This 6D study provides the first rigorous, approximation-free description of the bound state properties of (HCl)2, including the dissociation energy, tunneling splittings and their J, K dependence, frequencies of intermolecular vibrations and associated J=0→1 spacings, and quantum number assignments of the 6D eigenstates. Detailed comparison with 4D bound state calculations (for fixed HCl bond length) was made in order to assess the importance of including the intramolecular vibrations of the two HCl subunits for accurate calculation of various spectroscopic properties of (HCl)2. Comparison of the 6D results with experimental data, while confirming that the ES1 PES is substantially more accurate than the ab initio PES, shows that there is room for further refinements, preferably using 6D bound state calculations.

Relativistic bound-state equations in three dimensions.

First, a systematic procedure is derived for obtaining three-dimensional bound-state equations from four-dimensional ones. Unlike ``quasipotential approaches'' this procedure does not involve the use of delta-function constraints on the relative four-momentum. In the absence of negative-energy states, the kernels of the three-dimensional equations derived by this technique may be represented as sums of time-ordered perturbation theory diagrams. Consequently, such equations have two major advantages over quasipotential equations: They may easily be written down in any Lorentz frame, and they include the meson-retardation effects present in the original four-dimensional equation. Second, a simple four-dimensional equation with the correct one-body limit is obtained by a reorganization of the generalized ladder Bethe-Salpeter kernel. Third, our approach to deriving three-dimensional equations is applied to this four-dimensional equation, thus yielding a retarded interaction for use in the three-dimensional bound-state equation of Wallace and Mandelzweig. The resulting three-dimensional equation has the correct one-body limit and may be systematically improved upon. The quality of the three-dimensional equation, and our general technique for deriving such equations, is then tested by calculating bound-state properties in a scalar field theory using six different bound-state equations. It is found that equations obtained using the method espoused here approximate the wave functions obtained from their parent four-dimensional equations significantly better than the corresponding quasipotential equations do. \textcopyright{} 1996 The American Physical Society.

Uniform alpha -nucleus potential in a wide range of masses and energies.

We have reanalyzed elastic \ensuremath{\alpha} scattering data on many target nuclei from $^{40}\mathrm{Ca}$ up to $^{208}\mathrm{Pb}$ over a wide range of energies. Using double-folded potentials we have obtained excellent agreement between the experimental scattering data and our optical model calculations. In addition, bound state properties have been calculated successfully. A systematic behavior of the energy and mass dependence of the strengths of the real and imaginary potentials has been found. \textcopyright{} 1996 The American Physical Society.

Physical Mechanism of Neutron Halo on Drip Line Light Nuclei

In order to extend the conventional shell model calculation with harmonic oscillator bases to halo nuclei a self-similar-structure shell model(SSM) in which the single particle orbit has state(orbit)-dependent frequency was proposed. We do this by a rescaling of both the kinetic and potential energy term of the harmonic oscillator and a mean field imitation so that the physical mechanisms of both neutron skin and neutron halo as well as the bound state properties of Borromean nuclei such as 6He, 11Li and 14Be can be revealed in SSM.

Properties of Deuteron Bound State from Meson and Quark Theories for the Nucleon-Nucleon Interaction

The properties of the nucleon-nucleon bound state in the deuteron are considered. Nucleon-nucleon interactions of the Yukawa, Reid and Paris potential forms are used to describe the deuteron bound state. Also, the nucleon-nucleon interaction with different meson exchanges derived from the meson theory as well as the nucleon-nucleon interaction with quark exchange derived from the quark theory by introducing the quark-quark potential with one gluon exchange are used to investigate the deuteron properties. The deuteron binding energy, quadrupole moment, effective range, root-mean-square radius and the D/S ratio are calculated by using different nucleon-nucleon interactions. The obtained results of the present calculations are in good agreement with the experimental values.