Some necessary conditions for fermion N-representability

The analogues of the Q and B conditions for the N-representability of a p-particle fermion density operator are derived. These conditions impose some new necessary conditions for the N-representability of 2-density operators. It is shown that the new conditions are no more restrictive than the conventional Q and B conditions.     

Remarks on the density functional approach to the inhomogeneous electron gas

The density functional approach is reformulated by using the most general form of the Hohenberg-Kohn theorem based on p-particle densities. Comparison with the reduced density matrix theory is made, exhibiting fully the p-particle hierarchy of both theories. Some advantages and drawbacks of the generalized density functional approach are discussed. The 1-particle spin-polarized case is presented to indicate the place of the usual DFA within the framework of the generalized theory.     

Boson expansions and quantization of time-dependent self-consistent fields (I). Particle-hole excitations

Two concrete methods are presented for quantizing the time-dependent Hartree equations in terms of boson operators. The first is the well-known infinite boson expansion analogous to the Holstein-Primakoff representation of angular momentum operators. The second, a new development, consists of finite boson quadratic forms, and is analogous to the Schwinger representation of angular momenta. In each case, a physical boson subspace can easily be constructed within which the full fermion dynamics is exactly duplicated. It therefore follows that quantization of the time-dependent Hartree equations, including all degrees of freedom, retrieves the exact many-body problem. The discussion in this paper is limited to particle-hole excitations of an N-particle system. A generalization to one-nucleon transfer processes on the N-particle system is also given in terms of ideal odd nucleons, but this brings in infinite expansions.     

Integral equations for N-particle scattering

Integral equations are derived for the N-particle transition operators. The equations couple together only transition operators between two-body channels. The kernel of the equations becomes connected after a single iteration. Transition operators involving channels with three or more particles can be obtained by quadratures from the solution of the equations. It is also shown that the N-particle equations can be reduced to multichannel two-body equations by the use of the quasiparticle method.     

A multi-cluster,n-particle generalization of the three-particle faddeev wavefunction equations

Recent work applying certain forms of many-body scattering theory to problems such as molecular potential energy surfaces and equations for nonequilibrium statistical mechanics indicates that a formulation of the theory based directly on multi-cluster, n-particle, wave function components could be of some utility. Such a formulation is derived in this paper using techniques from the Baer-Kouri-Levin-Tobocman and Bencze-Redish-Sloan-Polyzou theories of multi-particle scattering. It is based on components corresponding to the various multi-cluster partitions of an n-particle scattering system and is a generalization of the three-body Faddeev wave function formalism, to which it reduces when n = 3. Except for the full breakup partition, which does not enter the equations, the new components are defined for all possible m-cluster partitions of the n-particles, 2 ≤ m ≤ n ? 1. The sum of all the components yields the solution to the Schrödinger equation for scattering and either the Schrödinger equation solution or an easily identified spurious solution in the case of bound states. Both the two-cluster components and two-cluster transition operators are shown to be solutions of equations involving quantities carrying only two-cluster partition labels. Discussions of the Born term and a multiple scattering representation for the non-rearrangement transition operator and the inclusion of distortion operators in the formalism are also included.     

Mermin's n-particle Bell inequality and operators' noncommutativity

The relationship between the noncommutativity of operators and the violation of the Bell inequality is exhibited in the light of the n-particle Bell-type inequality discovered by Mermin (Phys. Rev. Lett. 65 (1990) 1838). It is shown, in particular, that the maximal amount of violation of Mermin's inequality predicted by quantum mechanics decreases exponentially by a factor of 2^−m/2 whenever any m among the n single-particle commutators happen to vanish.     

Quantum Mechanical Virial Theorem in Systems with Translational and Rotational Symmetry

Generalized virial theorem for quantum mechanical nonrelativistic and relativistic systems with translational and rotational symmetry is derived in the form of the commutator between the generator of dilations G and the Hamiltonian H. If the conditions of translational and rotational symmetry together with the additional conditions of the theorem are satisfied, the matrix elements of the commutator [G,H] are equal to zero on the subspace of the Hilbert space. Normalized simultaneous eigenvectors of the particular set of commuting operators which contains H, J ², J _z and additional operators form an orthonormal basis in this subspace. It is expected that the theorem is relevant for a large number of quantum mechanical N-particle systems with translational and rotational symmetry.     

Kinematic effective charges in photonuclear reactions

It is shown that the Gartenhaus-Schwartz-transformation of the electric multipole operator Ω^[L], i.e. expressing it in lab frame coordinates, not only leads to the well known concept of kinematic effective charges but in addition gives 2-, 3-,...,N-particle operator contributions whereN=min(A, L). In particular forE2 transitions the electric quadrupole operator contains one- and two-particle operators which contribute to the single particle transition rate and which will lead to two particle transitions.     

A new mass measurement of29Mg. Observation of excited states via the13C(18O,2p)29Mg reaction

A direct measurement of the mass of the neutron rich nucleus²⁹Mg has been performed via the¹³C(¹⁸O,2p)²⁹Mg reaction. Excitation energies in²⁹Mg are also deduced from the 2p-particle spectra, and compared with theory.     

Sensitivity in the trajectory of long-range α-particle

The factors influencing the trajectory of long-range ??-particle in the cold ternary fission of ²⁵²Cf are discussed. The trajectory of the ??-particle is studied by considering the influence of the force on the ??-particle due to Coulomb and proximity potentials and is found to have sensitive dependence on the initial position and initial energy of the ??-particle. The sensitivity to initial conditions signifies the presence of deterministic chaos which is characterized by Lyapunov exponent (LE). The LE is calculated using Wolf??s algorithm and found positive which implies that the objectives of trajectory calculations are restricted.     

Messung der Elektronendriftgeschwindigkeit in N2 imE/p-Bereich von 0,05 bis 40 Volt/cm Torr (Funkenkammerverfahren)

A special spark chamber technique was used to measure drift velocities of electrons for N₂ over anE/p-range from 0.05 to 40 volts/cm·Torr. The inaccuracy is smaller than 5% in the mediumE/p-range and increases to 10% at the ends of the region. This method uses a single α-particle traversing a parallel plate gap. The α-particle triggers by a photomultiplier a high voltage pulse which initiates an avalanche discharge. By varying the delay time after which the high voltage pulse is triggered one deduces from the height of the avalanche discharge the time necessary for the electrons to cross the gap and thus the drift velocity.     

Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent

The quantal system of Bose particles described by the non-linear Schrödinger equation i?φ/?t = -$\text{1}\text{2}$?²φ/?x² + cφ1φ², with c= cxf∞ and via the ground state with finite particle density, is the 1- dimensional gas of impenetrable bosons studied by M. Girardeau, T.D. Schultz, A. Lenard, H.G. Vaidya and C.A. Tracy. We show that the 2-point (resp. 2n-point) function, or the 1-particle (resp. n-particle) reduced density matrix, of this system satisfies a non-linear differential equation (resp. a system of non-linear partial differential equations) of Painlevé type. Derivation of these equations is based on the link between field operators in a Clifford group and monodromy preserving deformation theory, which was previously established and applied to the 2-dimensional Ising model and other problems. Several related topics are also discussed.     

On the small and largep ⊥ behavior of hadronic processes. A new wave-particle duality?

A general Ansatz for the transverse momentum distributions of exclusiven-particle production cross-sections is discussed which is shown to be in qualitative agreement with the present trend of high energy data. In particular, the Ansatz is tailored to account for the small and largep _⊥ behavior of the single inclusive cross-section and it is then used to calculate all the physical quantities of interest in order to restrict their arbitraryness. It is also pointed out that the trend of hadronic reactions is suggestive of a new form of high energy wave-particle duality which discriminates between the low and largep _⊥ domains.     

Polarization of α-clusters in light nuclei?

The α-particle model of Brink is extended to allow for non-spherical clusters. This is done by admixingp-functions to thes-single particle states which represent, in the usual version of the model, the nucleons in a cluster. The results in the nuclei⁸Be,¹²C,¹⁶O, and²⁰Ne indicate that the spherical clusters represent the stable configurations.     

The Galilean and translationally invariant operator algebra describing nuclei

The deviation of the commutation relations of the Galilean and translationally invariant field operators (given in part I) from the exact Fermi commutation relations is investigated. For this purpose the invariant field operators are integrated with one-particle functions describing a compactn-particle system of nucleons and its low excitations. With this assumption an approximate expression for the (subtractive) deviation of both commutation rules from one another is given. It is carefully estimated that the exact deviation, taken in the operator norm, is of ordern ^?2/3. It is shown that the degree of compactness of nuclear matter in the phase space plays an essential role in the determination of this estimate.     

Unitary group decomposition of Hamiltonian operators. I. Structure and sizes in the Hartree-Fock basis

The extent to which the Hartree-Fock (HF) procedure converts a two-body interaction into an effective one-body operator has been studied. For this purpose, the nuclear Hamiltonian is classified according to its tensor properties under the unitary group U(N) and its direct-sum subgroup U(m) + U(N ? m) generated by the Hartree-Fock procedure. Here N is the total number of HF single particle states of which m are occupied. The sizes of different tensor parts in m-particle spaces have been determined for both U(N) and U(m) + U(N ? m). In terms of these sizes a ratio is defined which provides a measure of the conversion efficiency of HF and a global measure of the goodness of HF s.p. basis. This ratio is evaluated for N = Z even-even nuclei in 0d-1s shell and 0f-1p shell using realistic Hamiltonian operators.     

Integral equations for the scattering of N identical particles

Integral equations are obtained for the scattering of N identical particles using a form of the N-particle scattering equations derived previously. The equations couple together only transition operators between physical two cluster channels, the breakup amplitudes being expressed in terms of quadratures over two-cluster amplitudes. The kernel of the equations becomes connected after a single iteration. The number of coupled equations for identical particles is $\text{1}\text{2}\text{N}\text{or}\text{1}\text{2}\text{(N?1)}$ when N is even or odd respectively.     

Algebraic solution of the Hubbard model on the infinite interval

We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the infinite line at zero density. This enables us to diagonalize the Hamiltonian algebraically. The eigenstates can be classified as scattering states of particles, bound pairs of particles and bound states of pairs. We obtain the corresponding creation and annihilation operators and calculate the S-matrix. The Hamiltonian on the infinite line is invariant under the Yangian quantum group Y(su(2)). We show that the n-particle scattering states transform like n-fold tensor products of fundamental representations of Y(su(2) ) and that the bound states are Yangian singlet.     

Testing QCD trough inclusiveJ/ψ-production ine +e− annihilations

We study the cubic Schrödinger model for attractive coupling. Using the quantized version of the Zakharov-Shabat eigenvalue problem we define operators, which create the eigenstates of the corresponding quantum field theoretical Hamiltonian. In particular, we construct the well-knownn-particle bound states of this model.     

Dunkl operator,integrability, and pairwise scattering in rational Calogero model

The integrability of the Calogero model can be expressed as zero curvature condition using Dunkl operators. The corresponding flat connections are non-local gauge transformations, which map the Calogero wave functions to symmetrized wave functions of the set of N free particles, i.e. it relates the corresponding scattering matrices to each other. The integrability of the Calogero model implies that any k-particle scattering is reduced to successive pairwise scatterings. The consistency condition of this requirement is expressed by the analog of the Yang–Baxter relation.