Comparison of several equivalent local potentials for microscopic nonlocal Nα potentials

The phase shifts obtained in the Perey-Saxon, Horiuchi and Peierls-Vinh Mau approximations for the microscopic nonlocal Nα interaction of Lassaut and Vinh Mau have been compared at 10 and 20 MeV to the exact results, without the customary approximation of Perey and Buck, which neglects part of the angular dependence of the nonlocality and is inadequate. We have also compared the equivalent local potentials with the corresponding local wave functions and damping factors to their exact wronskian counterparts and obtained the corresponding nonlocal wave functions as a product of the approximate local wave function and the damping factor in all cases. The results show that of all the approximations the Peierls-Vinh Mau approximation is the most accurate one for s-waves and that the Perey-Saxon approximation is inadequate for Nα scattering. The accuracy of all the approximations is dependent on the degree of repulsiveness of the effective nuclear force. For the exact wronskian equivalent local potential and damping factor however, we reproduce the exact nonlocal wave function to high accuracy in all cases, confirming the accuracy of our numerical methods. The implications for nuclear reactions where the off-shell behaviour of the Nα interaction is important are discussed.     

Hartree-Fock calculations for finite nuclei with equivalent nonlocal potentials

The method of constructing equivalent regular two-body potentials by a unitary transformation of the two-body Hamiltonian has been generalized to spin-parity dependent nuclear potentials containing tensor- and spin-orbit terms. Starting from the Gammel-Christian-Thaler potential, which includes tensor forces, we obtained a class of equivalent regular, but nonlocal potentials depending on a parameterλ — the range of nonlocality. — These potentials have been used in a Hartree-Fock calculation for the closed-shell nuclei He⁴, C¹², O¹⁶, Si²⁸, S³², Ca⁴⁰. The calculated binding energies show a slowλ-variation with a minimum in the region of 0.7 f. The nuclear radii decrease with increasingλ and are in general too small. The sequence of single particle levels of the nuclei with closedl- shells is in agreement with that obtained with the usual nuclear shell model potential including spin-orbit coupling.     

Phase transition for Ising frustration potentials

A frustration potential is a sum of interactions the terms of which are not simultaneously minimized even in the ground-state spin configurations. Ising models with such potentials can be discussed by the use of contours. The Peierls condition for the phase transition can be properly generalized, taking into account the presence of zero-energy contours. Frustration has some special features in two dimensions, which we study in detail. The connection with models of spin-glasses is discussed.     

Decoupling potentials for the three-body final state Schrödinger equation of knockout reactions

In the conventional distorted wave impulse approximation (DWIA) approach the three-body final state of a knockout reaction is decoupled by assuming a plane wave form for the coupling term. The influence of this decoupling approximation on the analyses of cluster knockout reactions has been investigated for a test case where the exact solution is obtainable. A proper treatment of the coupling term causes large oscillations in the effective distorting optical potentials for the decoupled Schrödinger equation. These decoupling potentials depend strongly not only on the partial wave angular momentum,l but also on their azimuthal projection,m.     

Effective pair potentials in fluids in the presence of three-body forces

The physical properties of a fluid in which there is only a two-body potential, u_αβ , can be expressed in terms of the total correlation function, h ₁₂, which is a sum of all connected graphs with root-points on molecules 1 and 2, whose links are f bonds, where f_αβ = exp (-u_αβ/κT) - 1. It is shown that the total correlation function in the presence of a weak three-body potential, u_αβγ , is h ₁₂*, where h ₁₂* is the sum of all two-body connected graphs in which each f bond is replaced in turn by an f* bond, where

and where ? is a sub-set of the elementary graphs each of which contains one f_αβγ link. We call this sub-set the line-irreducible graphs, and its leading term is a graph discussed by Rushbrooke and Silbert.

The three-body potential is set equal to the dipole-dipole-dipole potential of Axilrod and Teller, and the analytic properties and numerical values of the first term ?₁ examined in detail.

Other effective potentials have been defined and the relations between them are elucidated. In particular it is shown that the first term in ? cannot be used to obtain the effective link f* at liquid densities, but that it can be compared with the dependence on density of the effective potential u* obtained by Mikolaj and Pings from the x-ray diffraction of compressed argon.     

Local potentials phase equivalent to separable two-nucleon interactions

Local energy-dependent potentials have been constructed phase equivalent to members of a family of phase-equivalent separable two-nucleon potentials in the¹ S ₀-state. It has been shown that these potentials obey the known off-shell constraints in the¹ S ₀-state and can therefore not be regarded as unrealistic in this sense. They have the same shape as the energy-independent local Kermode potentials. However we also find that the off-shell behaviour of a separable¹ S ₀ potential and its local equivalent can differ considerably.     

Some properties of bound states in the three-body problem with separable potentials

A system of three identical bosons with the pair separable S-interaction is considered. The monotonic (Yamaguchi potential) and oscillating pair potentials for the three-alpha model of¹²C have been investigated. In the case of the Yamaguchi potential many excited states (second, third, etc.) have been found.The author is thankful to Prof. V. G. Neudatchin and Prof. Yu. F. Smirnov for valuable discussions on the problems concerned.     

The structure of 4He and phase-shift equivalent potentials

The Hartree-Fock and Brueckner theories are applied to the nucleus ⁴He. A truncated finite space of single-particle oscillator states is used, and different choices of the particle spectrum in Brueckner theory are considered. Results for the total binding energies and wound integrals are presented for the Reid soft-core potential and sets of phase-shift equivalent potentials generated from the Reid potential by a rank-one unitary transformation. The relation of the results to the position of the Emery singularities is investigated.     

Effective pair potentials in fluids in the presence of three-body forces. II

Earlier calculations are extended to the second order in density thus providing the non-additive contributions to the fourth virial coefficient in the presence of a weak three-body force given by the triple-dipole dispersion potential of Axilrod and Teller. We compare the Percus-Yevick approximations of Rushbrooke and Silbert and of Rowlinson at the level of the fourth virial coefficient and find that the former is more accurate. We also compare our calculations of the effective pair potential of liquid argon with the results of Mikolaj and Pings obtained from X-ray diffraction measurements.     

Deformed nuclear halos

Deformation properties of weakly bound nuclei are discussed in the deformed single-particle model. It is demonstrated that in the limit of a very small binding energy the valence particles in specific orbitals, characterized by a very small projection of single-particle angular momentum onto the symmetry axis of a nucleus, can give rise to the halo structure which is completely decoupled from the rest of the system. The quadrupole deformation of the resulting halo is completely determined by the intrinsic structure of a weakly bound orbital, irrespective of the shape of the core.     

Phase separation in one-dimensional hard-core boson system with two- and three-body interactions

We investigate the ground state phase diagram of hard-core boson system with repulsive two-body and attractive three-body interactions in one-dimensional optical lattice. When these two interactions are comparable and increasing the hopping rate, physically intuitive analysis indicates that there exists a phase separation region between the solid phase with charge density wave order and superfluid phase. We identify these phases and phase transitions by numerically analyzing the density distribution, structure factor of density-density correlation function, three-body correlation function and von Neumann entropy estimator obtained by density matrix renormalization group method. These phases and phase transitions are expected to be observed in the ultra-cold polar molecule experiments by properly tuning interaction parameters as suggested in Methods by Büchler et al. [Nat. Phys. 3, 726 (2007)], which is constructive to understand the physics of ubiquitous insulating-superconducting phase transitions in condensed matter systems.     

Neutron halos in hypernuclei

Properties of single- Λ and double- Λ hypernuclei for even-N Ca isotopes ranging from the proton dripline to the neutron dripline are studied using the relativistic continuum Hartree-Bogoliubov theory with a zero-range pairing interaction. Compared with ordinary nuclei, the addition of one or two Λ-hyperons lowers the Fermi level. The predicted neutron dripline nuclei are, respectively, ⁷⁵ _ΛCa and ⁷⁶ _2ΛCa, as the additional attractive force provided by the Λ-N interaction shifts nuclei from outside to inside the dripline. Therefore, the last bound hypernuclei have two more neutrons than the corresponding ordinary nuclei. Based on the analysis of two-neutron separation energies, neutron single-particle energy levels, the contribution of continuum and nucleon density distribution, giant halo phenomena due to the pairing correlation, and the contribution from the continuum are suggested to exist in Ca hypernuclei similar to those that appear in ordinary Ca isotopes. Received: 21 October 2002 / Accepted: 11 January 2003 / Published online: 8 April 2003     

Phase diagram of the alternating-spin Heisenberg chain with extra isotropic three-body exchange interactions

For the time being isotropic three-body exchange interactions are scarcely explored and mostly used as a tool for constructing various exactly solvable one-dimensional models, although, generally speaking, such competing terms in generic Heisenberg spin systems can be expected to support specific quantum effects and phases. The Heisenberg chain constructed from alternating S = 1 and σ = 1/2 site spins defines a realistic prototype model admitting extra three-body exchange terms. Based on numerical density-matrix renormalization group (DMRG) and exact diagonalization (ED) calculations, we demonstrate that the additional isotropic three-body terms stabilize a variety of partially-polarized states as well as two specific non-magnetic states including a critical spin-liquid phase controlled by two Gaussinal conformal theories as well as a critical nematic-like phase characterized by dominant quadrupolar S-spin fluctuations. Most of the established effects are related to some specific features of the three-body interaction such as the promotion of local collinear spin configurations and the enhanced tendency towards nearest-neighbor clustering of the spins. It may be expected that most of the predicted effects of the isotropic three-body interaction persist in higher space dimensions.     

Universal three-body physics for fermionic dipoles

Our present study of the universal physics for three oriented fermionic dipoles in the hyperspherical adiabatic representation predicts a single long-lived three-dipole state, which exists in only one three-body symmetry and forms near a two-dipole resonance. Our analysis reveals the spatial configuration of the universal state and the scaling of its binding energy and lifetime with the strength of the dipolar interaction. In addition, three-body recombination of fermionic dipoles is found to be important even at ultracold energies. An additional finding is that an effective long-range repulsion arises between a dipole and a dipolar dimer that is tunable via dipolar interactions.     

Axion condensate as a model for dark matter halos

Localized solutions of an axion-like scalar model with a periodic self-interaction are analyzed as a model of dark matter halos. It is shown that such a cold Bose–Einstein type condensate can provide a substantial contribution to the observed rotations curves of galaxies, as well provide a soliton type interpretation of the dark matter ‘bullets’ observed via gravitational lensing in merging clusters.     

A unitary model for three-body collisions

A connected 3 → 3 formalism for three-body collision processes is reduced to a hierarchy of three on-energy-shell integral equations and one off-energy-shell integral equation. Only the on-energy-shell equations, which involve only on-energy-shell three-body and two-body amplitudes, need be solved exactly in order to obtain elastic and break-up amplitudes satisfying the unitarity constraints exactly. Applied to n-d break-up, the on-energy-shell equations ensure that the n-d initial-state interaction, the nucleon-nucleon final-state interactions, and more complicated 3 → 3 processes are correctly described. After angular momentum analysis the on-energy-shell equations are one-dimensional integral equations, even in the case of local two-body potentials. This unitary model provides a practical scheme for calculating approximate three-body elastic and break-up amplitudes when two-body local potentials are used to describe the two-body subsystems.