Structure of light unstable nuclei in continuum energies

The Coulomb breakup reaction of ⁶He into a ⁴He+n+n 3-body system is analyzed by applying the complex scaling method (CSM). We can derive the contributions to El and E2 transitions, not only from resonances, but also 2- and 3-body continuum states, which show the characteristic structure of the many-body unbound states in ⁶He.     

Irreducible U(3) tensor interactions in the symplectic collective model

The potential V(β, γ) of the Bohr-Mottelson and symplectic collective models is expressed as a linear combination of U(3) irreducible tensor operators in the symplectic enveloping algebra. This many-body collective potential is then projected onto the symplectic two-body tensor operators. The projected two-body potential is shown to give results similar to the many-body potential in ²⁰Ne. Hence, in the symplectic shell model, one has obtained a collective model with two-body forces.     

Boson-like quantum dynamics of association in ultracold Fermi gases

We study the collective association dynamics of a cold Fermi gas of 2N atoms in M atomic modes into a single molecular bosonic mode. When the atomic translational motion is slow compared to the atom-molecule conversion rate, the many-body fermionic problem for 2^M amplitudes is effectively reduced to a dynamical system of min{N, M} + 1 amplitudes, making the solution no more complex than the solution of a two-mode Bose-Einstein condensate and allowing realistic calculations with up to 10⁴ particles. The many-body dynamics is shown to be formally similar to the dynamics of the bosonic system under the mapping of boson particles to fermion holes, producing collective enhancement effects due to many-particle constructive interference.     

Accurate ab initio-based DMBE potential energy surface for HLi2(X 2A′) via scaling of the external correlation

A globally accurate potential energy surface is reported for the electronic ground-state HLi₂ by fitting ab initio energies to double many-body expansion formalism. The total 3726 ab initio energies used to map the HLi₂ potential energy surface are calculated using the multi-reference configuration interaction method, with their dynamical correlation being semiempirically corrected by the double many-body expansion-scaled external correlation method. The current potential energy surface generates an excellent fit of the ab initio energies, showing a small root-mean squared derivation of 0.636 ? kcal ? mol^-1. The topographical features of the HLi₂ potential energy surface are examined in detail, which concludes that the H + Li₂(X ? ¹ Σ _g ) → Li + LiH(X ? ¹ Σ) reaction is essentially barrierless and the exothermicity is calculated to be 33.668 ? kcal ? mol^-1, thus corroborates the available experimental and theoretical results.     

Schrödinger operators with symmetries

We consider the stationary Schrödinger operator H of a many-body system M with two-body rotation invariant interactions. The operator H is reduced with respect to the symmetries of permutation of identical particles, rotations and reflections, into a direct sum of operators H^τ̃, where τ̃ is an index of the irreducible representations of the symmetry group of the system.The spectra of the operators H^τ̃ were investigated in a series of papers of G.M. Zislin and A.G. Sigalov ([20], [21], [31]-[35]). In a recent paper [3] we have developed the spectral theory of these operators on the basis of the Weinberg equations.In the present work we complete and simplify this theory. In particular we treat in detail the case where the given system can be decomposed into two identical subsystems. For such systems there is a certain coupling between permutation and rotation-reflection symmetries, because a permutation, which interchanges the two subsystems, imposes a reflection on the relative position vector of the two centers of mass. This requires a modification of the theorem on essential spectrum as formulated in [3] in the case where such a division is not possible. The importance of this special case, as exemplified by diatomic molecules, fully justifies such a detailed treatment.This special case was treated by Zislin [34] under the assumption that the interactions are essentially multiplicative, relatively compact two-body interactions. Our method allows for general relatively compact two-body interactions, and can without difficulty be generalized to many-body interactions.Moreover, the method based on the Weinberg equation is suitable for a further analysis of the spectra of these operators.     

Correlations in charged bosons

A new chain diagram formula is derived for many-body systems in such a way that an ideal gas term does not explicitly appear. This form is simpler and more convenient than the previously known expression. The result is applied to a charged boson gas under different conditions. It is found that exponential type decrease of the correlations for large distances changes into 1/r⁸ type decrease at the transition point.     

Ab initio theory and calculations of X-ray spectra

There has been dramatic progress in recent years both in the calculation and interpretation of various x-ray spectroscopies. However, current theoretical calculations often use a number of simplified models to account for many-body effects, in lieu of first principles calculations. In an effort to overcome these limitations we describe in this article a number of recent advances in theory and in theoretical codes which offer the prospect of parameter free calculations that include the dominant many-body effects. These advances are based on ab initio calculations of the dielectric and vibrational response of a system. Calculations of the dielectric function over a broad spectrum yield system dependent self-energies and mean-free paths, as well as intrinsic losses due to multi-electron excitations. Calculations of the dynamical matrix yield vibrational damping in terms of multiple-scattering Debye–Waller factors. Our ab initio methods for determining these many-body effects have led to new, improved, and broadly applicable x-ray and electron spectroscopy codes. To cite this article: J.J. Rehr et al., C. R. Physique 10 (2009).     

N identical particles under quantum confinement: a many-body dimensional perturbation theory approach

Systems that involve N identical interacting particles under quantum confinement appear throughout many areas of physics, including chemical, condensed matter, and atomic physics. In this paper, we present the methods of dimensional perturbation theory, a powerful set of tools that uses symmetry to yield simple results for studying such many-body systems. We present a detailed discussion of the dimensional continuation of the N-particle Schrödinger equation, the spatial dimension D→∞ equilibrium (D⁰) structure, and the normal-mode (D⁻¹) structure. We use the FG matrix method to derive general, analytical expressions for the many-body normal-mode vibrational frequencies, and we give specific analytical results for three confined N-body quantum systems: the N-electron atom, N-electron quantum dot, and N-atom inhomogeneous Bose-Einstein condensate with a repulsive hard-core potential.     

The structure of the resonating group equation

The general structure of the Hamilton kernel $\text{H}{}_{\mathrm{\Omega }}$ of the resonating group method (RGM) equation is derived in the oscillator model. The many-body states Ψ_v corresponding to the redundant states are explicitly constructed for the example α-¹⁶O. Their energies E_v enter into the non-local part of $\text{H}{}_{\mathrm{\Omega }}$ which is of a very simple structure. For α- ¹⁶ only one of the energies E_v is positive. The corresponding state (PEB) has a finite width which is calculated for a model Hamilton kernel. This state must not be counted in the Levinson theorem. The quantitative connection of the Pauli-repulsion and its energy dependence to the redundant states and the energies E_v is given.     

Dynamic 13C NMR spectroscopy

Dynamic ¹³C NMR spectroscopy is a recent addition to the tools available to chemists to investigate dynamic processes in molecules. The ¹³C spectra are not complicated by coupling and separation of the signals is the order of five times as large (in Hz). Consequently the temperature range over which meaningful measurements can be obtained is increased. There is therefore a marked increase in the dynamic range and accuracy of the measurements. Both very slow processes, e.g. 0.017 s^?1 for N,N-dimethylformamide and very fast processes, e.g. ΔG³ = 17.6 kJ mol^?1 for cycloocta-1,3,5-triene can be examined. In addition the technique is becoming very important in observing dynamic processes in metal carbonyls.     

Subthreshold and near-threshold K +-meson photoproduction on nuclei

The inclusive K ⁺-meson production in photon-induced reactions in the near-threshold and subthreshold energy regimes is analyzed for the one-step (γN → K ⁺ Y, Y=Λ, Σ) incoherent production processes on the basis of an appropriate new folding model that takes properly into account the struck-target nucleonremoval energy and the internal momentum distribution (nucleon spectral function), extracted from recent quasielastic-electron-scattering experiments and from many-body calculations based on realistic models of NN interaction. Simple parametrizations of the total and differential cross sections for K ⁺ production in photon-nucleon collisions are presented. A comparison of the model calculations of the K ⁺ differential cross sections for γ¹²C interactions in the threshold region with existing experimental data is given, which displays the contributions to K ⁺ production at considered incident energies from the use of the single-particle part, as well as high momentum and high removal energy part, of the nucleon spectral function. Detailed predictions for the K ⁺ total and differential cross sections for γ²H, γ¹²C, and γ²⁰⁸Pb interactions at subthreshold and near-threshold energies are provided. The effect of the uncertainties in the elementary K ⁺-production cross sections on the K ⁺ yield is explored.     

Microscopic multichannel calculation of the molecular dipole degree of freedom in the18O nucleus

StrongB(E1) transitions have been recently observed between states in the¹⁸O nucleus which follow roughly the energy sequence of a dimolecular α+¹⁴C rotator. These findings have been interpreted by Gai et al. as evidence for a molecular dipole degree of freedom being present in the¹⁸O nucleus. However, this idea was contradicted by the results of a microscopic multichannel calculation performed by Descouvemont and Baye which was based on elastic α+¹⁴C and inelastic α+¹⁴C(2⁺) many-body cluster wave functions. We have improved this study by performing a microscopic multichannel calculation including additionally an+¹⁷O many-body fragmentation in order to enlarge our model space by those shell model components which dominate the structure of the (positive parity)¹⁸O ground state band. Like Descouvemont and Baye we find a positive parity α+¹⁴C molecular band in¹⁸O and, additionally, a rather strong collectivity in the lowest 1^?, 3^? and 5^? states in¹⁸O. However, since the internal structure is different within these states, the calculated states should not be interpreted as a negative parity α+¹⁴C molecular band. In this perspective, the microscopic multichannel calculations do not support the hypothesis of a molecular dipole degree of freedom being present in the¹⁸O nucleus.     

Thermal helium clusters at 3.2 Kelvin in classical and semiclassical simulations

The thermodynamic stability of⁴He_4–13 at 3.2 K is investigated with the classical Monte Carlo method, with the semiclassical path-integral Monte Carlo (PIMC) method, and with the semiclassical all-order many-body method. In the all-order many-body simulation the dipole-dipole approximation including short-range correction is used. The resulting stability plots are discussed and related to recent TOF experiments by Stephens and King. It is found that with classical Monte Carlo of course the characteristics of the measured mass spectrum cannot be resolved. With PIMC, switching on more and more quantum mechanics. by raising the number of virtual time steps results in more structure in the stability plot, but this did not lead to sufficient agreement with the TOF experiment. Only the all-order many-body method resolved the characteristic structures of the measured mass spectrum, including magic numbers. The result shows the influence of quantum statistics and quantum mechanics on the stability of small neutral helium clusters.     

Many-body field theoretic framework for inelastic pion-nucleus scattering

We consider inelastic scattering of pions from nuclei using many-body quantum field theory methods. We find that, in an inelastic amplitude for small energy transfer, one can separate out effects of particle-hole correlations in the final nuclear state. The ratio of π⁺ and π^? inelastic cross sections can differ substantially from the analogous ratio for free πN scattering.     

Calculation of the hyperfine structure of the 42 S 1/2, 42 P 1/2, 42 P 3/2 states in the 3d 10 nl configuration of Cu

The hyperfine structure of the 4² S _1/2, 4² P _1/2, 4² P _3/2 states in the 3d ¹⁰ nl configuration of Cu has been evaluated using many-body perturbation theory. Polarisation effects were included in all orders and correlation to third-order. By the use of iteration methods, a large number of higher order diagrams were also included. The correlation effects between the valence electron and the 3d shell were found to be very important. The results forA(² S _1/2) andA(² P _1/2) 5827MHz and 440 MHz, respectively, are in good agreement with the experimental results, whereas the result forA(² P _3/2)=83 MHz is far from the experimental value. No explanation was found for the discrepancy. The quadrupole values were found to be ?206 mb for⁶³Cu and ?185 mb for⁶⁵Cu.     

Four-Body CDCC Analysis for Breakup Reactions of Three-Body Projectiles

We present a new method of smoothing discrete breakup cross sections calculated by the continuum-discretized coupled-channels method based on the complex-scaling method. One of the advantages of this approach is to be applicable to many-body breakup reaction systems. In this work, we apply the new smoothing method to analyses of ¹²C(⁶He, nn ⁴He) and ²⁰⁸Pb(⁶He, nn ⁴He) reactions at 240 MeV/A.     

A study of many-body phenomena in metal nanoclusters (Au, Cu) close to their transition to the nonmetallic state

The results of a study of many-body phenomena in gold and copper nanoclusters are presented. The measured conductivity as a function of nanocluster height h was found to have a minimum at h ≈ 0.6 nm. Conductivity was local in character at nanocluster sizes l ≤ l _c ≈ 2.5 nm. Changes in core hole screening and an anomalous increase in the Anderson singularity index α in gold and copper nanoclusters could be caused by changes in permittivity from metallic (? → ∞) to nonmetallic (? ∝ l ²). The many-body phenomenon characteristics observed in the X-ray photoelectron and tunnel spectra of gold and copper nanoclusters as the size of the nanoclusters changed led us to suggest changes in the band structure of the nanoclusters and, therefore, their possible transition from the metallic to nonmetallic state.     

Alpha-like four-nucleon correlations in the ground state of 48Cr

The ground-state structure of ⁴⁸Cr is investigated by multiple α-like cluster model. The original model with only J = T = 0 α-like cluster is extended so as to deal with the contribution of J > 0 α-like units. The model reproduces the observed ground-state energy of ⁴⁸Cr well and explains the characteristic variation of the ground-state energies from ⁴⁴Ti to ⁴⁸Cr caused by many-body correlations. The properties of the ⁴⁸Cr ground state which originate in the α-like four-nucleon correlations are revealed by the model.