Study of the 3He(4He,γ)7Be and 3H(4He,γ)7Li Reactions in an Extended Two-Cluster Model

 The ³He(⁴He, γ)⁷Be and ³H(⁴He, γ)⁷Li reactions are studied in an extended two-cluster model which contains α + h/t and ⁶Li + p/n clusterizations. We show that the inclusion of the ⁶Li + p/n channels can significantly change the zero-energy reaction cross sections, S(0), and other properties of the ⁷Be and ⁷Li nuclei, like the quadrupole moments Q. However, the results agree with the known correlation trend between S(0) and Q. Moreover, we demonstrate that the value of the zero-energy derivatives of the astrophysical S-factors are more uncertain than currently believed. Received June 17, 1999; revised February 22, 2000; accepted for publication April 17, 2000     

Three-Body Calculation of the 4He（aH,γ）7Li and 4He（aHe,γ）7Be Reactions and Structure of the 7Li and 7Be at Solar Energies

The two 3H＋4He and 3He＋4He fusion reactions at low energies are usually viewed as an approximate external capture process. We study the 4He（3H,γ）rLi and 4He（SHe,γ）7Be reactions in a cluster model, which can take into account two- and three-body electromagnetic currents, using minimal substitution in the explicit momentum dependence of the two- and three-cluster interactions. Our main goal is to explore how the cross section of the low-energy 3H＋4He or 3He＋4He capture reactions depends on energy. The astrophysical S-factors for these reactions are calculated at very low energies. We construct the conserved realistic Argonne v18 for two nucleons and Urbana IX or Tucson-Melbourne three-cluster interactions, which are considered for calculation. We also calculate the binding energies and the structural properties of a Hq-4He or 3He＋4 He systems. The binding energies are found to be -37.72 （-36.32） MeV and -39.35 （-37.43） MeV, with （without） three-body interactions for 7Be and 7 Li, in satisfactory agreement with other theoretical results and experimental data, respectively.     

Nuclear vertex constants for the virtual decay <Superscript>7</Superscript>Be → <Superscript>3</Superscript>He + <Superscript>4</Superscript>He of the 7Be bound states from a phase-shift analysis in the effective-range theory

The phase-shift-analysis data for the ³He⁴He scattering are analyzed using the effective-range theory, with the Coulomb interaction taken into account. We find both the renormalized nuclear vertex constants for the vertex ⁷Be → ³He + ⁴He in the ground (3/2⁻) and in the first excited (1/2⁻) bound states of ⁷Be, and the corresponding asymptotic normalization constants of the radial wave functions in these states. The results obtained can be used in an astrophysical S-factor calculation for radiative capture reaction ⁴He(³He, γ)⁷Be     

What is the physics behind the 3He–4He anomaly?

We show that coalescence of nucleons emitted prior to thermalization in highly excited nuclei can explain the anomaly of kinetic energies of helium clusters. A new coalescence algorithm has been included in the statistical approach to nuclear reactions formerly used to describe intermediate mass fragment production. Received: 24 September 1999 / Revised version: 22 November 1999     

Observation of anomalously fast diffusion in 3He–4He solid solutions near the BCC-HCP transition

The pulsed NMR technique was used to investigate diffusion on the BCC-HCP phase-equilibrium and melting curves of a dilute solution of ³He in ⁴He. The contributions from all coexisting phases were identified using the spin-echo method. It is established that, along with the contributions from the equilibrium BCC and HCP phases or from bulk liquid (in the melting curve measurements), there is an additional diffusional process that is characterized by an anomalously high diffusion coefficient. It is found that the latter is close to the diffusion coefficient in liquid helium, while the diffusion itself is spatially restricted. The observed effect may be caused by the formation of liquid droplets in the course of the BCC-HCP transition.     

The 3He(α, γ)7Be and 3He(α, γ)7Li reactions at astrophysical energies

The radiative capture cross sections for ³He(α, γ)⁷Be and ³He(α, γ)⁷Li at astrophysical energies have been studied microscopically in terms of the resonating group method. It was found that the astrophysical S-factors correlate strongly to the nuclear size and deformation of ⁷Be and ⁷Li. With the help of measured nuclear properties of these nuclei, a safety range of the absolute values of the S-factor was determined; the most recommended S(0)-values are 0.50 ± 0.03 keV · b for the ³He(α, γ)⁷Be reaction and 0.098 ± 0.006 keV · b for the ³H(α, γ)⁷Li reaction.     

Microscopic calculation of the 3He(α,γ)7Be and 3H(α,γ)7Li capture cross sections using realistic interactions

The radiative capture cross sections for the 3He(α,γ)7Be and 3H(α,γ)7Li reactions are calculated in the fully microscopic fermionic molecular dynamics approach using a realistic effective interaction that reproduces the nucleon-nucleon scattering data. At large distances bound and scattering states are described by antisymmetrized products of 4He and 3He/3H ground states. At short distances the many-body Hilbert space is extended with additional many-body wave functions needed to represent polarized clusters and shell-model-like configurations. Properties of the bound states are described well, as are the scattering phase shifts. The calculated S factor for the 3He(α,γ)7Be reaction agrees very well with recent experimental data in both absolute normalization and energy dependence. In the case of the 3H(α,γ)7Li reaction the calculated S factor is larger than available experimental data by about 15%.     

Production of high energy deuterons in the reaction:3He+3He→4He+2H+e ++v

Experiments on the reaction:³He+³He→⁴He+²He using a single four detector telescope have shown evidence for the production of deuteron pulses, consistent with the²He→²H+e⁺+v fusion reaction in the final state. New measurements on the same reaction using improved techniques viz.A) a windowless³He gas target andB) α- d correlation detection with 5 ns resolving time and antipileup circuitry have been performed. Calibrations were obtained from the⁷Li+³He→²H+⁴He+⁴He reaction spectra. The correlation angles were 30° and 97° for the alphas and deuterons respectively. Deuteron pulses have been observed, correlated with alpha particles. A cross section of (1.7 ±0.5)nbsr^?1MeV^?1 was obtained consistent with previous measurements using a single telescope.     

Influence of D-state in 4He on S Factor for the 2H（d, γ）^4He Reaction

We employ a direct capture method to study the influence of D-state in ^4He on S factor for the ^2H（d,γ）^4He reaction, in which the D-state component of the colliding deuterons and D-state component in ^4He ground state are considered. The parameters of Woods-Saxon （WS） potentials are obtained by reproducing the binding energy of d-d （i.e. ^2H-^2H） system, and d-d elastic scattering phase shifts calculated by the resonating group method. The theoretical results are in good agreement with the experimental data at Ec.m〈 3 MeV. The impact of the D state probability in ^4He on the extrapolated value of the astrophysical S factor for ^2H（d, γ）^4He reaction is discussed.     

The Formation Mechanism and Binding Energy for the Octahedral Central Structure of the He7^＋ Cluster

The formation mechanism for the octahedral central structure of the He7^ cluster is proposed and its total energy curve is calculated by the method of a modified arrangement channel quantum mechanics (MACQM). The energy is a function of separation R between two nuclei at the center and an apex of the octahedral central structure. The result of the calculation shows that the curve has a minimM energy -19.7296 a.u. at R = 2.40α0. The binding energy of He7^ with respect to He^ 6He was calculated to be 0.6437 a.u. This means that the duster of He7^ may be formed in the stable octahedral central structure with R=2.40 α0.     

Forward vertex detector upgrade for the PHENIX experiment at RHIC

A new forward vertex detector is under construction for the PHENIX experiment and will be installed in 2011. The device consists of two sets of four disks of silicon mini-strips and matches the acceptance of the existing muon detectors, and will provide precise vertex measurement for charged tracks. The forward vertex detector is designed to greatly enhance the heavy-flavor physics capabilities on PHENIX. The structure of the proposed device and its performance from Monte Carlo studies are presented.     

A covariant representation of the Ball–Chiu vertex

In nonabelian gauge theory the three-gluon vertex function contains important structural information, in particular on infrared divergences, and is also an essential ingredient in the Schwinger–Dyson equations. Much effort has gone into analyzing its general structure, and at the one-loop level also a number of explicit computations have been done, using various approaches. Here we use the string-inspired formalism to unify the calculations of the scalar, spinor and gluon loop contributions to the one-loop vertex, leading to an extremely compact representation in all cases. The vertex is computed fully off-shell and in dimensionally continued form, so that it can be used as a building block for higher-loop calculations. We find that the Bern–Kosower loop replacement rules, originally derived for the on-shell case, hold off-shell as well. We explain the relation of the structure of this representation to the low-energy effective action, and establish the precise connection with the standard Ball–Chiu decomposition of the vertex. This allows us also to predict that the vanishing of the completely antisymmetric coefficient function S   of this decomposition is not a one-loop accident, but persists at higher-loop orders. The sum rule found by Binger and Brodsky, which leads to the vanishing of the one-loop vertex in N=4$N=4$ SYM theory, in the present approach relates to worldline supersymmetry.     

T invariance and polarization effects in the reactions p+3He → π++4He and π++4He → p+3He

On the basis of T invariance, it is established that the dependence of the effective cross section for a binary reaction of the a+b → c+d type on the polarization vectors of primary particles a and b determines completely the polarization vectors and spin correlations for the same particles in the inverse reaction c+d → a+b induced by collisions between unpolarized primary particles c and d. By using the formalism of helicity amplitudes, polarization effects are studied in the process p+³He → π⁺+⁴He and in the inverse process π⁺+⁴He → p+³He. It is shown that, in the reaction π⁺+⁴He → p+³He, the spins of the final-state particles (proton and ³He nucleus) are strongly correlated. An expression for the correlation tensor is obtained for arbitrary values of the (p, ³He) emission angle.     

Model-independent result for the imaginary part of forward πHe4 scattering amplitude in unphysical region

Evaluation of contributions from dispersion integrals to the real part of forwardHe⁴ scattering amplitude is reconsidered. By application of a generalized mean-value theorem to the dispersion integral from the lowest branch point to the elastic threshold, a model-independent conclusion on the imaginary part of forwardHe⁴ scattering amplitude in unphysical region is drawn.     

Light-scattering studies of the dynamical behaviour of liquid 4He close to the λ-line

The paper begins with a review of experiments carried out by the present authors and their collaborators to determine by light scattering the dynamic structure factor of liquid ⁴He at temperatures close to the superfluid transition. This review includes details of the experimental techniques and reports a number of new sets of experimental results ; it concentrates particularly on the low-frequency part of the dynamic structure factor (the second-sound Brillouin doublet and the Rayleigh line), and the results cover both the hydrodynamic and the critical regimes for one particular value of the wave-vector. A comparison is made with the results of other authors, particularly those of Greytak and his collaborators. Following this presentation of the experimental data, an attempt is made to describe the dynamical behaviour of helium near the superfluid transition in terms of simple physical pictures, and then to use these pictures as the basis of simple calculations. The results often seem to agree surprisingly well with experiment, although the agreement may well be fortuitous; this part of the paper is frankly speculative and ought not to be taken too seriously. Comparison is made with the results of rigorous theoretical work, including recent attempts to apply the techniques of the renormalization group ; although these latter attempts have led to a degree of success, some of the results obtained seem to be in serious disagreement with experiment.     

Nuclear vertex constants and asymptotic normalization coefficients for 8Be resonance states from effective-range expansions for αα scattering

The properties of the first excited state of the ⁸Be* nucleus (2⁺) are studied. This state corresponds to the resonance in αα scattering at the energy of E _α = E ₂ ≈ 3 MeV. Use is made of an expansion of the effective-range function K(k ²). The function K(k ²) is sensitive to the value of E ₂. A fit to experimental data on the dependence of the Coulomb-nuclear phase shift δ ₂ ^C on the energy E _α leads to an E ₂ value that is smaller than the average value obtained from an analysis of various reactions. The experimental behavior of δ ₂ ^C (E _α) cannot be described satisfactorily by fixing the average value of E ₂. The renormalized nuclear vertex function for the process α + α → ⁸Be*(2+) and the asymptotic normalization coefficient for the respectiveGamow wave function are calculated by using the set of parameter values found in the present study.