Brueckner G matrix for a planar slab of nuclear matter

The equation for the Brueckner G matrix is investigated for planar-slab geometry. A method for calculating the G matrix for a planar slab of nuclear matter is developed for a separable form of NN interaction. Actually, the separable version of the Paris NN potential is used. The singlet ¹ S ₀ and the triplet ³ S ₁–³ D ₁ channel are considered. The present analysis relies on the mixed momentum-coordinate representation, where use is made of the momentum representation in the slab plane and of the coordinate representation in the orthogonal direction. The full two-particle Hilbert space is broken down into the model subspace, where the two-particle propagator is considered exactly, and the complementary subspace, where the local-potential approximation is used, which was proposed previously for calculating the effective pairing potential. Specific calculations are performed for the case where the model subspace is constructed on the basis of negative-energy single-particle states. The G matrix is parametrically dependent on the total two-particle energy E and the total momentum P _⊥ in the slab plane. Since the G matrix is assumed to be further used to calculate the Landau-Migdal amplitude, the total two-particle energy is fixed at the value E=2μ, where μ is the chemical potential of the system under investigation. The calculations are performed predominantly for P _⊥=0. The role of nonzero values of P _⊥ is assessed. The resulting G matrix is found to depend greatly on μ in the surface region.     

Simple microscopic model for the scalar-isoscalar component of the Landau-Migdal amplitude

A simple microscopic model is proposed that describes the coordinate dependence of the zeroth harmonic f ₀(r) of the scalar-isoscalar component of the Landau-Migdal amplitude. In the theory of finite Fermi systems due to Migdal, such a dependence was introduced phenomenologically. The model presented in this study is based on a previous analysis of the Brueckner G matrix for a planar slab of nuclear matter; it expresses the function f ₀(r) in terms of the off-mass-shell T matrix for free nucleon-nucleon scattering. The result involves the T matrix taken at the negative energy value equal to the doubled chemical potential μ of the nucleus being considered. The amplitude f ₀(r) found in this way is substituted into the condition that, in the theory of finite Fermi systems, ensures consistency of the self-energy operator, effective quasiparticle interaction, and the density distribution. The calculated isoscalar component of the mean nuclear field V(r) agrees fairly well with a phenomenological nuclear potential. Owing to a strong E dependence of the T matrix at low energies, the potential-well depth V(0) depends sharply on μ, increasing as |μ| is reduced. This effect must additionally stabilize nuclei near the nucleon drip line, where μ vanishes.     

Spin and spin-isospin polarized nuclear matter

Properties of (N = Z) nuclear matter are investigated through a Brueckner method using the Paris potential for two special configurations, one when all spins are pointing in the same direction, the other when neutron spins are pointing upward and proton spins downward. The results of the calculations are used to evaluate the energy of the isoscalar giant spin dipole vibrations and the value of the spin-spin part of the nucleon-nucleus optical-model potential.     

Local-potential approximation for the Brueckner G matrix and problem of optimally choosing model subspace

The validity of the local-potential approximation, which was proposed previously for the singlet-pairing problem in semi-infinite nuclear matter, is investigated in the Bethe-Goldstone equation for the Brueckner G matrix. For this purpose, use is made of the method developed earlier for solving this equation for a planar slab of nuclear matter in the case of a separable form of NN interaction. The ¹ S ₀ singlet and the ³ S ₁+³ D ₁ triplet channel are considered. The complete two-particle Hilbert space is split into a model and the complementary subspace that are separated by an energy E ₀. The two-particle propagator is calculated precisely in the first subspace, and the local-potential approximation is used in the second subspace. With an eye to subsequently employing the G matrix to calculate the Landau-Migdal amplitude, the total two-particle energy is fixed at E=2μ, where μ is the chemical potential of the system under consideration. Specific numerical calculations are performed at μ=?8 MeV. The applicability of the local-potential approximation is investigated versus the cutoff energy E ₀. It is shown that, in either channel being considered, the accuracy of the local-potential approximation is rather high for E ₀≥10 MeV.     

Symmetry energy,unstable nuclei and neutron star crusts

We present an upgraded review of our microscopic investigation on the single-particle properties and the EOS of isospin asymmetric nuclear matter within the framework of the Brueckner theory extended to include a microscopic three-body force. We pay special attention to the discussion of the three-body force effect and the comparison of our results with the predictions by other ab initio approaches. Three-body force is shown to be necessary for reproducing the empirical saturation properties of symmetric nuclear matter within nonrelativistic microscopic frameworks, and also for extending the hole-line expansion to a wide density range. The three-body force effect on nuclear symmetry energy is repulsive, and it leads to a significant stiffening of the density dependence of symmetry energy at supra-saturation densities. Within the Brueckner approach, the three-body force affects the nucleon s.p. potentials primarily via its rearrangement contribution which is strongly repulsive and momentum-dependent at high densities and high momenta. Both the rearrangement contribution induced by the three-body force and the effect of ground-state correlations are crucial for predicting reliably the single-particle properties within the Brueckner framework.     

The energy of the spin-glass state of a binary mixture at T = 0 and its variational properties

In the random-bond model of Ising spins, the concept of a multiple-bond distribution of effective field was introduced in the pair approximation. The integral equation for a single-bond distribution was derived intuitively. The variational energy at T = 0 is expressed in terms of two parameters μ and η where μ is the probability of zero effective field in the single-bond distribution and η is the magnetization per spin. For η = 0, the energy of the spin-glass state corresponds to a local minimum as a function of μ, for an even z (number of the nearest neighbours) and to an inflection point for an odd z. It was shown that the spin-glass state corresponds to a local minimum with respect to μ and η for z = 4, to an inflection point with respect to μ and a local minimum with respect to η for z = 3. It is conjectured that the maximum of the energy of the spin-glass state of Sherrington and Kirkpatrick is attributed not to the replica method, but to the mean field approximation. Stationary properties of the energy as a function of both μ and η were examined in detail.     

On the Distribution of the Wave Function for Systems in Thermal Equilibrium

For a quantum system, a density matrix ρ that is not pure can arise, via averaging, from a distribution μ of its wave function, a normalized vector belonging to its Hilbert space ?. While ρ itself does not determine a unique μ, additional facts, such as that the system has come to thermal equilibrium, might. It is thus not unreasonable to ask, which μ, if any, corresponds to a given thermodynamic ensemble? To answer this question we construct, for any given density matrix ρ, a natural measure on the unit sphere in ?, denoted GAP(ρ). We do this using a suitable projection of the Gaussian measure on ? with covariance ρ. We establish some nice properties of GAP(ρ) and show that this measure arises naturally when considering macroscopic systems. In particular, we argue that it is the most appropriate choice for systems in thermal equilibrium, described by the canonical ensemble density matrix ρ_β = (1/Z) exp (?β H). GAP(ρ) may also be relevant to quantum chaos and to the stochastic evolution of open quantum systems, where distributions on ? are often used.     

Neutron matter properties in an extended Brueckner approach

Neutron matter properties are calculated both at zero and finite temperature within an extended Brueckner approach using the Paris potential. The binding energy turns out to be very close to the one calculated variationally with the Urbanav ₁₄ potential. Particular emphasis is put on the symmetry energy, on the isospin dependence of the mean field and on the effective mass. As an illustration, the masses of neutron stars are calculated.     

On the renormalization of the quantum field theory of point-like monopoles and charges

The quantum field theory of point-like monopoles and charges is first formulated on a euclidean lattice for a convenient regularization. The regularization preserves the peculiar features of the theory, namely those related to the invariance and to the quantization condition. The partition function is expressed as a path integral over the particle's closed paths and the action is constructed in terms of arbitrary surfaces having those paths as boundaries. The possible divergences of the continuum limit are discussed, in particular the vacuum polarization ones. It is found that, although both the electric charge Q and the magnetic charge G are renormalized as Q = Z_QQ_R and G = Z_GG_R, the quantization condition is preserved by the renormalization i.e. Z_QZ_G = 1 so that QG = Q_RG_R = 2πn. Due to the dual symmetry of the theory, then, for Q = G we get Z_Q = Z_G = 1.     

Approximation of the microscopic effective pairing interaction by the off-shell T matrix for free nucleon-nucleon scattering

The effective pairing interaction in the ¹ S ₀ channel as calculated microscopically within the Brueckner method for a planar slab of nuclear matter by using the separable version of the Paris nucleon-nucleon potential is investigated. The effective interaction is determined for the model space including all negative-energy single-particle states. An analysis is performed for two values of the chemical potential, μ=?8 and ?4 MeV. It is shown that, to a high precision, the effective interaction can be approximated by the off-shell T matrix for free nucleon-nucleon interaction, the T matrix in question being taken at a negative value of the total energy of two nucleons E=2μ.     

Reliable measurement of the FRET sensitized-quenching transition factor for FRET quantification in living cells

3-cube-based Förster resonance energy transfer (FRET) microscopy, a sensitized acceptor FRET quantification method, has been widely used to visualize dynamic protein–protein interaction in living cells. Determining the FRET sensitized-quenching transition factor (G factor) of a particular donor-acceptor pair and optical system is crucial for 3-cube FRET quantification. We here improved the acceptor photobleaching-based G factor determination method (termed as mPb-G) and the two-plasmid-based G factor determination method (termed as mTP-G) for rapid and reliable measurement of the G factor. mTP-G method determines G factor by simultaneously detecting three images of cells exclusively expressing each of two tandem constructs with multiple donors and multiple acceptors. This method circumvents switchover of the cells exclusively expressing each of the two constructs. mPb-G method images G factor by detecting three images of cells expressing a donor-acceptor tandem FRET construct before and after partially photobleaching acceptor. We performed the two methods on our dual-channel wide-field FRET microscope to obtain reliable G factor, and also measured the FRET efficiency and acceptor-to-donor concentration ratio of tandem constructs with different acceptor-donor stoichiometries in living HepG2 cells. mTP-G and mPb-G methods provide two simple and reliable tools for determining the G factor, in turn, quantitatively measuring FRET signal and monitoring dynamic biochemical processes in living cells.     

Scattering of charged particles by atoms

A closed variant of the Born approximation for calculating differential scattering cross sections in ion-atom collisions is developed. An expression in terms of the matrix elements J _ij with respect to the single-electron states of the atom is found for the matrix element describing the target atom in the formula for the differential cross section. The matrix elements J _ij are averaged over the relative orientation of the momentum transferred in the collision and the symmetry axis of the electronic orbitals of the target atom, using the single-electron Rutaan-Hartree-Fock wave functions. The algebraic representation of the matrix elements J _ij makes it possible to perform calculations for atoms with any value of Z. The model developed is used to calculate the cross sections σ_Σ and characteristic scattering angles θ_c for the process of electron loss by H^? ions with energy E = 0.1–100 MeV in targets consisting of atoms with Z = 2–54. It is shown that σ_Σ ∝ E ^?1 and θ_c ∝ E ^?1/2 for all Z, and for fixed E the behavior of σ_Σ(Z) and θ_c(Z) is determined by the order of filling of the electronic shells of the target atoms (the ionization potential). The computational results are analyzed and compared with the experimental data and the results of other calculations.     

Transport parameters in illuminated layers of semiinsulating GaAs

Measurements are reported on semiinsulating p-type Gallium Arsenide specimens illuminated with photons of energy greater than the energy gap.An excited layer is defined of thickness d given by the sum of the radiation penetration depth and the ambipolar diffusion length.Concentrations n and mobilities μ of the carriers in this layer are determined from galvanomagnetic effects in light and in darkness. The concentration n shows a slow decrease with increasing wavelength out to the absorption edge, where it falls abruptly; μ falls with rising photon energy. As a function of increasing intensity, the mobility remains constant, while n rises linearly with photon-excitation rate. The results are discussed in terms of the variations of d. Further an attempt has been made to find the dependence between electron and hole concentrations in the excited layer measuring the variations of short circuit photomagnetoelectric current (I_PME) as a function of excess conductance (ΔG).     

Three body clusters in finite nuclei (I). 4He

A method is developed for the treatment of the Bethe-Faddeev three body cluster equations in finite nuclei. A matrix method is employed to sum the three hole line graphs in ⁴He. For each value of a constant shift C in the intermediate state oscillator spectrum we have calculated: (i) the two body bound state binding energy self-consistently in the Brueckner approximation, (ii) the energy contribution from three hole line graphs, and (iii) the effect of single particle potential insertion in particle lines. The most important dependence on C comes from those graphs containing single particle insertions and their effect is to make the sum of (i) + (ii) + (iii) much less dependent upon C than (i) alone. The three hole line contribution for ⁴He comes mainly from third order graphs. Effects of truncation of the matrix are severe and calculations with a larger matrix could alter the quantitative but probably not the qualitative results.     

A new mass formula and new neutron and proton magic numbers in light nuclei

This mass formula explains gross features of the binding energy curves for all the elements from Li to Bi. It has no shell effects incorporated. Comparisons of separation energies computed from this formula and measured masses show extra-stability at N=6 (Z=3?8), Z=6 (N=6?9), N=14 (Z=7?10), Z=14 (N=14?19), N=16 (Z=7?8), Z=16 (N=24?26), loss of magicity at N=8 (Z=4), N=20 (Z=12?15) and quenching of N=50, 82, 126, Z=50 near driplines. Z=82 magicity rises at N=104 after strong quenching near N=107.     

Constraint on anomalous 4ν interaction

The features of a hypothetical 4ν interaction considered as the possible reason for massive-neutrino instability required in the cosmological scenario that involve neutrino dark matter are discussed. New constraints on the 4ν-interaction constant G _χ are obtained: G _χ<(15–42)G _F for m _χ>G _Z (G _F is the Fermi constant of weak interaction; m _χ is the mass of the 4ν-interaction gauge boson, also known as χ boson; and m _Z is the Z-boson mass) and G _χ<(2.8–5.6)G _F for m _χ?G _Z . These constraints virtually rule out the 4ν interaction as a possible version of solution to the cosmological neutrino-instability problem.     

Wave functions for low-lying states of light deformed nuclei using a “realistic” hamiltonian and their test by inelastic scattering: The case of 20Ne

Nuclear structure wave functions for the ground and low-lying excited states of ²⁰Ne, obtained from the angular momentum projected deformed particle-hole model using a “realistic” many-nucleon hamiltonian (kinetic energy plus a Brueckner G-matrix based on the Hamada-Johnston potential), are used as input to microscopic antisymmetrised DWBA analyses of inelastic proton scattering from ²⁰Ne. This nuclear structure model, which has been previously shown able to describe the essential features of the giant multipole resonances of both ²⁰Ne and ²⁸Si, predicts angular distributions for inelastic proton scattering, exciting a number of states below 9 MeV in ²⁰Ne, in qualitative agreement with the available data; a somewhat surprising result given the nuclear structure model's completely microscopic formulation. Anomalies observed in the assignment of some predicted levels to experimental states suggest some shortcomings in the form adopted for the hamiltonian.     

Momentum-dependent mean field in π<Subscript>0</Subscript> production in Nb + Nb collisions

The Boltzmann-Nordheim-Vlasov (BNV) equation has been solved by using a microscopic momentum-dependent (MD) nuclear mean field. This potential has been calculated in the framework of the self-consistent Brueckner theory up to the second order in the G-matrix. Comparison with the so-called soft and stiff Equation of State (EOS) is presented, using the Skyrme force. Calculations have been performed for the ⁹³Nb + ⁹³Nb reaction at E_lab = 100, 250, 400A MeV. Our results show that the subthreshold π₀ production cross-section is very sensitive to the momentum-dependent mean field, resulting, at the lowest energy, in a total cross-section a factor of 7 larger than that obtained with a local potential. The effect decreases as the bombarding energy increases.     

The sensitivity of allowed β-decay to the nuclear radius

The sensitivity to the nuclear radius of the phase-space factor for allowed β-decay is investigated as a function of energy release and Z for Z < 40 using a definition of the phasespace factor that takes into account in detail finite-size effects on the lepton wave functions and their convolution with the nucleon wave functions.