Effective theory of NN interactions in a separable representation

We consider the effective field theory of the NN system in a separable representation. The pionic part of the effective potential is included nonperturbatively and approximated by a separable potential. The use of a separable representation allows for the explicit solution of the Lippmann-Schwinger equation and a consistent renormalization procedure. The phase shifts in the ¹ S ₀ channel are calculated to subleading order.     

Inclusive photoproduction of polarized 3P1 quarkonium

We analyse inclusive photoproduction of polarized ³P₁ quarkonium in the framework of QCD. To separate non-perturbative and perturbative parts in the density matrix of the produced quarkonium we use a method, which is equivalent to the diagrammatic expansion widely used in analyzing deeply inelastic scattering. A systematic expansion in a small velocity v, with which a heavy quark moves inside the quarkonium in its rest frame, is performed for the non-perturbative parts, and they are expressed as matrix elements in non-relativistic QCD. At the leading order of v there are four matrix elements representing non-perturbative physics. The perturbative parts are calculated at the leading order of coupling constants. Some numerical results, especially numerical results for HERA, are given.     

Exact four-body calculation of the 4ΛHe-4ΛH binding energy difference

The coupled, two-variable integral equations that determine the ⁴_ΛHe and ⁴_ΛH bound states, when the NN and ΛN interactions are represented by separable potentials, are derived from the Schrödinger equation. The integral equations are solved numerically for simple s-wave potentials and for tensor potentials in the truncated t-matrix approximation without resort to separable expansion of the kernels. The Λ-separation energy difference ΔB_Λ resulting from the genuine four-body model is shown to be approximately twice as large as that coming from an “effective two-body” model calculation, when identical central potentials are used. The four-body model estimate of ΔB_Λ made with tensor forces is consistent with the experimental value, indicating that charge symmetry breaking implied by the low energy Λ N scattering parameters is compatible with that suggested by the known binding energy difference in the A = 4 hypernuclear isodoublet.     

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.     

Messung der Winkelverteilung der α-Teilchen der Kern-Reaktion11B (p, α1)8Be (2,9 MeV)

It is not possible to measure the angular distribution of the α-particles from¹¹B(p, α₁)⁸Be*(2,9 MeV) with a simple one-detector arrangement, because the back-ground α-particle spectrum from⁸Be* will change shape and contents with angle. Therefore a coincidence method is employed. Two detectors are arranged in such a way that with any angle in thelaboratory system the angle between the detectors is 180 degrees in the center ofmass system. By this method angular correlations are eliminated and the angular distribution of α₁ can be measured as long as the two coincident lines, recorded by each detector, are separable. Since this is not always the case the angular distributions are determined only for reactions proceeding through the two excited states in¹²C that are reached with 1.39 and 2.64 MeV proton energy. Angular distributions of the α_o radiation have been remeasured.     

Contribution ofp-wave (3)+1 subamplitudes to4He binding energy and scattering observables below four-body breakup threshold

The four-body equations of Alt, Grassberger and Sandhas, in the form that the (2)+(2) subsystem amplitudes are treated by the convolution method, are solved for separable two-body interactions between nucleon pairs in the channels³S₁-³D₁ (t ₀₀ alone) and¹S₀. AllL=0 andL=1 (3)+1 subamplitudes are represented in a separable form using the energy dependent pole expansion. The contribution ofp-wave (3)+1 subamplitudes to the⁴He binding energy, threshold scattering observables and low energy cross sections forn ³Hn ³H,p ³Hep ³He,dddd andddp ³H reactions is studied for different two-body potentials.     

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.     

The identification of two entrance channels in the reaction of metastable helium He(23S,21S) with SO2

The energy spectrum of electrons emitted in the reaction of He(2³S) and He(2¹S) with SO₂ indicates that in addition to the covalent entrance channel a strongly attractive ionic channel plays a role. We find upper limits for the well depth of the potential curve that corresponds to the latter channel of D_e ? 3.5 eV and D_e ? 4.3 eV for He(2³S) and He(2¹S) as the reaction partner, respectively. The partitioning between the two entrance channels can be understood by assuming the coupling matrix between both channels to depend strongly on the orientation of the SO₂ molecule with respect to the incident metastable He*.     

Thermal expansion behavior and chemical compatibility of BaxSr1−xCo1−yFeyO3−δ with 8YSZ and 20GDC

Perovskite oxides of the composition Ba_xSr_1−xCo_1−yFe_yO_3−δ(BSCF) were synthesized via a modified Pechini method and characterized by X-ray diffraction, dilatometry and thermogravimetry. Investigations revealed that single-phase perovskites with cubic structure can be obtained for x ≤ 0.6 and 0.2 ≤ y ≤ 1.0. The as-synthesized BSCF powders can be sintered in several hours to nearly full density at temperatures of over 1180 °C. Thermal expansion curves of dense BSCF samples show nonlinear behavior with sudden increase in thermal expansion rate between about 500 °C and 650 °C, due mainly to the loss of lattice oxygen caused by the reduction of Co⁴⁺ and Fe⁴⁺ to lower valence states. Thermal expansion coefficients (TECs) of BSCF were measured to be 19.2–22.9 × 10^− 6 K^− 1 between 25 °C and 850 °C. Investigations showed further that Ba_0.5Sr_0.5Co_0.8Fe_0.2O_3−δ is chemically compatible with 8YSZ and 20GDC for temperatures up to 800 °C, above which severe reactions were detected. After being heat-treated with 8YSZ or 20GDC for 5 h above 1000 °C, Ba_0.5Sr_0.5Co_0.8Fe_0.2O_3−δ was completely converted to phases like SrCoO_3−δ, BaCeO₃, BaZrO₃, etc.     

Ab-initio interpretation of 〈r−3〉 electronic quantities in the hfs of Mg I 3s 3p 3 P and1 P

It has been known for a long time that, in a two-electron arc spectrum, the properties of the³ P and¹ P terms of the lowests p configuration cannot be interpreted correctly in a pure-configuration model. Following the experimental determination of the hyperfine constantA(3s 3p ¹ P ₁) in Mg I by Kluge and Otten, this paper presents the ab-initio interpretation of the 〈r ^?3〉_3p hyperfine electronic quantities in 3s 3p through the use of the multiconfigurational Hartree-Fock method. It appears that taking into account the effects of the monoelectronic excitations 3s→nd, 2p→np and 3p→np leads to ab-initio evaluations in very good agreement with experiment. The case of the 3p→np excitation, to which Brillouin's theorem should apply in principle, is discussed. Using the same method, a refined evaluation is proposed for the nuclear electric-quadrupole moment of Mg²⁵ (Q=0.200 ± 0.01 barn).     

Thermodynamic properties of the CeSn3 mixed valence compound

We have measured on the CeSn₃ compound, the expansion coefficient between 80 and 800 K at normal pressure, the isothermal compressibility in the 0–8 GPa pressure range at room temperature and the heat capacity at constant pressure in the 60–300 K temperature range. The experimental data were compared with those previously found for the isomorphous LaSn₃ phase, assumed as a proper reference material for the study of the intermediate valency states in CeSn₃. Both the thermal expansion (3α) and the isothermal compressibility (k) of CeSn₃ show behaviours quite different from those of LaSn₃: for instance, in the standard conditions, 3α is 55 × 10^?6K^?1for CeSn₃ and 38 × 10^?6K^?1for LaSn₃; k is 15 × 10^?12 Pa^?1 and 12 × 10^?12 Pa^?1 respectively for CeSn₃ and LaSn₃. The thermal behaviour of the molar specific heat at constant pressure of CeSn₃ is similar to that of LaSn₃ for temperatures lower than 50 K. In the 70–300 K temperature range, the heat capacity of CeSn₃ is clearly higher than that of LaSn₃, ΔC_p being maximum near 150 K. The analysis of the calorimetric data show that the electronic coefficient γ of CeSn₃ is temperature dependent: its value varies from 53 mJ K^?2 mole^?1 at low temperature 24 mJ K^?2 mole^?1 at 300 K.     

An anomalous thermal expansion in the perovskite system,Gd1−xSrxMnO3 (0 ≤ x ≤ 0.3)

The thermal expansion behavior of sintered samples of Gd_1−xSr_xMnO₃ (X = 0.0–0.4) was studied. The sintered bodies in this system showed negative thermal expansion over a wide temperature range. The detailed crystal structure refinements with respect to temperature showed that the volume of the orthorhombic perovskite lattice monotonically increased with temperature, however, in addition to this, the release of distortion from the Jahn-Teller effect of Mn³⁺ ion occurred over a wide temperature range, which brought the negative expansion of the a-axis, although the b- and c-axes increased with temperature. The anomalous thermal expansion is explained by the sum of the effects of the shrinkage of the a-axis and absorption of the b- and c-axes' expansion by the pores in the sintered body.     

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.     

Stark effect investigations of the 4f 14 6s 6p 3 P 1 and1 P 1 levels of ytterbium

The tensor polarizabilities of the 4f ¹⁴ 6s 6p ³ P ₁ level were investigated for all stable Ytterbium isotopes by the method of optical double resonance. The tensor polarizabilities were deduced from the rf-resonance signals in parallel electric and magnetic fields. The value obtained for the even Yb isotopes is in good agreement with the results derived from the measurements on the odd isotopes. The mean value isα _ten(³ P ₁)0=5.99(34)kHz/(kV/cm)². The tensor polarizability of the 4f ¹⁴ 6s 6p ¹ P ₁ level of¹⁷¹Yb was measured by means of the level crossing technique with parallel electric and magnetic fields. The experimental result isα _ten(¹ P ₁)=?14.3(1.4)kHz/(kV/cm)². This is compared with the prediction of the LS coupling approximation using the experimental data of the³ P ₁ level. Only poor agreement is obtained which is due to the configuration mixing in the¹P₁ level.     

Measurements of theg J -factors of12C in the3 P 1 and3 P 2 states

Using the atomic beam magnetic resonance method the Zeeman interactions of¹²C in the³ P ₁ and³ P ₂ states at magnetic fields of about 3.4 kOe have been measured. The measured quantities areg _J (³ P ₁)?g_J(³ P ₂)=15.4(1.0)·10^?6 g _J (³ P ₂)=1.5010616 (50), from which the following value for g_J(³P₁) can be calculated:g _J (³ P ₁)=1.5010770 (50). The experimental results are in moderate agreement with theoretical calculations.     

Low-temperature investigations of the open-framework material HfMgMo3O12

The A₂Mo₃O₁₂ family, where A³⁺ is a large trivalent cation, can show interesting thermal properties such as negative thermal expansion. One member of this family, HfMgMo₃O₁₂, where the two A³⁺ cations have been replaced by Hf⁴⁺ and Mg²⁺, has been shown to have a low positive coefficient of thermal expansion above room temperature. This property makes HfMgMo₃O₁₂ an attractive candidate as a component for solid solutions with near-zero thermal expansion. However, its properties below room temperature were unexplored. In this work we report the phase transition from orthorhombic Pnma to monoclinic P2₁/a at T～175 K with an enthalpy change of 0.27 kJ mol^?1. Relaxation calorimetry, from 5 K to 300 K, show only the small anomaly associated with this transition. The thermal conductivity, determined from 2 K to 300 K, was low, but not as low as some other materials exhibiting negative thermal expansion. Analysis of the low-temperature heat capacity indicates the presence of low-energy phonon modes in HfMgMo₃O₁₂, consistent with the low thermal conductivity. The upper bound of the Young's modulus, estimated from the effective Debye temperature derived from the low-temperature heat capacity, is 20 GPa, a relatively low value due to the flexibility of the framework structure.     

The Triton from the Reid93 Potential in the UPA

The unitary pole approximation (UPA) provides an effective means to construct a rank one separable potential for calculations in which one requires a simple representation of the deuteron and/or triton ground-state wave function. By construction the deuteron wave function and the ¹S₀ anti-bound state wave function of the original potential are reproduced. We report results for the corresponding triton ground state. We choose to utilize the realistic Reid93 potential for this purpose. The Reid93 potential, generated by the Nijmegen group, is a Reid-like, partial-wave local potential that produces a χ² representation of the nucleon–nucleon (NN) scattering data that is as precise as an NN partial-wave analysis. Results for properties of ²H and ³H from the UPA are compared with those for the original potential. To further illustrate the precision of the method, results for properties of the deuteron and triton from the UPA are also compared with those for the original Reid68 potential.     

The Rank-One Separable Interaction Kernel for Nucleons with Scalar Propagator

In the paper the covariant kernel of the nucleon-nucleon interaction of particles with scalar propagators is analyzed. The Bethe–Salpeter equation for the T matrix is considered in the rank-one separable kernel. The parameters of the kernel for the specific partial-wave channels explicitly connect with the observables low energy scattering parameters and phase shifts, deuteron binding energy. Covariant separable kernels for the partial-wave channels with total angular momentum J = 0 (¹S₀, ³P₀) and J =1 (³S₁ ? ³D₁, ¹P₁, ³P₁) are constructed.     

On the unitary pole expansion of the potentials I and III of Malfliet and Tjon

The unitary pole expansion for the local soft-core potentials I and III of Malfliet and Tjon is obtained, and the Faddeev-Lovelace equations are solved for the separable potentials. The energyE _T of the triton and the doublet scattering length² a have been obtained. The results are ?8.59 MeV ≦E_T≦ ?8.57 MeV and 0.89 fm≦² a≦0.91 fm. For the quartet scattering length a value₄ a = 6.39 fm has been found.