Toric <Emphasis Type="Italic">G</Emphasis><Subscript>2</Subscript> and <Emphasis Type="Italic">Spin</Emphasis>(7) Holonomy Spaces from Gravitational Instantons and Other Examples

Non-compact G ₂ holonomy metrics that arise from a T ² bundle over a hyper-Kähler space are constructed. These are one parameter deformations of certain metrics studied by Gibbons, Lü, Pope and Stelle in [1]. Seven-dimensional spaces with G ₂ holonomy fibered over the Taub-Nut and the Eguchi-Hanson gravitational instantons are found, together with other examples. By using the Apostolov-Salamon theorem [2], we construct a new example that, still being a T ² bundle over hyper-Kähler, represents a non-trivial two parameter deformation of the metrics studied in [1]. We then review the Spin(7) metrics arising from a T ³ bundle over a hyper-Kähler and we find a two parameter deformation of such spaces as well. We show that if the hyper-Kähler base satisfies certain properties, a non-trivial three parameter deformation is also possible. The relation between these spaces with half-flat and almost G ₂ holonomy structures is briefly discussed.     

Symmetries of Einstein-Yang-Mills fields and dimensional reduction

LetE be a manifold on which a compact Lie groupS acts simply (all orbits of the same type);E can be written locally asM×S/I,M being the manifold of orbits (space-time) andI a typical isotropy group for theS action. We study the geometrical structure given by anS-invariant metric and anS-invariant Yang Mills field onE with gauge groupR. We show that there is a one to one correspondence between such structures and quadruplets of fields defined solely onM; _v is a metric onM,h are scalar fields characterizing the geometry of the orbits (internal spaces), ⁱ are other scalar fields (Higgs fields) characterizing theS invariance of the Lie(R)-valued Yang Mills field and is a Yang Mills field for the gauge groupN(I)|I×Z((I)),N(I) being the normalizer ofI inS, is a homomorphism ofI intoR associated to theS action, andZ((I)) is the centralizer of(I) inR. We express the Einstein-Yang-Mills Lagrangian ofE in terms of the component fields onM. Examples and model building recipes are given.     

Construction of kernels of the nonlinear collision integral in the Boltzmann equation using laplace transformation

It is shown that the relation between kernels L _l (v, v ₁) of the linear collision integral and kernels G _l,0 ^l (v, v ₁, v ₂) of the nonlinear collision integral can be reduced to the Laplace transformation. Analytic expressions for nonlinear kernels G _0,0 ⁺⁰ (v, v ₁, v ₂) and G _1,0 ⁺¹ (v, v ₁, v ₂) are determined for hard spheres and pseudo-Maxwellian molecules.     

Bivariate distributions in statistical spectroscopy studies: III. Non interacting particle strength densities for one-body transition operators

In statistical spectroscopy, it was shown by French et al. (Ann. Phys., N.Y. 181, 235 (1988)) that the bivariate strength densities take a convolution form with the non interacting particle (NIP) strength density being convoluted with a spreading bivariate Gaussian due to interactions. Leaving aside the question of determining the parameters of the spreading bivariate Gaussian, one needs good methods for constructing the NIP bivariate strength densitiesI _O ^h (E,E′) (h is a one-body hamiltonian andO is a transition operator) in large shell model spaces. A formalism for constructingI _O ^h is developed for one-body transition operators by using spherical orbits and spherical configurations. For rapid construction and also for applying the statistical theory in large shell model spacesI _O ^h is decomposed into partial densities defined by unitary orbit configurations (unitary orbit is a set of spherical orbits). Trace propagation formulas for the bivariate momentsM _rs with r+s ≤2 of the partial NIP strength densities, which will determine the Gaussian representation, are derived. In a large space numerical example with Gamow-Tellerβ ^? transition operator, the superposition of unitary orbit partial bivariate Gaussian densities is shown to give a good representation of the exact NIP strength densities. Trace propagation formulas forM _rs with r+<—4 are also derived inm-particle scalar spaces which are useful for many purposes.     

Analysis of average primary gamma-transition intensities and cross sections of the113Cd(n, γ) reaction

A combined analysis of the available data on the primaryγ-ray intensities from the¹¹³Cd(n, γ) reaction atE _n=1.9 and 24.3 keV neutron energies together with the data on¹¹³Cd neutron capture cross sections in theE _n=3–200 keV energy region was carried out. The neutron strength functions were determined asS _n0=(0.260±0.073) 10^?4 and S_n1=(5.06±0.67) 10^?4. No spin-orbit splitting of thep-wave neutron strength function was found. The energy dependence of theE 1 radiative strength function {ie147-01} was fitted by the Kadmenski-Furman model somewhat better than by a standard Lorentzian. TheM 1 giant resonance parameters were obtained as E _G ^{M 1} =8.8±1.6 MeV and Γ _G ^{M 1} = 4.7±2.6 MeV. The neutron capture cross section of¹¹³Cd from its isomeric state ({ie147-02}=11/2^?, E ₁ ^m =263.7 keV) was calculated.     

Yrast states in the π- particle ν- hole nucleus 65 146 Tb81

The nucleus ¹⁴⁶Tb was studied from in beam γγ-and conversion electron measurements. The level scheme was established up to ～5MeV above the (πh_11/2 vd _3/2 ^?1 )_5? β-isomer. In addition to the known (πh_11/2 vh _11/2 ^?1 )₁₀₊ E3-isomer, the 8⁺ and 11⁺ members of this configuration were located. The levels at the yrast line are dominated by the couplings of the πh_11/2 vh _11/2 ^?1 valence nucleons to the collective 3^? octupole state and to the πh_11/2d _5/2 ^?1 and πh_11/2g _7/2 ^?1 particle-hole excitations of ¹⁴⁶Gd.     

A measurement of the ratio GE/GE of the proton form factors at very low momentum transfer

The ratioμG _EG_M of the proton form factors was determined by measuring the electron scattering cross section of the proton relative to that of¹²C. Data were taken atq ²=0.09, 0.16, 0.25, and 0.36 fm^?2, yielding a weighted mean ofμG _E/G_M=1.01±0.03.     

The group of automorphisms of the galilei group

The group of automorphisms of the Galilei groupG: Aut(G) is calculated. It is shown that Aut(G) has the structure of a semi-direct product byG of the group ? _m ^* ×?_m where ?_m is the group of reals noted multiplicatively and ? _m ^* m is the subgroup of positive reals.     

The magnetic moment of the 10+ isomer in140Ce andE1 transitions inN=82 isotones caused by outer subshell configurations

Using the reaction¹³⁸Ba(α,2n)¹⁴⁰Ce the magnetic moment of the 10 ₁ ⁺ isomer atE _x =3714.7 keV in theN=82 nucleus¹⁴⁰Ce has been determined by means of the TDPAD method toμ=+10.3(4)μ _N . Measuredg-factors in¹⁴⁰Ce are compared to calculations within the shell model with configuration mixing. For the 10 ₁ ⁺ isomer in¹⁴⁰Ce the four proton configuration π(1g ₇ ^2/2 ,2d ₅ ^2/2 ) has been found to be dominant. From theg-factor measurement strong contributions of multiparticle excitations to thegp2d _3/2,π3s ₁ ² or π1h ₁₁ ² shells and admixtures of neutron excitations to the wave function of the 10 ₁ ⁺ state could be excluded. The strongE1γ-branch of the deexcitation of the 10 ₁ ⁺ isomer in¹⁴⁰Ce can be explained by means of small admixtures of configurations which contain the outer subshell excitationsπ2f _7/2 andπ1h _9/2. On this basisE1 transitions experimentally observed in theN=82 nuclei¹⁴⁰Ce,¹⁴¹Pr and¹⁴⁵Eu may be understood.     

Exotic mesons withJ PC=1−+, strange and non-strange

We analyse the QCD sum rules for the exotic quark-antiquark-gluon states called “glukonium” or “hermaphrodite” mesons. We predict a non-strange resonance of this type at ～1.5 GeV, a strange one at ～1.6 GeV and a strange-antistrange one at ～1.75 GeV. It should be noted that the above values of masses depend crucially on the vacuum expectation value of the gluon field operator <g ³ f _abc ·G _μv ^a G _vλ ^b G _λμ ^c >.     

Classical electrodynamics with nonlocal constitutive equations

It is assumed that the coupling of the field quantities D^μv (x) and F _αβ (x) is nonlocal. This hypothesis leads to a theory of an electromagnetic field that has the following properties.(1) The source of the field F _αβ (x) exhibits a center of charge and a center of mass that do not coincide, in general.(2) The field componentF _0i=?c²E_i is regular at the origin.(3) In the first-order approximation the new field equations are equivalent to the conventional Maxwell field equations.(4) The conventional cutoff procedure in momentum space as practiced in the Maxwell-Lorentz theory is equivalent to the first-order approximation in terms of an invariant length ξ².(5) The gyromagnetic ratio of the source of F _αβ (x) is equal toc/mc for a quantum of chargee and massm.     

MeanM-subshell fluorescence yields atZ=88, 90, 92, and 94

M x-ray —L x-ray coincidence measurements with high resolution, cooled Si(Li) x-ray detectors were made on transitions following the alpha decays of²²⁸Th,²³²U,²³⁸Pu, and²⁴⁴Cm, in order to determine the meanM-subshell fluorescence yields. The values obtained are:v ₄ ^M =0.032±0.002, andv ₅ ^M =0.024±0.002 atZ=88;v ₁ ^M =0.038±0.003,v ₄ ^M =0.042±0.002, andv ₅ ^M =0.038±0.002 atZ=90;v ₁ ^M =0.047±0.002,v ₄ ^M =0.048±0.002, andv ₅ ^M =0.044±0.002 atZ=92;v ₁ ^M =0.066±0.002,v ₄ ^M =0.062±0.002, andv ₅ ^M =0.063±0.002 atZ=94. The quantityΩ ₁ ^M +f ₁₂ ^MΩ ₂ ^M was measured as (56±10)×10^?4, (62±12)×10^?4, (99±18) ×10^?4, and (93±15)×10^?4 forZ=88, 90, 92, and 94, respectively, which agree well with the calculations of McGuire. The radiativeL ₁-L ₃ transition intensity was measured for the four atomic numbers and found to be consistently less than the calculations of Scofield by about 45 percent.     

Relative probabilities of spontaneous transitions in v″ progressions of the G1Σ g + , v′→B 1Σ u + , v″ bands of the H2 molecule

The probabilities of spontaneous transitions in v″ progressions of the G ¹Σ _g ⁺ →B ¹Σ _u ⁺ bands of the H₂ molecule (the 3D→2B electronic transition in notations of G.H. Dieke) are, for the first time, experimentally studied. The line strength ratios were measured for 78 G ¹Σ _g ⁺ , v′, J′→B ¹Σ _u ⁺ , v″, J″ electronic-vibrational-rotational spectral lines having a common upper level but belonging to different bands of v″ progressions (the vibrational branching coefficients). For this purpose, the intensities of lines of the P and R branches, emitted by a low-pressure plasma and corresponding to different values of the rotational (J′=0–11) and vibrational (v′=0–3 and v″=0–7) quantum numbers, were used. It was found that the changes in the vibrational branching coefficients with variation of v′ and v″ are significant (up to a factor of 20). For most bands studied, the dependences of the vibrational branching coefficients on the rotational quantum number J′ of an upper level are rather weak and do not exceed 30%. It was established that the difference between the experimental values of ratios of the vibronic transition probabilities (summed over J″) and the results of calculation in the adiabatic approximation strongly depends on v′, reaching a factor of 25 for a transition from the v′=2 level. At the same time, the discrepancy between the experimental data and the results of nonadiabatic ab initio calculations lies between 1.0 and 2.3.     

Exact solutions of the Bach field equations of general relativity

Conformally invariant gravitational field equations on the hand and fourth order field equations on the other were discussed in the early history of general relativity (Weyl Einstein, Bach et al.) and have recently gained some new interest (Deser, P. Günther, Treder, et al.). The equations B_αβ=0 or B_αβ=?T_αβ, where B_αβ denotes the Bach tensor and T_αβ a suitable energy-momentum tensor, possess both the mentioned properties. We construct exact solutions ds²=g_αβdx^αdx^β of the Bach equations: (2, 2)-decomposable, centrally symmetric and pp-wave solutions. The gravitational field g_αβ is coupled by B_αβ=?T_αβ to an electromagnetic field F_αβ=?F_αβ obeying the Maxwell equations or to a neutrino field ?A obeying the Weyl equations respectively. Among interesting new metrics ds² there appear some physically well-known ones, such as the De Sitter universe, the Weyl-Trefftz metric. and the plane-fronted gravitational waves with parallel rays (pp-waves) known from Einstein's theory. The solutions are built up by means of special techniques: A separation method for (2, 2)-decomposable solutions, simplification of centrally symmetric metrics by a suitable conformal transformation, and complex function methods for pp-wave solutions.     

Strong coupling 1/N c expansion in the gluonic sector of lattice quantum chromodynamics

The vacuum state of gluonic quantum chromodynamics on the lattice is determined up to fifth order in a 1/N _c expansion (N _c=number of colours). The vacuum expectation value of the gluon field squaredF _aμvF _a ^μv is deduced. The quark-antiquark and gluon-gluon potential is calculated in the same limit up to the 1/N _c ³ order.     

The static potential in quantum chromodynamics

The effective interaction between a static quark-antiquark pair is computed within the framework of 〈G_μv^aG_a^μv〉 ≠ 0. Due to the static approximation the interaction takes the form of a potential, which is in striking agreement with phenomenological potentials.     

Gravitational stability of cold Bose star

The maximum mass of cold Bose star that can sustain its own gravity is determined to be ≈0.6/Gm, wherem is the mass of boson. This is different from the Oppenheimer-Volkoff mass of ≈0.4/G ^3/2 m _N ² for the neutron star and may facilitate formation of smaller black holes made of cold invisible axions in the axion dominated universe.