Lifting Grobner bases from the exterior algebra

In the article "Non-commutative Grobner bases for commutative algebras", Eisenbud-Peeva-Sturmfels proved a number of results regarding Grobner bases and initial ideals of those ideals in the free associative algebra which contain the commutator ideal. We prove similar results for ideals which contains the anti-commutator ideal (the defining ideal of the exterior algebra). We define one notion of generic initial ideals in the free assoicative algebra, and show that gin's of ideals containing the commutator ideal, or the anti-commutator ideal, are finitely generated.Comment: 6 pages, LaTeX2

Methanol in W3(H2O) and Surrounding Regions

We present the results of an interferometric study of 38 millimeter-wave lines of CH3OH in the region around the water maser source W3(H2O) and a region extending about 30" to the south and west of the hydroxyl maser source W3(OH). The methanol emitting region around W3(H2O) has an extent of 2.0" x 1.2" (4400 x 2600 AU). The density is of order 1.e7 cm-3, sufficient to thermalize most of the methanol lines. The kinetic temperature is approximately 140 K and the methanol fractional abundance greater than 1.e-6, indicative of a high degree of grain mantle evaporation. The W3(H2O) source contains sub-structure, with peaks corresponding to the TW source and Wyrowski's B/C, separated by 2500 AU in projection. The kinematics are consistent with these being distinct protostellar cores in a wide binary orbit and a dynamical mass for the region of a few tens of Mo. The extended methanol emission to the southwest of W3(OH) is seen strongly only from the lowest excitation lines and from lines known elsewhere to be class I methanol masers, namely the 84.5 GHz 5(-1)-4(0)E and 95.2 GHz 8(0)-7(1)A+ lines. Within this region there are two compact clumps, which we denote as swA and swB, each about 15" (0.16 pc projected distance) away from W3(OH). Excitation analysis of these clumps indicates the presence of lines with inverted populations but only weak amplification. The sources swA and swB appear to have kinetic temperatures of order 50-100 K and densities of order 1.e5 - 1.e6 cm-3. The methanol fractional abundance for the warmer clump is of order 1.e-7, suggestive of partial grain mantle evaporation. The clumping occurs on mass scales of order 1 Mo.Comment: 28 pages including 6 figures and 4 tables, accepted by Ap

General Solutions of Relativistic Wave Equations II: Arbitrary Spin Chains

A construction of relativistic wave equations on the homogeneous spaces of the Poincar\'{e} group is given for arbitrary spin chains. Parametrizations of the field functions and harmonic analysis on the homogeneous spaces are studied. It is shown that a direct product of Minkowski spacetime and two-dimensional complex sphere is the most suitable homogeneous space for the physical applications. The Lagrangian formalism and field equations on the Poincar\'{e} and Lorentz groups are considered. A boundary value problem for the relativistically invariant system is defined. General solutions of this problem are expressed via an expansion in hyperspherical functions defined on the complex two-sphere.Comment: 56 pages, LaTeX2

Experimental and theoretical lifetimes and transition probabilities in Sb I

We present experimental atomic lifetimes for 12 levels in Sb I, out of which seven are reported for the first time. The levels belong to the 5p$^2$($^3$P)6s $^{2}$P, $^{4}$P and 5p$^2$($^3$P)5d $^{4}$P, $^{4}$F and $^{2}$F terms. The lifetimes were measured using time-resolved laser-induced fluorescence. In addition, we report new calculations of transition probabilities in Sb I using a Multiconfigurational Dirac-Hartree-Fock method. The physical model being tested through comparisons between theoretical and experimental lifetimes for 5d and 6s levels. The lifetimes of the 5d $^4$F$_{3/2, 5/2, 7/2}$ levels (19.5, 7.8 and 54 ns, respectively) depend strongly on the $J$-value. This is explained by different degrees of level mixing for the different levels in the $^4$F term.Comment: 10 page

A measurement of the differential cross section for the two-body photodisintegration of 3He at theta_LAB = 90deg using tagged photons in the energy range 14 -- 31 MeV

The two-body photodisintegration of 3He has been investigated using tagged photons with energies from 14 -- 31 MeV at MAX-lab in Lund, Sweden. The two-body breakup channel was unambiguously identified by the (nonsimultaneous) detection of both protons and deuterons. This approach was made feasible by the over-determined kinematic situation afforded by the tagged-photon technique. Proton- and deuteron-energy spectra were measured using four silicon surface-barrier detector telescopes located at a laboratory angle of 90deg with respect to the incident photon-beam direction. Average statistical and systematic uncertainties of 5.7% and 6.6% in the differential cross section were obtained for 11 photon-energy bins with an average width of 1.2 MeV. The results are compared to previous experimental data measured at comparable photon energies as well as to the results of two recent Faddeev calculations which employ realistic potential models and take into account three-nucleon forces and final-state interactions. Both the accuracy and precision of the present data are improved over the previous measurements. The data are in good agreement with most of the previous results, and favor the inclusion of three-nucleon forces in the calculations.Comment: 12 pages, 13 figures; further Referee comments addresse

Improved microscopic-macroscopic approach incorporating the effects of continuum states

The Woods-Saxon-Strutinsky method (the microscopic-macroscopic method) combined with Kruppa's prescription for positive energy levels, which is necessary to treat neutron rich nuclei, is studied to clarify the reason for its success and to propose improvements for its shortcomings. The reason why the plateau condition is met for the Nilsson model but not for the Woods-Saxon model is understood in a new interpretation of the Strutinsky smoothing procedure as a low-pass filter. Essential features of Kruppa's level density is extracted in terms of the Thomas-Fermi approximation modified to describe spectra obtained from diagonalization in truncated oscillator bases. A method is proposed which weakens the dependence on the smoothing width by applying the Strutinsky smoothing only to the deviations from a reference level density. The BCS equations are modified for the Kruppa's spectrum, which is necessary to treat the pairing correlation properly in the presence of continuum. The potential depth is adjusted for the consistency between the microscopic and macroscopic Fermi energies. It is shown, with these improvements, that the microscopic-macroscopic method is now capable to reliably calculate binding energies of nuclei far from stability.Comment: 66 pages, 29 figures, 1 tabl

Systematic trends in beta-delayed particle emitting nuclei: The case of beta-p-alpha emission from 21Mg

We have observed beta+-delayed alpha and p-alpha emission from the proton-rich nucleus 21Mg produced at the ISOLDE facility at CERN. The assignments were cross-checked with a time distribution analysis. This is the third identified case of beta-p-alpha emission. We discuss the systematic of beta-delayed particle emission decays, show that our observed decays fit naturally into the existing pattern, and argue that the patterns are to a large extent caused by odd-even effects.Comment: 6 pages, 5 figure

New Outlook on the Possible Existence of Superheavy Elements in Nature

A consistent interpretation is given to some previously unexplained phenomena seen in nature in terms of the recently discovered long-lived high spin super- and hyper-deformed isomeric states. The Po halos seen in mica are interpreted as due to the existence of such isomeric states in corresponding Po or nearby nuclei which eventually decay by gamma- or beta-decay to the ground states of 210Po, 214Po and 218Po nuclei. The low-energy 4.5 MeV alpha-particle group observed in several minerals is interpreted as due to a very enhanced alpha transition from the third minimum of the potential-energy surface in a superheavy nucleus with atomic number Z=108 (Hs) and atomic mass number around 271 to the corresponding minimum in the daughter.Comment: 8 pages, 8 figures, 5 tables. Paper presented at VII Int. School-Seminar on Heavy Ion Physics, May 27 - June 1, 2002, Dubna, Russi