Radio-frequency spectroscopy of weakly bound molecules in ultracold Fermi gas

We create weakly bound Feshbach molecules in ultracold Fermi gas40K by sweeping a magnetic field across a broad Feshbach resonance point 202.2 G with a rate of 20 ms/G and perform the dissociation process using radio-frequency(RF) technology. From RF spectroscopy, we obtain the binding energy of the weakly bound molecules in the vicinity of Feshbach resonance. Our measurement also shows that the number of atoms generated from the dissociation process is different at various magnetic fields with the same RF amplitude, which gives us a deeper understanding of weakly bound Feshbach molecules.

One-neutron stripping process in the^(209)Bi(^(6)Li,^(5)Li)^(210)Bi*reaction reaction

One-neutron stripping process between^(6)Li and^(209)Bi was studied at 28,30,and 34 MeV using the in-beamγ-ray spectroscopy method.Theγ-γcoincident analysis clearly identified twoγ-rays feeding the ground and long-lived isomeric states,which were employed to determine the cross section.The one-neutron stripping cross sections were similar to the cross sections of complete fusion in the^(6)Li+^(209)Bi system,but the one-neutron stripping cross sections decreased more gradually at the sub-barrier region.A coupled-reaction-channel calculation was performed to study the detailed reaction mechanism of the one-neutron stripping process in^(6)Li.The calculations indicated that the first excited state of 5 Li is critical in the actual one-neutron transfer mechanism,and the valence proton of 209Bi can be excited to the low-lying excited state in(^(6)Li,^(5)Li)reaction,unlike in the(d,p)reaction.

Finite Range Effects on Fusion and/or Breakup of ~6He+^(238)U and ^(11)Li+^(208)Pb Systems

We have studied the effects of the finite range on the fusion and/or breakup of ^6He^＋238U and ^11Li＋^208pb Pb dynamic polarization potential approach. It has been found of the interaction between the fragments of the projectile systems at near barrier energies within the framework of that at near barrier energies the maximum flux is lost to the breakup channel and at energies well above the Coulomb barrier the fusion coupled with the breakup channel opens up, initially with sharp rise and later becoming saturated at energy nearly twice of the Coulomb barrier. Further, it is found that the breakup cross section increases with the increasing range of the interaction between the fragments of the projectile while the fusion coupled with the breakup channel cross section decreases with the increasing range.

密度泛函理论及其数值方法新进展

综述了密度泛函理论及其数值方法的最新进展。密度泛函理论的发展以寻找合适的交换相关近似为主线 ,从最初的局域密度近似、广义梯度近似到现在的非局域泛函、自相互作用修正 ,多种泛函形式的相继出现使得密度泛函理论可以提供越来越精确的计算结果。除了交换相关近似的发展 ,近年来密度泛函理论向含时理论、相对论等方面的扩展也很活跃。另外 ,在密度泛函理论体系发展的同时 ,相应的数值计算方法的发展也非常迅速。从古老的有限差分、有限元到新兴的小波分析都被用来实现密度泛函理论的数值计算。与此同时 ,线性标度的密度泛函理论算法日趋成熟 ,使得通过密度泛函理论研究诸如生物大分子之类的体系成为可能。随着密度泛函理论本身及其数值方法的发展 ,它的应用也越来越广泛 ,一些新的应用领域和研究方向不断涌现。

Analysis on the Formation Reason of A Rare Big Hailstone Weather in Nantong City

By using the ground and high-altitude observation data,NCEP 6 h reanalysis data and CINRAD/SA radar observation data,the circulation situation,the atmospheric stability degree and the radar echo characteristics of a strong convection weather which occurred in Nantong area of Jiangsu Province on June 14 in 2009 were analyzed.The results showed that the hailstone happened in the large scale background of coastal trough rear which was established by the northeast low vortex.The warm air in the middle-low layer was covered with the cold air in 500 hPa,which provided the favorable condition for the occurrence of strong convection weather which included the hailstone,the thunderstorm,the strong wind and so on.Seen from the analysis on the radar echo,the windstorm which induced this strong convective weather had the characteristics of super monomer windstorm.In the northwest and the southeast,there were 2 obvious outflow boundaries and the overhanging structure characteristics.The strong vertical shear and the suitable frozen layer height in the middle-low layer of troposphere were also favorable to fall the hailstone.

Sharp weak bounds for n-dimensional fractional Hardy operators

We obtain the operator norms of the n-dimensional fractional Hardy operator Hα（0 〈 α 〈 n） from weighted Lebesgue spaces Lp｜x｜p（R^n） to weighted weak Lebesgue spacesLq,∞｜x｜β（R^n）.

Intra-and Intermolecular Rovibrational States of HCl-H_(2)O and DCl-H_(2)O Dimers from Full-Dimensional and Fully Coupled Quantum Calculations

We report full-dimensional and fully coupled quantum bound-state calculations of the J=1 intra-and intermolecular rovibrational states of two isotopologues of the hydrogen chloride-water dimer,HClH_(2)O(HH)and DCl-H_(2)O(DH).The present study complements our recent theoretical investigations of the J=0 nine-dimensional(9D)vibrational level structure of these and two other H/D isotopologues of this noncovalently bound molecular complex,and employs the same accurate 9D permutation invariant polynomial-neural network potential energy surface.The calculations yield all intramolecular vibrational fundamentals of the HH and DH dimers and the low-energy intermolecular rovibrational states in these intramolecular vibrational manifolds.The results are compared with those of the 9D J=0 calculations of the same dimers.The energy differences between the K=1 and K=0 eigenstates exhibit pronounced variations with the intermolecular rovibrational states,for which a qualitative explanation is provided.

On complete convergence in Marcinkiewicz-Zygmund type SLLN for random variables

We consider a generalization of Baum-Katz theorem for random variables satisfying some cover conditions.Consequently,we get the results for many dependent structures,such as END,ϱ^(*)mixing,ϱ^(-)mixing andφ-mixing,etc.

LOWER BOUNDS FOR WEAK BYZANTINE AGREEMENT

Lower bounds for Byzantine agreement obtained by Dolev and Strong are shown, by a simplermethod, also to be true for weak Byzantine agreement.

Study of weakly-bound odd-A nuclei with quasiparticle blocking

The coordinate-space Hartree-Fock-Bogoliubov（HFB） approach with quasiparticle blocking has been applied to study the odd-A weakly bound nuclei ^17,19B and ^37Mg,in which halo structures have been reported in experiments.The Skyrme nuclear forces SLy4 and UNEDF1 have been adopted in our calculations.The results with and without blocking have been compared to demonstrate the emergence of deformed halo structures due to blocking effects.In our calculations,^19B and ^37Mg have remarkable features of deformed halos.

Systematic extraction of the strong absorption distance and Coulomb barrier from elastic scattering

The reduced strong absorption distance d_(S) and Coulomb barrier height V_(B) are extracted from the quarter-point recipe from a series of experimental elastic scattering angle distributions.The nuclei with different binding energies are systematically studied as the projectile,including the tightly bound,weakly bound,and halo nuclei.It is found that the mean d_(S) for halo nuclei is significantly larger than that of tightly and weakly bound nuclei.The complex behavior of d_(S) regarding the binding energy and properties of the target is observed for halo nuclei.The linear relationship of the reduced distance with system size may be used to estimate the Coulomb barrier radius R_(B),which is difficult to obtain from fusion reactions.The rule of V_(B) concerning the Coulomb parameter z is in agreement with other theoretical barrier laws extracted from the fusion reaction.Furthermore,the reason why the binding energy or deformation has little effect on the linear relationship of V_(B) as a function of z is clarified.

Further investigation on the fusion of ^(6)Li with ^(209)Bi target at near-barrier energies

The complete and incomplete fusion cross sections for ^(6)Li+^(209)Bi were measured using the in-beamγ-ray method around the Coulomb barrier.The cross sections of(deuteron captured)incomplete fusion(ICF)products were re-quantified experimentally for this reaction system.The results reveal that the ICF cross section is equivalent to that of complete fusion(CF)above the Coulomb barrier and dominant near or below the Coulomb barrier.A theoretical calculation based on the continuum discretized coupled channel(CDCC)method was performed for the aforementioned CF and ICF cross sections;the result is consistent with the experiments.The universal fusion function(UFF)was also compared with the measured CF cross section for different barrier parameters,demonstrating that the CF suppression factor is significantly influenced by the choice of potential,which can reflect both dynamic and static effects of breakup on the fusion process.

Fusion and one-neutron stripping process for ^(6)Li+^(94)Zr system around the Coulomb Barrier

The complete and incomplete fusion cross section as well as one-neutron stripping process of ^(6)Li+^(94)Zr system were measured at the energies around the Coulomb barrier by onlineγ-ray method.In addition to a 30%suppression factor when compared with the measured total fusion process,the complete fusion cross section in ^(6)Li+^(94)Zr system was observed to be significantly lower than those in the nearby ^(6)Li+^(90,96)Zr system.The new experimental result implies that the coupling with breakup channel in the ^(6)Li-induced fusion processes can be affected by the inner structure of the target,which is still not clear in any available model calculation.For the one-neutron stripping process,the direct production cross sections for each level in 95Zr were extracted and compared with the coupled reaction channel calculation,offering a unique opportunity to examine the single-particle nature of the produced excited states.Given the fact that an overall overestimation of the production cross section for 954-keV and1618-keV levels was observed in the comparison,further investigation is highly demanded in order to understand the full reaction mechanism for the one-neutron stripping process induced by ^(6)Li.

THE VOLUME AND TOPOLOGY OF A COMPLETE RIEMANNIAN MANIFOLD

It is conjectured that the manifold with nonnegative Ricci curvature and weaked bounded geometry is of finite topological type, if The paper partially solves this conjecture. In the same time, the paper also discusses the volume growth of a manifold with asymptotically nonnegative Ricci curvature.

Single-Doppler Radar Observations of a High Precipitation Supercell Accompanying the 12 April 2003 Severe Squall Line in Fujian Province

In this study,single Doppler radar data were used to examine the structure and evolution of a high precipitation（HP） supercell embedded in a cold front near Jianyang,Fujian Province on 12 April 2003.The synoptic environment was characterized by high humidity at low levels,moderate CAPE（convective available potential energy;1601 J kg^（-1））,moderate wind shear（22 m s^（-1） in 0-5 km）,and veering of the horizontal winds with height,similar to those HP supercells previously observed in midlatitudes.In addition,the calculated bulk Richardson number was only 16,suggesting favorable environmental conditions for supercell development. The documented storm was located at the leading edge of a squall line.It was initiated from a single cell at 0732 UTC.It evolved into a bow shape gradually,and then split into two separate storms along the storm motion direction through the apex of the bow echo.The left-moving storm dissipated rapidly, but the right-moving storm strengthened and evolved into an HP supercell,lasting for more than 1 h.The radar reflectivity of the HP supercell during its mature stage showed a typical low-level hook echo at the front flank of the storm with its maximum reflectivity beyond 70 dBZ.Above the hook echo,an elevated maximum reflectivity core accompanied by a bounded weak-echo region（BWER） and a down-shear echo overhanging aloft were clearly identified.The elevated BWER,marked by 40-50-dBZ reflectivity values,was surrounded by values of 60-70 dBZ.A well-defined mesocyclone lasted about 1 h and was collocated with the low-level WER and middle-level BWER.The radar-estimated time-height profiles of mesocyclone rotational velocity and diameter indicated that this mesocyclone formed initially at middle level,then deepened and strengthened rapidly with the vertical depth deeper than 8 km and rotational velocity stronger than 24 m s^（-1） at the mature stage,and later decayed rapidly.The GBVTD（ground-based velocity track display）-derived primary circulation showed that the maximum tangential wind of the mesocyclone appeared at middle level （3-5 km） with a value of about 20 m s^（-1）.The mean radial wind field was characterized with a low-level inflow below 4 km,and accompanied by stronger updraft near the mesocyclone center.Between 4 and 7 km.the tangential wind profile resembled a Rankine combined vortex with the radius of maximum wind （RMW） at 3 km.and there was outflow/inflow inside/outside of the RMW.Correspondingly,the vertical velocity indicated a stronger updraft at the RMW and a weak downdraft inside the RMW.Above 7 km,the outflow strengthened and extended outside the RMW. In summary,the reflectivity structures of the storm and the accompanying mesocyclone were similar to those midlatitude HP supercells proposed in Miller＇s paper in 1994.However,the evolution of the HP supercell,including its three stages：ordinary storm,bow echo,and storm splitting,was quite different from those documented before.

Role of projectile breakup effects and intrinsic degrees of freedom on fusion dynamics

This article analyzes the fusion dynamics of loosely bound and stable projectiles with Zr-target isotopes within the context of the coupled channel approach and the energy-dependent Woods-Saxon potential model （EDWSP model）. In the case of the 2SSi＋90Zr reaction, the coupling to the inelastic surface excitations results in an adequate description of the observed fusion dynamics while in case of the 2Ssi ＋ 94Zr reaction, the coupling to collective surface vibrational states as well as the neutron （multi-neutron） transfer channel is necessary in the coupled channel calculations to reproduce the below-barrier fusion data. However, the EDWSP model calculation provides an accurate explanation of the fusion data of 2Ssi＋ 90,94Zr reactions in the domain of the Coulomb barrier. In the fusion of the 6Li＋90Zr reaction, the inclusion of the nuclear structure degrees of freedom recovers the observed sub-barrier fusion enhancement but results in suppression of the above barrier fusion data by 34% with respect to the coupled channel calculations. Using EDWSP model calculations, this suppression factor is reduced by 14% and consequently, the above-barrier fusion data of 6Li＋90Zr reaction is suppressed by 20% with reference to the EDWSP model calculations. Such fusion suppression at above-barrier energies can be correlated with the breakupof the projectile （6Li） before reaching the fusion barrier, as a consequence of low binding energy.

CDCC calculations of fusion of 6Li with targets 144Sm and 154Sm：effect of resonance states

Continuum Discretized Coupled-Channel（CDCC） model calculations of total, complete and incomplete fusion cross sections for reactions of the weakly bound 6Li with 144,154Sm targets at energies around the Coulomb barrier are presented. In the cluster structure frame of 6Li→α＋d, short-range absorption potentials are considered for the interactions between the ground state of the projectile 6Li and α-d fragments with the target. In order to separately calculate complete and incomplete fusion and to reduce double-counting, the corresponding absorption potentials are chosen to be of different range. Couplings to low-lying excited states 2＋, 3-of 144Sm and 2＋, 4＋ of 154Sm are included. So, the effect on total fusion from the excited states of the target is investigated. Similarly, the effect on fusion due to couplings to resonance breakup states of 6Li, namely, l = 2,Jπ= 3＋, 2＋, 1＋ is also calculated.The latter effect is determined by using two approaches,（a） by considering only resonance state couplings and（b）by omitting these states from the full discretized energy space. Among other things, it is found that both resonance and non-resonance continuum breakup couplings produce fusion suppression at all the energies considered.

Relative probabilities of breakup channels in reactions of^(6.7)Li with^(209)Biat energies around and above the Coulomb barrier

Coincidence measurements of breakup fragments in reactions of^(6.7)with^(209)Bi at energies around and above the Coulomb barrier were carried out using a large solid-angle covered detector array.Through the Q values along with the relative energies of the breakup fragments,different breakup components(prompt breakups and delayed breakups)and different breakup modes(α+t,α+d,α+p,andα+α)are distinguished.A new breakup mode,α+t,is observed in^(6)Li-induced reactions at energies above the Coulomb barrier.Correlations between breakup modes and breakup components as well as their variations with the incident energy are investigated.The results will help us better understand the breakup effects of weakly bound nuclei on the suppression of a complete fusion,particularly for the above-barrier energies.

Two New Lipschitz Type Spaces and Their Characterizations

In this paper,we first introduce the weak Lipschitz spaces WLip_(q,α),1<q<∞,0<α<1 which are the analog of weak Lebesgue spaces L^(q,∞)in the setting of Lipschitz space.We obtain the equivalence between the norm ||·||_(Lipα)and ||·||_(()WLip_(q,α)).As an application,we show that the commutator M_(β)~b is bounded from L~p to L^(q,∞) for some p ∈(1,∞) and 1/p-1/q=(α+β)/n if and only if b is in Lip_(α).We also introduce the weak central bounded mean oscillation space WCBMO_(q,α) and give a characterization of WCBMO_(q,α) via the boundedness of the commutators of Hardy type operators.