Probing the Structure of Unstable Nuclei Through the Recoiled Proton Tagged Knockout Reaction

Recoiled proton tagged knockout reaction experiments were carried-out for He-8 at 82.5 MeV/u in RIKEN and for He-6 at 65 MeV/u in Lanzhou. The very preliminary results for the distinguish of the reaction mechanism are presented and compared to the kinematics calculation.

Elastic Scattering of He-6 + p at 82.3 MeV/nucleon

Differential cross sections for the elastic scattering of halo nucleus He-6 on proton target were measured at 82.3 MeV/u. The experimental results are well reproduced by optical model calculations using global potential KD02 with a reduction of the depth of real volume part by a factor of 0.7. A systematic analysis shows that this behavior might be related to the weakly bound property of unstable nuclei.

EXPERIMENTAL INVESTIGATION OF THE STELLAR REACTION S-30(p, gamma)(31) Cl VIA COULOMB DISSOCIATION

The Coulomb dissociation of the proton-rich nuclei Cl-31 was studied experimentally using Cl-31 beams at 58 MeV/nucleon with a lead target. The relative energy between the reaction products, S-30 and proton, was obtained. The first excited state in Cl-31 was observed which is relevant to the resonant capture of stellar S-30(p, gamma)Cl-31 reaction

MEASUREMENT OF TWO-PROTON CORRELATION FROM THE BREAK-UP OF Al-23

Experiments of Al-23 and Mg-22 radioactive beams bombarding a C-12 target at an energy of 60 similar to 70 A MeV have been performed at the projectile fragment separator beamline (RIPS) in the RIKEN Ring Cyclotron Facility to study the two-proton emission from Al-23 and Mg-22 excited states, respectively. The trajectorie of the decay products, namely Na-21 + p + p from Al-23 and Ne-20 + p + p from Mg-22, are clean identified. The relative momentum and opening angle between two protons in the rest frame of three body decay channels are obtained by relativistic-kinematics reconstruction. The results demonstrate that there are some di-proton emission components from He-2 cluster for the excited Al-23 and Mg-22.

MEASUREMENT OF THE PROTON-PROTON CORRELATION FUNCTION FROM THE BREAK-UP OF Mg-22 AND Ne-20

An experiment of Mg-22 and Ne-20 beams bombarding on a C-12 target at an energy of 60 similar to 70 A MeV has been performed at the RIKEN projectile fragment separator (RIPS)in the RIKEN Ring Cyclotron Facility to study the two-proton correlated emission from Mg-22 and Ne-20 excited states. The two-protons momentum correlation functions have been obtained for Mg-22 and Ne-20, respectively. The trajectories of the Mg-22 decayed products (Ne-20 + p + p) were also measured to get the angular correlations between the two protons in Center of Mass of decaying system by relativistic-kinematics reconstruction. The results exhibit that Mg-22 has the features of He-2 cluster decay mechanism.

On subspace lattices II. Continuity of Lat

We study the continuity of the map Lat sending an ultraweakly closed operator algebra to its invariant subspace lattice. We provide an example showing that Lat is in general discontinuous and give sufficient conditions for the restricted continuity of this map. As consequences we obtain that Lat is continuous on the classes of von Neumann and Arveson algebras and give a general approximative criterion for reflexivity, which extends Arvesonâ??s theorem on the reflexivity of commutative subspace lattices.

On subspace lattices I. Closedness type properties and tensor products

We study properties of subspace lattices related to the continuity of the map Lat and the notion of reflexivity. We characterize various “closedness” properties in different ways and give the hierarchy between them. We investigate several properties related to tensor products of subspace lattices and show that the tensor product of the projection lattices of two von Neumann algebras, one of which is injective, is reflexive.

Graphs of relations and Hilbert series

We are discussing certain combinatorial and counting problems related to quadratic algebras. First we give examples which confirm the Anick conjecture on the minimal Hilbert series for algebras given by $n$ generators and $\frac {n(n-1)}{2}$ relations for $n \leq 7$. Then we investigate combinatorial structure of colored graph associated to relations of RIT algebra. Precise descriptions of graphs (maps) corresponding to algebras with maximal Hilbert series are given in certain cases. As a consequence it turns out, for example, that RIT algebra may have a maximal Hilbert series only if components of the graph associated to each color are pairwise 2-isomorphic.

Multiplicative spectra of Banach spaces

The multiplicative spectrum of a complex Banach space X is the class K(X) of all (automatically compact and Hausdorff) topological spaces appearing as spectra of Banach algebras (X,*) for all possible continuous multiplications on X turning X into a commutative associative complex algebra with the unity. The properties of the multiplicative spectrum are studied. In particular, we show that K(X^n) consists of countable compact spaces with at most n non-isolated points for any separable hereditarily indecomposable Banach space X. We prove that K(C[0,1]) coincides with the class of all metrizable compact spaces.

Non-trivial stably free modules over crossed products

We consider the class of crossed products of noetherian domains with universal enveloping algebras of Lie algebras. For algebras from this class we give a sufficient condition for the existence of projective non-free modules. This class includes Weyl algebras and universal envelopings of Lie algebras, for which this question, known as noncommutative Serre's problem, was extensively studied before. It turns out that the method of lifting of non-trivial stably free modules from simple Ore extensions can be applied to crossed products after an appropriate choice of filtration. The motivating examples of crossed products are provided by the class of RIT algebras, originating in non-equilibrium physics.

Multidimensional operator multipliers

We introduce multidimensional Schur multipliers and characterise them, generalising well-known results by Grothendieck and Peller. We define a multidimensional version of the two-dimensional operator multipliers studied recently by Kissin and Shulman. The multidimensional operator multipliers are defined as elements of the minimal tensor product of several C *-algebras satisfying certain boundedness conditions. In the case of commutative C*-algebras, the multidimensional operator multipliersreduce to continuousmul-tidimensional Schur multipliers. We show that the multiplierswith respect to some given representations of the corresponding C*-algebrasdo not change if the representations are replaced by approximately equivalent ones. We establish a non-commutative and multidimensional version of the characterisations by Grothendieck and Peller which shows that universal operator multipliers can be obtained ascertain weak limits of elements of the algebraic tensor product of the corresponding C *-algebras.

Compactness properties of operator multipliers

We continue the study of multidimensional operator multipliers initiated in~cite{jtt}. We introduce the notion of the symbol of an operator multiplier. We characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers. We give sufficient conditions for the sets of compact and completely compact multipliers to coincide and characterise the cases where an operator multiplier in the minimal tensor product of two C*-algebras is automatically compact. We give a description of multilinear modular completely compact completely bounded maps defined on the direct product of finitely many copies of the C*-algebra of compact operators in terms of tensor products, generalising results of Saar

Stable isomorphism of dual operator spaces

We prove that two dual operator spaces $X$ and $Y$ are stably isomorphic if and only if there exist completely isometric normal representations $phi$ and $psi$ of $X$ and $Y$, respectively, and ternary rings of operators $M_1, M_2$ such that $phi (X)= [M_2^*psi (Y)M_1]^{-w^*}$ and $psi (Y)=[M_2phi (X)M_1^*].$ We prove that this is equivalent to certain canonical dual operator algebras associated with the operator spaces being stably isomorphic. We apply these operator space results to prove that certain dual operator algebras are stably isomorphic if and only if they are isomorphic. We provide examples motivated by CSL algebra theory.

On the weak amenability of β(X)

We investigate the weak amenability of the Banach algebra ß(X) of all bounded linear operators on a Banach space X. Sufficient conditions are given for weak amenability of this and other Banach operator algebras with bounded one-sided approximate identities.