Isomeric transitions between shape coexisting states in iodine isotopes withA=115, 119 and 121

Applying delayed- r.f. coincidences and generalized centroid-shift analysis, nanosecond isomers in some odd-A iodine isotopes are studied in-beam. The reactions¹⁰⁶Cd(¹²C,p2n) and^116,118Sn(⁶Li,3n) have been used. The following half-lives were determined:T _1/2(565 keV)=0.50±0.10 ns andT _1/2(837 keV) =0.90±0.20 ns in¹¹⁵I,T _1/2(687 keV)=5.50±0.50 ns andT _1/2(2418 keV)=4.0±0.50 ns in¹¹⁹I as well asT _1/2(812 keV)=0.35±0.20 ns andT _1/2(445 keV)<0.10 ns=">¹²¹I. A systematics of the absolute probabilities for the transitions deexciting theg _9/2 9/2⁺ and _11/2 11/2 ₁ ^– band heads in^115–125I is presented and discussed.Partly supported by the Bulgarian National Research Foundation under contracts PH14, and PH31 and Kernforschungszentrum Karlsruhe, Stabsabteilung Internationale Beziehungen     

Temperature measurements in CO2-laser-induced pyrolysis flames for SiC and ternary SiC/C/B powder synthesis by means of CARS

The hot luminescent reaction zones of CO₂-laser-induced pyrolysis flames using SiH₄/C₂H₂ gas mixtures with different silane to acetylene ratios and with and without diborane additives were investigated by means of H₂ Q-branch CARS spectroscopy, leading to spatial temperature profiles in gas flow direction. In the case of B₂H₆ additive to the stoichiometric SiH₄/C₂H₂ mixture a high temperature plateau ( 800–1000 K) of the reactant gas volume develops already several millimetres before reaching the CO₂-laser focus line. This precursor preheating zone could be explained by the catalytic effect of boron atoms or boron-containing intermediate species in the flame. A similar behaviour for acetylene-rich flames operating at half laser power was not observed.     

Inclusion-exclusion: Exact and approximate

It is often required to find the probability of the union of givenn eventsA ₁ ,...,A _n . The answer is provided, of course, by the inclusion-exclusion formula: Pr(A _i )= _i – _i<j Pr(A _i A _j )±.... Unfortunately, this formula has exponentially many terms, and only rarely does one manage to carry out the exact calculation. From a computational point of view, finding the probability of the union is an intractable, #P-hard problem, even in very restricted cases. This state of affairs makes it reasonable to seek approximate solutions that are computationally feasible. Attempts to find such approximate solutions have a long history starting already with Boole [1]. A recent step in this direction was taken by Linial and Nisan [4] who sought approximations to the probability of the union, given the probabilities of allj-wise intersections of the events forj=1,...k. The developed a method to approximate Pr(A _i ), from the above data with an additive error of exp . In the present article we develop an expression that can be computed in polynomial time, that, given the sums _|S|=j Pr( _iS A _i ) forj=1,...k, approximates Pr(A _i ) with an additive error of exp . This error is optimal, up to the logarithmic factor implicit in the notation.The problem of enumerating satisfying assignments of a boolean formula in DNF formF=v _l ^m C _i is an instance of the general problem that had been extensively studied [7]. HereA _i is the set of assignments that satisfyC _i , and Pr( _iS A _i )=a _S /2ⁿ where _iS C _i is satisfied bya _S assignments. Judging from the general results, it is hard to expect a decent approximation ofF's number of satisfying assignments, without knowledge of the numbersa _S for, say, all cardinalities . Quite surprisingly, already the numbersa _S over |S|log(n+1)uniquely determine the number of satisfying assignments for F.We point out a connection between our work and the edge-reconstruction conjecture. Finally we discuss other special instances of the problem, e.g., computing permanents of 0,1 matrices, evaluating chromatic polynomials of graphs and for families of events whose VC dimension is bounded.Work supported in part by a grant of the Binational Israel-US Science Foundation.Work supported in part by a grant of the Binational Israel-US Science Foundation and by the Israel Science Foundation.     

Common supports as fixed points

A family S of sets in R ^d is sundered if for each way of choosing a point from rd+1 members of S, the chosen points form the vertex-set of an (r–1)-simplex. Bisztriczky proved that for each sundered family S of d convex bodies in R ^d , and for each partition (S , S ), of S, there are exactly two hyperplanes each of which supports all the members of S and separates the members of S from the members of S . This note provides an alternate proof by obtaining each of the desired supports as (in effect) a fixed point of a continuous self-mapping of the cartesian product of the bodies.     

Survey of experimental results on μCF including hyperfine effects

Complementary to the investigations of the most efficient dt cycle, also the other muon-induced fusion cycles in mixtures of hydrogen isotopes have been studied. The results of these dedicated experiments provide rich information about muon-induced few-body reactions and contribute significantly to a better overall understanding of CF. A summary of the recent progress will be presented. Special emphasis will be put on two characteristic examples, namely a new experimental approach to study the muonic cascade in H-D mixtures and the systematic study of hyperfine effects in muon-induced reactions.     

The kinetics of muon-catalyzed dt fusion

A main source of information about the muon-catalyzed fusion cycle in D-T mixtures are the cycling rates _c, which are characteristic for the kinetic equilibrium of states attained rapidly in dense targets. The measurement, analysis and interpretation of these rates will be discussed, concentrating on the extensive set of rates observed at PSI over the last decade in gaseous, liquid and solid targets.Invited talk presented by Peter Kammel.     

Two-proton multiplets in theN=82 nucleus 62 144 Sm82 from in-beamγ-measurements

In a high sensitivity (,2n) in-beam study of ₆₂ ¹⁴⁴ Sm₈₂, with the Kölner Würfel OSIRIS -detector array including a Compton polarimeter, we have identified the complete two-proton multiplets d ₅ ^2/–2 , d ₅ ^2/–1 g ₇ ^2/–1 , g ₇ ^2/–2 , h_11/2d ₅ ^2/–1 and the 9^– to 4^– members of the h_11·/2g ₇ ^2/–1 multiplet.Work partially supported by CICYT (Spain).