246 research outputs found
p-wave phase shift and scattering length of Li
We have calculated the p-wave phase shifts and scattering length of Li.
For this we solve the partial wave Schr\"odinger equation and analyze the
validity of adopting the semiclassical solution to evaluate the constant
factors in the solution. Unlike in the wave case, the semiclassical
solution does not provide unique value of the constants. We suggest an
approximate analytic solution, which provides reliable results in special
cases. Further more, we also use the variable phase method to evaluate the
phase shifts. The p-wave scattering lengths of Cs and Cs are
calculated to validate the schemes followed. Based on our calculations, the
value of the wave scattering length of Li is .Comment: 10 figure
Bounds for graph regularity and removal lemmas
We show, for any positive integer k, that there exists a graph in which any
equitable partition of its vertices into k parts has at least ck^2/\log^* k
pairs of parts which are not \epsilon-regular, where c,\epsilon>0 are absolute
constants. This bound is tight up to the constant c and addresses a question of
Gowers on the number of irregular pairs in Szemer\'edi's regularity lemma.
In order to gain some control over irregular pairs, another regularity lemma,
known as the strong regularity lemma, was developed by Alon, Fischer,
Krivelevich, and Szegedy. For this lemma, we prove a lower bound of
wowzer-type, which is one level higher in the Ackermann hierarchy than the
tower function, on the number of parts in the strong regularity lemma,
essentially matching the upper bound. On the other hand, for the induced graph
removal lemma, the standard application of the strong regularity lemma, we find
a different proof which yields a tower-type bound.
We also discuss bounds on several related regularity lemmas, including the
weak regularity lemma of Frieze and Kannan and the recently established regular
approximation theorem. In particular, we show that a weak partition with
approximation parameter \epsilon may require as many as
2^{\Omega(\epsilon^{-2})} parts. This is tight up to the implied constant and
solves a problem studied by Lov\'asz and Szegedy.Comment: 62 page
A quantitative version of the non-abelian idempotent theorem
Suppose that G is a finite group and A is a subset of G such that 1_A has
algebra norm at most M. Then 1_A is a plus/minus sum of at most L cosets of
subgroups of G, and L can be taken to be triply tower in O(M). This is a
quantitative version of the non-abelian idempotent theorem.Comment: 82 pp. Changed the title from `Indicator functions in the
Fourier-Eymard algebra'. Corrected the proof of Lemma 19.1. Expanded the
introduction. Corrected typo
Measurement of W Polarisation at LEP
The three different helicity states of W bosons produced in the reaction e+
e- -> W+ W- -> l nu q q~ at LEP are studied using leptonic and hadronic W
decays. Data at centre-of-mass energies \sqrt s = 183-209 GeV are used to
measure the polarisation of W bosons, and its dependence on the W boson
production angle. The fraction of longitudinally polarised W bosons is measured
to be 0.218 \pm 0.027 \pm 0.016 where the first uncertainty is statistical and
the second systematic, in agreement with the Standard Model expectation
Search for Anomalous Couplings in the Higgs Sector at LEP
Anomalous couplings of the Higgs boson are searched for through the processes
e^+ e^- -> H gamma, e^+ e^- -> e^+ e^- H and e^+ e^- -> HZ. The mass range 70
GeV < m_H < 190 GeV is explored using 602 pb^-1 of integrated luminosity
collected with the L3 detector at LEP at centre-of-mass energies
sqrt(s)=189-209 GeV. The Higgs decay channels H -> ffbar, H -> gamma gamma, H
-> Z\gamma and H -> WW^(*) are considered and no evidence is found for
anomalous Higgs production or decay. Limits on the anomalous couplings d, db,
Delta(g1z), Delta(kappa_gamma) and xi^2 are derived as well as limits on the H
-> gamma gamma and H -> Z gamma decay rates
Measurement of W Polarisation at LEP
The three different helicity states of W bosons produced in the reaction e+
e- -> W+ W- -> l nu q q~ at LEP are studied using leptonic and hadronic W
decays. Data at centre-of-mass energies \sqrt s = 183-209 GeV are used to
measure the polarisation of W bosons, and its dependence on the W boson
production angle. The fraction of longitudinally polarised W bosons is measured
to be 0.218 \pm 0.027 \pm 0.016 where the first uncertainty is statistical and
the second systematic, in agreement with the Standard Model expectation
Bose-Einstein Correlations of Neutral and Charged Pions in Hadronic Z Decays
Bose-Einstein correlations of both neutral and like-sign charged pion pairs
are measured in a sample of 2 million hadronic Z decays collected with the L3
detector at LEP. The analysis is performed in the four-momentum difference
range 300 MeV < Q < 2 GeV. The radius of the neutral pion source is found to be
smaller than that of charged pions. This result is in qualitative agreement
with the string fragmentation model
Z Boson Pair-Production at LEP
Events stemming from the pair-production of Z bosons in e^+e^- collisions are
studied using 217.4 pb^-1 of data collected with the L3 detector at
centre-of-mass energies from 200 GeV up to 209 GeV. The special case of events
with b quarks is also investigated.
Combining these events with those collected at lower centre-of-mass energies,
the Standard Model predictions for the production mechanism are verified. In
addition, limits are set on anomalous couplings of neutral gauge bosons and on
effects of extra space dimensions
Neutral-Current Four-Fermion Production in e+e- Interactions at LEP
Neutral-current four-fermion production, e+e- -> ffff is studied in 0.7/fb of
data collected with the L3 detector at LEP at centre-of-mass energies
root(s)=183-209GeV. Four final states are considered: qqvv, qqll, llll and
llvv, where l denotes either an electron or a muon. Their cross sections are
measured and found to agree with the Standard Model predictions. In addition,
the e+e- -> Zgamma* -> ffff process is studied and its total cross section at
the average centre-of-mass energy 196.6GeV is found to be 0.29 +/- 0.05 +/-
0.03 pb, where the first uncertainty is statistical and the second systematic,
in agreement with the Standard Model prediction of 0.22 pb. Finally, the mass
spectra of the qqll final states are analysed to search for the possible
production of a new neutral heavy particle, for which no evidence is found
Measurement of Exclusive rho+rho- Production in Mid-Virtuality Two-Photon Interactions and Study of the gamma gamma* -> rho rho Process at LEP
Exclusive rho+rho- production in two-photon collisions between a quasi-real
photon, gamma, and a mid-virtuality photon, gamma*, is studied with data
collected at LEP at centre-of-mass energies root(s)=183-209GeV with a total
integrated luminosity of 684.8pb^-1. The cross section of the gamma gamma* ->
rho+ rho- process is determined as a function of the photon virtuality, Q^2,
and the two-photon centre-of-mass energy, W_gg, in the kinematic region:
0.2GeV^2 < Q^2 <0.85GeV^2 and 1.1GeV < W_gg < 3GeV. These results, together
with previous L3 measurements of rho0 rho0 and rho+ rho- production, allow a
study of the gamma gamma* -> rho rho process over the Q^2-region 0.2GeV^2 < Q^2
< 30 GeV^2
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