Search results for "Matrix"
showing 10 items of 3205 documents
On a differential system arising in the network control theory
2016
We investigate the three-dimensional dynamical system occurring in the network regulatory systems theory for specific choices of regulatory matrix { { 0, 1, 1 } { 1, 0, 1 } { 1, 1, 0 } } and sigmoidal regulatory function f(z) = 1 / (1 + e-μz), where z = ∑ Wij xj - θ. The description of attracting sets is provided. The attracting sets consist of respectively one, two or three critical points. This depends on whether the parameters (μ,θ) belong to a set Ω or to the complement of Ω or to the boundary of Ω, where Ω is fully defined set.
Study of odd-mass N = 82 isotones with realistic effective interactions
1997
The microscopic quasiparticle-phonon model, MQPM, is used to study the energy spectra of the odd $Z=53 - 63$, N=82 isotones. The results are compared with experimental data, with the extreme quasiparticle-phonon limit and with the results of an unrestricted $2s1d0g_{7/2}0h_{11/2}$ shell model (SM) calculation. The interaction used in these calculations is a realistic two-body G-matrix interaction derived from modern meson-exchange potential models for the nucleon-nucleon interaction. For the shell model all the two-body matrix elements are renormalized by the $\hat{Q}$-box method whereas for the MQPM the effective interaction is defined by the G-matrix.
$\gamma W$-box Inside-Out: Nuclear Polarizabilities Distort the Beta Decay Spectrum
2019
I consider the $\gamma W$-box correction to superallowed nuclear $\beta$-decays in the framework of dispersion relations. I address a novel effect of a distortion of the emitted electron energy spectrum by nuclear polarizabilities and show that this effect, while neglected in the literature, is sizable. I estimate its size in the approximation of a linear energy dependence, and using two models that are expected to give the lower and the upper bound. The respective correction to the $\beta^+$ spectrum is estimated to be $\Delta_R(E)=(1.6\pm1.6)\times10^{-4}{E}/{\rm MeV}$ assuming a conservative 100\% uncertainty. The effect is positive-definite and can be observed if a high-precision measur…
Has the neutral double hypernucleus nΛΛ4 been observed?
2019
Abstract The BNL-AGS E906 experiment was the first fully electronic experiment to produce and study double hypernuclei with large statistics. Two dominant structures were observed in the correlated π − – π − momentum matrix at ( p π − H , p π − L ) = ( 133 , 114 ) MeV / c and at ( 114 , 104 ) MeV / c . In this work we argue that the interpretation of the structure at ( 133 , 114 ) MeV / c in terms of Λ 3 H+ Λ 4 H pairs is questionable. We show, that neither a scenario where these single-Λ hypernuclei are produced after capture of a stopped Ξ − by a 9Be nucleus nor interactions of energetic Ξ − with 9Be nuclei in the target material can produce a sufficient amount of such twin pairs. We have…
Couplings in coupled channels versus wave functions: Application to theX(3872)resonance
2010
We perform an analytical study of the scattering matrix and bound states in problems with many physical coupled channels. We establish the relationship of the couplings of the states to the different channels, obtained from the residues of the scattering matrix at the poles, with the wave functions for the different channels. The couplings basically reflect the value of the wave functions around the origin in coordinate space. In the concrete case of the $X(3872)$ resonance, understood as a bound state of ${D}^{0}{\overline{D}}^{*0}$ and ${D}^{+}{D}^{*\ensuremath{-}}$ (and $c.c.$ From now on, when we refer to ${D}^{0}{\overline{D}}^{*0}$ , ${D}^{+}{D}^{*\ensuremath{-}}$, or $D{\overline{D}}…
Couplings in coupled channels versus wave functions in the case of resonances: Application to the twoΛ(1405)states
2011
In this paper we develop a formalism to evaluate wave functions in momentum and coordinate space for the resonant states dynamically generated in a unitary coupled channel approach. The on-shell approach for the scattering matrix, commonly used, is also obtained in quantum mechanics with a separable potential, which allows one to write wave functions in a trivial way. We develop useful relationships among the couplings of the dynamically generated resonances to the different channels and the wave functions at the origin. The formalism provides an intuitive picture of the resonances in the coupled channel approach, as bound states of one bound channel, which decays into open ones. It also pr…
Isospin dependence of electromagnetic transition strengths among an isobaric triplet
2019
*Aydın, Sezgin ( Aksaray, Yazar )
Consistent large-scale shell-model analysis of the two-neutrino ββ and single β branchings in 48Ca and 96Zr
2020
Abstract Two-neutrino double-beta-decay matrix elements M 2 ν and single beta-decay branching ratios were calculated for 48Ca and 96Zr in the interacting nuclear shell model using large single-particle valence spaces with well-tested two-body Hamiltonians. For 48Ca the matrix element M 2 ν = 0.0511 is obtained, which is 5.5% smaller than the previously reported value of 0.0539. For 96Zr this work reports the first large-scale shell-model calculation of the nuclear matrix element, yielding a value M 2 ν = 0.0747 with extreme single-state dominance. These matrix elements, combined with the available ββ-decay half-life data, yield effective values of the weak axial coupling which in turn are u…
Measurement of the W-pair cross section in $e^+ e^-$ collisions at 172 GeV
1997
The e(+)e(-) --> W+W- cross section is measured in a data sample collected by ALEPH at a mean centre-of-mass energy of 172.09 GeV, corresponding to an integrated luminosity of 10.65 pb(-1). Cross sections are given for the three topologies, fully leptonic, semi-leptonic and hadronic of a W-pair decay. Under the assumption that no other decay modes are present, the W-pair cross section is measured to be 11.7 +/- 1.2(stat.) +/- 0.3(syst.) pb. The existence of the triple gauge boson vertex of the Standard Model is clearly preferred by the data. The decay branching ratio of the W boson into hadrons is measured to be B(W --> hadrons) = 67.7 +/- 3.1(stat.) +/- 0.7(syst.) %, allowing a determinati…
Microscopic description of low-lying two-phonon states: Electromagnetic transitions
2003
Microscopic description of low-lying two-phonon states in even-even nuclei is introduced. The main building blocks are the quasiparticle random-phase approximation (QRPA) phonons. A realistic microscopic nuclear Hamiltonian, based on the Bonn one-boson-exchange potential, is diagonalized in a basis containing one-phonon and two-phonon components, coupled to a given angular momentum and parity. The QRPA equations are directly used in deriving the equations of motion for the two-phonon states. The Pauli principle is taken into account by diagonalizing the metric matrix and discarding the zero-norm states. The electromagnetic transition matrix elements are derived in terms of the metric matrix…