Search results for "Functional analysis"
showing 10 items of 1059 documents
General treatment of vortical, toroidal, and compression modes
2011
The multipole vortical, toroidal, and compression modes are analyzed. Following the vorticity concept of Ravenhall and Wambach, the vortical operator is derived and related in a simple way to the toroidal and compression operators. The strength functions and velocity fields of the modes are analyzed in $^{208}$Pb within the random-phase-approximation using the Skyrme force SLy6. Both convection and magnetization nuclear currents are taken into account. It is shown that the isoscalar (isovector) vortical and toroidal modes are dominated by the convection (magnetization) nuclear current while the compression mode is fully convective. The relation between the above concept of the vorticity to …
Coupled-cluster singles, doubles and triples (CCSDT) calculations of atomization energies
2000
Atomization energies have been calculated for CO, H2O, F-2, HF, N-2 and CH2 (the (1)A(1) state) using the coupled-duster singles, doubles and triples (CCSDT) model as well as the coupled-cluster singles and doubles model with a perturbative correction for triples [CCSD(T)]. TheCCSD(T) model provides an excellent approximation to the CCSDT model; at the cc-pV5Z basis set level, the CCSDT valence triples contribution is underestimated by 9.1% (0.8 kJ/mol) for CH, and overestimated for the remaining molecules by as little as 4.3%(1.3 kJ/mol) for F-2,and as much as 8.4% (3.0 kJ/mol) for N-2. At the CCSDT level, the agreement with experiment is not improved, suggesting that some cancellation of …
Spectrum-shape method and the next-to-leading-order terms of the β-decay shape factor
2017
Effective values of the axial-vector coupling constant ${g}_{\mathrm{A}}$ have lately attracted much attention due to the prominent role of ${g}_{\mathrm{A}}$ in determining the half-lives of double $\ensuremath{\beta}$ decays, in particular their neutrinoless mode. The half-life method, i.e., comparing the calculated half-lives to the corresponding experimental ones, is the most widely used method to access the effective values of ${g}_{\mathrm{A}}$. The present paper investigates the possibilities offered by a complementary method: the spectrum-shape method (SSM). In the SSM, comparison of the shapes of the calculated and measured $\ensuremath{\beta}$ electron spectra of forbidden nonuniq…
Improved determination of the β−ν¯e angular correlation coefficient a in free neutron decay with the aSPECT spectrometer
2020
We report on a precise measurement of the electron-antineutrino angular correlation ($a$ coefficient) in free neutron beta-decay from the $a$SPECT experiment. The $a$ coefficient is inferred from the recoil energy spectrum of the protons which are detected in 4$\pi$ by the $a$SPECT spectrometer using magnetic adiabatic collimation with an electrostatic filter. Data are presented from a 100 days run at the Institut Laue Langevin in 2013. The sources of systematic errors are considered and included in the final result. We obtain $a = -0.10430(84)$ which is the most precise measurement of the neutron $a$ coefficient to date. From this, the ratio of axial-vector to vector coupling constants is …
Forbidden nonuniqueβdecays and effective values of weak coupling constants
2016
Forbidden nonunique $\ensuremath{\beta}$ decays feature shape functions that are complicated combinations of different nuclear matrix elements and phase-space factors. Furthermore, they depend in a very nontrivial way on the values of the weak coupling constants, ${g}_{\mathrm{V}}$ for the vector part and ${g}_{\mathrm{A}}$ for the axial-vector part. In this work we include also the usually omitted second-order terms in the shape functions to see their effect on the computed decay half-lives and electron spectra ($\ensuremath{\beta}$ spectra). As examples we study the fourth-forbidden nonunique ground-state-to-ground-state ${\ensuremath{\beta}}^{\ensuremath{-}}$ decay branches of $^{113}\ma…
Octupole states in Tl207 studied through β decay
2020
The β decay of 207Hg into the single-proton-hole nucleus 207Tl has been studied through γ-ray spectroscopy at the ISOLDE Decay Station (IDS) with the aim of identifying states resulting from coupling of the πs−11/2, πd−13/2, and πh−111/2 shell model orbitals to the collective octupole vibration. Twenty-two states were observed lying between 2.6 and 4.0 MeV, eleven of which were observed for the first time, and 78 new transitions were placed. Two octupole states (s1/2-coupled) are identified and three more states (d3/2-coupled) are tentatively assigned using spin-parity inferences, while further h11/2-coupled states may also have been observed for the first time. Comparisons are made with st…
Radiative vector meson decay
2004
We study the radiative $\rho$, $\omega$ and $\phi$ decay into $\pi^0 \pi^0 \gamma$ and $\pi^0 \eta \gamma $ taking into account mechanisms in which there are two sequential vector-vector-pseudoscalar or axial-vector--vector--pseudoscalar steps followed by the coupling of a vector meson to the photon, considering the final state interaction of the two mesons. Other mechanisms in which two kaons are produced through the same sequential mechanisms or from vector meson decay into two kaons which undergo final state interaction leading to the final pair of pions or $\pi^0 \eta$, are also considered. The results of the parameter free theory, together with the theoretical uncertainties, are compar…
Direct excitation of the “dark”b3Πstate predicted by deperturbation analysis of theA1Σ+−b3Πcomplex in KCs
2010
The diode-laser-induced fluorescence spectra $b {}^{3}{\ensuremath{\Pi}}_{\ensuremath{\Omega}=0}^{+}\ensuremath{\rightarrow}{X}^{ 1}{\ensuremath{\Sigma}}^{+}$ originated from the rovibronic levels of the ``dark'' triplet $b {}^{3}{\ensuremath{\Pi}}_{\ensuremath{\Omega}=0}^{+}$ state of KCs dimers were recorded with a Fourier transform spectrometer with a resolution of 0.03 cm${}^{\ensuremath{-}1}$. Term values of 30 rovibronic levels $({v}_{b0}^{*}\ensuremath{\in}[14,18];{J}^{\ensuremath{'}}\ensuremath{\in}[47,134])$ below the minimum of perturbing $A {}^{1}{\ensuremath{\Sigma}}^{+}$ state were determined with 0.003--0.01 cm${}^{\ensuremath{-}1}$ uncertainty. The optimal excitation and dete…
Estimation of the Repeatedly-Projected Reduced Density Matrix under Decoherence
2007
Decoherence is believed to deteriorate the ability of a purification scheme that is based on the idea of driving a system to a pure state by repeatedly measuring another system in interaction with the former and hinder for a pure state to be extracted asymptotically. Nevertheless, we find a way out of this difficulty by deriving an analytic expression of the reduced density matrix for a two-qubit system immersed in a bath. It is shown that we can still extract a pure state if the environment brings about only dephasing effects. In addition, for a dissipative environment, there is a possibility of obtaining a dominant pure state when we perform a finite number of measurements.
Rotational band in 12C based on the Hoyle state
2014
t. α + 12C inelastic differential cross-sections were measured at the energies 65 and 110 MeV. A new broad state at 13.75 MeV was observed. Its spin-parity has been determined as 4+ and the diffraction radius of the corresponding L = 4 transition is ~ 0.8 fm larger than that of the excitation of the 4+, 14.8 MeV level. The 13.75 MeV state was considered to be the third member of the rotational band based on the Hoyle state. peerReviewed