Search results for "Sum rule in quantum mechanics"
showing 10 items of 153 documents
QCD sum rule calculation ofK ℓ3 form factors
1992
We present a combined finite energy sum rule (FESR) and analytic continuation by duality (ACD) calculation of the (neutral)K l3 decay. We confirm the Callan-Treiman relation and investigate the validity of a linear fit for the form factors. Furthermore, we obtain ζ=−0.1...−0.3, consistent with the mean experimental value ζ=−0.1±0.09.
Towards nonlocal density functionals by explicit modelling of the exchange-correlation hole in inhomogeneous systems
2013
We put forward new approach for the development of a non-local density functional by a direct modeling of the shape of exchange-correlation (xc) hole in inhomogeneous systems. The functional is aimed at giving an accurate xc-energy and an accurate corresponding xc-potential even in difficult near-degeneracy situations such as molecular bond breaking. In particular we demand that: (1) the xc hole properly contains -1 electron, (2) the xc-potential has the asymptotic -1/r behavior outside finite systems and (3) the xc-potential has the correct step structure related to the derivative discontinuities of the xc-energy functional. None of the currently existing functionals satisfies all these re…
Gamow-Teller response in the configuration space of a density-functional-theory–rooted no-core configuration-interaction model
2018
Background: The atomic nucleus is a unique laboratory in which to study fundamental aspects of the electroweak interaction. This includes a question concerning in medium renormalization of the axial-vector current, which still lacks satisfactory explanation. Study of spin-isospin or Gamow-Teller (GT) response may provide valuable information on both the quenching of the axial-vector coupling constant as well as on nuclear structure and nuclear astrophysics.Purpose: We have performed a seminal calculation of the GT response by using the no-core configuration-interaction approach rooted in multireference density functional theory (DFT-NCCI). The model treats properly isospin and rotational sy…
QCD sum rule determination of the charm-quark mass
2011
QCD sum rules involving mixed inverse moment integration kernels are used in order to determine the running charm-quark mass in the $\bar{MS}$ scheme. Both the high and the low energy expansion of the vector current correlator are involved in this determination. The optimal integration kernel turns out to be of the form $p(s) = 1 - (s_0/s)^2$, where $s_0$ is the onset of perturbative QCD. This kernel enhances the contribution of the well known narrow resonances, and reduces the impact of the data in the range $s \simeq 20 - 25 GeV^2$. This feature leads to a substantial reduction in the sensitivity of the results to changes in $s_0$, as well as to a much reduced impact of the experimental u…
Recently published line strengths for the transition array 3s–3p in C I, N II and O III: a critical review
2014
Recently calculated atomic structure data for C I, N II and O III are reviewed and analyzed by performing J-file sum rule tests. The line strengths of the 3s–3p transition array are analyzed. In the case of neutral carbon and ionized nitrogen data, the LS-forbidden transitions are included in the analysis.
Compton scattering off pions and electromagnetic polarizabilities
2019
The electric ($\alpha_\pi$) and magnetic ($\beta_\pi$) Compton polarizabilities of both the charged and the neutral pion are of fundamental interest in the low-energy sector of quantum chromodynamics (QCD). Pion polarizabilities affect the shape of the $\gamma\pi\to\gamma\pi$ Compton scattering angular distribution at back scattering angles and $\gamma\gamma\to\pi\pi$ absolute cross sections. Theory derivations are given of the $\gamma\pi\to\gamma\pi$ Compton scattering differential cross section, dispersion relations, and sum rules in terms of the polarizabilities. We review experimental charged and neutral polarizability studies and theoretical predictions. The $\pi^0$ polarizabilities we…
Dispersion Approach to Pion Photoproduction and GDH Sum Rule
1999
Pion photoproduction has been analyzed in the framework of dispersion relations at constant t. The results for S-wave pion production at threshold and P-wave production in the Δ (1232) resonance region are presented and compared to the data and theoretical expectations. The predictions for the GDH sum rule are shown to be very sensitive to the threshold S-wave amplitude.
Multipole strength distributions and form factors forE1,E2/E0, andE3 fromU238(e,e’f) coincidence experiments
1987
A model-independent multipole analysis of $^{238}\mathrm{U}$(e,e'f) coincidence data, taken at four momentum transfers (0.2\ensuremath{\le}${q}_{\mathrm{eff}\mathrm{\ensuremath{\le}}0.7}$ ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$; \ensuremath{\omega}=4--22 MeV) yields both E1, E2/E0, and E3 form factors and strength distributions. The E2/E0 strength distribution in the fission channel shows two distinct bumps centered at \ensuremath{\omega}\ensuremath{\simeq}10 and 14 MeV, exhausting up to 12 MeV (19\ifmmode\pm\else\textpm\fi{}2)% of the isoscalar E2 sum rule. The extracted form factors can be described within a hydrodynamical model by use of parameters ${c}_{\mathrm{tr}/{c}_{0}=1.2}$ and …
Quasielastic proton knockout from 16O.
1994
The spectral function of the $^{16}\mathrm{O}$(e,e'p${)}^{15}$N reaction has been measured in quasielastic parallel kinematics. Momentum distributions are extracted for transitions to several discrete states, with emphasis on the low-lying positive parity states of $^{15}\mathrm{N}$. Spectroscopic factors and bound state wave functions are deduced from a DWIA analysis employing five different optical potentials. Coupled channels effects are investigated for the first four states of $^{15}\mathrm{N}$ and are found to be minimal. The spectroscopic results of the 1/${2}^{\mathrm{\ensuremath{-}}}$ ground state and the first 3/${2}^{\mathrm{\ensuremath{-}}}$ excited state indicate a 28%\ifmmode\…
Dissecting the Hadronic Contributions to (g−2)μ by Schwinger’s Sum Rule
2018
The theoretical uncertainty of $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$ is currently dominated by hadronic contributions. In order to express those in terms of directly measurable quantities, we consider a sum rule relating $g\ensuremath{-}2$ to an integral of a photoabsorption cross section. The sum rule, attributed to Schwinger, can be viewed as a combination of two older sum rules: Gerasimov-Drell-Hearn and Burkhardt-Cottingham. The Schwinger sum rule has an important feature, distinguishing it from the other two: the relation between the anomalous magnetic moment and the integral of a photoabsorption cross section is linear, rather than quadratic. The linear property makes it suitable …