Search results for "Formula"
showing 10 items of 755 documents
Microscopic calculations of isospin-breaking corrections to superallowed beta-decay
2011
The superallowed beta-decay rates that provide stringent constraints on physics beyond the Standard Model of particle physics are affected by nuclear structure effects through isospin-breaking corrections. The self-consistent isospin- and angular-momentum-projected nuclear density functional theory is used for the first time to compute those corrections for a number of Fermi transitions in nuclei from A=10 to A=74. The resulting leading element of the CKM matrix, |V_{ud}|= 0.97447(23), agrees well with the recent result by Towner and Hardy [Phys. Rev. C {\bf 77}, 025501 (2008)].
Introduction to the Standard Model of Particle Physics
2015
The Standard Model (SM) of particle physics is a gauge field theory based on the gauge group \(SU(3)_C \otimes SU(2)_L \otimes U(1)_Y\) that describes the fundamental electromagnetic, weak and strong interactions.
Muon (g− 2) in the Standard Model and supersymmetric extensions
2016
Recent new results on the SM and the SUSY prediction for the muon ( g – 2) are briefly reviewed, and a SUSY scenario with particularly large contributions is discussed.
QED one-loop corrections to radiative muon decay
1994
Based upon the Fermi interaction, the differential decay rate of the radiative muon decay including one-loop radiative corrections is determined to the order ${G}_{F}^{2}{\ensuremath{\alpha}}^{2}$. Essential aspects of the calculation are exhibited. After cancellation of IR divergences, the double radiative muon decay is included. Some initial applications are considered.
Lattice QCD: A Brief Introduction
2014
A general introduction to lattice QCD is given. The reader is assumed to have some basic familiarity with the path integral representation of quantum field theory. Emphasis is placed on showing that the lattice regularization provides a robust conceptual and computational framework within quantum field theory. The goal is to provide a useful overview, with many references pointing to the following chapters and to freely available lecture series for more in-depth treatments of specifics topics.
Examples for Calculating Path Integrals
2001
We now want to compute the kernel K(b, a) for a few simple Lagrangians. We have already found for the one-dimensional case that $$\displaystyle{ K{\bigl (x_{2},t_{2};x_{1},t_{1}\bigr )} =\int _{ x(t_{1})=x_{1}}^{x(t_{2})=x_{2} }[dx(t)]\,\text{e}^{(\mathrm{i}/\hslash )S} }$$ (19.1) with $$\displaystyle{ S =\int _{ t_{1}}^{t_{2} }dt\,L(x,\dot{x};t)\;. }$$ First we consider a free particle, $$\displaystyle{ L = m\dot{x}^{2}/2\;, }$$ (19.2) and represent an arbitrary path in the form, $$\displaystyle{ x(t) =\bar{ x}(t) + y(t)\;. }$$ (19.3) Here, \(\bar{x}(t)\) is the actual classical path, i.e., solution to the Euler–Lagrange equation: $$\displaystyle{ \frac{\partial L} {\partial x}\Big\vert _{…
Resonant three-photon ionization spectroscopy of atomic Fe
2013
Laser spectroscopic investigations on high-lying states around the ionization potential (IP) in the atomic spectrum of Fe have been carried out for the development of a practical three-step resonance ionization scheme accessible by Ti: sapphire lasers. A hot cavity laser ion source, typically used at on-line radioactive ion beam production facilities, was employed in this work. Ionization schemes employing high-lying Rydberg and autoionizing states populated by three-photon excitations were established. Five new Rydberg and autoionizing Rydberg series converging to the ground and to the first four excited states of Fe II are reported. Analyses of the Rydberg series yield the value 63 737.68…
Three-step resonant photoionization spectroscopy of Ni and Ge: ionization potential and odd-parity Rydberg levels
2007
In preparation of a laser ion source, we have investigated multi-step laser ionization via Rydberg and autoionizing states for atomic Ni and Ge using a mass separator with an ion beam energy of 20 keV. For both elements resonant three-step excitation schemes suitable for modern Ti:sapphire laser systems were developed. Rydberg series in the range of principal quantum numbers 20 n 80 were localized, assigned and quantum numbers were allocated to the individual resonances. Ionization potentials (IP) were extracted from fits of the individual series and quantum defects of individual levels were analysed for confirmation of series assignment. For Ni the ionization potential could be extracted w…
Mass of astrophysically relevantCl31and the breakdown of the isobaric multiplet mass equation
2016
The mass of $^{31}\mathrm{Cl}$ has been measured with the JYFLTRAP double-Penning-trap mass spectrometer at the Ion Guide Isotope Separator On-Line (IGISOL) facility. The determined mass-excess value, $\ensuremath{-}7034.7(34)$ keV, is 15 times more precise than in the Atomic Mass Evaluation 2012. The quadratic form of the isobaric multiplet mass equation for the $T=3/2$ quartet at $A=31$ fails $({\ensuremath{\chi}}_{n}^{2}=11.6)$ and a nonzero cubic term, $d=\ensuremath{-}3.5(11)$ keV, is obtained when the new mass value is adopted. $^{31}\mathrm{Cl}$ has been found to be less proton-bound, with a proton separation energy of ${S}_{p}=264.6(34)$ keV. Energies for the excited states in $^{31…
Mean field methods in large amplitude nuclear collective motion
1984
The time dependent Hartree-Fock method (TDHF) is reviewed and its success and failure are discussed. It is demonstrated that TDHF is a semiclassical theory which is basically able to describe the time evolution of one-body operators, the energy loss in inclusive deep inelastic collisions, and fusion reactions above the Coulomb barrier. For genuine quantum mechanical processes as e.g. spontaneous fission, subbarrier fusion, phase shifts and the description of bound vibrations, the quantized adiabatic time dependent Hartree-Fock theory (quantized ATDHF) is suggested and reviewed. Realistic three-dimensional calculations for heavy ion systems of A1+A2<32 are presented. Applications to various …