Related papers: Nuclear critical charge for two-electron ion in La…
In this paper we confirm that $2^*(\gamma)=\frac{2(N+\gamma)}{N-2}$ with $\gamma>0$ is exactly the critical exponent for the embedding from $H_r^1(\mathbb{R}^N)$ into $L^q(\mathbb{R}^N;|x|^\gamma)$($N\geqslant 3$) (see…
The quadratic Zeeman effect is calculated for the ground $^2P_{1/2}$ state of light boron-like ions in the range of nuclear-charge numbers $Z = 10-24$. The calculations are performed in the Furry picture using three models for the…
Shell model studies have been done for very neutron - rich nuclei in the range Z=50-55 and N=82-87. Good agreement of the theoretical level spectra with the experimental one for N=82, 83 I and Te nuclei is shown. Then the results for three…
We consider two-component fermions on the lattice in the unitarity limit. This is an idealized limit of attractive fermions where the range of the interaction is zero and the scattering length is infinite. Using Euclidean time projection,…
The complete calculation of the 2-loop electroweak corrections to the renormalization of the electric charge in the Standard Model allows to discuss in detail the value of the MSbar effective coupling $\hat e(m_Z)$. We discuss the…
We report lattice QCD results on the axial charges of ground and excited nucleon states of both parities. This is the first study of these quantities with approximately chiral (CI) fermions. Two energy levels in the range of the negative…
We compute the free energy in the presence of a chemical potential coupled to a conserved charge in effective O($n$) scalar field theory (without explicit symmetry breaking terms) to NNL order for asymmetric volumes in general…
We report a calculation of all two-loop QED corrections with closed fermion loops for the n=1 and n=2 states of H-like ions and for a wide range of the nuclear charge numbers Z=1-100. The calculation is performed to all orders in the…
Neutron scattering results for the tetragonal compound CeRhIn5 give evidence for two crystal field (CF) excitations at 6.9 and 23.6 meV. The scattering can be fit assuming a set of CF parameters B$^{0}_{2}$ = -1.03 meV, B$^{0}_{4}$ = 0.044…
We propose a novel method for measuring the neutron skin of heavy nuclei using collider experiments. Specifically, we demonstrate that the neutron skin thickness of the lead nucleus can be extracted in $p$+$^{208}$Pb collisions by analyzing…
We present a new dimensional scaling transformation of the Schrodinger equation for the two electron bond. This yields, for the first time, a good description of the two electron bond via D-scaling. There also emerges, in the large-D limit,…
We obtain analytic solution of the time-independent Schrodinger equation in two dimensions for a charged particle moving in the field of an electric quadrupole. The solution is written as a series in terms of special functions that support…
We prove dynamical dichotomy into scattering and blow-up (in a weak sense) for all radial solutions of the Zakharov system in the energy space of four spatial dimensions that have less energy than the ground state, which is written using…
For any arbitrary values of $n$ and $l$ quantum numbers, we present a simple exact analytical solution of the $D$-dimensional ($D\geq 2$) hyperradial Schr% \"{o}dinger equation with the Kratzer and the modified Kratzer potentials within the…
We present a theory of the pair distribution function $g(z)$ and many-body effective electron-electron interaction for one dimensional (1D) electron liquid. Our approach involves the solution of a zero-energy scattering Schr\"odinger…
We study here a number of mathematical problems related to our recently introduced neoclassical theory for the electromagnetic phenomena in which charges are represented by complex valued wave functions as in the Schrodinger wave mechanics.…
Recent advances in muonic x-ray experiments have reinvigorated efforts in measurements of absolute nuclear charge radii. Here, a modern approach is presented, and demonstrated through determination of the charge radii of the two stable…
We found that the two-dimensional Schr\"odinger equation for 3 electrons in an homogeneous magnetic field (perpendicular to the plane) and a parabolic scalar confinement potential (frequency $\omega_0$) has exact analytical solutions in the…
Charge exchange between highly charged ions and neutral atoms and molecules has been considered as one of the important mechanisms controlling soft X ray emissions in many astrophysical objects and environments. However, for modeling charge…
Using a straightforward extension of the analysis of Lieb and Wu, we derive a simple analytic form for the ground state energy of a one-dimensional Hubbard ring in the atomic limit. This result is valid for an \textit{arbitrary} number of…