Deuteron properties from muonic atom spectroscopy

Leading order ($\alpha^4$) finite size corrections in muonic deuterium are evaluated within a few body formalism for the $\mu^- p n$ system in muonic deuterium and found to be sensitive to the input of the deuteron wave function. We show that this sensitivity, taken along with the precise deuteron charge radius determined from muonic atom spectroscopy can be used to determine the elusive deuteron D-state probability, $P_D$, for a given model of the nucleon-nucleon (NN) potential. The radius calculated with a $P_D$ of 4.3\% in the chiral NN models and about 5.7\% in the high precision NN potentials is favoured most by the $\mu^-d$ data.Comment: 14 pages, 2 figure

On Quasibound N* Nuclei

The possibility for the existence of unstable bound states of the S11 nucleon resonance N$^*$(1535) and nuclei is investigated. These quasibound states are speculated to be closely related to the existence of the quasibound states of the eta mesons and nuclei. Within a simple model for the N N$^*$ interaction involving a pion and eta meson exchange, N$^*$-nucleus potentials for N*-$^3$He and N*-$^{24}$Mg are evaluated and found to be of a Woods-Saxon like form which supports two to three bound states. In case of N*-$^3$He, one state bound by only a few keV and another by 4 MeV is found. The results are however quite sensitive to the N N$^*$ $\pi$ and N N$^*$ $\eta$ vertex parameters. A rough estimate of the width of these states, based on the mean free path of the exchanged mesons in the nuclei leads to very broad states with $\Gamma \sim$ 80 and 110 MeV for N*-$^3$He and N*-$^{24}$Mg respectively.Comment: Presented at the Jagiellonian Symposium on Fundamental and Applied Subatomic Physics, Cracow, Poland, June 2015; to be published in Acta Physica Polonica B (2016

Short Range Interactions in the Hydrogen Atom

In calculating the energy corrections to the hydrogen levels we can identify two different types of modifications of the Coulomb potential $V_{C}$, with one of them being the standard quantum electrodynamics corrections, $\delta V$, satisfying $\left|\delta V\right|\ll\left|V_{C}\right|$ over the whole range of the radial variable $r$. The other possible addition to $V_{C}$ is a potential arising due to the finite size of the atomic nucleus and as a matter of fact, can be larger than $V_{C}$ in a very short range. We focus here on the latter and show that the electric potential of the proton displays some undesirable features. Among others, the energy content of the electric field associated with this potential is very close to the threshold of $e^+e^-$ pair production. We contrast this large electric field of the Maxwell theory with one emerging from the non-linear Euler-Heisenberg theory and show how in this theory the short range electric field becomes smaller and is well below the pair production threshold

Lorentz Contracted Proton

The proton charge and magnetization density distributions can be related to the well known Sachs electromagnetic form factors $G_{E,M}({\bm q}^{2})$ through Fourier transforms, only in the Breit frame. The Breit frame however moves with relativistic velocities in the Lab and a Lorentz boost must be applied to the form factors before extracting the static properties of the proton from the corresponding densities. Apart from this, the Fourier transform relating the densities and form factors is inherently a non-relativistic expression. We show that the relativistic corrections to it can be obtained by extending the standard Breit equation to higher orders in its $1/c^2$ expansion. We find that the inclusion of the above corrections reduces the size of the proton determined from electron proton scattering data. Indeed the central value of the latest proton radius of $r_p = 0.879$ fm as determined from e-p scattering changes to $r_p = 0.8404$ fm after applying corrections.Comment: 15 page