/pdf/laser-spectroscopy-for-the-study-of-exotic-nuclei-e74lz4uc.pdf

Laser spectroscopy for the study of exotic nuclei

Etude de dix structures hyperfines et deduction des constantes d'interaction dipolaire magnetique et quadripolaire electrique et des niveaux d'energie

Newly observed lines and hyperfine structure in the infrared spectrum of indium obtained by using a Fourier-transform spectrometer

We investigate "Posner molecules", calcium phosphate clusters with chemical formula Ca$_9$(PO$_4$)$_6$. Originally identified in hydroxyapatite, Posner molecules have also been observed as free-floating molecules $in$ $vitro$. The formation and aggregation of Posner molecules have important implications for bone growth, and may also play a role in other biological processes such as the modulation of calcium and phosphate ion concentrations within the mitochondrial matrix. In this work, we use a first-principles computational methodology to study the structure of Posner molecules, their vibrational spectra, their interactions with other cations, and the process of pairwise bonding. Additionally, we show that the Posner molecule provides an ideal environment for the six constituent $^{31}\text{P}$ nuclear spins to obtain very long spin coherence times. $In$ $vitro$, the spins could provide a platform for liquid-state nuclear magnetic resonance quantum computation. $In$ $vivo$, the spins may have medical imaging applications. The spins have also been suggested as "neural qubits" in a proposed mechanism for quantum processing in the brain.

Posner molecules: From atomic structure to nuclear spins

Recently Fraser and Schoen showed that the solution of a certain extremal Steklov eigenvalue problem on a compact surface with boundary can be used to generate a free boundary minimal surface, i.e. , a surface contained in the ball that has (i) zero mean curvature and (ii) meets the boundary of the ball orthogonally (doi:10.1007/s00222-015-0604-x). In this paper, we develop numerical methods that use this connection to realize free boundary minimal surfaces. Namely, on a compact surface, Σ, with genus γ and b boundary components, we maximize σ j (Σ, g ) L (∂ Σ, g ) over a class of smooth metrics, g , where σ j (Σ, g ) is the j th nonzero Steklov eigenvalue and L (∂ Σ, g ) is the length of ∂ Σ. Our numerical method involves (i) using conformal uniformization of multiply connected domains to avoid explicit parameterization for the class of metrics, (ii) accurately solving a boundary-weighted Steklov eigenvalue problem in multi-connected domains, and (iii) developing gradient-based optimization methods for this non-smooth eigenvalue optimization problem. For genus γ = 0 and b = 2, …, 9, 12, 15, 20 boundary components, we numerically solve the extremal Steklov problem for the first eigenvalue. The corresponding eigenfunctions generate a free boundary minimal surface, which we display in striking images. For higher eigenvalues, numerical evidence suggests that the maximizers are degenerate, but we compute local maximizers for the second and third eigenvalues with b = 2 boundary components and for the third and fifth eigenvalues with b = 3 boundary components.

/pdf/computation-of-free-boundary-minimal-surfaces-via-extremal-280gxr9vzb.pdf

Computation of free boundary minimal surfaces via extremal Steklov eigenvalue problems

The accuracy of atomic theory calculations limits the extraction of nuclear charge radii from isotope shift measurements of odd-proton nuclei. For Na isotopes, though precise spectroscopic measurements have existed for more than half a century, calculations by different methods offer a wide range of values. Here, we present accurate atomic calculations to reliably extract the Na charge radii. By combining experimental matter radii with nuclear coupled-cluster calculations based on nucleon-nucleon and three-nucleon forces, we constrain the parameters obtained from the atomic calculations. Therefore, this study guides atomic theory and highlights the importance of using accurate atomic and nuclear computations in our understanding of the size of light nuclei. 

Nuclear charge radii of Na isotopes: Interplay of atomic and nuclear theory

This work reports on the application of a novel electric field-ionization setup for high-resolution laser spectroscopy measurements on bunched fast atomic beams in a collinear geometry. In combination with multi-step resonant excitation to Rydberg states using pulsed lasers, the field ionization technique demonstrates increased sensitivity for isotope separation and measurement of atomic parameters over previous non-resonant laser ionization methods. The setup was tested at the Collinear Resonance Ionization Spectroscopy experiment at ISOLDE-CERN to perform high-resolution measurements of transitions in the indium atom from the $$\text {5s}^2\text {5d}\,^2\text {D}_{5/2}$$ and $$\text {5s}^2\text {5d}\,^2\text {D}_{3/2}$$ states to $$\text {5s}^2n$$p $$^2$$P and $$\text {5s}^2n\text {f}\,^2$$F Rydberg states, up to a principal quantum number of $$n=72$$. The extracted Rydberg level energies were used to re-evaluate the ionization potential of the indium atom to be $$46,670.107(4)\,\hbox {cm}^{-1}$$. The nuclear magnetic dipole and nuclear electric quadrupole hyperfine structure constants and level isotope shifts of the $$\text {5s}^2\text {5d}\,^2\text {D}_{5/2}$$ and $$\text {5s}^2\text {5d}\,^2\text {D}_{3/2}$$ states were determined for $$^{113,115}$$In. The results are compared to calculations using relativistic coupled-cluster theory. A good agreement is found with the ionization potential and isotope shifts, while disagreement of hyperfine structure constants indicates an increased importance of electron correlations in these excited atomic states. With the aim of further increasing the detection sensitivity for measurements on exotic isotopes, a systematic study of the field-ionization arrangement implemented in the work was performed at the same time and an improved design was simulated and is presented. The improved design offers increased background suppression independent of the distance from field ionization to ion detection.

/pdf/laser-spectroscopy-of-indium-rydberg-atom-bunches-by-4s729343hk.pdf

Laser spectroscopy of indium Rydberg atom bunches by electric field ionization.

This work reports on the application of a novel electric field-ionization setup for high-resolution laser spectroscopy measurements on bunched fast atomic beams in a collinear geometry. In combination with multi-step resonant excitation to Rydberg states using pulsed lasers, the field ionization technique demonstrates increased sensitivity for isotope separation and measurement of atomic parameters over non-resonant laser ionization methods. The setup was tested at the Collinear Resonance Ionization Spectroscopy experiment at ISOLDE-CERN to perform high-resolution measurements of transitions in the indium atom from the 5s$^2$5d~$^2$D$_{5/2}$ and 5s$^2$5d~$^2$D$_{3/2}$ states to 5s$^2$($n$)p~$^2$P and 5s$^2$($n$)f~$^2$F Rydberg states, up to a principal quantum number of $n$ = 72. The extracted Rydberg level energies were used to re-evaluate the ionization potential of the indium atom to be 46670.1055(21) cm$^{-1}$. The nuclear magnetic dipole and nuclear electric quadrupole hyperfine structure constants and level isotope shifts of the 5s$^2$5d~$^2$D$_{5/2}$ and 5s$^2$5d~$^2$D$_{3/2}$ states were determined for $^{113,115}$In. The results are compared to calculations using relativistic coupled-cluster theory. A good agreement is found with the ionization potential and isotope shifts, while disagreement of hyperfine structure constants indicates an increased importance of electron correlations in these excited atomic states. With the aim of further increasing the detection sensitivity for measurements on exotic isotopes, a systematic study of the field-ionization arrangement implemented in the work was performed and an improved design was simulated and is presented. The improved design offers increased background suppression independent of the distance from field ionization to ion detection.

/pdf/laser-spectroscopy-of-indium-rydberg-atom-bunches-by-imunb9vdm4.pdf

F. J. Waso

Papers

Laser spectroscopy of indium Rydberg atom bunches by electric field ionization.

Laser spectroscopy of indium Rydberg atom bunches by electric field ionization