A cryogenic buffer gas beam, an electrostatic hexapole lens, and 2D transverse Doppler laser cooling are combined to produce a bright beam of barium monofluoride ($^{138}$Ba$^{19}$F) molecules. Experimental results and trajectory simulations are used to study the laser cooling effect as a function of laser detuning, laser power, laser alignment, and interaction time. A scattering rate of 6.1(1.4) $\times 10^{5}$ s$^{-1}$ on the laser cooling transition is obtained; this is $14 \%$ of the expected maximum, which is attributed to limited control of the magnetic field used to remix dark states. Using 3 tuneable lasers with appropriate sidebands and detuning, each molecule scatters approximately 400 photons during 2D laser cooling, limited by the interaction time and scattering rate. Leaks to dark states are less than 10$\%$. The experimental results are used to benchmark the trajectory simulations to predict the achievable flux 3.5 m downstream for a planned $e$EDM experiment.

We demonstrate a method to determine the longitudinal phase-space distribution of a cryogenic buffer gas cooled beam of barium-fluoride molecules based on a two-step laser excitation scheme. Temporal resolution is achieved by a transversely aligned laser beam that drives molecules from the ground state X2 Sigma+ to the A2 Pi 1/2 state around 860 nm, while the velocity resolution is obtained by a laser beam that is aligned counter-propagating with respect to the molecular beam and that drives the Doppler shifted A2 Pi 1/2 to D2 Sigma+ transition around 797 nm. Molecules in the D-state are detected background-free by recording the fluorescence from the D - X transition at 413 nm. A temporal resolution of 11 mu s and a velocity resolution of 6 m s-1 is obtained. In order to calibrate the absolute velocity, we have determined the Doppler free transition frequencies for the X - A and X - D transitions with an absolute accuracy below 0.3 MHz. The high resolution of the phase-space distributions allows us to observe a variation of the average velocity and velocity spread over the duration of the molecular beam pulse. Our method hence gives valuable insight into the dynamics in the source.

We demonstrate a spin-precession method to observe and analyze multilevel coherence between all hyperfine levels in the X-2 Sigma(+), N = 0 ground state of barium monofluoride ((BaF)-Ba-138-F-19). The signal is sensitive to the state-preparation Rabi frequency and external electric and magnetic fields applied in searches for a permanent electric dipole moment (EDM). In the obtained interference spectrum, the electric field and Rabi frequency become observable simultaneously with the EDM. This method reduces systematic biases and the number of auxiliary measurements for such precision measurements.

Recently, we have demonstrated a method to record the longitudinal phase-space distribution of a pulsed cryogenic buffer gas cooled beam of barium fluoride molecules with high resolution. In this paper, we use this method to determine the influence of various source parameters. Besides the expected dependence on temperature and pressure, the forward velocity of the molecules is strongly correlated with the time they exit the cell, revealing the dynamics of the gas inside the cell. Three observations are particularly noteworthy: (1) The velocity of the barium fluoride molecules increases rapidly as a function of time, reaches a maximum 50-200 mu s after the ablation pulse and then decreases exponentially. We attribute this to the buffer gas being heated up by the plume of hot atoms released from the target by the ablation pulse and subsequently being cooled down via conduction to the cell walls. (2) The time constant associated with the exponentially decreasing temperature increases when the source is used for a longer period of time, which we attribute to the formation of a layer of isolating dust on the walls of the cell. By thoroughly cleaning the cell, the time constant is reset to its initial value. (3) The velocity of the molecules at the trailing end of the molecular pulse depends on the length of the cell. For short cells, the velocity is significantly higher than expected from the sudden freeze model. We attribute this to the target remaining warm over the duration of the molecular pulse giving rise to a temperature gradient within the cell. Our observations will help to optimize the source parameters for producing the most intense molecular beam at the target velocity.

An electrostatic hexapole lens is used to manipulate the transverse properties of a beam of barium fluoride molecules from a cryogenic buffer gas source. The spatial distribution of the beam is measured by recording state-selective laser-induced fluorescence on an emccd camera, providing insight into the intensity and transverse position spread of the molecular beam. Although the high mass and unfavorable Stark shift of barium fluoride pose a considerable challenge, the number of molecules in the low-field seeking component of the N=1 state that pass a 4 mm diameter aperture 712 mm behind the source is increased by a factor of 12. Furthermore, it is demonstrated that the molecular beam can be displaced by up to +/-5 mm by moving the hexapole lens. Our measurements agree well with numerical trajectory simulations. We discuss how electrostatic lenses may be used to increase the sensitivity of beam experiments such as the search for the electric dipole moment of the electron.

Searches for a permanent electric dipole moment (EDM) of a fundamental particle started with the key idea by Ramsey and Purcell of exploitation of discrete symmetries, such as parity, more than seven decades ago. These searches provide a model-independent test of theoretical frameworks, in particular, the Standard Model of particle physics. Over time, a large number of experimentally suitable systems, also atoms and molecules, provided more stringent limits on possible EDMs. We discuss some perspectives on such experiments in the context of statistics, systematics, and sensitivities to beyond the Standard Model physics.

We demonstrate a spin-precession method to observe and analyze multi-level coherence between all hyperfine levels in the $X ^2\Sigma^+,N=0$ ground state of barium monofluoride ($^{138}$Ba$^{19}$F). The signal is sensitive to the state-preparation Rabi frequency and external electric and magnetic fields applied in searches for a permanent electric dipole moment (EDM). In the obtained interference spectrum, the electric field and Rabi frequency become observable simultaneously with the EDM. This method reduces systematic biases and the number of auxiliary measurements for such precision measurements.

The toolbox for material characterization has never been richer than today. Great progress with all kinds of particles and interaction methods provide access to nearly all properties of an object under study. However, a tomographic analysis of the subsurface region remains still a challenge today. In this regard, the Muon-Induced X-ray Emission (MIXE) technique has seen rebirth fueled by the availability of high intensity muon beams. We report here a study conducted at the Paul Scherrer Institute (PSI). It demonstrates that the absence of any beam time-structure leads to low pile-up events and a high signal-to-noise ratio (SNR) with less than one hour acquisition time per sample or data point. This performance creates the perspective to open this technique to a wider audience for the routine investigation of non-destructive and depth-sensitive elemental compositions, for example in rare and precious samples. Using a hetero-structured sample of known elements and thicknesses, we successfully detected the characteristic muonic X-rays, emitted during the capture of a negative muon by an atom, and the gamma-rays resulting from the nuclear capture of the muon, characterizing the capabilities of MIXE at PSI. This sample emphasizes the quality of a continuous beam, and the exceptional SNR at high rates. Such sensitivity will enable totally new statistically intense aspects in the field of MIXE, e.g. elemental 3D-tomography and chemical analysis. Therefore, we are currently advancing our proof-of-concept experiments with the goal of creating a full fledged permanently operated user station to make MIXE available to the wider scientific community as well as industry.

We present an investigation of the performance of the relativistic multi-reference Fock-space coupled cluster (FSCC) method for predicting molecular hyperfine structure (HFS) constants, including a thorough computational study to estimate the associated uncertainties. In particular, we considered the $^{19}$F HFS constant in the ground and excited states of BaF. Due to a larger basis set dependence, the uncertainties on the excited state results (16-85%) were found to be significantly larger than those on the ground state constants ($\sim$2%). The ab initio values were compared to the recent experimental results, and good overall agreement within the theoretical uncertainties was found. This work demonstrates the predictive power of the FSCC method and the reliability of the established uncertainty estimates, which can be crucial in cases where the calculated property cannot be directly compared to experiment.

The toolbox for material characterization has never been richer than today. Great progress with all kinds of particles and interaction methods provide access to nearly all properties of an object under study. However, a tomographic analysis of the subsurface region remains still a challenge today. In this regard, the Muon Induced X-ray Emission (MIXE) technique has seen rebirth fueled by the availability of high intensity muon beams. We report here a study conducted at the Paul Scherrer Institute (PSI). It demonstrates that the absence of any beam time-structure leads to low pile-up events and a high signal-to-noise ratio (SNR) with less than one hour acquisition time per sample or data point. This performance creates the perspective to open this technique to a wider audience for the routine investigation of non-destructive and depth-sensitive elemental compositions, for example in rare and precious samples. Using a hetero-structured sample of known elements and thicknesses, we successfully detected the characteristic muonic X-rays, emitted during the capture of a negative muon by an atom, and the gamma-rays resulting from the nuclear capture of the muon, characterizing the capabilities of MIXE at PSI. This sample emphasizes the quality of a continuous beam, and the exceptional SNR at high rates. Such sensitivity will enable totally new statistically intense aspects in the field of MIXE, e.g., elemental 3D-tomography and chemical analysis. Therefore, we are currently advancing our proof-of-concept experiments with the goal of creating a full fledged permanently operated user station to make MIXE available to the wider scientific community as well as industry.

The MACS experiment performed at PSI in the 1990s provided an yet unchallenged upper bound on the probability for a spontaneous conversion of the muonium atom, { M=}({\mu^+e^-})M=(μ+e−), into its antiatom, antimuonium {\overline{{M}} = }({\mu^-e^+})M¯=(μ−e+). It comprises the culmination of a series of measurements at various accelerator laboratories worldwide. The experimental limits on the process have provided input and steering for the further development of a variety of theoretical models beyond the standard theory, in particular for models which address lepton number violating processes and matter-antimatter oscillations. Several models beyond the standard theory could be strongly disfavored. There is interest in a new measurement and improved sensitivity could be reached by exploiting the time evolution of the conversion process, e.g., at intense pulsed muonium sources.

A measurement of the magnitude of the electric dipole moment of the electron (eEDM) larger than that predicted by the Standard Model (SM) of particle physics is expected to have a huge impact on the search for physics beyond the SM. Polar diatomic molecules containing heavy elements experience enhanced sensitivity to parity (P) and time-reversal (T)-violating phenomena, such as the eEDM and the scalar-pseudoscalar (S-PS) interaction between the nucleons and the electrons, and are thus promising candidates for measurements. The NL-eEDM collaboration is preparing an experiment to measure the eEDM and S-PS interaction in a slow beam of cold BaF molecules [P. Aggarwal et al., Eur. Phys. J. D 72, 197 (2018)]. Accurate knowledge of the electronic structure parameters, Wd and Ws, connecting the eEDM and the S-PS interaction to the measurable energy shifts is crucial for the interpretation of these measurements. In this work, we use the finite field relativistic coupled cluster approach to calculate the Wd and Ws parameters in the ground state of the BaF molecule. Special attention was paid to providing a reliable theoretical uncertainty estimate based on investigations of the basis set, electron correlation, relativistic effects, and geometry. Our recommended values of the two parameters, including conservative uncertainty estimates, are 3.13 ±0.12×1024Hzecm for Wd and 8.29 ± 0.12 kHz for Ws.

The fundamental symmetries, charge conjugation (C), parity (P) and time reversal (T), play a significant role in the Standard Model (SM) of elementary particle physics. Of these, T symmetry and the combined CP symmetry are the least well understood, and they hold valuable clues for unraveling the secrets of nature. All subatomic particles are postulated to possess an intrinsic property known as a permanent electric dipole moment (EDM). The EDM of an atom is a combination of those of each constituent particle and also CP-violating interactions between the particles. Being many-particle systems, atoms and molecules arc ideal candidates for probing a rich variety of both T- and CP-violating interactions. Paramagnetic atoms, which have a single valence electron in their outer shell, are sensitive to subtle signals associated with CP violations in the leptonic sector, i.e., the EDM of the electron. At present, we are developing a high-intensity laser-cooled Fr factory at RIKEN accelerator facility in an attempt to evaluate the EDM of Fr to an accuracy of 10(-30) ecm. Laser cooling is important for achieving highly accurate EDM measurements, since it allows long interaction times using an optical lattice. The current status of the laser-cooled Fr EDM experiments is presented in this paper.

A supersonic beam source for SrF and BaF molecules is constructed by combining the expansion of carrier gas (a mixture of 2% SF6 and 98% argon) from an Even-Lavie valve with laser ablation of a barium/strontium metal target at a repetition rate of 10 Hz. Molecular beams with a narrow translational velocity spread are produced at relative values of Δv/v = 0.053(11) and 0.054(9) for SrF and BaF, respectively. The relative velocity spread of the beams produced in our source is lower in comparison with the results from other metal fluoride beams produced in supersonic laser ablation sources. The rotational temperature of BaF is measured to be 3.5 K. The source produces 6 × 108 and 107 molecules per steradian per pulse in the X2Σ+ (ν = 0, N = 1) state of BaF and SrF molecules, respectively, a state amenable to Stark deceleration and laser cooling.

We report on the electrostatic trapping of neutral SrF molecules. The molecules are captured from a cryogenic buffer-gas beam source into the moving traps of a 4.5-m-long traveling-wave Stark decelerator. The SrF molecules in X^{2}Σ^{+}(v=0,N=1) state are brought to rest as the velocity of the moving traps is gradually reduced from 190  m/s to zero. The molecules are held for up to 50 ms in multiple electric traps of the decelerator. The trapped packets have a volume (FWHM) of 1  mm^{3} and a velocity spread of 5(1)  m/s, which corresponds to a temperature of 60(20) mK. Our result demonstrates a factor 3 increase in the molecular mass that has been Stark decelerated and trapped. Heavy molecules (mass>100  amu) offer a highly increased sensitivity to probe physics beyond the standard model. This work significantly extends the species of neutral molecules of which slow beams can be created for collision studies, precision measurement, and trapping experiments.

The hyperfine splitting of the 5g -> 4f transitions in muonic 185,187-Re has been measured using high resolution HPGe detectors and compared to state-of-the-art atomic theoretical predictions. The spectroscopic quadrupole moment has been extracted using modern fitting procedures and compared to the values available in literature obtained from muonic X rays of natural rhenium. The extracted values of the nuclear spectroscopic quadrupole moment are 2.07(5) barn and 1.94(5) barn, respectively for 185-Re and 187-Re. This work is part of a larger effort at the Paul Scherrer Institut towards the measurement of the nuclear charge radii of radioactive elements.

The article "Electro-optic sensor for static fields", written by "J. O. Grasdijk, X. F. Bai, I. Engin, K. Jungmann, H. J. Krause, B. Niederländer, A. Off enhäuser, M. Repetto, L. Willmann, S. Zimmer

The NL-eEDM collaboration is building an experimental setup to search for the permanent electric dipole moment of the electron in a slow beam of cold barium fluoride molecules [NL-eEDM Collaboration, Eur. Phys. J. D 72, 197 (2018)]. Knowledge of the molecular properties of BaF is thus needed to plan the measurements and, in particular, to determine the optimal laser-cooling scheme. Accurate and reliable theoretical predictions of these properties require the incorporation of both high-order correlation and relativistic effects in the calculations. In this work, theoretical investigations of the ground and lowest excited states of BaF and its lighter homologs, CaF and SrF, are carried out in the framework of the relativistic Fock-space coupled cluster and multireference configuration interaction methods. Using the calculated molecular properties, we determine the Franck-Condon factors (FCFs) for the A2Π1/2→X2Σ1/2+ transition, which was successfully used for cooling CaF and SrF and is now considered for BaF. For all three species, the FCFs are found to be highly diagonal. Calculations are also performed for the B2Σ1/2+→X2Σ1/2+ transition recently exploited for laser-cooling of CaF; it is shown that this transition is not suitable for laser-cooling of BaF, due to the nondiagonal nature of the FCFs in this system. Special attention is given to the properties of the A′2Δ state, which in the case of BaF causes a leak channel, in contrast to CaF and SrF species where this state is energetically above the excited states used in laser-cooling. We also present the dipole moments of the ground and excited states of the three molecules and the transition dipole moments (TDMs) between the different states. Finally, using the calculated FCFs and TDMs, we determine that the A2Π1/2→X2Σ1/2+ transition is suitable for transverse cooling in BaF.