Combining Slater-type orbitals and effective core potentials

We present a general methodology to evaluate matrix elements of the effective core potentials (ECPs) within one-electron basis set of Slater-type orbitals (STOs). The scheme is based on translation of individual STO distributions in the framework of Barnett-Coulson method. We discuss different types of integrals which naturally appear and reduce them to few basic quantities which can be calculated recursively or purely numerically. Additionally, we consider evaluation of the STOs matrix elements involving the core polarisation potentials (CPP) and effective spin-orbit potentials. Construction of the STOs basis sets designed specifically for use with ECPs is discussed and differences in comparison with all-electron basis sets are briefly summarised. We verify the validity of the present approach by calculating excitation energies, static dipole polarisabilities and valence orbital energies for the alkaline earth metals (Ca, Sr, Ba). Finally, we evaluate interaction energies, permanent dipole moments and ionisation energies for barium and strontium hydrides, and compare them with the best available experimental and theoretical data.Comment: submitted to Phys. Rev.

High count rate {\gamma}-ray spectroscopy with LaBr3:Ce scintillation detectors

The applicability of LaBr3:Ce detectors for high count rate {\gamma}-ray spectroscopy is investigated. A 3"x3" LaBr3:Ce detector is used in a test setup with radioactive sources to study the dependence of energy resolution and photo peak efficiency on the overall count rate in the detector. Digitized traces were recorded using a 500 MHz FADC and analysed with digital signal processing methods. In addition to standard techniques a pile-up correction method is applied to the data in order to further improve the high-rate capabilities and to reduce the losses in efficiency due to signal pile-up. It is shown, that {\gamma}-ray spectroscopy can be performed with high resolution at count rates even above 1 MHz and that the performance can be enhanced in the region between 500 kHz and 10 MHz by using pile-up correction techniques

Precise study of asymptotic physics with subradiant ultracold molecules

Weakly bound molecules have physical properties without atomic analogues, even as the bond length approaches dissociation. In particular, the internal symmetries of homonuclear diatomic molecules result in formation of two-body superradiant and subradiant excited states. While superradiance has been demonstrated in a variety of systems, subradiance is more elusive due to the inherently weak interaction with the environment. Here we characterize the properties of deeply subradiant molecular states with intrinsic quality factors exceeding $10^{13}$ via precise optical spectroscopy with the longest molecule-light coherent interaction times to date. We find that two competing effects limit the lifetimes of the subradiant molecules, with different asymptotic behaviors. The first is radiative decay via weak magnetic-dipole and electric-quadrupole interactions. We prove that its rate increases quadratically with the bond length, confirming quantum mechanical predictions. The second is nonradiative decay through weak gyroscopic predissociation, with a rate proportional to the vibrational mode spacing and sensitive to short-range physics. This work bridges the gap between atomic and molecular metrology based on lattice-clock techniques, yielding new understanding of long-range interatomic interactions and placing ultracold molecules at the forefront of precision measurements.Comment: 12 pages, 6 figure

Analytical two-center integrals over Slater geminal functions

We present analytical formulas for the calculation of the two-center two-electron integrals in the basis of Slater geminals and products of Slater orbitals. Our derivation starts with establishing a inhomogeneous fourth-order ordinary differential equation that is obeyed by the master integral, the simplest integral with inverse powers of all interparticle distances. To solve this equation it was necessary to introduce a new family of special functions which are defined through their series expansions around regular singular points of the differential equation. To increase the power of the interparticle distances under the sign of the integral we developed a family of open-ended recursion relations. A handful of special cases of the integrals is also analysed with some remarks on simplifications that occur. Additionally, we present some numerical examples of the master integral that validate the usefulness and correctness of the key equations derived in this paper. In particular, we compare our results with the calculations based on the series expansion of the exp(-\gamma r12) term in the master integral.Comment: 28 pages, 0 figures, 7 table

Control of Ultracold Photodissociation with Magnetic Fields

Photodissociation of a molecule produces a spatial distribution of photofragments determined by the molecular structure and the characteristics of the dissociating light. Performing this basic chemical reaction at ultracold temperatures allows its quantum mechanical features to dominate. In this regime, weak applied fields can be used to control the reaction. Here, we photodissociate ultracold diatomic strontium in magnetic fields below 10 G and observe striking changes in photofragment angular distributions. The observations are in excellent qualitative agreement with a multichannel quantum chemistry model that includes nonadiabatic effects and predicts strong mixing of partial waves in the photofragment energy continuum. The experiment is enabled by precise quantum-state control of the molecules.Comment: 8 pages, 3 figure

Performance of a Large Area Avalanche Photodiode in a Liquid Xenon Ionization and Scintillation Chamber

Scintillation light produced in liquid xenon (LXe) by alpha particles, electrons and gamma-rays was detected with a large area avalanche photodiode (LAAPD) immersed in the liquid. The alpha scintillation yield was measured as a function of applied electric field. We estimate the quantum efficiency of the LAAPD to be 45%. The best energy resolution from the light measurement at zero electric field is 7.5%(sigma) for 976 keV internal conversion electrons from Bi-207 and 2.6%(sigma) for 5.5 MeV alpha particles from Am-241. The detector used for these measurements was also operated as a gridded ionization chamber to measure the charge yield. We confirm that using a LAAPD in LXe does not introduce impurities which inhibit the drifting of free electrons.Comment: 13 pages, 8 figure

Experimental and Theoretical Investigation of the Crossover from the Ultracold to the Quasiclassical Regime of Photodissociation

At ultralow energies, atoms and molecules undergo collisions and reactions that are best described in terms of quantum mechanical wave functions. In contrast, at higher energies these processes can be understood quasiclassically. Here, we investigate the crossover from the quantum mechanical to the quasiclassical regime both experimentally and theoretically for photodissociation of ultracold diatomic strontium molecules. This basic reaction is carried out with a full control of quantum states for the molecules and their photofragments. The photofragment angular distributions are imaged, and calculated using a quantum mechanical model as well as the WKB and a semiclassical approximation that are explicitly compared across a range of photofragment energies. The reaction process is shown to converge to its high-energy (axial recoil) limit when the energy exceeds the height of any reaction barriers. This phenomenon is quantitatively investigated for two-channel photodissociation using intuitive parameters for the channel amplitude and phase. While the axial recoil limit is generally found to be well described by a commonly used quasiclassical model, we find that when the photofragments are identical particles, their bosonic or fermionic quantum statistics can cause this model to fail, requiring a quantum mechanical treatment even at high energies.Comment: 13 pages, 6 figure

Crossover from the Ultracold to the Quasiclassical Regime in State-Selected Photodissociation

Processes that break molecular bonds are typically observed with molecules occupying a mixture of quantum states and successfully described with quasiclassical models, while a few studies have explored the distinctly quantum mechanical low-energy regime. Here we use photodissociation of diatomic strontium molecules to demonstrate the crossover from the ultracold, quantum regime where the photofragment angular distributions strongly depend on the kinetic energy, to the energy-independent quasiclassical regime. Using time-of-flight velocity map imaging for photodissociation channels with millikelvin reaction barriers, we explore photofragment energies in the 0.1-300 mK range experimentally and up to 3 K theoretically, and discuss the energy scale at which the crossover occurs. Furthermore, we find that the effects of quantum statistics can unexpectedly persist to high photodissociation energies.Comment: 6 pages, 4 figure