Many interacting fermions in a one-dimensional harmonic trap: a quantum-chemical treatment

We employ \textit{ab initio} methods of quantum chemistry to investigate spin-1/2 fermions interacting via a two-body contact potential in a one-dimensional harmonic trap. The convergence of the total energy with the size of the one-particle basis set is analytically investigated for the two-body problem and the same form of the convergence formula is numerically confirmed to be valid for the many-body case. Benchmark calculations for two to six fermions with the full configuration interaction method equivalent to the exact diagonalization approach, and the coupled cluster method including single, double, triple, and quadruple excitations are presented. The convergence of the correlation energy with the level of excitations included in the coupled cluster model is analyzed. The range of the interaction strength for which single-reference coupled cluster methods work is examined. Next, the coupled cluster method restricted to single, double, and noniterative triple excitations, CCSD(T), is employed to study a two-component Fermi gas composed of 6 to 80 atoms in a one-dimensional harmonic trap. The density profiles of trapped atomic clouds are also reported. Finally, a comparison with experimental results for few-fermion systems is presented. Upcoming possible applications and extensions of the presented approach are discussed.Comment: 25 pages, 12 figures, 1 tabl

Prasowa działalność wydawnicza krakowskiego Towarzystwa Gospodarczo-Rolniczego w latach 1850–1862

The first part of the article ”Press Publishing Activities of Cracow Economic and Agricultural Society in the years 1850–1862” presents the Society’s attempts to establish its press organ in Cracow’s newspaper market for a longer time. Appendix to the “Time” Dedicated to Industry, Agriculture, and Farming Technology (1850), independent semi-annual Annual of the Imperial-Royal Cracow Economic and Agricultural Society (1851–1853), and Agro-Industrial Weekly (1854–1862) were established. Journalistic genres and columns characteristic of these three periodicals were discussed in the article. Also presented was the unrealized plan of the Society: to publish a magazine „for the people”. During these several years, the Society did not lack determination and flexibility in their attempts to publish their own magazine

Ab initio potential energy curves, scattering lengths, and rovibrational levels of the He2+_2^+ molecular ion in excited electronic states

We calculate accurate potential energy curves for a ground-state He$^+$ ion interacting with a He atom in the lowest-energy metastable $^3\!S$ electronic state. We employ the full configuration interaction method, equivalent to exact diagonalization, with results extrapolated to the complete basis set limit. The leading relativistic and adiabatic corrections are included using perturbation theory. We calculate rovibrational levels and spectroscopic constants of the He$_2^+$ molecular ion in excited electronic states for three stable isotopologues. We predict the scattering lengths for ultracold ion-atom collisions. The theoretical data are presented with their uncertainties and agree well with previous results for the ground state. The reported results may be useful for the spectroscopy of the He$_2^+$ molecular ion in the excited electronic state and collisional studies of He$^+$ ions immersed in ultracold gases of metastable He atoms.Comment: 18 pages, 6 figures, 7 table