Related papers: Precise Variational Calculation For The Doubly Exc…
The nonrelativistic energies of the homonuclear ion T$_2^+$ are calculated for the ground state using the Lagrange-mesh method as was done for the isotopomers H$_2^+$ and D$_2^+$ ({\it J. Phys. B: At. Mol. Opt. Phys.} {\bf 45} 065101 and…
The application of the hyperspherical harmonic approach to the case of non-local two-body potentials is described. Given the properties of the hyperspherical harmonic functions, there are no difficulties in considering the approach in both…
We have investigated some of the thermodynamic properties of spin polarized liquid $^3\mathrm{He}$ at finite temperature using the lowest order constrained variational method. For this system, the free energy, entropy and pressure are…
A new state of the H$_2^+$ molecular ion with binding energy of 1.09$\times10^{-9}$ a.u. below the first dissociation limit is predicted, using highly accurate numerical nonrelativistic quantum calculations. It is the first L=0 excited…
We perform ab initio QED calculations of energy levels for the $n=1$ and $n=2$ states of He-like ions with the nuclear charge in the range $Z = 12$-100. The complete set of two-electron QED corrections is evaluated to all orders in the…
Consider $N$ bosons in a finite box $\Lambda= [0,L]^3\subset \mathbf R^3$ interacting via a two-body smooth repulsive short range potential. We construct a variational state which gives the following upper bound on the ground state energy…
Highly accurate closed-form approximations are given for the ground state and first excited state wavefunctions and energies for a nonrelativistic particle in a one-dimensional double square well potential with a square barrier in between…
A trial function is presented for the $H_2$ molecule which provides the most accurate (the lowest) Bohr-Oppenheimer ground state energy among few-parametric trial functions (with $\leq 14$ parameters). It includes the electronic correlation…
We study the lowest energy E of a semirelativistic system of N identical massless bosons with Hamiltonian H= sum{i=1 to N} sqrt(p_i^2)+ sum{j>i=1 to N} g |r_i - r_j|^2, g > 0. We prove the inequalities A [g N^2 (N-1)^2]^{1/3} < E < B [g N^2…
The nonrelativistic energy together with relativistic and quantum electrodynamic corrections for all the molecular hydrogen isotopologues (D$_2$, T$_2$, HD, HT, DT) were evaluated without expansion in the electron-nucleus mass ratio. The…
Variational and perturbative relativistic energies are computed and compared for two-electron atoms and molecules with low nuclear charge numbers. In general, good agreement of the two approaches is observed. Remaining deviations can be…
We calculate the energy of the state closest to threshold for two and three identical, spinless particles confined to a cubic spatial volume with periodic boundary conditions and with zero total momentum in the finite-volume frame. The…
We have calculated ac polarizabilities of the $2 \ ^3S$ and $2 \ ^1S$ states of both $^4$He and $^3$He in the range 318 nm to 2.5 $\mu$m and determined the magic wavelengths at which these polarizabilities are equal for either isotope. The…
We present calculations of the electron angular distributions in the single ionization of helium by 1-MeV proton impact at momentum transfer of 0.75 a.u. and ejected-electron energy of 6.5 eV. The results using the first and second Born…
Phase-shift differences and amplitude ratios of the outgoing $s$ and $d$ continuum wave packets generated by two-photon ionization of helium atoms are determined from the photoelectron angular distributions obtained using velocity map…
We present a nonperturbative numerical evaluation of the one-photon electron self energy for hydrogenlike ions with low nuclear charge numbers Z=1 to 5. Our calculation for the 1S state has a numerical uncertainty of 0.8 Hz for hydrogen and…
The \textit{ab initio} approach is used to evaluate the excitation energies of the $2s2p \, ^{2S+1}P_J$ states from the ground state as well as the $2s2p \, ^3P_1 \rightarrow 2s2p \, ^3P_0$ and $2s2p \, ^3P_2 \rightarrow 2s2p \, ^3P_1$…
We present the detection of the highly forbidden $2^{3\!}S_1 \rightarrow 3^{3\!}S_1$ atomic transition in helium, the weakest transition observed in any neutral atom. Our measurements of the transition frequency, upper state lifetime, and…
Collisional (de-)excitation of H$_{2}$ by helium plays an important role in the thermal balance and chemistry of various astrophysical environments, making accurate rate coefficients essential for the interpretation of observations of the…
We build the first analytic empirical potential for the most deeply bound $\mbox{Li}_{2}$ state: $b\left(1^{3}\Pi_{u}\right)$. Our potential is based on experimental energy transitions covering $v=0-34$, and very high precision theoretical…