arXiv subjects

J. Mitroy

Publications and source records attributed to J. Mitroy.

33 records · Page 2Linked to original sources

arXiv2008

Positron-atom scattering using pseudo-state energy shifts

A method to generate low-energy phase shifts for elastic scattering using bound-state calculations is applied to the problem of e+ - Mg and e+ - Zn scattering after an initial validation on the e+ - Cu system. The energy shift between a small reference calculation and the largest possible configuration interaction calculation of the lowest energy pseudo-state is used to tune a semi-empirical optical potential. The potential was further fine-tuned by utilizing the energy of the second lowest pseudo-state. The s- and p-wave phase shifts for positron scattering from Mg and Zn are given from threshold to the first excitation threshold. The e+ - Mg cross section has a prominent p-wave shape resonance at an energy of about 0.096 eV with a width of 0.106 eV. The peak cross section for e+ - Mg scattering is about 4800 a_0^2 while Z_eff achieves a value of 1310 at an energy of 0.109 eV.

physics.atom-ph↗

arXiv2007

Positronic complexes with unnatural parity

The structure of the unnatural parity states of PsH, LiPs, NaPs and KPs are investigated with the configuration interaction and stochastic variational methods. The binding energies (in hartree) are found to be 8.17x10-4, 4.42x10-4, 15.14x10-4 and 21.80x10-4 respectively. These states are constructed by first coupling the two electrons into a configuration which is predominantly 3Pe, and then adding a p-wave positron. All the active particles are in states in which the relative angular momentum between any pair of particles is at least L = 1. The LiPs state is Borromean since there are no 3-body bound subsystems (of the correct symmetry) of the (Li+, e-, e-, e+) particles that make up the system. The dominant decay mode of these states will be radiative decay into a configuration that autoionizes or undergoes positron annihilation.

physics.atom-ph↗

arXiv2006

Generating phase shifts from pseudo state energy shifts

A simple way to generate low energy phase shifts for elastic scattering using bound-state calculations is postulated, validated and applied to the problem of e+ - Mg scattering. The essence of the method is to use the energy shift between a small reference calculation and the largest possible calculation of the lowest energy pseudo-state to tune a semi-empirical optical potential. The L = 1 partial wave for e+ - Mg scattering is predicted to have a shape resonance at an energy of about 0.13 eV. The value of Zeff at the center of the resonance is about 1500.

physics.atom-ph↗

arXiv2006

Second bound state of PsH

The existence of a second bound state of PsH that is electronically stable and also stable against positron annihilation by the normal 2gamma and 3gamma processes is demonstrated by explicit calculation. The state can be found in the 2,4So symmetries with the two electrons in a spin triplet state. The binding energy against dissociation into the H(2p) + Ps(2p) channel was 6.06x10-4 Hartree. The dominant decay mode of the states will be radiative decay into a configuration that autoionizes or undergoes positron annihilation. The NaPs system of the same symmetry is also electronically stable with a binding energy of 1.553x10-3 Hartree with respect to the Na(3p) + Ps(2p) channel.

physics.atom-ph↗

arXiv2006

The existence of a 2Po excited state for the e+Ca system

The Configuration Interaction method is used to demonstrate that there is an electronically stable state of positronic calcium with an orbital angular momentum of L=1. This prediction relies on the use of an asymptotic series to estimate the variational limit of the energy. The best estimate of the binding energy is 37 meV. A discussion of the structure of the system is also presented.

physics.atom-ph↗

arXiv2006

Convergence of an s-wave calculation of the He ground state

The Configuration Interaction (CI) method using a large Laguerre basis restricted to l = 0 orbitals is applied to the calculation of the He ground state. The maximum number of orbitals included was 60. The numerical evidence suggests that the energy converges as Delta E^N approx A/N^(7/2) + B/N^(8/2) + >... where N is the number of Laguerre basis functions. The electron-electron delta-function expectation converges as Delta delta^N approx A/N^(5/2) + B/N^(6/2) + ... and the variational limit for the l = 0 basis is estimated as 0.1557637174(2) a_0^3. It was seen that extrapolation of the energy to the variational limit is dependent upon the basis dimension at which the exponent in the Laguerre basis was optimized. In effect, it may be best to choose a non-optimal exponent if one wishes to extrapolate to the variational limit. An investigation of the Natural Orbital asymptotics revealed the energy converged as Delta E^N approx A/N^6 + B/N^7 + ... while the electron-electron delta-function expectation converged as Delta delta^N approx A/N^4 + B/N^5 + >... . The asymptotics of expectation values other than the energy showed fluctuations that depended on whether $N$ was even or odd.

physics.atom-ph↗

arXiv2006

Convergence of the partial wave expansion of the He ground state

The Configuration Interaction (CI) method using a very large Laguerre orbital basis is applied to the calculation of the He ground state. The largest calculations included a minimum of 35 radial orbitals for each l ranging from 0 to 12 resulting in basis sets in excess of 400 orbitals. The convergence of the energy and electron-electron delta-function with respect to J (the maximum angular momenta of the orbitals included in the CI expansion) were investigated in detail. Extrapolations to the limit of infinite in angular momentum using expansions of the type Delta X_J = A_X/(J+1/2)^p + B_X/(J+1/2)^(p+1) + ..., gave an energy accurate to 10^(-7) Hartree and a value of accurate to about 0.5%. Improved estimates of and , accurate to 10^(-8) Hartree and 0.01% respectively, were obtained when extrapolations to an infinite radial basis were done prior to the determination of the J -> infty limit. Round-off errors were the main impediment to achieving even higher precision since determination of the radial and angular limits required the manipulation of very small energy and differences.

physics.atom-ph↗

arXiv2006

Energy and expectation values of the PsH system

Close to converged energies and expectation values for PsH are computed using a ground state wave function consisting of 1800 explicitly correlated gaussians. The best estimate of the PsH$^{\infty}$ energy was -0.789196740 hartree which is the lowest variational energy to date. The 2$γ$ annihilation rate for PsH$^{\infty}$ was $2.47178\times 10^{9}$ s$^{-1}$.

physics.atom-ph↗

arXiv2006

Convergence of CI single center calculations of positron-atom interactions

The Configuration Interaction (CI) method using orbitals centered on the nucleus has recently been applied to calculate the interactions of positrons interacting with atoms. Computational investigations of the convergence properties of binding energy, phase shift and annihilation rate with respect to the maximum angular momentum of the orbital basis for the e^+Cu and PsH bound states, and the e^+-H scattering system were completed. The annihilation rates converge very slowly with angular momentum, and moreover the convergence with radial basis dimension appears to be slower for high angular momentum. A number of methods of completing the partial wave sum are compared, an approach based on a Delta X_J = a/(J + 1/2)^n + b/(J + 1/2)^(n+1) form (with n = 4 for phase shift (or energy) and n = 2 for the annihilation rate) seems to be preferred on considerations of utility and underlying physical justification.

physics.atom-ph↗

arXiv2006

Configuration Interaction calculations of positron binding to Be(3Po)

The Configuration Interaction method is applied to investigate the possibility of positron binding to the metastable beryllium (1s^22s2p 3Po) state. The largest calculation obtained an estimated energy that was unstable by 0.00014 Hartree with respect to the Ps + Be^+(2s) lowest dissociation channel. It is likely that positron binding to parent states with non-zero angular momentum is inhibited by centrifugal barriers.

physics.atom-ph↗

arXiv2006

Large dimension Configuration Interaction calculations of positron binding to the group II atoms

The Configuration Interaction (CI) method is applied to the calculation of the structures of a number of positron binding systems, including e+Be, e+Mg, e+Ca and e+Sr. These calculations were carried out in orbital spaces containing about 200 electron and 200 positron orbitals up to l = 12. Despite the very large dimensions, the binding energy and annihilation rate converge slowly with l, and the final values do contain an appreciable correction obtained by extrapolating the calculation to the l to infinity limit. The binding energies were 0.00317 hartree for e+Be, 0.0170 hartree for e+Mg, 0.0189 hartree for e+Ca, and 0.0131 hartree for e+Sr.

physics.atom-ph↗

arXiv2004

The higher-order C_n dispersion coefficients for hydrogen

The complete set of 2nd, 3rd and 4th order van der Waals coefficients, C_n up to n=32 for the H(1s)-H(1s) dimer are computed using pseudo-states to evaluate the appropriate sum rules. A study of the convergence pattern for n<=16 indicates that all the C_n (n<=16) coefficients are accurate to 13 significant digits. The relative size of the 4th-order C^4_n to the 2nd-order C^2_n coefficients is seen to increase as n increases and at n=32 the 4th-order term is actually larger.

physics.atom-ph↗

arXiv2004

The higher order C_n dispersion coefficients for the alkali atoms

The van der Waals coefficients, from C_11 through to C_16 resulting from 2nd, 3rd and 4th order perturbation theory are estimated for the alkali (Li, Na, K and Rb) atoms. The dispersion coefficients are also computed for all possible combinations of the alkali atoms and hydrogen. The parameters are determined from sum-rules after diagonalizing the fixed core Hamiltonian in a large basis. Comparisons of the radial dependence of the C_n/r^n potentials give guidance as to the radial regions in which the various higher-order terms can be neglected. It is seen that including terms up to C_10/r^10 results in a dispersion interaction that is accurate to better than 1 percent whenever the inter-nuclear spacing is larger than 20 a_0. This level of accuracy is mainly achieved due to the fortuitous cancellation between the repulsive (C_11, C_13, C_15) and attractive (C_12, C_14, C_16) dispersion forces.

physics.atom-ph↗

arXiv2004

Properties of the triplet metastable states of the alkaline-earth atoms

The static and dynamic properties of the alkaline-earth atoms in their metastable state are computed in a configuration interaction approach with a semi-empirical model potential for the core. Among the properties determined are the scalar and tensor polarizabilities, the quadrupole moment, some of the oscillator strengths and the dispersion coefficients of the van der Waals interaction. A simple method for including the effect of the core on the dispersion parameters is described.

physics.atom-ph↗

arXiv1997

Positronic lithium, an electronically stable Li-e$^+$ ground state

Calculations of the positron-Li system were performed using the Stochastic Variational Method and yielded a minimum energy of -7.53208 Hartree for the L=0 ground state. Unlike previous calculations of this system, the system was found to be stable against dissociation into the Ps + Li$^+$ channel with a binding energy of 0.00217 Hartree and is therefore electronically stable. This is the first instance of a rigorous calculation predicting that it is possible to combine a positron with a neutral atom and form an electronically stable bound state.

physics.atom-ph↗