Lamb shifts and fine-structure splittings for light muonic ions: Hyperfine-structure corrections

Our previous calculations for the energy splittings of the states 2s1/2-2p1/2 and 2s1/2-2p3/2 for the muonic ions - Li, - Be, and - B are extended to include hyperfine-structure corrections. The results show that there is a rich spectrum of well-resolved hyperfine transitions lying throughout the visible and infrared parts of the spectrum. A measurement of the transition frequencies would provide a precise determination of the nuclear radius and the hyperfine-structure coupling constants. © 1986 The American Physical Society

A unified treatment of the non-relativistic and relativistic hydrogen atom: III. The reduced Green functions

The last in a series of three papers in which it is shown how the radial part of non-relativistic and relativistic hydrogenic bound-state calculations involving the Green functions can be presented in a unified manner. The work presented here is concerned with the reduced Green functions which arise in second-order stationary state perturbation theory. Using a simple linear transformation of the four radial parts of the relativistic reduced Green function it is shown how the non-relativistic and relativistic functions are special instances of the solution of a general second-order differential equation. The general solution of this equation is exhibited in the form of a Sturmian expansion, and complete solutions in both cases are presented. Recursion relations are deduced for the radial parts of both reduced Green functions and their matrix elements are examined in detail. As a test of the given functions the second-order effect of a perturbation of the nuclear charge is calculated and is shown to agree exactly with the value expected from a simple Taylor expansion of the hydrogenic energy formula

Bethe logarithms for hydrogen up to n=20, and approximations for two-electron atoms

Bethe logarithms accurate to 14 or 15 places to the right of the decimal are tabulated for all states of hydrogen up to n=20. Approximation methods for Rydberg states of two-electron atoms are discussed. © 1990 The American Physical Society

Expectation values of rP for arbitrary hydrogenic states

Expectation values of rP for an arbitrary nl hydrogenic state are expressed in terms of state-independent coefficients that are determined by a simple recursion relation. Explicit results are given for negative P down to -16 and, by an algebraic transformation, for positive P up to 13. Closed-form expressions are obtained for the coefficients of the two highest-order terms in l multiplying each power of n. The result is an asymptotic expression valid for each P and sufficiently large l. © 1990 The American Physical Society

An alternative proof of some relations between hydrogenic matrix elements

A relationship between certain integrals of the product of two Laguerre polynomials is obtained. It is shown how this relationship, together with two known Hankel transforms, allows for an alternative derivation of some relations between matrix elements of r k for hydrogenic ions. A further relation, involving matrix elements of logarithmic functions, is obtained in a similar manner. © 1990 IOP Publishing Ltd

A unified treatment of the non-relativistic and relativistic hydrogen atom: III. The reduced Green functions

The last in a series of three papers in which it is shown how the radial part of non-relativistic and relativistic hydrogenic bound-state calculations involving the Green functions can be presented in a unified manner. The work presented here is concerned with the reduced Green functions which arise in second-order stationary state perturbation theory. Using a simple linear transformation of the four radial parts of the relativistic reduced Green function it is shown how the non-relativistic and relativistic functions are special instances of the solution of a general second-order differential equation. The general solution of this equation is exhibited in the form of a Sturmian expansion, and complete solutions in both cases are presented. Recursion relations are deduced for the radial parts of both reduced Green functions and their matrix elements are examined in detail. As a test of the given functions the second-order effect of a perturbation of the nuclear charge is calculated and is shown to agree exactly with the value expected from a simple Taylor expansion of the hydrogenic energy formula

Quantum defects and the 1/n dependence of Rydberg energies: Second-order polarization effects

The principal result of this paper is a general expression for the second-order dipole polarization energy of a Rydberg electron resulting from the term -1/r4 in the asymptotic potential, where 1 is the core polarizability. It is shown that the second-order term contributes even as well as odd powers of 1/n in a 1/n expansion of the energies for Rydberg states. The results are used to extend the interpretation of the terms in a quantum-defect expansion. It is shown that the Ritz expansion for the quantum defect, which contains only even inverse powers of the effective quantum number n*, provides a powerful method for deducing the even-order terms in the second-order energy. Least-squares fits to high-precision variational calculations for the Rydberg states of helium, using 1/n and quantum-defect expansions, are presented. The results reveal well-defined Ritz defects, which represent the degree to which the data cannot be represented by a Ritz expansion for the quantum defect. The implications for extrapolations of quantum defects are discussed. Finally, it is shown that the second-order polarization energy plays a significant role in understanding the quantum defects for the alkali metals. © 1991 The American Physical Society

A unified treatment of the non-relativistic and relativistic hydrogen atom II: The Green functions

This is the second in a series of three papers in which it is shown how the radial part of non-relativistic and relativistic hydrogenic bound-state calculations involving the Green functions can be presented in a unified manner. In this paper the nonrelativistic Green function is examined in detail; new functional forms are presented and a clear mathematical progression is shown to link these and most other known forms. A linear transformation of the four radial parts of the relativistic Green function is given which allows for the presentation of this function as a simple generalization of the non-relativistic Green function. Thus, many properties of the non-relativistic Green function are shown to have simple relativistic generalizations. In particular, new recursion relations of the radial parts of both the non-relativistic and relativistic Green functions are presented, along with new expressions for the double Laplace transforms and recursion relations between the radial matrix elements. A novel proof of the Sturmian form of the radial Green functions is given in an appendix

A novel non-Fermi-liquid state in the iron-pnictide FeCrAs

We report transport and thermodynamic properties of stoichiometric single crystals of the hexagonal iron-pnictide FeCrAs. The in-plane resistivity shows an unusual "non-metallic" dependence on temperature T, rising continuously with decreasing T from ~ 800 K to below 100 mK. The c-axis resistivity is similar, except for a sharp drop upon entry into an antiferromagnetic state at T_N 125 K. Below 10 K the resistivity follows a non-Fermi-liquid power law, rho(T) = rho_0 - AT^x with x<1, while the specific heat shows Fermi liquid behaviour with a large Sommerfeld coefficient, gamma ~ 30 mJ/mol K^2. The high temperature properties are reminiscent of those of the parent compounds of the new layered iron-pnictide superconductors, however the T -> 0 properties suggest a new class of non-Fermi liquid.Comment: 6 pages, 4 figure