arXiv subjects

J. Sapirstein

Publications and source records attributed to J. Sapirstein.

14 recordsLinked to original sources

arXiv2023

Simplified partial wave expansion of the Lamb shift

A method for calculating the self energy part of the Lamb shift is revisited. When the electron propagator in an external field is represented as an expansion in partial waves, the original method converges relatively slowly, requiring the calculation of dozens of partial waves. Here we show an improved method in which accurate results can be obtained using a much smaller number of partial waves. The method is illustrated for the ground states of hydrogenlike and lithiumlike boron, and the possibility of high accuracy calculations on lower Z hydrogenic ions is discussed.

physics.atom-ph↗

arXiv2018

Green Function of the Poisson Equation: D=2,3,4

We study the Green function of the Poisson equation in two, three and four dimensions. The solution g of the equation nabla^2 g(x - x') = delta^(D)(x - x'), where x and x are D-dimensional position vectors, is customarily expanded into radial and angular coordinates. For the two-dimensional case (D=2), we find a subtle interplay of the necessarily introduced scale L with the radial component of zero magnetic quantum number. For D=3, the well-known expressions are briefly recalled; this is done in order to highlight the analogy with the four-dimensional case, where we uncover analogies of the four-dimensional spherical harmonics with the familiar three-dimensional case. Remarks on the SO(4) symmetry of the hydrogen atom complete the investigations.

math-ph↗

arXiv2014

Stark shift and parity non-conservation for near-degenerate states of xenon

We identify a pair of near-degenerate states of opposite parity in atomic Xe, the $5p^5 10s \,\, ^2[3/2]_2^o$ at $\rm{E}=94759.927$ cm$^{-1}$ and $5p^5 6f \,\, ^2[5/2]_2$ at $\rm{E}= 94759.935$ cm$^{-1}$, for which parity- and time-odd effects are expected to be enhanced by the small energy separation. We present theoretical calculations which indicate narrow widths for both states and we report a calculated value for the weak matrix element, arising from configuration mixing, of $|W|=2.1$ Hz for $^{132}$Xe. In addition, we measured the Stark effect of the $5p^5\,6f$ $^2[5/2]_{2}$ and $5p^5 \,6f \ ^2[3/2]_2$ ($\rm{E} =94737.121\,\rm{cm}^{-1}$) states. The Stark-shift of the $6f$ states is observed to be negative, revealing the presence of nearby $6g$ states at higher energies, which have not been observed before. The Stark-shift measurements imply an upper limit on the weak matrix element of $|W|\!<\!5$ Hz for the near-degenerate states ($10s \,\, ^2[3/2]_2^o$ and $6f \,\, ^2[5/2]_2$), which is in agreement with the presented calculations.

physics.atom-ph↗

arXiv2014

Coordinate-space approach to vacuum polarization

The vacuum-polarization correction for bound electrons or muons is examined. The objective is to formulate a framework for calculating the correction from bound-state quantum electrodynamics entirely in coordinate space, including the Uehling potential which is usually isolated and treated separately. Pauli-Villars regularization is applied to the coordinate-space calculation and the most singular terms are shown to be eliminated, leaving the physical correction after charge renormalization. The conventional derivation of the Uehling potential in momentum space is reviewed and compared to the coordinate-space derivation.

quant-ph↗

arXiv2013

Bound-state field theory approach to proton structure effects in muonic hydrogen

A bound-state field theory approach to muonic hydrogen is set up using a variant of the Furry representation in which the lowest-order Hamiltonian describes a muon in the presence of a point Coulomb field, but the origin of the binding field is taken to be three charged quarks in the proton which are modeled as Dirac particles that move freely within a spherical well. Bound-state field theory techniques are used to evaluate one- and two-photon effects. Particular attention is paid to two-photon exchange diagrams, which include the effect of proton polarizability. In addition the modification of the electromagnetic self energy of the proton by the electric field of the muon is examined. Finally, the model is used to carry out a calculation of the static electric polarizability of the proton.

hep-ph↗

arXiv2012

Field-theory calculation of the electric dipole moment of the neutron and paramagnetic atoms

Electric dipole moments (edms) of bound states that arise from the constituents having edms are studied with field-theoretic techniques. The systems treated are the neutron and a set of paramagnetic atoms. In the latter case it is well known that the atomic edm differs greatly from the electron edm when the internal electric fields of the atom are taken into account. In the nonrelativistic limit these fields lead to a complete suppression, but for heavy atoms large enhancement factors are present. A general bound-state field theory approach applicable to both the neutron and paramagnetic atoms is set up. It is applied first to the neutron, treating the quarks as moving freely in a confining spherical well. It is shown that the effect of internal electric fields is small in this case. The atomic problem is then revisited using field-theory techniques in place of the usual Hamiltonian methods, and the atomic enhancement factor is shown to be consistent with previous calculations. Possible application of bound-state techniques to other sources of the neutron edm is discussed.

hep-ph↗

arXiv2005

Recoil corrections in the hydrogen isoelectronic sequence

A version of the Bethe-Salpeter equation appropriate for calculating recoil corrections in highly charged hydrogenlike ions is presented. The nucleus is treated as a scalar particle of charge Z, and the electron treated relativistically. The known recoil corrections of order $m^2/M(Zα)^4$ are derived in both this formalism and in NRQED.

hep-ph↗

arXiv2004

Calculation of Radiative Corrections to E1 matrix elements in the Neutral Alkalis

Radiative corrections to E1 matrix elements for ns-np transitions in the alkali metal atoms lithium through francium are evaluated. They are found to be small for the lighter alkalis but significantly larger for the heavier alkalis, and in the case of cesium much larger than the experimental accuracy. The relation of the matrix element calculation to a recent decay rate calculation for hydrogenic ions is discussed, and application of the method to parity nonconservation in cesium is described.

physics.atom-ph↗

arXiv2004

Accurate S-state helium wave functions in momentum space

High accuracy helium wave functions based on exponentials with random coefficients are transformed into momentum space. The utility of the wave functions is demonstrated through calculation of the expectation value of various operators needed to evaluate relativistic and QED corrections.

physics.atom-ph↗

arXiv2003

Radiative Corrections to One-Photon Decays of Hydrogenic Ions

Radiative corrections to the decay rate of n=2 states of hydrogenic ions are calculated. The transitions considered are the M1 decay of the 2s state to the ground state and the E1(M2) decays of the $2p_{1/2}$ and $2p_{3/2}$ states to the ground state. The radiative corrections start in order $α(Z α)^2$, but the method used sums all orders of $Zα$. The leading $α(Zα)^2$ correction for the E1 decays is calculated and compared with the exact result. The extension of the calculational method to parity nonconserving transitions in neutral atoms is discussed.

hep-ph↗

arXiv2003

Vacuum polarization calculations for hydrogenlike and alkalilike ions

Complete vacuum polarization calculations incorporating finite nuclear size are presented for hydrogenic ions with principal quantum numbers n=1-5. Lithiumlike, sodiumlike, and copperlike ions are also treated starting with Kohn-Sham potentials, and including first-order screening corrections. In both cases dominant Uehling terms are calculated with high accuracy, and smaller Wichmann- Kroll terms are obtained using numerical electron Green's functions.

physics.atom-ph↗

arXiv2003

Two-loop corrections to the decay rate of parapositronium

Order $α^2$ corrections to the decay rate of parapositronium are calculated. A QED scattering calculation of the amplitude for electron-positron annihilation into two photons at threshold is combined with the technique of effective field theory to determine an NRQED Hamiltonian, which is then used in a bound state calculation to determine the decay rate. Our result for the two-loop correction is $5.1243(33)$ in units of $(α/π)^2$ times the lowest order rate. This is consistent with but more precise than the result $5.1(3)$ of a previous calculation.

hep-ph↗

arXiv2003

Radiative Corrections to Parity Nonconserving Transitions in Atoms

The matrix element of a bound electron interacting with the nucleus through exchange of a Z boson is studied for the gauge invariant case of $2s_{1/2}-2p_{1/2}$ transitions in hydrogenic ions. The QED radiative correction to the matrix element, which is $-α/2π$ in lowest order, is calculated to all orders in $Zα$ using exact propagators. Previous calculation of the first-order binding correction are confirmed both analytically and by fitting the exact function at low $Z$. Consequences for the interpretation of parity nonconservation in cesium are discussed.

hep-ph↗

arXiv2000

Order α^2 corrections to the decay rate of orthopositronium

Order α^2 corrections to the decay rate of orthopositronium are calculated in the framework of nonrelativistic QED. The resulting contribution is found to be in significant disagreement with one set of experimental measurements though another experiment is in agreement with theory.

hep-ph↗