Overlap Amplitudes Research Articles

Atomic Electron Shell Excitations in Double-β Decay

The problem of the transition of electron shells of atoms to excited states in the process of neutrinoless double-βdecay is investigated. This subject is crucial for modeling the energy spectrum ofβ-electrons, which is sensitive to the mass and Majorana nature of neutrinos. The dependence of the obtained results on the atomic number indicates an important role of the Feinberg–Migdal effect in the electron shell excitations. We report the overlap amplitudes of the electron shells of the parent atom and the daughter ion for eleven atoms, the two-neutrino double-βdecay of which was observed experimentally. In around one-fourth of the cases where the structure of the electron shells is inherited from the parent atom, there is a transition to the ground state or the excited state with the lowest energy. The de-excitation of the daughter ion in the latter scenario is accompanied by the emission of photons in the ultraviolet range, which can serve as an auxiliary signature of double-βdecay. The average excitation energy of the electron shells ranges between 300 and 800 eV, with the variance ranging from (1.7 keV)2in calcium to (14 keV)2in uranium.

Atomic Electron Shell Excitations in Double-β Decay

The problem of the transition of electron shells of atoms to excited states in the process of neutrinoless double-beta decay is investigated. This subject is crucial for modeling the energy spectrum of beta -electrons, which is sensitive to the mass and Majorana nature of neutrinos. The dependence of the obtained results on the atomic number indicates an important role of the Feinberg–Migdal effect in the electron shell excitations. We report the overlap amplitudes of the electron shells of the parent atom and the daughter ion for eleven atoms, the two-neutrino double-beta decay of which was observed experimentally. In around one-fourth of the cases where the structure of the electron shells is inherited from the parent atom, there is a transition to the ground state or the excited state with the lowest energy. The de-excitation of the daughter ion in the latter scenario is accompanied by the emission of photons in the ultraviolet range, which can serve as an auxiliary signature of double-beta decay. The average excitation energy of the electron shells ranges between 300 and 800 eV, with the variance ranging from (1.7 keV)2 in calcium to (14 keV)2 in uranium.

Eigenvalues of uncorrelated, density-difference matrices and the interpretation of Δ-self-consistent-field calculations.

Two theorems on the eigenvalues of differences of idempotent matrices determine the natural occupation numbers and orbitals of electronic detachment, attachment, or excitation that pertain to transitions between wavefunctions that each consist of a single Slater determinant. They are also applicable to spin density matrices associated with Slater determinants. When the ranks of the matrices differ, unit eigenvalues occur. In addition, there are ±w pairs of eigenvalues where |w| ≤ 1, whose values are related to overlaps, t, between the corresponding orbitals of Amos and Hall, and Löwdin by the formula w=±1-t2 12. Generalized overlap amplitudes, including Dyson orbitals and their probability factors, may be inferred from these eigenvalues, which provide numerical criteria for: classifying transitions according to the number of holes and particles in final states with respect to initial states, identifying the most important effects of orbital relaxation produced by self-consistent fields, and the analysis of Fukui functions. Two similar theorems that apply to sums of idempotent matrices regenerate formulae for the natural orbitals and occupation numbers of an unrestricted Slater determinant that were published first by Amos and Hall.

Overlap of electron shells in $$\beta $$ and double-$$\beta $$ decays

The $\beta$ and double-$\beta$ decay channels, which are not accompanied by excitation of the electron shells, are suppressed due to the nonorthogonality of the electron wave functions of the parent and daughter atoms. The effect is sensitive to the contribution of the outer electron shells. Since valence electrons participate in chemical bonding and collectivize in metals, the decay rates of the unstable nuclides are modified when they are embedded in a host material. Core electrons are less affected by the environment, and their overlap amplitudes are more stable. The suppression effect is estimated for $ \beta^- $ decay of $^{87}$Kr, electron capture in $^{163}$Ho, and $2\beta^-$ decays of $^{76}$Ge, $^{100}$Mo, $^{130}$Te, and $^{136}$Xe. The overlap amplitude of the electron shells enters the relationship between the half-life of neutrinoless $2\beta$ decay and the effective electron neutrino Majorana mass.

Calculation of the amplitudes to the electron propagator from a minimal basis CI calculation on N2

A comparison between overlap amplitudes and ionization energies calculated by the method of configuration interaction and by the electron propagator for a model problem is presented. Details of the approximations in both types of calculations made are outlined. The close, but not exact, agreement reported between CI and propagator calculations is encouraging and indicates that truncations of the propagator equations can be performed in a systematic manner with results comparable to those obtained from methods relying on the variational principle.

Boundary RG flow associated with the AKNS soliton hierarchy

We introduce and study an integrable boundary flow possessing an infinite number of conserving charges which can be thought of as quantum counterparts of the Ablowitz, Kaup, Newell and Segur Hamiltonians. We propose an exact expression for overlap amplitudes of the boundary state with all primary states in terms of solutions of certain ordinary linear differential equation. The boundary flow is terminated at a nontrivial infrared fixed point. We identify a form of whole boundary state corresponding to this fixed point.

Coherent ultrafast photoelectron spectroscopy in Br2: An alternative method for measuring Δv≠ transitions in Rydberg-to-Rydberg excitations

A two-state vibrational wave packet is prepared in a low-lying 4d[12](1 or 2) Rydberg state of jet cooled Br(2) (4d, v(')=3 and v(')=4) by two-photon excitation with 266.5 nm pulses from an ultrafast laser. The wave packet is detected by autoionization following excitation with time-delayed 800 nm pulses to the n=8 (v(+)=4) and n=9 (v(+)=3) Rydberg states in the (2)Pi(12) angular momentum core state. Autoionization of each state occurs to the (2)Pi(32) state of the ion through spin-orbit ionization. Photoelectron spectroscopy is used to differentiate between the n=8 and n=9 ejected photoelectrons. Detection of the wave packet recurrences via the n=8 and n=9 Rydberg states reveals a pi phase-shift difference of the recurrences between the two final states. In each case, Delta v not equal 0 transitions are observed since wave packet recurrences are detected. By fitting the observed phase change of the recurrences with a simple model for the overlap amplitudes and assumptions about the potentials, we estimate, within the context of the model, that approximately 0.6% of the transitions may be attributed to Delta v= +/- 1 transitions between the initial Rydberg superposition state and the final Rydberg detection state.

Integrable model of boundary interaction: the paperclip

We consider a model of 2D quantum field theory on a disk, whose bulk dynamics is that of a two-component free massless Bose field X =(X,Y) , and interaction occurs at the boundary, where the boundary values ( X B , Y B ) are constrained to special curve—the “paperclip brane”. The interaction breaks conformal invariance, but we argue that it preserves integrability. We propose exact expression for the disk partition function (and more general overlap amplitudes 〈 P |B〉 of the boundary state with all primary states) in terms of solutions of certain ordinary linear differential equations.

Compton scattering beyond the impulse approximation

We treat the nonrelativistic Compton scattering process in which an incoming photon scatters from an N-electron many-body state to yield an outgoing photon and a recoil electron, without invoking the commonly used frameworks of either the impulse approximation (IA) or the independent particle model (IPM). An expression for the associated triple differential scattering cross section is obtained in terms of Dyson orbitals, which give the overlap amplitudes between the N-electron initial state and the $(N\ensuremath{-}1)$ electron singly ionized quantum states of the target. We show how in the high-energy transfer regime, one can recover from our general formalism the standard IA based formula for the cross section which involves the ground-state electron momentum density of the initial state. Our formalism will permit the analysis and interpretation of electronic transitions in correlated electron systems via inelastic x-ray scattering spectroscopy beyond the constraints of the IA and the IPM.

Chemical bonding in the hydrogen molecule

The chemical bond in the hydrogen molecule is examined using the electron density and the generalized overlap amplitudes. Logarithmic derivatives of the electron density provide clear picture of its behavior in the bonding region as well as in the outer region. The GOA expansion of the density is used to examine the dependence of the rate of decay of the density on the GOA ionization potentials. The increase in the electron density at the nuclei and in the bonding region coincides with the higher ionization potential of H{sub 2} over the H atom. The density in the bonding region along the internuclear axis does not decay exponentially, but its shape is very nearly an inverted Gaussian. 31 refs., 11 figs., 1 tab.

Generalized overlap amplitudes for the lithium atom

Generalized overlap amplitudes (GOAS) are calculated between the lithium atom and several states of Li+. An examination of the long-range behavior of the GOAS indicates that they are coupled, appearing to have the same exponential decay at large r. At intermediate distances from the nucleus, the GOAS decay with their unique exponential rate and the decay rates only merge at large r. Although many of the GOAS appear to be similar, their distinctness indicates that they may, in fact, be linearly independent. © 1996 John Wiley & Sons, Inc.

Chemical bonding in the hydrogen molecule

The chemical bond in the hydrogen molecule is examined using the electron density and the generalized overlap amplitudes. Logarithmic derivatives of the electron density provide a clear picture of its behavior in the bonding region as well as in the outer region. The GOA expansion of the density is used to examine the dependence of the rate of decay of the density on the GOA ionization potentials. The increase in the electron density at the nuclei and in the bonding region coincides with the higher ionization potential of H2 over the H atom. The density in the bonding region along the internuclear axis does not decay exponentially, but its shape is very nearly an inverted Gaussian. © 1996 John Wiley & Sons, Inc.

Generalized overlap amplitudes for the lithium atom

Generalized overlap amplitudes for the lithium atom

A local one‐electron operator for the generalized‐overlap amplitudes

AbstractAn approach to the N‐electron behavior is presented which emphasizes the dynamics of an individual electron. The generalized overlap amplitudes (GOAS), although formally defined by an integration over the coordinates of N − 1 electrons, are, instead, resolved as a column vector, eigenfunction to a local one‐electron differential operator. These amplitudes have no restrictions of linear independence between them, but each satisfies the one‐electron boundary conditions at the nuclei and at large distances. The one‐electron (or charge) density is the sum of the squares of the elements of the column. The energy density, a constant times the one‐electron density, maintains this one‐to‐one relationship throughout modifications in total number of electrons or external potential, although the constant of proportionality, the total energy of the system, may change in the process. Indistinguishability of electrons and antisymmetry is always observed by the dynamics of each electron. A numerical example, the ground state of helium, is presented. © 1995 John Wiley & Sons, Inc.

Generalized overlap amplitudes using the extended Koopmans’ theorem for Be

Approximate generalized overlap amplitudes (GOAs), also called Feynman–Dyson amplitudes, have been calculated from a full configuration interaction (CI) wave function for the ground state of beryllium using the extended Koopmans’ theorem (EKT). The GOAs were also calculated from the ground state CI wave function for Be and the ground state and excited state CI wave functions for Be+. The EKT GOAs are nearly identical to the corresponding CI GOAs for the lower 2S states of Be+ and for the Be+ 1s2s2 state which has a large GOA occupation number. There are many CI GOAs for which there is not a corresponding EKT GOA. This may be due in part to the limited size of the basis set and to the inability to include natural spin orbitals with small occupation numbers in the EKT calculations.

Occupation function in extended systems

The occupation function in the sense of occupation numbers for the natural spin orbitals for a solid is analyzed from several points of view. The connection with the generalized overlap amplitudes is pointed out and the theory is developed for general spin orbitals both in position and momentum space. The symmetry properties of the occupation function and its Fourier coefficients are analyzed. General expressions for the gradient of the occupation function are derived. The special restricted Hartree-Fock case, where the occupation function is a step function is described as an illustration.

An efficient method for the calculation of generalized overlap amplitudes for core photoelectron shake-up spectra

Using a Gelfand-Tsetlin N-electron basis and a graphical unitary group approach, an efficient method is derived for the calculation of generalized overlap amplitudes of the form X (n) p = < Ψ (n) )( N-1) ¦ψ a p ¦ψ (0) ( N) >, whereψ ( n) ( N-1) and ψ (0)( N) denote complete active space wavefunctions and p is a core orbital index. Using this method the computational effort to obtain X n p is negligible compared to the wavefunction optimization.

A diabatic model for photoionization. Application to the inner valence x-ray photoelectron spectrum of acetylene

A two-state diabatic model for high-energy photoionization is proposed and applied to the inner valence x-ray photoelectron spectrum of acetylene. The diabatic electronic representation is accomplished by calculating the first order nonadiabatic coupling over the vibrational normal modes. The photoionization overlap amplitudes are expressed in terms of this new basis which is related to the adiabatic representation via an orthogonal transformation. The nonadiabatic (vibronic) coupling leads to a significant redistribution of photoelectron intensity for the totally symmetric states in the inner valence region. This finding resolves previous ambiguities in the analysis of the spectrum.

The full 2p-h tda and other self-energy approximants: a comparative investigation

A super-operator formulation for decoupling symmetry blocks of the full 2p-h TDA electron propagator matrix is presented, accuracy is explored using the full 2p-h TDA overlap amplitudes to calculate relative ionization intensities for N 2 and H 2O. The effect of excluding orbitais on IPs and relative ionization cross sections is reported.

16O, 24, 26Mg, 28Si, 32S, 40Ca(α, 12C) and multi-α-cluster transfer reactions

The (α, 12C) reaction has been studied on a variety of nuclei, A = 16 to 40, at E α = 90.3 MeV. The data indicate a rapid fall-off of cross sections with increasing target mass, approximately as A t −5 ± 1. This and other systematics are used to estimate cross sections for multi-α-cluster transfer reactions in heavy nuclei and suggest σ T < 10 −34 cm 2 consistent with present experimental limits. The data for 24Mg(α, 12C) 16O has been studied in more detail and indicates a selective population of final states including 16O g.s., with oscillatory angular distributions in some instances. Finite-range distorted-wave Born approximation calculations for direct 8Be pickup have been performed utilizing cluster overlap amplitudes obtained with zero-order SU(3) wave functions. The calculations are in qualitative, and often quantitative, agreement with shapes and absolute magnitudes of the measured angular distributions although the cross sections for certain α-cluster states (2 +, E x ≈ 7 MeV; 4 +, E x ≈ 10.3 MeV) are greatly overestimated with this model. Other more complicated mechanisms, such as successive α-transfer, cannot be excluded. The systematics of the calculated 8Be cluster overlaps and the calculated and measured (α, 12C) cross sections are investigated, and implications for multi-α-cluster transfer reactions are discussed.