Nuclear Recoil Effect Research Articles

Comprehensive constraints on fermionic dark matter-quark tensor interactions in direct detection experiments* *Supported in part by the Major Project of Basic and Applied Basic Research of Guangdong Province, China(2020B0301030008) and the National Natural Science Foundation of China(12035008, 12247151, 12305110, 12347121)

Effective field theory (EFT) provides a model-independent framework for interpreting the results of dark matter (DM) direct detection experiments. In this study, we demonstrate that the two fermionic DM-quark tensor operators and can contribute to the DM electric and magnetic dipole moments via nonperturbative QCD effects, in addition to the well-studied contact DM-nucleon operators. We then investigate the constraints on these two operators by considering both the contact and dipole contributions using the XENON1T nuclear recoil and Migdal effect data. We also recast other existing bounds on the DM dipole operators, derived from electron and nuclear recoil measurements in various direct detection experiments, as constraints on the two tensor operators. For , our results significantly extend the reach of constraints on the DM-quark tensor operators to masses as low as , with the bound exceeding that obtained by the Migdal effect with only contact interactions by approximately an order of magnitude. In particular, for the operator with DM mass , the latest PandaX constraint on the DM electric dipole moment puts more stringent bounds than the previous direct detection limit. We also briefly discuss the constraints obtained from experiments other than direct detection.

The excitation energies and hyperfine structures for 2l, 3l states in lithiumlike ions

Combining the multi-configuration Dirac–Hartree–Fock method and the model-quantum electrodynamics (QED) approach, the wave functions, transition energies and hyperfine structure constants for 2l, 3l states in Li-like Ne7+, Mg9+, Al10+, P12+, Ar15+ and Ca17+ ions are calculated. The effects of electron correlation, Breit interactions, nuclear recoil and QED effects are analyzed in detail. We find that the contribution of the non-diagonal elements of the self-energy is significant for the 2p1/2→2s1/2 and 2p3/2→2s1/2 transitions. However, for the 3l→2s1/2 transitions, the contribution of non-diagonal elements is small. The accuracy of the currently calculated hyperfine structure constants is expected to be within 1%.

The Landé g factors of highly charged Sn47+ and Bi80+ ions

The wavefunctions and eigenvalues of the ground states of Sn47+, and Bi80+ ions are calculated using the fully relativistic multiconfiguration Dirac-Hartree–Fock (MCDHF) method. Detailed investigation are carried out to study the effects of electron correlation, Breit interaction, quantum electrodynamics (QED), and nuclear recoil. Based on these calculations, the theoretical predictions for the g factors of the ground states of Sn47+ and Bi80+ ions are 1.980429 and 1.934759, respectively. The accuracy of these calculations is expected to be on the order of 10−5.

Formula omitted][formula omitted] MCDHF/RCI calculations of mass- and field shifts isotopes parameters of the [formula omitted][formula omitted][formula omitted] and [formula omitted][formula omitted][formula omitted] transitions in He-like ions for the sequence 2 [formula omitted][formula omitted][formula omitted] 83

Based on the multiconfiguration Dirac–Hartree–Fock method, the field shift and mass shift parameters of the 1s21S0−1s2p1P1o and 1s21S0−1s2p3P0,1,2o transitions in He-like ions for the sequence 2 ≤Z≤ 83 are calculated with high precision. The total value of the isotope shift is determined by the sum of the mass- and field-shifts. With the inclusion of the Breit interaction and the leading QED corrections, we find that the mass shift parameters of these transitions do not change monotonously along the isoelectronic sequence in the high-Z range due to the relativistic nuclear recoil effects. In addition, the field shifts and mass shifts of these four transitions are estimated and compared along the isoelectronic sequence.

QED calculations of the nuclear recoil effect in muonic atoms

QED calculations of the nuclear recoil effect in muonic atoms

Calculations of energy levels, radiative transition parameters, hyperfine structure constants [formula omitted] - [formula omitted], Landé [formula omitted] factors and isotope shifts for Sc XX using the MCDF-RCI method

Large scale calculations for the energy levels, transition rates, oscillator strengths, lifetimes, hyperfine interaction constants, Landé gJ factors, and isotope shift factors have been performed for 1s2 and 1snl(n=2−8andl≤n−1) levels of He-like Sc XX ion. The general-purpose relativistic atomic structure package (GRASP2018) based on the fully relativistic multiconfiguration Dirac–Fock (MCDF) method is used to carry out the calculations. The leading quantum electrodynamic corrections, Breit interaction and nuclear recoil effects are also included in the succeeding relativistic configuration interaction (RCI) calculations. The relativistic isotope shift (RIS4) programme is used to determine the mass and field shifts factors. Furthermore, the percentage uncertainty in the transition parameters and lifetimes is estimated. A detailed comparison of the present results with the corresponding values from the NIST database and other theoretical and experimental works, wherever available, has been done, and an excellent agreement is achieved. A large section of the results is reported for the first time in the present work.

Ab initio calculations of the 2p3/2→2s transition in He-, Li-, and Be-like uranium

The bound-state QED approach is applied to calculations of the $2p_{3/2} \rightarrow 2s$ transition energies in He-, Li-, and Be-like uranium. For U$^{90+}$ and U$^{89+}$, standard perturbation theory for a single level is employed, while the calculations of U$^{88+}$ have required its counterpart for quasidegenerate levels. The utilized approach merges the rigorous QED treatment up to the second order of perturbation theory with the higher-order electron-correlation contributions evaluated within the Breit approximation. The higher-order screened QED effects are estimated by means of the model-QED operator. The nuclear recoil, nuclear polarization, and nuclear deformation effects are taken into account as well. Along with the transition energies, their pairwise differences are calculated. The comprehensive analysis of the uncertainties due to uncalculated effects is carried out, and the most accurate theoretical predictions, which are in perfect agreement with available experimental data, are obtained.

Complex-scaled ab initio QED approach to autoionizing states

Ab initio method based on a complex-scaling approach and aimed at a rigorous QED description of autoionizing states is worked out. The autoionizing-state binding energies are treated nonperturbatively in $\alpha Z$ and include all the many-electron QED contributions up to the second order. The higher-order electron correlation, nuclear recoil, and nuclear polarization effects are taken into account as well. The developed formalism is demonstrated on the $LL$ resonances in heliumlike argon and uranium. The most accurate theoretical predictions for the binding energies are obtained.

Study of 211Bi and 211Pb Recoils Release from 223Ra Labelled TiO2 Nanoparticles

Nanoparticles of various materials were proposed as carriers of nuclides in targeted alpha particle therapy to at least partially eliminate the nuclear recoil effect causing the unwanted release of radioactive progeny originating in nuclear decay series of so-called in vivo generators. Here, we report on the study of 211Pb and 211Bi recoils release from the 223Ra surface-labelled TiO2 nanoparticles in the concentration range of 0.01-1 mg/mL using two phase separation methods different in their kinetics in order to test the ability of progeny resorption. We have found significant differences between the centrifugation and the dialysis used for labelled NPs separation as well as that the release of 211Pb and 211Bi from the nanoparticles also depends on the NPs dispersion concentration. These findings support our previously proposed recoils-retaining mechanism of the progeny by their resorption on the NPs surface. At the 24 h time-point, the highest overall released progeny fractions were observed using centrifugation (4.0% and 13.5% for 211Pb and 211Bi, respectively) at 0.01 mg/mL TiO2 concentration. The lowest overall released fractions at the 24 h time-point (1.5% and 2.5% for 211Pb and 211Bi respectively) were observed using dialysis at 1 mg/mL TiO2 concentration. Our findings also indicate that the in vitro stability tests of such radionuclide systems designed to retain recoil-progeny may end up with biased results and particular care needs to be given to in vitro stability test experimental setup to mimic in vivo dynamic conditions. On the other hand, controlled and well-defined progeny release may enhance the alpha-emitter radiation therapy of some tumours.

Model-QED-operator approach to relativistic calculations of the nuclear recoil effect in many-electron atoms and ions

A model-operator approach to fully relativistic calculations of the nuclear recoil effect on energy levels in many-electron atomic systems is worked out. The one-electron part of the model operator for treating the normal mass shift beyond the Breit approximation is represented by a sum of semilocal and nonlocal potentials. The latter ones are constructed by employing the diagonal and off-diagonal matrix elements rigorously evaluated for hydrogenlike ions to first order in the electron-to-nucleus mass ratio. The specific mass shift beyond the lowest-order relativistic approximation has a form which can be directly employed in calculations. The capabilities of the method are probed by comparison of its predictions with the results of ab initio QED calculations. The proposed operator can be easily incorporated into any relativistic calculation based on the Dirac-Coulomb-Breit Hamiltonian.

Oscillator strengths and interstate transition energies involving [formula omitted] and [formula omitted] states of the Li atom

We report high accuracy calculations of the ground and excited doublet S and P states of lithium atom. Overall, 24 states corresponding to dominant electronic configurations 1s2ns and 1s2np (n=2,…,13) are considered in the framework of the Ritz variational method. The nonrelativistic wave function of each of these states is generated in an independent calculation by expanding it in terms of a large number (K=11,000−17,000) of all-electron explicitly correlated Gaussian functions (ECG) whose nonlinear parameters are extensively optimized with a procedure that employs analytic energy gradient determined with respect to these parameters. The Hamiltonian used in the calculations explicitly depends on the mass of the nucleus. The leading relativistic and quantum electrodynamics (QED) corrections to the energy levels are subsequently computed using the perturbation-theory approach and the variational nonrelativistic wave functions as the zeroth-order functions. As these functions are generated in the finite-nuclear-mass (FNM) calculations, the energy corrections include the nuclear recoil effects. The obtained energy levels allow us to determine highly accurate interstate transition frequencies for both the naturally occurring stable lithium isotopes, 6Li and 7Li, and the lithium atom with an infinitely heavy nucleus, ∞Li. The nonrelativistic wave functions are used to compute the transition dipole moments and the corresponding oscillator strengths. These quantities are reported for 144 S–P transitions of each isotope. The data set generated in this work is considerably more accurate and comprehensive than the data available from the previous theoretical calculations. It can be useful in guiding future spectroscopic measurements of the lithium atom.

Calculations of relativistic, correlation, nuclear and quantum-electrodynamics corrections to the energies and ionization potentials of the ground state of lithium-like ions

This paper presents all the leading contributions to the relativistic binding energies and ionization potentials of the ground state of lithium-like ions with a nuclear charge in the range Z=3-20. Correlation, relativistic and quantum-electrodynamics corrections as well as the contributions due to the finite size of the nucleus (the field shift) and finite mass of the nucleus (the recoil effect) are evaluated. Relativistic calculations are performed by means of the configuration-interaction method in the basis of the Dirac-Fock-Sturm orbitals using the Dirac-Coulomb-Breit Hamiltonian. Keywords: Li-like ions, ionization potential, relativistic calculations, configuration interaction, electron correlations, Breit interaction, field shift, nuclear recoil effect, QED corrections

Benchmark Calculations of the Energy Spectra and Oscillator Strengths of the Beryllium Atom

In this work, we present a series of benchmark variational calculations for the ground and 19 lowest bound excited singlet S and P states of the beryllium atom. The nonrelativistic wave functions of the states that represent the motion of the nucleus and the four electrons around the center of mass of the atom are expanded in terms of up to 17 000 all-particle explicitly correlated Gaussians. The Gaussians are optimized independently for each state. The leading relativistic corrections to the energy levels are computed in the framework of the perturbation theory and they explicitly include the nuclear recoil effects. We also calculate the leading quantum electrodynamics (QED) corrections for each considered state. Using the obtained energy levels and the corresponding wave functions, we compute the transition frequencies, transition dipole moments, and oscillator strengths. A comparison with the available experimental data shows very good agreement. The results of this most comprehensive set of calculations of spectroscopic accuracy for Be to date may open up new applications pertinent to the precision tests of QED, determination of the nuclear charge radius, and modeling matter-radiation equilibria of the beryllium gas that has relevance to the physics of interstellar media.

Abinitio Calculations of Energy Levels in Be-Like Xenon: Strong Interference between Electron-Correlation and QED Effects.

The strong mixing of close levels with two valence electrons in Be-like xenon greatly complicates abinitio QED calculations beyond the first-order approximation. Because of a strong interplay between the electron-electron correlation and QED effects, the standard single-level perturbative QED approach may fail, even if it takes into account the second-order screened QED diagrams. In the present Letter, the corresponding obstacles are overcome by working out the QED perturbation theory for quasidegenerate states. The contributions of all the Feynman diagrams up to the second order are taken into account. The many-electron QED effects are rigorously evaluated in the framework of the extended Furry picture to all orders in the nuclear-strength parameter αZ. The higher-order electron-correlation effects are considered within the Breit approximation. The nuclear recoil effect is accounted for as well. The developed approach is applied to high-precision QED calculations of the ground and singly excited energy levels in Be-like xenon. The most accurate theoretical predictions for the binding and excitation energies are obtained. These results deviate from the most precise experimental value by 3σ but perfectly agree with a more recent measurement.

QED theory of the normal mass shift in few-electron atoms

The electron-electron interaction correction of first order in $1/Z$ to the one-electron part of the nuclear recoil effect on binding energies in atoms and ions is considered within the framework of the rigorous QED approach. The calculations to all orders in $\alpha Z$ are performed for the $1s^2$ state in heliumlike ions and the $1s^2 2s$ and $1s^2 2p_{1/2}$ states in lithiumlike ions in the range $Z=5$--$100$. The results obtained are compared with the Breit-approximation values. The performed calculations complete a systematic treatment of the QED nuclear recoil effect up to the first order in $1/Z$. The correction obtained is combined with the previously studied two-electron part as well as the higher-order electron-correlation corrections evaluated within the Breit approximation to get the total theoretical predictions for the mass shifts.

Relativistic Calculation of the Nuclear Recoil Effect on the g Factor of the 2P3/2 State in Highly Charged B-like Ions

The nuclear recoil effect on the $^2 P_{3/2}$-state $g$ factor of B-like ions is calculated to first order in the electron-to-nucleus mass ratio $m/M$ in the range $Z=18$--$92$. The calculations are performed by means of the $1/Z$ perturbation theory. Within the independent-electron approximation, the one- and two-electron recoil contributions are evaluated to all orders in the parameter $\alpha Z$ by employing a fully relativistic approach. The interelectronic-interaction correction of first order in $1/Z$ is treated within the Breit approximation. Higher orders in $1/Z$ are partially taken into account by incorporating the screening potential into the zeroth-order Hamiltonian. The most accurate to date theoretical predictions for the nuclear recoil contribution to the bound-electron $g$ factor are obtained.

Complex Rotated Relativistic Configuration-Interaction Calculations of 1s2l2l ' States in O5+ Ion

Relativistic calculations of the energies and Auger widths of the lowest autoionizing states of lithium-like oxygen are performed. All leading corrections to the energy, including the contribution of electronic correlations, nuclear recoil effect, and quantum electrodynamic (QED) corrections, are included. The calculations have been performed using the Dirac–Coulomb–Breit Hamiltonian by the method of configuration interaction with complex rotation. The results obtained have been compared with the known experimental and theoretical values.

Interelectronic-interaction contribution to the nuclear recoil effect on the g factor of boronlike ions

The nuclear recoil effect on the ground-state $g$ factor of highly charged boronlike ions is considered within the relativistic formalism. The interelectronic-interaction contribution is evaluated in the Breit approximation, employing two independent approaches: the second-order perturbation theory and the configuration-interaction Dirac-Fock-Sturm method. The uncertainty of the nuclear recoil $g$-factor contributions is significantly reduced, especially for low- and middle-$Z$ ions.

QED calculations of the nuclear recoil effect on the bound-electrongfactor

Fully relativistic approach is applied to evaluation of the nuclear recoil effect on the bound-electron $g$ factor in hydrogenlike ions to first order in the electron-to-nucleus mass ratio $m/M$ and to all orders in $\alpha Z$. The calculations are performed in the range $1 \leqslant Z \leqslant 20$ for the $g$ factors of $1s$, $2s$, $2p_{1/2}$, and $2p_{3/2}$ states. The $\alpha Z$-dependence of the nontrivial QED recoil contribution as a function of $Z$ is studied.

Effective neutrino masses in KATRIN and future tritium beta-decay experiments

Past and current direct neutrino mass experiments set limits on the so-called effective neutrino mass, which is an incoherent sum of neutrino masses and lepton mixing matrix elements. The electron energy spectrum which neglects the relativistic and nuclear recoil effects is often assumed. Alternative definitions of effective masses exist, and an exact relativistic spectrum is calculable. We quantitatively compare the validity of those different approximations as function of energy resolution and exposure in view of tritium beta decays in the KATRIN, Project 8 and PTOLEMY experiments. Furthermore, adopting the Bayesian approach, we present the posterior distributions of the effective neutrino mass by including current experimental information from neutrino oscillations, beta decay, neutrinoless double-beta decay and cosmological observations. Both linear and logarithmic priors for the smallest neutrino mass are assumed.