Nuclear Polarizability Research Articles

Constraining Symmetry Energy from Pygmy Dipole Resonances in 68Ni and 132Sn

Abstract We make a new investigation on the correlation at saturation (subsaturation) density between the density dependence of symmetry energy and the percentage of energy-weighted sum rule (EWSR) exhausted by the pygmy dipole resonances (PDR) in $^{68}$Ni and $^{132}$Sn. The calculations are performed within Skyrme HF (or HF+BCS) plus random phase approximation (RPA) (or quasiparticle RPA) by using SAMi-J effective interactions. The effect of pairing on the dipole strength distribution of $^{68}$Ni and the density dependence of symmetry energy is discussed. The slope parameter L and symmetry energy J at saturation (subsaturation) density are 41.8-90.2 MeV (39.3-64.1 MeV) and 28.0-32.5 MeV (23.0-23.8 MeV). They are consistent with the currently accepted values except for the symmetry energy J at subsaturation density, it is slightly smaller than the data from nuclear mass differences and electric dipole polarizability.

Optical magnetic combination method for suppressing the Rb polarization-induced magnetic gradient in Rb-Xe NMR co-magnetometers.

The Rb polarization-induced magnetic field gradient affects the Xe nuclear spin relaxation properties and degrades the long-term stability of the NMR co-magnetometers. This paper proposes a combination suppressing scheme, which uses the second-order magnetic field gradient coils to compensate for the Rb polarization-induced magnetic gradient under counter-propagating pump beams. Based on the theoretical simulation, we find that the spatial distribution of the Rb polarization-induced magnetic gradient and the magnetic field distribution generated by gradient coils are complementary. The experimental results indicate that the compensation effect is 10% higher under the counter-propagating pump beams scheme compared with the compensation effect under the conventional single beam. Besides, due to a more uniform spatial distribution of electronic spin polarization, the Xe nuclear spin polarizability is improved and the signal-to-noise ratio (SNR) of NMR co-magnetometers could be further enhanced. The study provides an ingenious method for suppressing magnetic gradient in the optically polarized Rb-Xe ensemble, which is expected to improve the performance of the atomic spin co-magnetometers.

Nuclear polarizability effects in He+3 hyperfine splitting

The nuclear polarizability effects in hyperfine splitting of light atomic systems are not well known. The only system for which they were previously calculated is the hydrogen atom, where these effects were shown to contribute about 5\% of the total nuclear correction. One generally expects the polarizability effects to become more pronounced for composite nuclei. In the present work we determine the nuclear polarizability correction to the hyperfine splitting in He$^+$ by comparing the effective Zemach radius deduced from the experimental hyperfine splitting with the Zemach radius obtained from the electron scattering. We obtain a surprising result that the nuclear polarizability of the helion yields just 3\% of the total nuclear correction, which is smaller than for the proton.

Ground state energy of the hydrogen atom inside penetrable spherical cavities; variational approach

In this work we calculate the ground state energy of the hydrogen atom confined in a sphere of penetrable walls of radius Rc. Inside the sphere the system is subject to a Coulomb potential, whereas outside of it the potential is a finite constant V0. The energy is obtained as a function of Rc and V0 by means of the Rayleigh-Ritz variational method, in which, the trial function is proposed as a free particle wave function within a finite square well potential but including an exponential factor that takes into account the electron-nucleus Coulomb attraction. For an impenetrable sphere, , the energy grows fast as Rc approaches zero. On the other hand, when the height of the barrier V0 is finite, the energy increases slowly as Rc goes to zero. We also compute the Fermi contact term, nuclear magnetic screening, polarizability, pressure and tunneling as a function of Rc and V0. As expected, these physical quantities approach the corresponding values of the free hydrogen atom as Rc grows. We also discuss the pressure-induced ionization of the hydrogen atom. The present results are found in good agreement with those previously published in the literature.

Constraints on Nuclear Symmetry Energy Parameters

A review is made of constraints on the nuclear symmetry energy parameters arising from nuclear binding energy measurements, theoretical chiral effective field predictions of neutron matter properties, the unitary gas conjecture, and measurements of neutron skin thicknesses and dipole polarizabilities. While most studies have been confined to the parameters SV and L, the important roles played by, and constraints on Ksym, or, equivalently, the neutron matter incompressibility KN, are discussed. Strong correlations among SV,L, and KN are found from both nuclear binding energies and neutron matter theory. However, these correlations somewhat differ in the two cases, and those from neutron matter theory have smaller uncertainties. To 68% confidence, it is found from neutron matter theory that SV=32.0±1.1 MeV, L=51.9±7.9 MeV and KN=152.2±38.1 MeV. Theoretical predictions for neutron skin thickness and dipole polarizability measurements of the neutron-rich nuclei 48Ca, 120Sn, and 208Pb are compared to recent experimental measurements, most notably the CREX and PREX neutron skin experiments from Jefferson Laboratory. By themselves, PREX I+II measurements of 208Pb and CREX measurement of 48Ca suggest L=121±47 MeV and L=−5±40 MeV, respectively, to 68% confidence. However, we show that nuclear interactions optimally satisfying both measurements imply L=53±13 MeV, nearly the range suggested by either nuclear mass measurements or neutron matter theory, and is also consistent with nuclear dipole polarizability measurements. This small parameter range implies R1.4=11.6±1.0 km and Λ1.4=228−90+148, which are consistent with NICER X-ray and LIGO/Virgo gravitational wave observations of neutron stars.

Bayesian analysis of nuclear polarizability corrections to the Lamb shift of muonic H-atoms and He-ions

The extraction of nuclear charge radii from spectroscopy experiments in muonic atoms is currently limited by the large uncertainties associated with the theoretical evaluation of the nuclear polarizability effects. To facilitate calculations, these polarizability corrections are conventionally expressed as an expansion in a dimensionless parameter η, which has been argued in previous literature to hold an approximate value of 0.33 in light-nuclear systems. In this work, we check this claim by doing a Bayesian analysis of the nuclear-polarizability corrections to the Lamb shift in μ 2H and μ 3H atoms and in μ 3He+ and μ 4He+ ions at various orders in the η-expansion. Our analysis supports the claim that η ≪ 1 in these systems and finds truncation uncertainties that are similar to the previous estimate, the only exception being the truncation uncertainties in the μ 3He+ ion, which are found to be larger.

Precision nuclear-spin effects in atoms: EFT methods for reducing theory errors

We use effective field theory to compute the influence of nuclear structure on precision calculations of atomic energy levels. As usual, the EFT’s effective couplings correspond to the various nuclear properties (such as the charge radius, nuclear polarizabilities, Friar and Zemach moments etc.) that dominate its low-energy electromagnetic influence on its surroundings. By extending to spinning nuclei the arguments developed for spinless ones in Burgess, et al. (2018), we use the EFT to show – to any fixed order in Zα (where Z is the atomic number and α the fine-structure constant) and the ratio of nuclear to atomic size – that nuclear properties actually contribute to electronic energies through fewer parameters than the number of these effective nuclear couplings naively suggests. Our result is derived using a position-space method for matching effective parameters to nuclear properties in the EFT, that more efficiently exploits the simplicity of the small-nucleus limit in atomic systems. By showing that precision calculations of atomic spectra depend on fewer nuclear uncertainties than naively expected, this observation allows the construction of many nucleus-independent combinations of atomic energy differences whose measurement can be used to test fundamental physics (such as the predictions of QED) because their theoretical uncertainties are not limited by the accuracy of nuclear calculations. We provide several simple examples of such nucleus-free predictions for Hydrogen-like atoms.

Nuclear predictions for H spectroscopy without nuclear errors

Nuclear-structure effects often provide an irreducible theory error that prevents using precision atomic measurements to test fundamental theory. We apply newly developed effective field theory tools to Hydrogen atoms, and use them to show that (to the accuracy of present measurements) all nuclear finite-size effects (e.g. the charge radius, Friar moments, nuclear polarizabilities, recoil corrections, Zemach moments etc.) only enter into atomic energies through exactly two parameters, independent of any nuclear-modeling uncertainties. Since precise measurements are available for more than two atomic levels in Hydrogen, this observation allows the use of precision atomic measurements to eliminate the theory error associated with nuclear matrix elements. We apply this reasoning to the seven atomic measurements whose experimental accuracy is smaller than 10 kHz to provide predictions for nuclear-size effects whose theoretical accuracy is not subject to nuclear-modeling uncertainties and so are much smaller than 1 kHz. Furthermore, the accuracy of these predictions can improve as atomic measurements improve, allowing precision fundamental tests to become possible well below the ‘irreducible’ error floor of nuclear theory.

Microscopic theory of pygmy- and giant resonances: accounting for complex 1p1h$$\otimes $$phonon configurations

The Green function formalism with a consistent account for phonon coupling (PC), based on the self-consistent theory of finite Fermi systems, is applied for pygmy- and giant multipole resonances in magic nuclei with the aim to consider particle–hole (ph) and complex 1p1h $$\otimes $$ phonon configurations. A new equation for the effective field, which describes nuclear polarizability, is obtained. It contains new PC contributions, which are of interest in the energy region under consideration. They are due to: (1) the tadpole effect in the standard ph-propagator, (2) two new induced interactions (caused by the exchange of the ph-phonon) in the second ph-channel and in the particle–particle channels, and (3) the first and second variations of the effective interaction in the phonon field. The general expressions for energies and probabilities of transitions between the ground and excited states are obtained. The qualitative analysis and discussion of the new terms are performed.

Polarizability effects in atomic nuclei

This work sheds light upon how the atomic nucleus polarizes throughout the nuclear chart. Deviations from the well-known behavior of the nuclear dipole polarizability — which smoothly increases with increasing atomic mass number — are investigated. Relative enhancements are found for light nuclei as the nuclear symmetry energy decreases and, within a nucleus, as its excitation energy increases. These two properties are related by a diminishing binding energy of the nuclear system. Contrarily, hindrances of nuclear polarizability are observed in the photo-neutron cross-section data and photon-strength functions of semi-magic nuclei with [Formula: see text], 50 and 82, which support the presence of shell effects at low-lying excitations and — assuming validity of the Brink-Axel hypothesis — at high-excitation energies up to the quasi-continuum region. These features assign the nuclear dipole polarizability as a sensitive measure of the long-range correlations of the nuclear force, and provide a new spectroscopic probe to investigate collective phenomena, shell closures, and the elusive nuclear symmetry energy. Particular cases of quadrupole collectivity are also discussed in terms of the available, and yet so scarce, information on nuclear polarizability (e.g. Sn and Ni isotopes).

Elastic electron scattering by halocarbon radicals in the independent atom model approach

In order to study the elastic scattering of electrons by CFn (n = 1 − 4) molecular targets the independent atom model (IAM) is used with the optical potential (OP) method. The scattering cross sections were calculated in two approximations of the model – the IAM approach is used for the differential, while the Additivity Rule (IAM-AR) is used for the integral cross sections. The amplitudes of electron scattering by the carbon and fluorine atoms of the target molecules are calculated from the corresponding phase shifts, using the real and complex optical potential method. The parameter-free real part of the OP is calculated from the corresponding atomic characteristics – nuclear charge, electron density and static dipole polarizability. The differential and integral cross sections are calculated at equilibrium internuclear distances of the CFn molecules. They were compared with the available experimental data and with other theoretical results. A good overall agreement was observed while comparing our integral cross sections with the measured data. The level of the agreement however strongly depends on the target molecule, and a good consistency is observed typically above certain collision energies: from 10 eV in case of CF2, above 15-20 eV for CF3 and from 40 eV in case of CF4. Similar tendencies were found in case of the differential cross sections for a wide range of scattering angles at collision energies above 10 eV in case of CF2, above 15–20 eV for CF3, while in case of CF4 – above 20 eV.Graphical abstract

Probing uncertainties of nuclear structure corrections in light muonic atoms

Recent calculations of nuclear structure corrections to the Lamb shift in light muonic atoms are based on an expansion in a parameter eta, where only terms up to second order are retained. The parameter eta can be shown to be proportional to the square root of the muon/proton mass ratio, so that it is small and the expansion is expected to converge. However, practical implementations show that the eta convergence may be slower than expected. In this work we probe the uncertainties due to this expansion using a different formalism, which is based on a multipole expansion of the longitudinal and transverse response functions and was first introduced by Leidemann and Rosenfelder. We refer to this alternative expansion as the eta-less formalism. We generalize this formalism to account for the cancellation of elastic terms such as the third Zemach moment (or Friar moment) and embed it in a computationally efficient framework. We implement and test this approach in the case of muonic deuterium. The comparison of results in the point nucleon limit for both methods achieve sub-percent agreement. When nucleon form factors are introduced we find a 4% and 2% difference in the third Zemach moment and nuclear polarizability, respectively, compared to the eta-less expansion, indicating that the nucleon form factor approximations should be improved. However, we find that the sum of these terms removes this dependence and the uncertainty due to the eta-expansion and the related second-order approximation in the nucleon form factors amounts only to 0.2% and thus is fully justified in muonic deuterium. This computationally efficient framework paves the way to further studies in light muonic systems with more than two nucleons, where controlling and reducing uncertainties in nuclear structure corrections is key to the experimental efforts of the CREMA collaboration.

Combined analysis of the low-energy enhancement of the gamma-strength function and the giant dipole resonance

The nuclear dipole polarizability is mainly governed by the dynamics of the giant dipole resonance and has been investigated along with the effects of the low-energy enhancement of the photon strength function for nuclides in medium- and heavy-mass nuclei. Cubic-spline interpolations to both data sets show a significant reduction of the nuclear dipole polarizability for semi-magic and doubly magic nuclei, with magic numbers N = 28, 50, 82 and 126, which supports shell effects at high-excitation energies from the quasi-continuum to the giant dipole resonance. This work expands on the data analysis of our recent publication in Ngwetsheni and Orce (Phys. Lett. B 792, 335, 2019), which reveals a new spectroscopic probe to search for “old” and “new” magic numbers at high-excitation energies. New results presented in this work suggest an even higher sensitivity of the nuclear polarizability to shell effects when extrapolating the low-energy enhancement at lower gamma-ray energies.

γW Box Inside Out: Nuclear Polarizabilities Distort the Beta Decay Spectrum.

I consider the γW-box correction to superallowed nuclear β decays in the framework of dispersion relations. I address a novel effect of a distortion of the emitted electron energy spectrum by nuclear polarizabilities and show that this effect, while neglected in the literature, is sizable. The respective correction to the β^{+} spectrum is estimated to be Δ_{R}(E)=(1.6±1.6)×10^{-4}E/MeV assuming a conservative 100% uncertainty. The effect is positive definite and can be observed if a high-precision measurement of the positron spectrum is viable. If only the full rate is observed, it should be included in the calculated Ft values of nuclear decays. I argue that this novel effect should be included in the analyses of nuclear beta decay experiments to ensure the correct extraction of V_{ud} from decay rates, and of the Fierz interference term from precision measurements of decay spectra.

Continuing influence of shell effects at high-excitation energies

Empirical drops in ground-state nuclear polarizabilities indicate deviations from the effect of giant dipole resonances and may reveal the presence of shell effects in semi-magic nuclei with neutron magic numbers N=50, 82 and 126. Similar drops of polarizability in the quasi-continuum of nuclei with, or close to, magic numbers N=28, 50 and 82, could reflect the continuing influence of shell closures up to the nucleon separation energy. These findings open a new avenue to investigating magic numbers at high-excitation energies and strongly support recent large-scale shell-model calculations in the quasi-continuum region, which describe the origin of the low-energy enhancement of the photon strength function as induced paramagnetism. The nuclear-structure dependence of the photon-strength function asserts the generalized Brink-Axel hypothesis as more universal than originally expected.

How do we infer shell effects at high-excitation energies? A new spectroscopic probe to search for magic numbers

The nuclear dipole polarizability is mainly governed by the dynamics of the giant dipole resonance and, assuming validity of the brink-Axel hypothesis, has been investigated along with the effects of the low-energy enhancement of the photon strength function for nuclides in medium- and heavy-mass nuclei. Cubic-polynomial fitsto both data sets extrapolated down to a gamma-ray energy of 0.1 MeV show a significantreduction of the nuclear dipole polarizability for semi-magic nuclei, with magic numbers N =28, 50 and 82, which supports shell effects at high-excitation energies in the the quasi-continuum region. This work assigns σ-2 values as sensitive measures of long-range correlations of the nuclear force and provides a new spectroscopic probe to search for “old” and “new” magic numbers at high-excitation energies.

Nucleon effective mass and its isovector splitting

Using an energy density functional (EDF) based on the thermodynamic Gibbs-Duhem relation, found equivalent to the standard Skyrme EDF for infinite nuclear matter, it is demonstrated that the parameters of this EDF are not uniquely determined from the fit of the empirical and theoretical data related to nuclear matter. This prevents an unambiguous determination of the nucleon effective mass ($\frac{m_0^*}{m}$) and its isovector splitting ($\Delta m_0^*$). Complementary information from dipole polarizability of atomic nuclei helps in removing this ambiguity and plausible values of $\frac{m_0^*}{m}$ and $\Delta m_0^*$ can be arrived at. Presently considered fit data on infinite nuclear matter and dipole polarizability of finite nuclei yield $\frac{m_0^*}{m} =0.68 \pm 0.04 $ and $\Delta m_0^* =(-0.20 \pm 0.09)\delta $. This EDF is consistent with the constraint on the maximum mass of the neutron star.

Phenomenological critical interaction distance from elastic scattering measurements on a 208Pb target

We have surveyed a series of elastic scattering measurements from the literature involving tightly bound (9Li, 10Be, 12C, 16O, 19F), weakly bound (6Li, 7Li, 8Li, 8He, 9Be, 17F), and exotic (6He and 11Li) nuclei on a 208Pb target at energies close to the Coulomb barrier. The corresponding data were then converted and analyzed in terms of the interaction distance, where critical-interaction and strong-absorption distances were extracted. Larger values were obtained for the exotic 6He and 11Li nuclei, as compared with both weakly bound and tightly bound projectiles. The influence of long-range nuclear interactions and Coulomb dipole polarizability are discussed. A correlation between the critical interaction distance and binding energy for a given configuration is observed.

The influence of relativistic effects on nuclear magnetic resonance spin-spin coupling constant polarizabilities of H2 O2 , H2 S2 , H2 Se2 , and H2 Te2.

Relativistic and nonrelativistic calculations have been performed on hydrogen peroxide, dihydrogen disulfide, dihydrogen diselenide, and dihydrogen ditelluride, H2 X2 (X = O, S, Se, Te), to investigate the consequences of relativistic effects on their structures as well as their nuclear magnetic resonance (NMR) spin-spin coupling constants and spin-spin coupling constant polarizabilites. The study has been performed using both one-component nonrelativistic and four-component relativistic calculations at the density functional theory (DFT) level with the B3LYP exchange-correlation functional. The calculation of nuclear spin-spin coupling constant polarizabilities has been performed by evaluating the components of the third order tensor, nuclear spin-spin coupling polarizability, using quadratic response theory. From this, the pseudoscalar associated with this tensor has also been calculated. The results show that relativistic corrections become very important for H2 Se2 and H2 Te2 and hint that a new chiral discrimination technique via NMR spectroscopy might be possible for molecules containing elements like Se or Te. © 2018 Wiley Periodicals, Inc.

Isotope shift, nonlinearity of King plots, and the search for new particles

We derive a mean-field relativistic formula for the isotope shift of an electronic energy level for arbitrary angular momentum; we then use it to predict the spectra of superheavy metastable neutron-rich isotopes belonging to the hypothetical island of stability. Our results may be applied to the search for superheavy atoms in astrophysical spectra using the known values of the transition frequencies for the neutron deficient isotopes produced in the laboratory. An example of a relevant astrophysical system may be the spectra of the Przybylski's star where superheavy elements up to Z=99 have been possibly identified. In addition, it has been recently suggested to use the measurements of King plot non-linearity in a search for hypothetical new light bosons. On the other hand, one can find the non-linear corrections to the King-plot arising already in the Standard Model framework. We investigate contributions to the non-linearity arising from relativistic effects in the isotope field-shift, the nuclear polarizability and many-body effects. It is found that the nuclear polarizability contribution can lead to the significant deviation of the King plot from linearity. Therefore, the measurements of the non-linearity of King plots may be applied to obtain the nuclear polarizability change between individual isotopes. We then proceed with providing a rough analytical estimate of the non-linearity arising solely from the effect of a hypothetical scalar boson. Our predictions give theoretical limitations on the sensitivity of the search for new interactions and should help to identify the most suitable atoms for corresponding experiments.