D-wave Resonances Research Articles

Status of experimental knowledge on the unbound nucleus 13Be

The structure of the unbound nucleus 13Be is important for understanding the Borromean, two-neutron halo nucleus 14Be. The experimental studies conducted over the last four decades are reviewed in the context of the beryllium chain of isotopes and some significant theoretical studies. The focus of this paper is the comparison of new data from a 12Be(d,p) reaction in inverse kinematics, which was analyzed using Geant4 simulations and a Bayesian fitting procedure, with previous measurements. Two possible scenarios to explain the strength below 1 MeV above the neutron separation energy were proposed in that study: a single p-wave resonance or a mixture of an s-wave virtual state with a weaker p- or d-wave resonance. Comparisons of recent invariant mass and the (d,p) experiments show good agreement between the transfer measurement and the two most recent high-energy nucleon removal measurements.

Collective excitation of Bose–Einstein condensate of 23Na via high-partial wave Feshbach resonance

We experimentally observe the collective excitation (called surface-mode excitation) of Bose–Einstein condensate of 23Na by ramping the external magnetic field across the high-partial wave magnetic Feshbach resonance corresponding to vary the atomic interaction. We check the collective surface mode excitation of state for the three d-wave and three g-wave Feshbach resonances below 600 G and find that only two d-wave resonances present the strong excitation, another d-wave resonance only creates a weak excitation, and all g-wave resonances do not, which reflects the strength of these magnetic Feshbach resonances. For the collective excitation, the excitation of surface modes along the axial weak-confinement and radial strong-confinement of optical dipole trap shows different characteristics. We also study the lifetime of the collective oscillation by measuring the damping rate of the oscillation amplitude, which is caused by the mechanisms of dephasing effect and collisional relaxation. This excitation method gives us a new tool for investigating the properties of ultracold quantum gases without changing the trap frequencies.

Semiempirical Calculations on Low-Energy Electron Scattering by Zn and Cd Atoms

Since total cross section measurements for electron scattering by Zn and Cd performed in the 1970s, the existence of p-wave shape resonances below 1 eV are well established in the literature. It was suggested that a second d-wave shape resonance could exist in both systems at an energy slightly higher than the one recorded for the p-wave but still below the inelastic threshold. We report elastic scattering calculations for electron collisions with Zn and Cd atoms below 4 eV using a semiempirical approach, as well the scattering length for both targets. Our results show that, indeed, the d-wave shape resonance is found in Zn but absent in Cd. In fact, our cross sections and the few other ones available for this energy range are in discrepancy with the available experimental total cross sections for Cd.

Contributions of S-, P-, and D-wave resonances to the quasi-two-body decays B^{0}_{s} rightarrow psi (3686,3770)K pi in the perturbative QCD approach

Based on the perturbative quantum chromodynamics (pQCD) approach and the quasi-two-body approximation, we have studied the three-body decays B^{0}_{s}rightarrow psi (3686,3770)K pi , which include the contributions of the intermediate resonances overline{K }^{*}_{0}(1430)^{0}, overline{K }^{*}(892)^{0}, overline{K }^{*}(1410)^{0}, overline{K }^{*}(1680)^{0}, and overline{K }^{*}_{2}(1430)^{0}. The time-like form factors corresponding to the distribution amplitudes of the S-, P-, and D-wave of the kaon–pion pair were adopted in parameterized form, and describe the interactions between K and pi in the resonance region. First, the decays B^{0}_{s}rightarrow psi (2S,1D)K ^{-}pi ^{+} were calculated, followed by the calculation of the branching ratios of the decays B^{0}_{s}rightarrow psi (3686,3770)K ^{-}pi ^{+} using the 2S–1D mixing scheme. In addition, the pQCD predictions for the decays B^{0}_{s}rightarrow psi (2S,1D)K pi and B^{0}_{s}rightarrow psi (3686,3770)K pi were obtained using the narrow-width approximation relation given by the Clebsch–Gordan coefficients. Our work shows that the overline{K }^{*}(892)^{0} resonance is the main contributor to the total decay, and the branching ratio and the longitudinal polarization fraction of the psi (2S)overline{K }^{*}(892)^{0} decay mode agree well with the currently available data within errors. Furthermore, the theoretical predictions of the psi (2S) and psi (3686) decay modes are very close, indicating that they can be regarded as the same meson state. Finally, the pQCD predictions for branching ratios of decays B^{0}_{s}rightarrow psi (3686,3770)K pi are of the order of 10^{-5} and 10^{-6}, respectively, which can be verified using the ongoing LHCb and Belle II experiments.

Alpha-alpha scattering in the Multiverse

We investigate the phase shifts of low-energy α-α scattering under variations of the fundamental parameters of the Standard Model, namely the light quark mass, the electromagnetic fine-structure constant as well as the QCD θ-angle. As a first step, we recalculate α-α scattering in our Universe utilizing various improvements in the adiabatic projection method, which leads to an improved, parameter-free prediction of the S- and D-wave phase shifts for laboratory energies below 10 MeV. We find that positive shifts in the pion mass have a small effect on the S-wave phase shift, whereas lowering the pion mass adds some repulsion in the two-alpha system. The effect on the D-wave phase shift turns out to be more pronounced as signaled by the D-wave resonance parameters. Variations of the fine-structure constant have almost no effect on the low-energy α-α phase shifts. We further show that up-to-and-including next-to-leading order in the chiral expansion, variations of these phase shifts with respect to the QCD θ-angle can be expressed in terms of the θ-dependent pion mass.

Pseudogap in a crystalline insulator doped by disordered metals

Key to our understanding of how electrons behave in crystalline solids is the band structure that connects the energy of electron waves to their wavenumber. Even in phases of matter with only short-range order (liquid or amorphous solid), the coherent part of electron waves still has a band structure. Theoretical models for the band structure of liquid metals were formulated more than five decades ago1-15, but, so far, band-structure renormalization and the pseudogap induced by resonance scattering have remained unobserved. Here we report the observation of the unusual band structure at the interface of a crystalline insulator (black phosphorus) and disordered dopants (alkali metals). We find that a conventional parabolic band structure of free electrons bends back towards zero wavenumber with a pseudogap of 30-240millielectronvolts from the Fermi level. This is wavenumber renormalization caused by resonance scattering, leading to the formation of quasi-bound states in the scattering potential of alkali-metal ions. The depth of this potential tuned by different kinds of disordered alkali metal (sodium, potassium, rubidium and caesium) allows the classification of the pseudogap of p-wave and d-wave resonance. Our results may provide a clue to the puzzling spectrum of various crystalline insulators doped by disordered dopants16-20, such as the waterfall dispersion observed in copper oxides.

Effects of conical intersections on hyperfine quenching of hydroxyl OH in collision with an ultracold Sr atom

The effect of conical intersections (CIs) on electronic relaxation, transitions from excited states to ground states, is well studied, but their influence on hyperfine quenching in a reactant molecule is not known. Here, we report on ultracold collision dynamics of the hydroxyl free-radical OH with Sr atoms leading to quenching of OH hyperfine states. Our quantum-mechanical calculations of this process reveal that quenching is efficient due to anomalous molecular dynamics in the vicinity of the conical intersection at collinear geometry. We observe wide scattering resonance features in both elastic and inelastic rate coefficients at collision energies below k_{text {B}}times 10 , hbox {mK}. They are identified as either p- or d-wave shape resonances. We also describe the electronic potentials relevant for these non-reactive collisions, their diabatization procedure, as well as the non-adiabatic coupling between the diabatic potentials near the CIs.

Degenerate Bose gases near a d-wave shape resonance

Understanding quantum many-body systems with strong interactions and unconventional phases therein is one of the most challenging tasks in physics. In cold atom physics, this has been a focused research topic for nearly two decades, where strong interactions are naturally created and well manipulated by bringing the system close to a scattering resonance. However, most of the studies thus far have been limited to the s-wave resonance. Here, we report the experimental observation of a tunable and broad d-wave shape resonance in a quantum degenerate 41K gas, hallmarked by the fact that the molecular binding energies are split into three branches. The measured lifetime in the resonance regime is found to be much longer than the characteristic timescale for many-body relaxations. The analysis of the breathing mode, excited by ramping through the resonance, suggests that a low-temperature atom–molecule mixture is produced. Our system offers great promise for studying a d-wave molecular superfluid. A scattering resonance associated with quasi-bound diatomic levels trapped behind the centrifugal barrier has been observed in a quantum-degenerate potassium gas. Various measurements reveal the d-wave character of the collisions.

Three-body problem of bosons near a d -wave resonance

Motivated by recent experimental progresses, we investigate few-body properties of interacting spinless bosons nearby a d-wave resonance. Using the Skorniakov-Ter-Martirosion (STM) equations, we calculate the scattering length between an atom and a d-wave dimer, and we find that the atom-dimer scattering length is positive and is much smaller the result from the mean-field approximation. We also reveal unique properties of the three-body recombination rate for a degenerate Bose condensate nearby the d-wave resonance. We find that the total recombination rate is nearly a constant at the quasi-bound side, in contrast to the behavior of a thermal gas nearby high-partial wave resonance. We also find that the recombination rate monotonically increases across the unitary point toward the bound side, which is due to the largely enhanced coupling between the atom and the d-wave dimer with deeper binding energy. This monotonic behavior is also qualitatively different from that of a degenerate gas nearby an s-wave resonance counterpart.

Resonant d-wave interaction induced quantum droplet in dipolar atoms

Motivated by recent experimental advances on dipolar atoms, we study the Bose gas with anisotropic short-range interaction theoretically. Starting with an anisotropic square well potential, we demonstrate that near the zero-crossing of the s-wave scattering length, there always exists a d-wave resonance. We find that the inter-channel scattering can be characterized by a scattering length. To explore the many-body effect of the short-range anisotropic inter-particle potential, we construct a pseudo-potential which captures the low-energy physics of the raw potential properly. By means of the pseudo-potential, we find the resonant d-wave interaction can inhibit the collapse of the Bose gas induced by the s-wave and dipole–dipole interaction, leading to the formation of the quantum droplet.

Feshbach spectroscopy of an ultracold K41−Li6 mixture and K41 atoms

We have observed 69 $^{41}$K-$^6$Li interspecies Feshbach resonances including 13 elastic p-wave resonances and 6 broad d-wave resonances of $^{41}$K atoms in different spin-state combinations at fields up to 600~G. Multi-channel quantum defect theory calculation is performed to assign these resonances and the results show perfect agreement with experimental values after improving input parameters. The observed broad p- and d- wave resonances display a full resolved multiplet structure. They may serve as important simulators to nonzero partial wave dominated physics.

Feshbach loss spectroscopy in an ultracold Na23−K40 mixture

We perform Feshbach spectroscopy in an ultracold mixture of $^{23}$Na and $^{40}$K with different spin-state combinations. We have observed 24 new interspecies Feshbach resonances at magnetic field up to 350 G. A full coupled-channel calculation is performed to assign these resonances. Among them, 12 resonances are identified as d-wave Feshbach resonances. These d-wave Feshbach resonances are about 5 G systematically smaller than the predications based on previous model potential. Taking into account these new experimental results, we improve the Born-Oppenheimer potentials between Na and K, and achieve good agreement between the theory and experiment for all the observed Feshbach resonances.

Observation of Broad d-Wave Feshbach Resonances with a Triplet Structure.

High partial-wave (l≥2) Feshbach resonance (FR) in an ultracold mixture of ^{85}Rb-^{87}Rb atoms is investigated experimentally aided by a partial-wave insensitive analytic multichannel quantum-defect theory. Two "broad" resonances from coupling between d waves in both the open and closed channels are observed and characterized. One of them shows a fully resolved triplet structure with a splitting ratio well explained by the perturbation to the closed channel due to interatomic spin-spin interaction. These tunable "broad" d-wave resonances, especially the one in the lowest-energy open channel, could find important applications in simulating d-wave coupling dominated many-body systems. In addition, we find that there is generally a time and temperature requirement, associated with tunneling through the angular momentum barrier, to establish and observe resonant coupling in nonzero partial waves.

Positronium-dipole induced resonances in e+-H and e+-alkali systems

We derive general universal scaling relations governing resonances induced by the dipole moment of excited positronium interacting with atomic ions. A single non-universal parameter, which contains all the system-dependent information, is defined. Our results are compared to numerical calculations, using complex scaling, for S, P, and D-wave resonances below the positronium n = 2 threshold in the -(H, Li, Na, K) systems. The energy and width ratios of the successive resonances are found to agree well with the analytically derived scaling law.

Natural and Unnatural Parity Resonance States in the Positron-Hydrogen System with Screened Coulomb Interactions

In the present work, we report calculations of resonances in the positron-hydrogen system interacting with screened Coulomb potentials using the method of complex scaling together with employing correlated Hylleraas wave functions. Resonances with natural and unnatural parities are investigated. For the natural parity case, resonance parameters (energy and width) for D-wave resonance states with even parity lying below various positronium and hydrogen thresholds up to the H(N = 4) level are determined. For the unnatural parity case, results for P-even and D-odd resonance states with various screened Coulomb interaction strengths are located below different lower-lying Ps and H thresholds.

Population ofBe13in a nucleon exchange reaction

The neutron-unbound nucleus 13Be was populated with a nucleon-exchange reaction from a 71 MeV/u secondary 13B beam. The decay energy spectrum was reconstructed using invariant mass spectroscopy based on 12Be fragments in coincidence with neutrons. The data could be described with an s-wave resonance at E = 0.73(9) MeV with a width of Gamma = 1.98(34) MeV and a d-wave resonance at E = 2.56(13) MeV with a width of Gamma = 2.29(73) MeV. The observed spectral shape is consistent with previous one-proton removal reaction measurements from 14B.

A chiral quark model for meson electroproduction in the region of D-wave resonances

The meson scattering and electroproduction amplitudes in the D13, D33 and D15 partial waves are calculated in a coupled-channel formalism incorporating quasi-bound quark-model states, extending our previous studies of the P11, P33 and S11 partial waves. The vertices of the baryon-meson interaction including the s- and d-wave pions and $\rho$-mesons, the s-wave $\eta$-meson, and the $s$- and p-wave $\sigma$-mesons are determined in the Cloudy Bag Model, with some changes of the parameters to reproduce the widths of the resonances. The helicity amplitudes and the electroproduction amplitudes exhibit consistent behavior in all channels but tend to be too weak compared to the experiment. We discuss possible origins of this discrepancy which arises also in the constituent quark model calculations.

Elastic collision properties of ultracold calcium atoms

The s-wave scattering lengths are obtained for all stable isotope combinations of Ca atoms and those values are very sensitive to small changes of the reduced mass. These results rely on a recent measurement of the 40Ca–40Ca scattering length in a Bose condensate of 40Ca and making small corrections to a Born–Oppenheimer potential that reproduces all known spectroscopic data. We find that the 42Ca isotope has a scattering length of 417.5a0 and, thus, can be Bose condensed. The large interisotope scattering length between 43Ca and 42Ca indicates that sympathetic cooling of 43Ca by 42Ca atoms will be effective, and 43Ca–42Ca can also be used to study isotopic Bose–Fermi mixtures. We also predict a d-wave shape resonance for collisions of fermionic 43Ca atoms in different spin components.

Recent Results on New Resonances at Belle

The current generation of B-factories have given a major contributions in completing the spectrum of heavy quarkonia. New questions are raised above the thresholds, where many new states, the so called XYZʼs were found. Insight into their nature can come from the investigation of EM and hadronic transitions between them. This review will cover Belleʼs recent progress in this sector, which exploits the record samples of data taken on the peaks of the ϒ(2, 4, 5S) resonances: the discovery of two multiplets of charged bottomonia (Zbʼs) and of four S=1 states (parabottomonia), the studies on η transitions and on D-wave resonances in both charmonium and bottomonium. Prospects for future studies are given.

Resonance phenomena and threshold features in positron—helium scattering

Investigations of resonances and threshold behaviors in positron—helium scattering have been made using the momentum-space coupled-channels optical method. The positronium formation channels are considered via an equivalent-local complex potential. The s-wave resonances and the Wigner cusp feature at the positronium (n = 1) formation threshold are compared with the previous reports. The p- and the d-wave resonances and a Wigner cusp feature at the positronium (n = 2) formation threshold are reported for the first time.