Scattering Phase Shifts Research Articles

Hadron-hadron potentials coupled to quark degrees of freedom for X (3872)

To study the internal structure of the exotic hadron X(3872), considering the coupled-channel potential between quarks and hadrons is necessary because X(3872) is regarded as a mixture state of cc¯ and D0D¯*0. In this work, we construct the hadron-hadron potentials coupled to the quark channel and study the properties of the D0D¯*0 potentials for X(3872). In particular, we compare various local approximations by focusing on the scattering phase shifts.

Low Energy Analysis of Phase Shifts and Cross-Section for n – 3He System

"Considering the Hulth´en potential as the nuclear part of interaction regular solution is derived by exploiting the Frobenius method. The Jost function is constructed by utilizing its integral representation in terms of regular solution. The scattering phase shifts and cross-sections are calculated for the n−3He system from the on-shell Jost function. The results obtained are in close conformity with the previous works that exist in the literature."

Quantum theory of dark matter scattering

Dark matter self-scattering is one of key ingredients for small-scale structure of the Universe, while dark matter annihilation is important for the indirect measurements. There is a strong correlation between the velocity-dependent self-scattering cross section and the Sommerfeld enhancement factor for the dark matter annihilation cross section. In this study, we formulate a direct relation between them by the use of Watson’s (initial state/final state) theorem and Omnès solution, and our formulation reproduces the Sommerfeld enhancement factor, which directly computed by solving the Schrödinger equation, from the scattering phase shift.

Jost function analysis of elastic and inelastic nucleon–nucleon scattering with a new model potential

The analysis of nucleon–nucleon elastic and inelastic scattering data is presented by considering the combined interaction of nuclear and electromagnetic potentials of equal range. The exact analytical off-shell solutions of the nonrelativistic Schrödinger equation for the effective potential with the centrifugal term are investigated using ordinary differential equation approach. Numerical results of scattering phase shifts, differential cross-sections and Transition matrices are in sensible conformity with previous works.

Uncertainties in the transport properties of helium gas at cryogenic temperatures determined using molecular dynamics simulation

In this study, the transport properties, such as diffusivity, viscosity, and thermal conductivity, of 4He at the gaseous phase are computed for state points in the temperature range of 10 K to 150 K and pressure range of 0.10 MPa (1 atm) to 0.21 MPa using classical and quantum frameworks. Within the classical molecular dynamics simulation (MDS), the Green–Kubo (GK) approach is used. The GK method has an inherent uncertainty associated with it due to the random fluctuations in the flux autocorrelation functions. Moreover, in the temperature range of 10 K to 40 K, the quantum nature of the helium gas particles becomes prominent. The classical MDS performed does not include these effects and hence introduces uncertainties in the calculated results. We discuss efficient ways of time averaging the autocorrelation function to reduce statistical fluctuations and perform the quantum scattering phase shift calculations within the Chapman–Cowling theory to study the quantum effects. Furthermore, this study also provides the transport properties data in the cryogenic temperature limit of 10 K to 150 K, which is scarcely studied in the literature and can be applied in complex systems.

Toward extracting the scattering phase shift from integrated correlation functions

Toward extracting the scattering phase shift from integrated correlation functions

Transport cross sections and collision integrals for C+(2P)–H(2S), C(3P)–H+(1S), C(1D)–H+(1S), and C+(4P)–H(2S) interactions

Transport collision integrals of interacting atoms or ions play a crucial role in modeling transport properties of high-temperature gases and plasmas. Here, we obtained the potential energy curves (PECs) of CH+ using the internally contracted multireference configuration interaction method with the Davidson correction (icMRCI+Q) method. The PECs were then used to investigate the transport cross sections and transport collision integrals for the C+(2P)–H(2S), C(3P)–H+(1S), C(1D)–H+(1S), and C+(4P)–H(2S) interactions using the classical mechanical approach and a quantum mechanical treatment of the scattering with Wentzel–Kramers–Brillouin approximations of the scattering phase shifts. The transport cross sections were obtained in the collision energy of 10−6–1 hartree, which were used to compute transport collision integrals for C–H+ and C+–H systems over the temperature range of 500–40 000 K. The C(1D)–H+(1S) and C+(4P)–H(2S) interactions are considered for the first time. Our transport collision integrals can provide data references for computing transport properties of high-temperature plasmas involving C and H atoms/ions.

Many-body theory calculations of positron scattering and annihilation in noble-gas atoms via the solution of Bethe–Salpeter equations using the Gaussian-basis code EXCITON+

Scattering phase shifts and annihilation rates for low-energy positrons interacting with noble gas atoms are calculated ab initio using many-body theory implemented in the Gaussian-orbital code EXCITON+. Specifically, we construct the positron–atom correlation potential (self-energy) as the sum of three classes of infinite series describing the screened polarization, virtual positronium formation, and positron-hole repulsion found via the solution of Bethe–Salpeter equations for the two-particle propagators. The normalization of the continuum states is determined using the shifted pseudostates method [A. R. Swann and G. F. Gribakin, Phys. Rev. A 101, 022702 (2020)]. Comparison with the previous sophisticated B-spline many-body approach, which is restricted to atoms [J. Ludlow, D. G. Green, and G. F. Gribakin, Phys. Rev. A 90, 032712 (2014)], validates the EXCITON+ code, which can be used for multicentered targets including molecules, clusters, and condensed matter. Moreover, the relative effects of higher-order diagrams are quantified. It is found that the screening of the electron–positron Coulomb interaction represented by the infinite ring-diagram series (random-phase approximation) is compensated effectively by the additional electron-hole attraction corrections to it (the Bethe–Salpeter equation approximation) and that the use of the screened Coulomb interaction (screened at BSE level) in place of the bare Coulomb interaction in the virtual positronium and positron-hole ladder diagrams has negligible effect on both the phase shifts and Zeff. Our scattering length for Ne and Kr is in improved agreement with the convergent close-coupling result, and for Ar, the scattering length is in better agreement with the experiment compared with the previous B-spline many-body approach.

Low and intermediate energy cross section analysis of p-p and p-d elastic scattering using modified phase amplitude method for electromagnetic distorted nuclear interaction

The traditional phase function method is regarded as a resourceful tool for computing scattering phase shifts for quantum mechanical potential scattering involving local interactions. For the local plus a nonlocal potential the conventional phase function method does not hold good. In such a situation one has to modify it. The modified variable phase method is adapted here to treat the Manning-Rosen (MR) plus Graz nonlocal separable potential for constructing an exact expression for the phase function with rigorous inclusion of the electromagnetic effect. The merit of our analytical result is demonstrated by computing elastic scattering phase parameters and differential scattering cross sections for proton-proton (p − p) and proton-deuteron (p − d) systems which are in sensible agreement with previous works.

Observation of suppressed viscosity in the normal state of 3He due to superfluid fluctuations

Evidence of fluctuations in transport have long been predicted in 3He. They are expected to contribute only within 100μK of Tc and play a vital role in the theoretical modeling of ordering; they encode details about the Fermi liquid parameters, pairing symmetry, and scattering phase shifts. It is expected that they will be of crucial importance for transport probes of the topologically nontrivial features of superfluid 3He under strong confinement. Here we characterize the temperature and pressure dependence of the fluctuation signature, by monitoring the quality factor of a quartz tuning fork oscillator. We have observed a fluctuation-driven reduction in the viscosity of bulk 3He, finding data collapse consistent with the predicted theoretical behavior.

Rescattering effects in nucleon-to-meson form factors and application to tau-lepton-induced proton decay

Nucleon decays put extremely stringent bounds on baryon-number-violating interactions. However, in case the corresponding operators involve only τ leptons, the direct two-body decays, e.g., p→π0τ+, are kinematically not allowed and nucleon decay can only proceed via an off-shell τ, leading to p→π0ℓ+νℓν¯τ. To calculate such processes, the momentum dependence of the form factors for nucleon-to-meson transitions, which describe the hadronization of the underlying process at the quark level, is needed. In this work, we point out new isospin and Fierz relations among such proton–kaon matrix elements and calculate the momentum dependence of the nucleon-to-meson form factors from the universal final-state interactions in terms of pion–nucleon or kaon–nucleon scattering phase shifts. We use these results to derive novel limits on the Wilson coefficients of the baryon-number-violating dimension-6 operators involving a τ lepton, which were previously unconstrained.

Nucleon-Nucleon Elastic Scattering for Motion in The Shifted Deng-Fan Potential

The scattering theory's main objective is to comprehend an object by hurling something at it. One can learn details about an object by observing how it bounces off other objects. The potential that exists between the two particles is the thing that one seeks to comprehend. In time-independent approach to scattering, one assumes that the incident beam has been activated for a very long time and that the entire system is in a stationary state. For short-range local potentials, the variable phase methodology is highly useful in solving quantum mechanical scattering problems. Variable phase methodology/phase-function technique has been explicitly utilized for non-relativistic nucleon-nucleon scattering phenomenon with the fundamental central local potential term and without spin-orbit force. Working under this methodology, scattering phase shifts, total scattering cross section and Differential cross section have been investigated for a new nuclear potential model “Shifted Deng-Fan potential”. Real nucleon-nucleon scattering systems (n-p) and (p-p) have been treated for this purpose with partial waves up to l = 2 in the low and moderate energy region. For l > 0 waves, interacting repulsive barrier potential has been incorporated with the existing central part. Our results for the considered potential model show a close contest with that of the experimental data.

Analytical solution for nuclear plus atomic Hulthén potential — A perturbative approach

In this work, we construct the analytical solution of the Schrödinger equation for a combined nuclear plus atomic Hulthén potential with different range parameters, using the Frobenius method. The atomic Hulthén potential acts as the screened Coulomb potential to represent the very short-range electromagnetic interaction. It is intended to emphasize how the impact of the combined potential in these situations is routinely examined within the context of nuclear physics. The Jost function is calculated from its integral representation in terms of the regular solution. From the phase of the Jost function, the scattering phase shifts for different partial waves, and further differential scattering cross-section and total cross-sections are calculated for alpha-proton and proton–proton systems. On comparing with the existing experimental data, we conclude that the results obtained are in close conformity with the previous works that exist in the literature.

Inverse potentials for all ℓ channels of neutron-proton scattering using reference potential approach

Reference potential approach (RPA) has been successful in obtaining inverse potentials for weakly bound diatomic molecules using the Morse function. In this work, our goal is to construct inverse potentials for all the available ℓ-channels of np-scattering using RPA. Riccati-type phase equations for various ℓ-channels are solved using 5th order Runge-Kutta method to obtain the scattering phase shifts (SPS) in tandem with an optimisation procedure to minimize mean squared error (MSE). Interaction potentials for a total of 18 states have been constructed using only a three parameter Morse interaction model. The obtained MSE is <1% for 1 S 0, 3 P 1 and 3 D 1 channels and <2% for 1 P 1 channel and <0.1% for rest of the 14 channels. Total scattering cross-sections at various lab energies obtained using RPA are found to match well with experimental ones. A complete study of the np-scattering using RPA has been undertaken using Morse function as zeroth reference for the first time.

Finite-range effect in the two-dimensional density-induced BCS–BEC crossover

Abstract We theoretically investigate the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) crossover in a two-dimensional Fermi gas with the finite-range interaction by using the Hartree–Fock–Bogoliubov theory. Expanding the scattering phase shift in terms of the scattering length and effective range, we discuss the effect of the finite-range interaction on the pairing and thermodynamic properties. By solving the gap equation and the number equation self-consistently, we numerically calculate the effective-range dependence of the pairing gap, chemical potential, and pair size throughout the BCS–BEC crossover. Our results would be useful for further understanding of low-dimensional many-body problems.

Conductance oscillations of antiferromagnetic layer tunnel junctions

We study conductance oscillations of antiferromagnetic layer tunnel junctions composed of antiferromagnetic topological insulators such as ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$. In the presence of an in-plane magnetic field, we find that the two terminal differential conductances across the junction oscillates as a function of field strength. Notably, the quantum interference at weak fields for the even-layer case is distinctive from the odd-layer case due to the scattering phase shift $\ensuremath{\pi}$. Consequently, the differential conductance vanishes (maximized) at integer magnetic flux quanta for even-layer (odd-layer) junctions. The conductance oscillations manifest the layer-dependent quantum interference in which symmetries and scattering phases play essential roles. In numerical calculations, we observe that the quantum interference undergoes an evolution from superconducting quantum interference device-like to Fraunhofer-like oscillations as the junction length increases.

Cold collisions between alkali metals and alkaline-earth metals in the heteronuclear atom-ion system Li+Ba+

In a recent experiment [P. Weckesser et al., Nature (London) 600, 429 (2021)], the quantum $s$-wave regime was attained for an alkali-metal and alkaline-earth atom-ion combination $({\mathrm{LiBa}}^{+})$. We investigate possible outcomes from the interaction of this ion-atom pair at quantum regimes from a theoretical point of view. For this purpose, Born-Oppenheimer potential energy surfaces are constructed for the three lowest dissociation channels of the ${(\mathrm{Ba}\text{\ensuremath{-}}\mathrm{Li})}^{+}$ molecular system using a multireference configuration interaction electronic-structure calculation. We present elastic, spin-exchange (SE), and diffusion cross sections in different energy regimes. The collisional properties of this system are calculated in terms of the scattering phase shifts and scattering cross sections, and the semiclassical behavior at a relatively high energy limit is also examined. For SE collisions, phase locking is obtained towards lower partial waves.

5p1/2nℓj autoionizing states of strontium for 0≤ℓ≤5

We report a comprehensive experimental and theoretical study of the autoionization of core-excited $5{p}_{1/2}n{\ensuremath{\ell}}_{j}$ strontium Rydberg states for intermediate values of ${\ensuremath{\ell}}_{j}$ in the range $0\ensuremath{\lesssim}{\ensuremath{\ell}}_{j}\ensuremath{\lesssim}5$. For a given value of ${\ensuremath{\ell}}_{j}$ autoionization, which results from the energy exchange between the two excited valence electrons, is found to scale as $\ensuremath{\sim}1/{n}^{3}$, mirroring the decrease in the Rydberg electron probability density in the vicinity of the inner $5{p}_{1/2}$ electron cloud. In contrast, the ${\ensuremath{\ell}}_{j}$ dependence of the autoionization rate is more complex. For the larger values of ${\ensuremath{\ell}}_{j}$ $(\ensuremath{\ge}4)$, the autoionization rate decreases as ${\ensuremath{\ell}}_{j}^{\ensuremath{-}5}$ due to the centrifugal barrier, which prevents the Rydberg electron from penetrating the core and inner $5{p}_{1/2}$ electron cloud. For the low-${\ensuremath{\ell}}_{j}$ core-penetrating Rydberg states, the scattering phase shift induced by the effective core potential becomes important in determining both the autoionization rates, which no longer show a monotonic variation with ${\ensuremath{\ell}}_{j}$, and the quantum defects.

Many-body theory of positronium scattering and pickoff annihilation in noble-gas atoms

The many-body-theory approach to positronium-atom interactions developed in [Phys. Rev. Lett. \textbf{120}, 183402 (2018)] is applied to the sequence of noble-gas atoms He-Xe. The Dyson equation is solved separately for an electron and positron moving in the field of the atom, with the entire system enclosed in a hard-wall spherical cavity. The two-particle Dyson equation is solved to give the energies and wave functions of the Ps eigenstates in the cavity. From these, we determine the scattering phase shifts and cross sections, and values of the pickoff annihilation parameter $^1Z_\text{eff}$ including short-range electron-positron correlations via vertex enhancement factors. Comparisons are made with available experimental data for elastic and momentum-transfer cross sections and $^1Z_\text{eff}$. Values of $^1Z_\text{eff}$ for He and Ne, previously reported in [Phys. Rev. Lett. \textbf{120}, 183402 (2018)], are found to be in near-perfect agreement with experiment, and for Ar, Kr, and Xe within a factor of 1.2.

A new efficient approach for the calculation of cross-sections with application to Yukawa potential

Large-scale and systematic calculations of scattering amplitudes and cross-sections for charged particle collisions are of fundamental importance for understanding the physical properties of materials in different research fields. However, the elaborated theoretical methods for cross-sections are generally restricted to a finite range of impact energies. Here, we present an efficient approach for the calculation of the scattering amplitude and cross-sections ranging from low to high collision energies based on the variable phase method, where the Wentzel–Kramers–Brillouin and Born approximations for scattering phase shifts (SPSs) are incorporated into the numerical algorithm to alleviate the computational cost. For this purpose, quantitative criteria for the validity of these approximations are established based on the properties of the turning points of the potentials. For different scattering potentials, the corresponding planes can be established as a guideline to select the optimal combination for calculating the scattering amplitude and cross-section. The demand for quantum treatment of phase shifts is reduced by one to two orders of magnitude, which strongly benefits the computation of cross-sections for high-energy scattering. It has been found that the quantum treatment for SPSs is necessary near the quantum states involving quantum tunneling and resonance. To testify the validity of the approach, the SPSs and also transport cross-sections are calculated for Yukawa potentials, and good agreements are obtained in comparison with other available high-precision calculations. The proposed numerical approach can be straightforwardly generalized to other scattering potentials and permits one to efficiently calculate the scattering cross-sections for a large energy range.