Longitudinal Momentum Distributions Research Articles

The Bethe-Salpeter approach to bound states: from Euclidean to Minkowski space

The challenge to obtain from the Euclidean Bethe–Salpeter amplitude the amplitude in Minkowski is solved by resorting to un-Wick rotating the Euclidean homogeneous integral equation. The results obtained with this new practical method for the amputated Bethe–Salpeter amplitude for a two-boson bound state reveals a rich analytic structure of this amplitude, which can be traced back to the Minkowski space Bethe–Salpeter equation using the Nakanishi integral representation. The method can be extended to small rotation angles bringing the Euclidean solution closer to the Minkowski one and could allow in principle the extraction of the longitudinal parton density functions and momentum distribution amplitude, for example.

Core longitudinal momentum distributions in the stripping reactions of two-neutron halo nuclei

The core longitudinal momentum distributions in two-neutron stripping reactions for halo nuclei of 20C and 22C are computed and compared to the experimental data obtained by detecting the core nucleus. The three-body wave function from the zero-range renormalized model is used as input in our calculations. We approximate the wave function of the projectile with a three-body structure, namely neutron-neutron-core, to an effective two-body one by integrating over neutron-neutron relative distance, such that the one has a core-dineutron wave function. The eikonal approximation is used in the description of the fragment-target interactions where the São Paulo optical potential is used for modeling the core-target and a Woods-Saxon potential is used for the dineutron-target interaction.

Multielectron polarization effects in strong-field ionization: Narrowing of momentum distributions and imprints in interference structures

We extend the semiclassical two-step model [Phys. Rev. A 94, 013415 (2016)] to include a multielectron polarization-induced dipole potential. Using this model we investigate the imprints of multielectron effects in the momentum distributions of photoelectrons ionized by a linearly polarized laser pulse. We predict narrowing of the longitudinal momentum distributions due to electron focusing by the induced dipole potential. We show that the polarization of the core also modifies interference structures in the photoelectron momentum distributions. Specifically, the number of fanlike interference structures in the low-energy part of the electron momentum distribution may be altered. We analyze the mechanisms underlying this interference effect. The account of the multielectron dipole potential seems to improve the agreement between theory and experiment.

Evidence of a Proton Halo in 23Al: A Mean Field Analysis

We have studied the nuclear structure properties like binding energy, charge radius, quadrupole deformation parameter for various isotopes of Al from the valley of stability to drip line region using the well known relativistic mean field formalism (RMF) with NL3 parameter set. We have compared our results with experimental data and found reasonable agreement. Further, we have taken spherical and deformed RMF densities to estimate the reaction dynamics of $^{23-28}$Al isotopes as projectiles and $^{12}$C as target by conjunction in Glauber model. The estimated results are also compared with the experimental data. The analysis of angular elastic differential and one proton removal cross sections are also studied with Glauber model many body system to investigate the structural feature of $^{23}$Al. The evidence of enhanced total reaction cross section, higher value of rms radius, narrow longitudinal momentum distribution and small proton separation energy of $^{23}$Al support its proton halo structure.

Phase- and intensity-resolved measurements of above threshold ionization by few-cycle pulses

We investigate the carrier-envelope phase (CEP) and intensity dependence of the longitudinal momentum distribution of photoelectrons resulting from above threshold ionization of argon by few-cycle laser pulses. The intensity of the pulses with a center wavelength of 750 nm is varied in a range between 0.7 × 1014 and . Our measurements reveal a prominent maximum in the CEP-dependent asymmetry at photoelectron energies of 2 UP (UP being the ponderomotive potential), that is persistent over the entire intensity range. Further local maxima are observed around 0.3 and 0.8 UP. The experimental results are in good agreement with theoretical results obtained by solving the three-dimensional time-dependent Schrödinger equation. We show that for few-cycle pulses, the amplitude of the CEP-dependent asymmetry provides a reliable measure for the peak intensity on target. Moreover, the measured asymmetry amplitude exhibits an intensity-dependent interference structure at low photoelectron energy, which could be used to benchmark model potentials for complex atoms.

Momentum peak shift and width of longitudinal momentum distribution of projectilelike fragments produced at E=290MeV/nucleon

Longitudinal momentum (${P}_{\mathrm{L}}$) distributions of projectilelike fragments produced at $E=290\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}/\mathrm{nucleon}$ are investigated. ${P}_{\mathrm{L}}$ distributions of fragments produced by Ar and Kr beams with a wide variety of targets (C, Al, Nb, Tb, and Au) were measured using the fragment separator at HIMAC. ${P}_{\mathrm{L}}$ distributions observed for fragments with a wide range of mass losses $\mathrm{\ensuremath{\Delta}}A$ (1--30 for Ar beam and 1--64 for Kr beam), show a slightly, but definitely asymmetric nature. The peak shift and width were obtained from the observed ${P}_{\mathrm{L}}$ distributions. No significant target dependence was found in either the peak shift or width. For the practical application, the variation in momentum peak shift with fragment mass (${A}_{\mathrm{F}}$) was represented by a parabolic function. The width on the high-${P}_{\mathrm{L}}$ side (${\ensuremath{\sigma}}_{\mathrm{High}}$) is well reproduced by the Goldhaber formula, which is obtained from the contribution of the Fermi momentum. The behavior of the reduced width, ${\ensuremath{\sigma}}_{0}$, obtained from ${\ensuremath{\sigma}}_{\mathrm{High}}$ via the Goldhaber formulation, is consistent with the mass-dependent Fermi momentum of a nucleon. The width on the low-${P}_{\mathrm{L}}$ side (${\ensuremath{\sigma}}_{\mathrm{Low}}$) is markedly larger than ${\ensuremath{\sigma}}_{\mathrm{High}}$ and exhibits a clear ${A}_{\mathrm{F}}$ dependence.

Kramers–Henneberger Form of Strong Field Theory with the Correction of Dipole Approximation**Supported by the National Natural Science Foundation of China under Grant Nos 11274149 and 11304185, and the Program of Shenyang Key Laboratory of Optoelectronic Materials and Technology under Grant No F12-254-1-00.

We show that the breakdown of dipole approximation can be adopted to explain the asymmetry structure in the photoelectron momentum distributions along the beam propagation direction, which is defined as the photoelectron longitudinal momentum distributions (PLMD), in tunneling regime (γK ≪ 1), based on the strong field approximation theory. The nondipole Hamiltonian for photoelectrons interacting with laser fields from a hydrogen-like atom is transformed into the Kramers–Henneberger frame in our model. To introduce the correction of dipole approximation, the spatial variable is kept in a vector potential A(r, t), demonstrating that the breakdown of dipole approximation is the major reason for the shift of the peak in PLMD. The nondipole effects are apparent when circularly polarized lasers are adopted to ionize the atoms, and clear tendency to increase offsets is found for increasing laser intensities.

Impact of Coulomb potential on peak structures arising in momentum and low-energy photoelectron spectra produced in strong-field ionization of laser-irradiated atoms

The phenomenon of pronounced peak structure(s) of longitudinal momentum distributions as well as a spike-like structure of low-energy spectra of photoelectrons emitted from laser-irradiated Ar and Ne atoms in a single ionization process is theoretically studied in the tunneling and multiphoton regimes of ionization. The problem is addressed assuming only the direct above-threshold ionization (ATI) as a physical mechanism underlying the phenomenon under consideration (viz. solely contributing to observed photoelectron momentum distributions (PMD)) and using the Coulomb–Volkov (CV) ansatz within the frame of conventional strong-field approximation (SFA) applied in the length-gauge formulation. The developed CV-SFA approach also incorporates the density functional theory essentially exploited for numerical composition of initial (laser-free) atomic state(s) constructed from atomic orbitals of Gaussian type. Our presented CV-SFA based (and laser focal-volume averaged) calculation results proved to be well reproducing both the pronounced double-peak and/or ATI-like multi-peak structure(s) experimentally observed in longitudinal PMD under conditions of tunneling and/or multiphoton regime, respectively. In addition, our CV-SFA results presented for tunneling regime also suggest and remarkably reproduce a pronounced structure observed in relevant experiments as a ‘spike-like’ enhanced maximum arising in low-energy region (around the value of about 1 eV) of photoelectron spectra. The latter consistency allows to identify and interpret these results as the so-called low-energy structure (LES) since the phenomenon proved to appear as the most prominent if the influence of Coulomb potential on photoelectron continuum states is maximally taken into account under calculations (viz. if the parameter Z in CV’s functions is put equal to 1). Moreover, the calculated LES proved to correspond (viz., established as closely related) to the mentioned double-peak structure arising in the low-momentum region ( a.u.) of longitudinal PMDs calculated under condition of the tunneling regime. Thus, the phenomena under consideration can be well understood and adequately interpreted beyond the terms and/or concepts of various different alternative strong-field approaches and models (such as e.g., extensively invoked and exploited nowadays though, more sophisticated SFA-based ‘rescattering’ mechanism) compared to which, the currently applied CV-SFA model (through the same underlying physical mechanism of solely direct ATI suggested) is additionally able to provide and reveal an intimate and transparent interrelation between the phenomena of LES and double-peak structure arising in PMDs observed in the tunneling regime.

Benchmarking theoretical formalisms for ( p,pn ) reactions: The C15(p,pn)C14 case

[Background] Proton-induced knockout reactions of the form $(p,pN)$ have experienced a renewed interest in recent years due to the possibility of performing these measurements with rare isotopes, using inverse kinematics. Several theoretical models are being used for the interpretation of these new data, such as the distorted-wave impulse approximation (DWIA), the transition amplitude formulation of the Faddeev equations due to Alt, Grassberger and Sandhas (FAGS) and, more recently, a coupled-channels method here referred to as transfer-to-the-continuum (TC). [Purpose] Our goal is to compare the momentum distributions calculated with the DWIA and TC models for the same reactions, using whenever possible the same inputs (e.g. distorting potential). A comparison with already published results for the FAGS formalism is performed as well. [Method] We choose the $^{15}$C($p$,$pn$)$^{14}$C reaction at an incident energy of 420 MeV/u, which has been previously studied with the FAGS formalism. The knocked-out neutron is assumed to be in a $2s$ single-particle orbital. Longitudinal and transverse momentum distributions are calculated for different assumed separation energies. [Results] For all cases considered, we find a very good agreement between DWIA and TC results. The energy dependence of the distorting optical potentials is found to affect in a modest way the shape and magnitude of the momentum distributions. Moreover, when relativistic kinematics corrections are omitted, our calculations reproduce remarkably well the FAGS result. [Conclusions] The results found in this work provide confidence on the consistency and accuracy of the DWIA and TC models for analyzing momentum distributions for $(p,pn)$ reactions at intermediate energies.

Re-examining the transition into the N = 20 island of inversion: Structure of 30Mg

Intermediate energy single-neutron removal from 31Mg has been employed to investigate the transition into the N=20 island of inversion. Levels up to 5 MeV excitation energy in 30Mg were populated and spin-parity assignments were inferred from the corresponding longitudinal momentum distributions and γ-ray decay scheme. Comparison with eikonal-model calculations also permitted spectroscopic factors to be deduced. Surprisingly, the 02+ level in 30Mg was found to have a strength much weaker than expected in the conventional picture of a predominantly 2p−2h intruder configuration having a large overlap with the deformed 31Mg ground state. In addition, negative parity levels were identified for the first time in 30Mg, one of which is located at low excitation energy. The results are discussed in the light of shell-model calculations employing two newly developed approaches with markedly different descriptions of the structure of 30Mg. It is concluded that the cross-shell effects in the region of the island of inversion at Z=12 are considerably more complex than previously thought and that np−nh configurations play a major role in the structure of 30Mg.

How sharp is the transition into the N=20 island of inversion for the Mg isotopes ?

The N=20 island of inversion is an excellent playground for testing shell model calculations. The Mg chain is a region of shell evolution still far from being well understood. In this paper we present preliminary results of a single-neutron knockout experiment from 31Mg performed at GANIL to study the structure of 31Mg and of the core 30Mg. The level scheme and longitudinal momentum distributions were mesured and spectroscopic factors were deduced. Negative parity states arise at low energy and the spectroscopic factor for the isomeric in 30Mg was determined to be smaller than foreseen in the standard picture. The preliminary experimental results are compared to state-of the art shell model calculations revealing opposed interpretations.

Collinear and TMD quark and gluon densities from parton branching solution of QCD evolution equations

We study parton-branching solutions of QCD evolution equations and present a method to construct both collinear and transverse momentum dependent (TMD) parton densities from this approach. We work with next-to-leading-order (NLO) accuracy in the strong coupling. Using the unitarity picture in terms of resolvable and non-resolvable branchings, we analyze the role of the soft-gluon resolution scale in the evolution equations. For longitudinal momentum distributions, we find agreement of our numerical calculations with existing evolution programs at the level of better than 1% over a range of five orders of magnitude both in evolution scale and in longitudinal momentum fraction. We make predictions for the evolution of transverse momentum distributions. We perform fits to the high-precision deep inelastic scattering (DIS) structure function measurements, and we present a set of NLO TMD distributions based on the parton branching approach.

Neutron removal from the deformed halo nucleus Ne31

Experimental data on Coulomb breakup and neutron removal indicate that 31Ne is one of the heaviest halo nuclei discovered so far. The possible ground state of 31Ne is either 3/2- coming from p-wave halo or 1/2+ from s-wave halo. In this work, we develop a treatable model to include deformed wave functions and a dynamical knockout formalism which includes the dependence on the nuclear orientation to study the neutron removal from 31Ne projectiles at energies around E=200 MeV/nucleon. A detailed account of the effects of deformation on cross sections and longitudinal momentum distributions is made. Our numerical analysis indicates a preference for the 31Ne ground state with spin parity 3/2-.

Photoelectron longitudinal momentum distributions containing nondipole effects**Project supported by the National Natural Science Foundation of China (Grant No. 11274149) and the Program of Shenyang Key Laboratory of Optoelectronic Materials and Technology, China (Grant No. F12-254-1-00).

This paper proposes a modified strong field approximation model for evaluating nondipole effects on the ionization of an atom in an intense laser field. The photoelectron longitudinal momentum distributions (PLMD) of a hydrogen-like atom exposed to a mid-infrared laser field is calculated. The theoretical results indicate an obvious asymmetry in the PLMD, and an offset of the PLMD peak appears in the opposite direction of the beam propagation due to nondipole effects. The peak offsets of the PLMD increased with the laser intensity, imposed by the initial state of the hydrogen-like atom.

Identification of doubly excited states in nonsequential double ionization of Ar in strong laser fields

We use the semiclassical model to study the intensity dependence of nonsequential double ionization (NSDI) of Ar in short strong laser pulses. The contributions to NSDI through sequential ionization of doubly excited states (SIDE) are identified by tracking the energy trajectories of the two outgoing electrons. The correlated electron momentum distributions are calculated from which the longitudinal momentum distributions of the fast and the slow electrons for the side-by-side and the back-to-back emissions are obtained. The simulated momentum distributions of the fast and the slow electrons for NSDI of Ar by linearly polarized fields with a wavelength of 795 nm at an intensity of 7 × 1013 W cm−2 are in good agreement with the experimental measurements of Liu et al (2014 Phys. Rev. Lett. 112 013003). We demonstrate that the process of double ionization through SIDE dominates NSDI only when the laser intensities are below the recollision threshold; nevertheless, for higher intensities the SIDE process still takes place although the contribution to the NSDI yields decreases rapidly as the intensity increases. It has been found that for SIDE at different intensities, both the correlated electron momentum spectra and the momentum distributions of the fast and the slow electrons remain the same.

Experimental verification of the nonadiabatic effect in strong-field ionization with elliptical polarization

We perform high-resolution measurement of ellipticity-resolved momentum distributions from tunneling ionization of atoms along the major and minor axes in strong elliptically polarized fields, respectively. With developing a subcycle nonadiabatic strong-field tunneling theory for arbitrary laser polarization, we show that the electron initial conditions for positions and momenta after the tunneling are nonadiabatically intertwined with the instantaneous laser field. We extract the transverse and longitudinal momentum distributions at the tunnel exit with respect to the field ellipticity. We calibrate the laser intensity with ab initio calculation by solving the time-dependent Schr\"odinger equation. The nonadiabatic effects are confirmed experimentally and theoretically. Disentangling the effect of the long-range Coulomb potential from the laser field, we have further demonstrated that the momentum-time structure of the tunneling wave packet in strong laser fields can be approximatively imaged when treating the Coulomb effect perturbatively.

Numerical Detector Theory for the Longitudinal Momentum Distribution of the Electron in Strong Field Ionization.

The lack of analytical solutions for the exit momentum in the laser-driven tunneling theory is a well-recognized problem in strong field physics. Theoretical studies of electron momentum distributions in the neighborhood of the tunneling exit depend heavily on adhoc assumptions. In this Letter, we apply a new numerical method to study the exiting electron's longitudinal momentum distribution under intense short-pulse laser excitation. We present the first realizations of the dynamic behavior of an electron near the so-called tunneling exit region without adopting a tunneling approximation.

Analysis of longitudinal momentum distribution data of 26–29P isotopes in stripping reactions

The orbital occupancy of the stripped proton in the phosphors isotopes with mass number 26–29 have been determined through the analysis of longitudinal momentum distributions (LMDs) of [Formula: see text] core fragments coming from [Formula: see text] and [Formula: see text] stripping reactions at high energies. It has been found that the probability of occupying [Formula: see text]-orbital by the stripped proton is 40–60%, 30–50%, 30–50% and 0–20% in [Formula: see text] isotopes, respectively. The effects of Coulomb barrier for the possibility of halo structure in proton-rich nuclei has also been examined and found that it decreases the chance of possessing halo structure in proton-rich nuclei.

Tunneling wave packets of atoms from intense elliptically polarized fields in natural geometry

We study strong-field tunneling of atoms in intense elliptically polarized laser fields in natural tunneling geometry. We obtain the temporal- and spatial-dependent tunneling ionization rates, the transverse and longitudinal momentum distributions, and the position distributions of the tunnel exit in parabolic coordinates. The tunneling electron wave packets at the tunnel exit are three dimensionally characterized for both momentum and spatial distributions. The conjunction between the tunneling point and the classical propagation of the widely used semiclassical model are naturally connected. We further calculate the ellipticity-dependent photoelectron momentum distributions on the detector, which are validated by comparison with the exact results through numerically solving the time-dependent Schr\odinger equation. The theory clarifies crucial questions about strong-field tunneling ionization, which has important implications for the attoclock with elliptical or circular fields, photoelectron holography, molecular orbital imaging, etc.

Production of the doubly charmed baryons at the SELEX experiment – The double intrinsic charm approach

The high production rate and $\langle x_{F} \rangle > 0.33$ of the doubly charmed baryons measured by the SELEX experiment is not amenable to perturbative QCD analysis. In this paper we calculate the production of the doubly heavy baryons with the double intrinsic charm Fock states whose existence is rigorously predicted by QCD. The production rate and the longitudinal momentum distribution are both reproduced. We also show that the production rates of the doubly charmed baryons and double $J/\psi $ production observed by NA3 collaboration are comparable. Recent experimental results are reviewed. The production cross section of the doubly charmed baryons at a fixed-target experiment at the LHC is presented.