Longitudinal Momentum Distributions Research Articles

Tight focusing of the vector optical field with polarization varying along complex curves of the Poincaré sphere.

Different from the scalar optical field with spatially uniform polarization, the vector optical field exhibits inhomogeneous distribution of polarization on the cross section. Manipulating the variation of polarization in a single optical beam is important to acquire a flexible and controllable focused optical field. Previous studies mainly focused on the vector optical field with its polarization varying along a circular trajectory of the Poincaré sphere. Here, we demonstrate the tight focusing behaviors of the vector optical field with the polarization varying along complex curves of the Poincaré sphere, which is generated by the joint modulation of azimuthal phase and amplitude distributions of orthogonally polarized components. The longitudinal polarization component with a multipolar pattern in rotational symmetry can be achieved with similar distribution of the total focused field. The transverse and longitudinal spin angular momentum distributions in the focal space are discussed. Approximately pure transverse spin angular momentum can be constructed and manipulated in the focal space, which provides the possibility to manipulate the 3D spin flux for the applications of nano and spin photonics.

A unified description of the halo nucleus 37Mg from microscopic structure to reaction observables

Based on the structure input directly from the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), we fully study reaction observables to search for halo evidence of 37Mg with the Glauber model. In this scheme, we evaluate the reaction cross sections of 20–37Mg bombarding a C target at 240 MeV/nucleon and find that most of the results agree well with the experimental data within 1σ uncertainty, especially good for the case of 37Mg. Our predicted doubling of the cross section change from 36Mg to 37Mg over that from 34Mg to 35Mg is consistent with a halo structure in 37Mg. Additionally, our calculated narrow longitudinal momentum distribution of 36Mg residues from 37Mg + 12C breakup agrees well with data and imply a nuclear size much larger than 35Mg. Furthermore, our study shows a dominant p-wave contribution to the longitudinal momentum distribution, supporting the conclusion that 37Mg is a p-wave halo nucleus. Our study provides the first unified description of the halo characteristics of 37Mg from nuclear structure to reaction dynamics.

Diverse mechanisms in proton knockout reactions from the Borromean nucleus ^{17}text {Ne}

Nucleon knockout experiments using beryllium or carbon targets reveal a strong dependence of the quenching factors, i.e., the ratio (hbox {R}_{textrm{s}}) of theoretical to the experimental spectroscopic factors (hbox {C}^2{textrm{S}}), on the proton-neutron asymmetry in the nucleus under study. However, this dependence is greatly reduced when a hydrogen target is used. To understand this phenomenon, exclusive ^{1}text {H}(^{17}text {Ne},2hbox {p}~^{16}text {F}) and inclusive ^{12}text {C}(^{17}text {Ne},2hbox {p}~^{16}text {F})hbox {X}, ^{12}text {C}(^{17}text {Ne},^{16}text {F})hbox {X} as well as ^{1}text {H}(^{17}text {Ne},^{16}text {F})hbox {X} (X-denotes undetected reaction products) reactions with ^{16}text {F} in the ground and excited states were analysed. The longitudinal momentum distribution of ^{16}{textrm{F}} and the correlations between the detached protons were studied. In the case of the carbon target, there is a significant deviation from the predictions of the eikonal model. The eikonal approximation was used to extract spectroscopic factor values hbox {C}^2{textrm{S}}. The experimental hbox {C}^2hbox {S} value obtained with C target is markedly lower than that for H target. This is interpreted as rescattering due to simultaneous nucleon knockout from both reaction partners, ^{17}text {Ne} and ^{12}text {C}.

Anisotropic momentum distribution of 11B and 11C produced from 12C beam at 100 MeV/nucleon

Longitudinal (P L) and transverse (P T) momentum distributions of 11B and 11C produced from a 12C beam with C, Al, Nb, Tb, and Au targets observed at E = 100 MeV/nucleon are investigated. The observed P T distribution systematically changes according to the target and this change in behavior can be consistently explained by the orbital deflection effect, which is determined by the competitive contributions of attractive nuclear and repulsive Coulomb potentials acting between the projectile and target. The comprehensive examination of the observed P L and P T distributions resolves the fragmentation reaction into two reaction channels. One is the pure abrasion channel, which is characterized by small momentum transfer and an isotropic Gaussian function. The second is the two-step reaction channel, which is characterized by large momentum transfer and an anisotropic Gaussian function. The anisotropy of the second channel is consistently explained by the momentum of a picked-up nucleon.

Proton quark distributions from a light-front Faddeev-Bethe-Salpeter approach

The projection onto the Light-Front of a Minkowski space Faddeev-Bethe-Salpeter equation model truncated at the valence level is applied to study the proton structure with constituent quarks. The dynamics of the model has built-in: (i) a bound diquark brought by a contact interaction, and (ii) the separation by ∼ΛQCD of the infrared and ultraviolet interaction regions. The model parameters are fine tuned to reproduce the proton Dirac electromagnetic form factor and mass. From that, the non-polarized longitudinal and transverse momentum distributions were computed. The results for the evolved non-polarized valence parton distributions suggest that: (i) the explicit consideration of the spin degree of freedom of both quark and diquark seems not relevant to it, and (ii) the comparison with the global fit from the NNPDF4.0 calls for higher Fock components of the wave function beyond the valence one.

Femtosecond-resolved imaging of a single-particle phase transition in energy-filtered ultrafast electron microscopy

Using an energy filter in transmission electron microscopy has enabled elemental mapping at the atomic scale and improved the precision of structural determination by gating inelastic and elastic imaging electrons, respectively. Here, we use an energy filter in ultrafast electron microscopy to enhance the temporal resolution toward the domain of atomic motion. Visualizing transient structures with femtosecond temporal precision was achieved by selecting imaging electrons in a narrow energy distribution from dense chirped photoelectron packets with broad longitudinal momentum distributions and thus typically exhibiting picosecond durations. In this study, the heterogeneous ultrafast phase transitions of vanadium dioxide (VO2) nanoparticles, a representative strongly correlated system, were filmed and attributed to the emergence of a transient, low-symmetry metallic phase caused by different local strains. Our approach enables electron microscopy to access the time scale of elementary nuclear motion to visualize the onset of the structural dynamics of matter at the nanoscale.

Exploiting dissipative reactions to perform in-beam γ -ray spectroscopy of the neutron-deficient isotopes Ca38,39

The neutron-deficient Ca isotopes continue to attract attention due to their importance for testing isospin symmetry and their relevance in capture reactions of interest for nova nucleosynthesis and the shape of light curves in Type I x-ray bursts. To date, spectroscopic information on $^{38,39}\mathrm{Ca}$ is largely limited to data on lower-spin excited states. Here, we report in-beam $\ensuremath{\gamma}$-ray spectroscopy of complementary higher-spin, complex-structure states in $^{39}\mathrm{Ca}$ populated in fast-beam-induced, momentum-dissipative processes leading to neutron pickup onto excited configurations of the projectile, $^{9}\mathrm{Be}(^{38}\mathrm{Ca}^{*},^{39}\mathrm{Ca}+\ensuremath{\gamma})X$. Such a dissipative reaction was recently characterized for the case of inelastic scattering of $^{38}\mathrm{Ca}$ off $^{9}\mathrm{Be}, ^{9}\mathrm{Be}(^{38}\mathrm{Ca}, ^{38}\mathrm{Ca}+\ensuremath{\gamma})X$. Additional data and discussion on the nuclear structure of $^{38}\mathrm{Ca}$ is also presented. An explanation for the more-complex-structure states, populated with small cross sections in one-nucleon knockout reactions, and observed in the tails of their longitudinal momentum distributions, is also offered.

Measurements of jet observables sensitive to b -quark fragmentation in tt¯ events at the LHC with the ATLAS detector

Several observables sensitive to the fragmentation of $b$-quarks into $b$-hadrons are measured using 36 fb${}^{-1}$ of $\sqrt s = 13$ TeV proton-proton collision data collected with the ATLAS detector at the LHC. Jets containing $b$-hadrons are obtained from a sample of dileptonic $t\bar{t}$ events, and the associated set of charged-particle tracks is separated into those from the primary $pp$ interaction vertex and those from the displaced $b$-decay secondary vertex. This division is used to construct observables that characterize the longitudinal and transverse momentum distributions of the $b$-hadron within the jet. The measurements have been corrected for detector effects and provide a test of heavy-quark-fragmentation modeling at the LHC in a system where the top-quark decay products are color-connected to the proton beam remnants. The unfolded distributions are compared with the predictions of several modern Monte Carlo parton-shower generators and generator tunes, and a wide range of agreement with the data is observed, with $p$-values varying from $5 \times 10^{-4}$ to 0.98. These measurements complement similar measurements from $e^+e^-$ collider experiments in which the $b$-quarks originate from a color-singlet $Z/\gamma^*$.

Pion inspired by QCD: Nakanishi and light-front integral representations

The pion structure in Minkowski space is explored using the Nakanishi integral representation. A general framework is developed for the pion Bethe-Salpeter amplitude based on the K\"allen-Lehmann representation of the dressed quarks with an ansatz for the pseudoscalar $\ensuremath{\pi}\ensuremath{-}q\overline{q}$ vertex fulfilling the axial Ward-Takahashi identity. The Nakanishi weight functions are derived for the scalar amplitudes associated with the decomposition of the pion Bethe-Salpeter amplitude in different operator bases in the Dirac spinor space in terms of the involved spectral densities. The approach is applied to an analytical model of the pion Bethe-Salpeter amplitude, which is combined with Landau gauge lattice QCD results for the quark running mass at spacelike momentum. From the Nakanishi integral representation several pion observables were calculated, such as the decay constant, the spin decomposition of the valence probabilities, longitudinal and transverse momentum distributions from the valence component of the light-front wave function.

Study of the deformed halo nucleus 31Ne with Glauber model based on microscopic self-consistent structures

The exotic deformed nucleus 31Ne is studied with an approach that combines self-consistent structure and reaction theories. The deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) is utilized to demonstrate that deformation and pairing correlations give rise to a halo structure with a large-amplitude p-wave configuration in 31Ne. Then the valence nucleon wave functions and angle-averaged density distributions of 30Ne from this theory are used as input for the Glauber reaction model to study the observables of neutron-rich neon isotopes to search halo signatures. With NL1 effective interaction, our predictions of the reaction cross sections for these exotic neon isotopes on a carbon target can better reproduce the experimental data than those from the relativistic mean field model for a spherical shape with resonances and pairing correlation contributions, and are roughly 3.3% (∼ 50 mb) larger than those with Gaussian function-fitted densities of the core nuclei. The calculated one-neutron removal cross section at 240 MeV/nucleon, and the inclusive longitudinal momentum distribution of the 30Ne residues from the 31Ne breakup reaction are largely improved over previous theoretical predictions and agree well with data. These reaction evaluations indicate a dilute density distribution in coordinate space and are a canonical signature of a halo structure. Moreover, our predictions with the NL3 and PK1 effective interactions give slightly better descriptions of reaction observables for exotic neon isotopes.

Self-consistent description of the halo nature of 31Ne with continuum and pairing correlations

Background: A relativistic structure model has previously been used to predict a halo structure for 31Ne (Zhang et al 2014 Phys. Lett. B 730 30), consistent with halo signatures from measured reaction cross sections of Ne isotopes bombarding Carbon targets. However, previous attempts to calculate those cross sections with reaction models were missing contributions from resonances and pairing correlations in their structure input. Purpose: Use a reaction model with our relativistic fully microscopic structure model input to predict these cross sections and momentum distributions and analyze for possible halo signatures. Methods: Structure input for exotic Ne isotopes were obtained via the analytical continuation of the coupling constant (ACCC) method based on the relativistic mean field (RMF) theory with Bardeen–Cooper–Schrieffer (BCS) pairing approximation, the RAB approach. Total reaction cross sections, one-neutron removal cross sections, and momentum distributions of breakup reaction products were calculated with a Glauber model using our relativistic structure input. Results: Our predictions of total reaction and one-neutron removal cross sections of 31Ne on a Carbon target were significantly enhanced compared with those of neighboring Neon isotopes, agreeing with measurements at 240 MeV/nucleon and consistent with a single neutron halo. Furthermore, our calculations of the inclusive longitudinal momentum distribution of the 30Ne and valence neutron residues from the 31Ne breakup reaction indicate a dilute density distribution in coordinate space, another halo signature. Conclusions: We give a full description of the halo nature of 31Ne that includes a self-consistent use of pairing and continuum contributions that makes predictions consistent with reaction cross section measurements. This approach can be utilized to determine the halo structure of other exotic nuclei.

Proton image and momentum distributions from light-front dynamics

We apply a dynamical three-constituent quark light-front model to study the proton. The dynamics is based on the notion of a diquark (bound or virtual) as the dominant interaction channel, which paramaterizes a contact interaction between the quarks in order to build the three-body Faddeev Bethe-Salpeter equations for the valence state, and we focus on the totally symmetric part of the wave function. The Dirac electromagnetic form factor is used to fix the model parameters, and the valence wave function is obtained. From that we investigate its Ioffe-time image, non-polarized longitudinal and transverse momentum distributions, and the double momentum distribution.

Ionic-state-resolved electron–electron correlation in strong-field double ionization

In this paper, we theoretically investigate the nonsequential double ionization (NSDI) process of Ne induced by 400 nm linearly polarized laser field with a intensity above the recollision threshold using the S-matrix theory. It is unexpected to find that, significantly different from the results for wavelength longer than 800 nm, both the electron momentum correlated distribution and the longitudinal momentum distribution of Ne2+ exhibit a strong dependence on the wave function of the intermediate ionic state from which the second electron is ionized. This observation provides a potential way to extract the information about the ionic-state wave function based on NSDI process.

Comparative study of classical theoretical descriptions of the ionization of atoms induced by few-cycle laser pulses

We have investigated the performance of classical models in the description of the single and double ionization of argon induced by 4-fs, 750-nm linearly polarized laser pulses by comparing the calculated quantities with existing experimental data, primarily the results of the systematic measurements of K\"ubel at al. [Phys. Rev. A 93, 053422 (2016)], in the intensity range (1--10)$\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}{10}^{14}\phantom{\rule{0.28em}{0ex}}{\mathrm{Wcm}}^{\ensuremath{-}2}$. The comparison involved different one- and two-electron models based on the classical ensemble approximation. The analysis covered single- and double-ionization probabilities and their ratios, longitudinal momentum distributions of the ${\mathrm{Ar}}^{+}$ and ${\mathrm{Ar}}^{2+}$ recoiled ions, and the carrier-envelope-phase-dependent asymmetry of the yield of the ${\mathrm{Ar}}^{+}$ and ${\mathrm{Ar}}^{2+}$ ions.

Relaxation of bosons in one dimension and the onset of dimensional crossover

We study ultra-cold bosons out of equilibrium in a one-dimensional (1D) setting and probe the breaking of integrability and the resulting relaxation at the onset of the crossover from one to three dimensions. In a quantum Newton's cradle type experiment, we excite the atoms to oscillate and collide in an array of 1D tubes and observe the evolution for up to 4.8 seconds (400 oscillations) with minimal heating and loss. By investigating the dynamics of the longitudinal momentum distribution function and the transverse excitation, we observe and quantify a two-stage relaxation process. In the initial stage single-body dephasing reduces the 1D densities, thus rapidly drives the 1D gas out of the quantum degenerate regime. The momentum distribution function asymptotically approaches the distribution of quasimomenta (rapidities), which are conserved in an integrable system. In the subsequent long time evolution, the 1D gas slowly relaxes towards thermal equilibrium through the collisions with transversely excited atoms. Moreover, we tune the dynamics in the dimensional crossover by initializing the evolution with different imprinted longitudinal momenta (energies). The dynamical evolution towards the relaxed state is quantitatively described by a semiclassical molecular dynamics simulation.

Evidence of potential change in nonsequential double ionization* *Project supported by the National Natural Science Foundation of China (Grant No. 11274219), the Science and Technology Planning Project of Guangdong Province of China (Grant No. 180917124960522), and the Program for Promotion of Science at Universities in Guangdong Province of China (Grant No. 2018KTSCX062).

Recently, the quantitative rescattering model (QRS) for nonsequential double ionization (NSDI) is modified by taking into account the potential change (PC) due to the presence of electric field at the time of recollision. Using the improved QRS model, we simulate the longitudinal momentum distributions of doubly charged ions He2+ by projecting the correlated two-electron momentum distributions for NSDI of He onto the main diagonal. The obtained results are compared directly with the experimental data at different intensities. It is found that when the PC is considered, the width of momentum distributions reduces and the agreement between theory and experiment is improved.

Hadron-in-jet production at partonic threshold

We consider the longitudinal momentum distribution of hadrons inside jets in proton-proton collisions. At partonic threshold large double logarithmic corrections arise which need to be resummed to all orders. We develop a factorization formalism within SCET that allows for the joint resummation of threshold and jet radius logarithms. We achieve next-to-leading logarithmic NLL′ accuracy by including non-global logarithms in the leading-color approximation. Overall, we find that the threshold resummation leads to a sizable enhancement of the cross section and a reduced QCD scale dependence, suggesting that the all-order resummation can be important for the reliable extraction of fragmentation functions in global analyses when jet substructure data is included.

Jet fragmentation functions for Z-tagged jets

Recently the LHCb collaboration has measured both longitudinal and transverse momentum distribution of hadrons produced inside Z-tagged jets in proton-proton collisions at the Large Hadron Collider. These distributions are commonly referred to as jet fragmentation functions and are characterized by the longitudinal momentum fraction zh of the jet carried by the hadron and the transverse momentum j⊥ with respect to the jet direction. We derive a QCD formalism within Soft-Collinear Effective Theory to describe these distributions and find that the zh-dependence provides information on standard collinear fragmentation functions, while j⊥-dependence probes transverse momentum dependent (TMD) fragmentation functions. We perform theoretical calculations and compare our results with the LHCb data. We find good agreement for the intermediate zh region. For j⊥-dependence, we suggest binning in both zh and j⊥, which would lead to a more direct probing of TMD fragmentation functions.

Microscopic analysis of quasielastic scattering and breakup reactions of the neutron-rich nuclei Be12,14

A microscopic analysis of the optical potentials (OPs) and cross sections of quasielastic scattering of $^{12,14}$Be on $^{12}$C at 56 MeV/nucleon and on protons at energy near 700 MeV is carried out. For lower energy scattering the real part of the OP is calculated by using of double-folding procedure accounting for the anti-symmetrization effects, while the imaginary part is obtained on the base of the high-energy approximation (HEA). The HEA is also applied to the calculations of both real and imaginary OPs when solving the relativistic equation for the high-energy proton-nucleus elastic scattering. The neutron and proton density distributions computed in different microscopic models for $^{12}$Be and $^{14}$Be are used. In the present hybrid model of the optical potential the only free parameters are the depths of the real and imaginary parts of OP obtained by fitting the experimental data. The role of the inelastic scattering channel to the first excited $2^{+}$ and $3^{-}$ states in $^{12}$C when calculating the quasielastic cross sections, as well as the modified density of the $^{12}$C target accounting for the surface effects are studied. In addition, the cluster model, in which $^{14}$Be consists of a $2n$-halo and the $^{12}$Be core, is applied to calculate the cross sections of diffraction breakup and stripping reactions in $^{14}$Be+$^{12}$C scattering and longitudinal momentum distributions of $^{12}$Be fragments at energy of 56 MeV/nucleon. A good agreement of the theoretical results with the available experimental data of both quasielstic scattering and breakup processes is obtained.

Exploring the Structure of the Bound Proton with Deeply Virtual Compton Scattering

In the past two decades, deeply virtual Compton scattering of electrons has been successfully used to advance our knowledge of the partonic structure of the free proton and investigate correlations between the transverse position and the longitudinal momentum of quarks inside the nucleon. Meanwhile, the structure of bound nucleons in nuclei has been studied in inclusive deep-inelastic lepton scattering experiments off nuclear targets, showing a significant difference in longitudinal momentum distribution of quarks inside the bound nucleon, known as the EMC effect. In this Letter, we report the first beam spin asymmetry (BSA) measurement of exclusive deeply virtual Compton scattering off a proton bound in ^{4}He. The data used here were accumulated using a 6GeV longitudinally polarized electron beam incident on a pressurized ^{4}He gaseous target placed within the CLAS spectrometer in Hall-B at the Thomas Jefferson National Accelerator Facility. The azimuthal angle (ϕ) dependence of the BSA was studied in a wide range of virtual photon and scattered proton kinematics. The Q^{2}, x_{B}, and t dependencies of the BSA on the bound proton are compared with those on the free proton. In the whole kinematical region of our measurements, the BSA on the bound proton is smaller by 20% to 40%, indicating possible medium modification of its partonic structure.