High-momentum Tail Research Articles

Reconstruction of Bremsstrahlung γ-rays spectrum in heavy ion reactions with Richardson-Lucy algorithm

The high momentum tail (HMT) in the momentum distribution of nucleons above the Fermi surface has been regarded as an evidence of short-range correlations (SRCs) in atomic nuclei. It has been showcased recently that the np Bremsstrahlung radiation in heavy ion reactions can be used to extract HMT information. The Richardson-Lucy (RL) algorithm is introduced to the reconstruction of the original Bremsstrahlung γ-ray energy spectrum from experimental measurements. By solving the inverse problem of the detector response to the γ-rays, the original energy spectrum of the Bremsstrahlung γ in 25 MeV/u 86Kr + 124Sn has been reconstructed and compared to the isospin- and momentum-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) simulations. The analysis based on hypothesis test suggests the existence of the HMT of nucleons in nuclei, in accordance with the previous conclusions. With its effectiveness being demonstrated, it is feasible to apply the RL algorithm in future experiments of measuring the Bremsstrahlung γ-rays in heavy ion reactions.

High-resolution momentum distributions from low-resolution wave functions

Nucleon momentum distributions calculated with a common one-body operator vary with the resolution scale (and scheme) of the Hamiltonian used. For high-resolution potentials such as Argonne v18 (AV18) there is a high-momentum tail, reflecting short-range correlations in the nuclear wave function, which is reduced or absent for softer, lower-resolution interactions. We explore if the similarity renormalization group (SRG) can be used to quantitatively reproduce the high-resolution distributions from variational Monte Carlo at all momenta using SRG-evolved operators and empirically fit single-particle orbitals rather than a full RG evolution of many-body wave functions. The goal of this approach is to enable calculations of high-resolution distributions for a wider range of nuclei as well as for other interactions, and provides connections to phenomenological analyses of experiments.

Gluon radiation from a classical point particle: recoil effects

The gluon radiation spectrum of a classical particle struck by a sheet of colored glass, is a key ingredient in understanding the distribution of energy and baryon density in the fragmentation region, particularly in the initial stages of heavy ion collisions. However, the currently known classical spectrum has a troublesome high-momentum tail (Kajantie et al. in Phys. Rev. D 100(5):054011, 2019; Phys Rev D 101(5):054012, 2020). By comparing tree-level bremsstrahlung of a spin-less quark to the above-mentioned known result, we propose an interpolating formula that takes into account the recoil of the struck particle, and therefore produces the correct perturbative behaviour at high momentum of the radiated gluon.

Forbidden dark matter annihilation into leptons with full collision terms

The standard approach of calculating the relic density of thermally produced dark matter based on the assumption of kinetic equilibrium is known to fail for forbidden dark matter models since only the high momentum tail of the dark matter phase space distribution function contributes significantly to dark matter annihilations. Furthermore, it is known that the computationally less expensive Fokker-Planck approximation for the collision term describing elastic scattering processes between non-relativistic dark matter particles and the Standard Model thermal bath breaks down if both scattering partners are close in mass. This, however, is the defining feature of the forbidden dark matter paradigm. In this paper, we therefore include the full elastic collision term in the full momentum-dependent Boltzmann equation as well as in a set of fluid equations that couple the evolution of the number density and dark matter temperature for a simplified model featuring forbidden dark matter annihilations into muon or tau leptons through a scalar mediator. On the technical side, we perform all angular integrals in the full collision term analytically and take into account the effect of dark matter self-interactions on the relic density. The overall phenomenological outcome is that the updated relic density calculation results in a significant reduction of the experimentally allowed parameter space compared to the traditional approach, which solves only for the abundance. In addition, almost the entire currently viable parameter space can be probed with CMB-S4, next-generation beam-dump experiments or at a future high-luminosity electron-position collider, except for the resonant region where the mediator corresponds to approximately twice the muon or tau mass.

Entanglement entropy, single-particle occupation probabilities, and short-range correlations

For quantum many-body systems with short-range correlations (SRCs), the intimate relationship between their magnitude, the behavior of the single-particle occupation probabilities at momenta larger than the Fermi momentum, and the entanglement entropy is a new qualitative aspect not studied and exploited yet. A large body of recent condensed matter studies indicates that the time evolution of the entanglement entropy describes the nonequilibrium dynamics of isolated and strongly interacting many-body systems, in a manner similar to the Boltzmann entropy, which is strictly defined for dilute and weakly interacting many-body systems. Both theoretical and experimental studies in nuclei and cold atomic gases have shown that the fermion momentum distribution has a generic behavior $n(k)=C/{k}^{4}$ at momenta larger than the Fermi momentum, due to the presence of SRCs, with approximately 20% of the particles having momenta larger than the Fermi momentum. The presence of the long momentum tails in the presence of SRCs changes the textbook relation between the single-particle kinetic energy and occupation probabilities, ${n}_{\text{mf}}(k)=1/{1+exp\ensuremath{\beta}[\ensuremath{\epsilon}(k)\ensuremath{-}\ensuremath{\mu}]}$ for momenta very different form the Fermi momentum, particularly for dynamics processes. SRCs induced high-momentum tails of the single-particle occupation probabilities increase the entanglement entropy of fermionic systems, which in its turn affects the dynamics of many nuclear reactions, such as heavy-ion collisions and nuclear fission.

Probing heavy-ion collisions with the yield ratios of neutron-proton at intermediate energy

Within an isospin- and momentum-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, we investigate effects of nucleon-nucleon short-range correlations (SRCs) and the nuclear symmetry energy on the yield ratios of neutron-proton (n/p) in four reaction systems K94r+94Kr, Z94r+94Zr, M94o+94Mo and R94u+94Ru. It is found that effects of the symmetry energy and the high momentum tails (HMTs), caused by the SRCs of nucleon-nucleon in the target and projectile, on the kinetic energy distribution of n/p yield ratio are almost same in four reaction systems. While the effect of the HMTs on the double ratio of n/p from neutron-rich and neutron-deficient reaction systems K94r+94Kr and R94u+94Ru is enlarged, and it is about two times than that of the symmetry energy in the high kinetic energies. Meanwhile, we find that the dependence of isospin-fractionation (i.e., the double ratio of n/p of gas-liquid phase) on the isospin asymmetry of reaction system is completely not sensitive to the HMTs but keeping high sensitivity to the symmetry energy. It indicates that the distribution of isospin-fractionation on the isospin asymmetry of reaction system can be taken as an experimental observable to extract information on nuclear symmetry energy.

Effects of high-momentum tail of nucleon momentum distribution on initiation of cluster production in heavy-ion collisions at intermediate energies

Based on the transport model isospin-dependent Boltzmann-Uehling-Uhlenbeck coupled with a phase-space coalescence afterburner, we studied the effects of the high-momentum tail (HMT) of nucleon momentum distribution in initialization in 197Au+197Au reactions at a beam energy of 400 MeV/nucleon with different impact parameters.We found remarkable impact parameter-dependent HMT effects on the fragment multiplicity distribution. The average neutron to proton ratio of produced isotopes is also affected by the HMT. The rapidity distributions of triton and 3He and their elliptic flows are all evidently affected by the HMT. All the effects of the HMT on the cluster production in heavy-ion collisions are centrality dependent.

Role of the effective range in the density-induced BEC-BCS crossover

We elucidate the role of the effective range in the Bose-Einstein-condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) crossover regime of two-component fermions in three dimensions. In contrast to ultracold Fermi gases near the broad Feshbach resonance, where the interaction can be characterized by the contact-type interaction, the interaction range in general becomes important in the density-induced BEC-BCS crossover discussed in the context of condensed-matter and nuclear systems. By characterizing the nonlocal interaction in terms of the low-energy constants such as scattering length $a$ and effective range $r$, we show how the crossover phenomena are affected by nonzero effective ranges. In particular, we show that the superfluid order parameter is strongly suppressed in the high-density regime and the sound velocity exhibits a nonmonotonic behavior reflecting the mechanical stability of the system. Moreover, we point out that the high-momentum tail associated with the contact parameter can be visible when the magnitude of momentum $k$ is much less than $1/r$. We also discuss the relation between the high-momentum tail and the nuclear contact formalism.

A local-density-approximation description of high-momentum tails in isospin asymmetric nuclei

We adapt the local density approximation to add the high-momentum tails (HMTs) to finite nuclei's Slater-determinant momentum distributions. The HMTs are extracted by the extended Brueckner-Hartree-Fock (EBHF) method or by the lowest order cluster approximation. With a correction factor being added to EBHF, it is sufficiently in agreement with the experimental benchmark, i.e., the high-momentum N/Z ratios approximately equal to 1, and the low-momentum N/Z ratios approximately equal to N/Z of the systems. It is also found that the tensor force makes the nucleon-nucleon correlations appear more easily on the nuclear surface region and the percentage of high-momentum (p>300 MeV/c) nucleons, around 17%–18%, independent of isospin asymmetry.

On the survival of the quantum depletion of a condensate after release from a magnetic trap

We present observations of the high momentum tail in expanding Bose–Einstein condensates of metastable Helium atoms released from a harmonic trap. The far-field density profile exhibits features that support identification of the tails of the momentum distribution as originating in the in-situ quantum depletion prior to release. Thus, we corroborate recent observations of slowly-decaying tails in the far-field beyond the thermal component. This observation is in conflict with the hydrodynamic theory, which predicts that the in-situ depletion does not survive when atoms are released from a trap. Indeed, the depleted tails even appear stronger in the far-field than expected before release, and we discuss the challenges of interpreting this in terms of the Tan contact in the trapped gas. In complement to these observations, full quantum simulations of the experiment show that, under the right conditions, the depletion can persist into the far field after expansion. Moreover, the simulations provide mechanisms for survival and for the the large-momentum tails to appear stronger after expansion due to an acceleration of the depleted atoms by the mean-field potential. However, while in qualitative agreement, the final depletion observed in the experiment is much larger than in the simulation.

Embedding short-range correlations in relativistic density functionals through quasi-deuterons

The formation of clusters at sub-saturation densities, as a result of many-body correlations, constitutes an essential feature for a reliable modelization of the nuclear matter equation of state (EoS). Phenomenological models that make use of energy density functionals (EDFs) offer a convenient approach to account for the presence of these bound states of nucleons when introduced as additional degrees of freedom. However, in these models clusters dissolve, by construction, when the nuclear saturation density is approached from below, revealing inconsistencies with recent findings that evidence the existence of short-range correlations (SRCs) even at larger densities. The idea of this work is to incorporate SRCs in established models for the EoS, in light of the importance of these features for the description of heavy-ion collisions, nuclear structure and in the astrophysical context. Our aim is to describe SRCs at supra-saturation densities by using effective quasi-clusters immersed in dense matter as a surrogate for correlations, in a regime where cluster dissolution is usually predicted in phenomenological models. Within the EDF framework, we explore a novel approach to embed SRCs within a relativistic mean-field model with density dependent couplings through the introduction of suitable in-medium modifications of the cluster properties, in particular their binding energy shifts, which are responsible for describing the cluster dissolution. As a first exploratory step, the example of a quasi-deuteron within the generalized relativistic density functional approach is investigated. The zero temperature case is examined, where the deuteron fraction is given by the density of a boson condensate. For the first time, suitable parameterizations of the cluster mass shift at zero temperature are derived for all baryon densities. They are constrained by experimental results for the effective deuteron fraction in nuclear matter near saturation and by microscopic many-body calculations in the low-density limit. A proper description of well-constrained nuclear matter quantities at saturation is kept through a refit of the nucleon meson coupling strengths. The proposed parameterizations allow to also determine the density dependence of the quasi-deuteron mass fraction at arbitrary isospin asymmetries. The strength of the deuteron-meson couplings is assessed to be of crucial importance. Novel effects on some thermodynamic quantities, such as the matter incompressibility, the symmetry energy and its slope, are finally discerned and discussed. The findings of the present study represent a first step to improve the description of nuclear matter and its EoS at supra-saturation densities in EDFs by considering correlations in an effective way. In a next step, the single-particle momentum distributions in nuclear matter can be explored using proper wave functions of the quasi-deuteron in the medium. The momentum distributions are expected to exhibit a high-momentum tail, as observed in the experimental study of SRCs by nucleon knockout with high-energy electrons. This will be studied in a forthcoming publication with an extensive presentation of the theoretical method and the results.

Short-range correlations in the extended quantum molecular dynamics model

Short-range potential has been added into an extended quantum molecular dynamics (EQMD) model. The rms radius, binding energy, and momentum distribution of $^{12}\mathrm{C}$ with different initial structures and short-range potential parameters have been checked. The separation energy of $^{12}\mathrm{C}(p,2p)^{11}\mathrm{B}$ reaction is calculated and compared with the experimental data, which indicates that our modified EQMD model can be taken as a reliable tool for studying proton pair knock-out reaction. Furthermore, the short-range correlation effects on emission time and momentum spectrum of two protons are discussed. Finally, the momentum correlation function of the emitted proton pair is calculated by Lednicky and Lyuboshitz's analytical method. The result explains that short-range repulsion causes high momentum tail and weakens the momentum correlation function.

Over-barrier crossing in multidimensional tunneling

Studies of the dissociative chemisorption of N2 using two-dimensional empirical potential energy surfaces that differ by the position of the saddle point, all show high tunneling probabilities at energies well below the saddle-point energy of the reaction. This is highly unusual for a heavy-atom system and contradicted by one-dimensional analysis along the minimum-energy path. A mechanism of over-barrier crossing, related to the high-momentum tail of the vibrational wave function of N2, is demonstrated. We analyze the two-dimensional wave-packet propagation and compares to the probability of having vibrational momenta that exceeds the value required to overcome the relevant barrier.

In-medium $$\Delta (1232)$$ potential, pion production in heavy-ion collisions and the symmetry energy

Using the dcQMD transport model, the isoscalar and isovector in-medium potentials of the $\Delta$(1232) baryon are studied and information regarding their effective strength is obtained from a comparison to experimental pion production data in heavy-ion collisions below 800 MeV/nucleon impact energy. The best description is achieved for an isoscalar potential moderately more attractive than the nucleon optical potential and a rather small isoscalar relative effective mass m$^*_\Delta \approx$ 0.45. For the isovector component only a constraint between the potential's strength at saturation and the isovector effective mass difference can be extracted, which depends on quantities such as the slope of the symmetry energy and the neutron-proton effective mass difference. These results are incompatible with the usual assumption, in transport models, that the $\Delta$(1232) and nucleon potentials are equal. The density dependence of symmetry energy can be studied using the high transverse momentum tail of pion multiplicity ratio spectra. Results are however correlated with the value of neutron-proton effective mass difference. This region of spectra is shown to be affected by uncertain model ingredients such as the pion potential or in-medium correction to inelastic scattering cross-sections at levels smaller than 10$\%$. Extraction of precise constraints for the density dependence of symmetry energy above saturation will require experimental data for pion production in heavy-ion collisions below 800 MeV/nucleon impact energy and experimental values for the high transverse momentum tail of pion multiplicity ratio spectra accurate to better than 5$\%$.

Imprints of high-momentum nucleons in nuclei on hard photons from heavy-ion collisions near the Fermi energy

The short-range correlation (SRC) induced by the tensor force in the isosinglet neutron-proton interaction channel leads to a high-momentum tail (HMT) in the single-nucleon momentum distributions n(k) in nuclei. Owing to the remaining uncertainties about the tensor force, the shape of the nucleon HMT may be significantly different from the dilute interacting Fermi gas model prediction $n(k) \sim1/k^4$ similar to the HMT in cold atoms near the unitary limit. Within an isospin- and momentum-dependent Boltzmann-Uehling-Uhlenbeck transport model incorporating approximately the nucleon HMT, we investigate hard photon emissions in $^{14}$N+$^{12}$C and $^{48}$Ca+$^{124}$Sn reactions at beam energies around the Fermi energy. Imprints of different shapes of the HMT on the energy spectrum, angular distribution and transverse momentum spectrum of hard photons are studied. While the angular distribution does not carry any information about the shape of the nucleon HMT, the energy spectra and especially the mid-rapidity transverse momentum spectra of hard photons are found to bare strong imprints of the shapes of nucleon HMTs in the two colliding nuclei.

Symmetry energy extracted from the SπRIT pion data in Sn+Sn systems

With the improved particular Isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model (impIBUU) including the nucleon-nucleon short-range correlations, the ratios and yields of $\pi^{-}$ and $\pi^{+}$ in Sn+Sn systems with different asymmetries at 270 MeV/nucleon are studied. It is found that the yields of $\pi^{-}$ and $\pi^{+}$ and their ratios in Sn+Sn systems characterized by different neutron to proton ratios obtained from the very recent S$\pi$RIT pion data, are quite well described by the model, especially when a soft symmetry energy with $L(\rho_{0})$ = 66.75$\pm$24.75 MeV is used. The calculations also clearly demonstrate that the high-momentum tail of the nucleon initialization in momentum space strongly affects the yields and ratios of pion production in Sn+Sn systems with different asymmetries near or below threshold. In addition, given many insoluble theoretical uncertainties in transport models, multi-system experimental measurements with various N/Z asymmetries are proposed to extract the symmetry energy less model-dependently by using heavy-ion collisions.

Impacts of nucleon-nucleon short-range correlations on neutron stars

Nucleon-nucleon short-range correlations (SRCs) are inevitable consequences of realistic nucleon-nucleon interactions. The corresponding SRC pairs, characterized by high relative momenta, have been verified experimentally to be important in finite nuclei. In this work, we study the impacts of nucleon-nucleon SRCs on the physical properties of neutron stars. Considering the small center-of-mass momenta of SRC pairs, new nucleon momentum distributions with high-momentum tails (HMTs) are proposed by extrapolating well-established experimental results of SRCs in finite nuclei to neutron star matter. HMTs with different shapes are adopted to estimate theoretical uncertainties. It is found that nucleon-nucleon SRCs generally stiffen the equation of state of neutron star matter and increase the maximum mass of neutron stars.

Structure Factors of Neutron Matter at Finite Temperature.

We compute continuum and infinite volume limit extrapolations of the structure factors of neutron matter at finite temperature and density. Using a lattice formulation of leading-order pionless effective field theory, we compute the momentum dependence of the structure factors at finite temperature and at densities beyond the reach of the virial expansion. The Tan contact parameter is computed and the result agrees with the high momentum tail of the vector structure factor. All errors, statistical and systematic, are controlled for. This calculation is a first step towards a model-independent understanding of the linear response of neutron matter at finite temperature.

Novel observation of isospin structure of short-range correlations in calcium isotopes

Short Range Correlations (SRCs) have been identified as being responsible for the high momentum tail of the nucleon momentum distribution, n(k). Hard, short-range interactions of nucleon pairs generate the high momentum tail and imprint a universal character on n(k) for all nuclei at large momentum. Triple coincidence experiments have shown a strong dominance of np pairs, but these measurements involve large final state interactions. This paper presents the results from Jefferson Lab experiment E08014 which measured inclusive electron scattering cross-section from Ca isotopes. By comparing the inclusive cross section from 48Ca to 40Ca in a kinematic region dominated by SRCs we provide a new way to study the isospin structure of SRCs.

N+H3, p+He3, p+H3, and n+He3 scattering with the hyperspherical harmonic method

The $n+^{3}\mathrm{H},$ $p+^{3}\mathrm{He},$ $p+^{3}\mathrm{H},$ and $n+^{3}\mathrm{He}$ elastic and charge exchange reactions at low energies are studied by means of the hyperspherical harmonic method. The considered nuclear Hamiltonians include modern two- and three-nucleon interactions, and in particular results are reported in case of chiral two-nucleon potentials, with and without the inclusion of chiral three-nucleon (3N) interactions. A detailed study of the convergence and numerical stability of the method is presented. We have found that the effect the 3N force is in general tiny except for $p+^{3}\mathrm{H}$ scattering below the opening of the $n+^{3}\mathrm{He}$ channel. In such a case, the effect of 3N forces is appreciable and a clear dependence on the cutoff used to regularize the high-momentum tail of the interactions is observed. Such a dependence is related to the presence of the poorly known sharp ${0}^{+}$ resonance, considered to be the first excited state of $^{4}\mathrm{He}$.