High-momentum Tail Research Articles

The normal liquid 3He one-body momentum distribution at zero and finite temperature

The normal liquid helium 3 one-body momentum distribution, n(k), at zero and finite temperature is evaluated by using the cluster expansion theory for the occupation probability of Ristig-Clark formalism. The lowest order constrained variational (LOCV) and the extended LOCV (ELOCV) method are used to calculate the correlation functions at zero and finite temperatures. The input inter-atomic potential is the familiar 6–12 Lennard-Jones interaction. The gap in n(k) at the Fermi surface is found to be about 0.41 comparing to 1.0 (0.72) for the noninteracting (dilute hard-sphere) Fermi gas model at zero temperature and it decreases by increasing the temperature. It is also demonstrated that the high-momentum tail of n(k) gets larger as we increase the temperature and finally, we find a good agreement between present calculated n(k) and those coming from more sophisticated approaches such as Diffusion and Green-function Monte Carlo techniques.

The one-body momentum distribution of nuclear matter at finite temperature

The one-body momentum distribution of nuclear matter at finite temperature, n ( k ) , is evaluated by using the cluster expansion theory for the occupation probability. The lowest order constrained variational (LOCV) method at finite temperature is used to calculate the correlation functions. The input nucleon–nucleon interactions are the Nijmegen- Reid93 and A v 18 as well as Reid68 and Δ - Reid soft core, phenomenological potentials. The gap in n ( k ) at the Fermi surface is found to be about 97 per cent comparing to 1.0 for the noninteracting Fermi gas model at zero temperature and it is shown to decrease by increasing the temperature. It is also demonstrated that the high-momentum tail of n ( k ) gets larger as we increase the temperature and the application of different interactions do not have dramatic effect on its behavior.

Anomalous Behavior of Proton Zero Point Motion in Water Confined in Carbon Nanotubes

The momentum distribution of the protons in ice Ih, ice VI, high density amorphous ice, and water in carbon nanotubes has been measured using deep inelastic neutron scattering. We find that at 5 K the kinetic energy of the protons is 35 meV less than that in ice Ih at the same temperature, and the high momentum tail of the distribution, characteristic of the molecular covalent bond, is not present. We observe a phase transition between 230 and 268 K to a phase that does resemble ice Ih. Although there is yet no model for water that explains the low temperature momentum distribution, our data reveal that the protons in the hydrogen bonds are coherently delocalized and that the low temperature phase is a qualitatively new phase of ice.

Condensate fraction and atomic kinetic energy of liquidHe3−He4mixtures

We present neutron-scattering measurements of the momentum distribution of liquid $^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}$ mixtures. The experiments were performed at wave vectors $Q$, $26\ensuremath{\leqslant}Q\ensuremath{\leqslant}29\phantom{\rule{0.3em}{0ex}}{\mathrm{\AA{}}}^{\ensuremath{-}1}$, on the MARI time-of-flight spectrometer at the ISIS Facility, Rutherford Appleton Laboratory, a spallation neutron source. Mixtures with $^{3}\mathrm{He}$ concentrations $x$ between 0 and 20% were investigated both in the superfluid and normal phases. From the data, we extract the Bose-Einstein condensate fraction ${n}_{0}$ and the momentum distributions of $^{3}\mathrm{He}$ and $^{4}\mathrm{He}$ atoms. We find that ${n}_{0}$ increases somewhat above the pure $^{4}\mathrm{He}$ value when $^{3}\mathrm{He}$ is added; e.g., from ${n}_{0}=(7.25\ifmmode\pm\else\textpm\fi{}0.75)%$ at $x=0$ to $(11\ifmmode\pm\else\textpm\fi{}3)%$ at $x=15--20\phantom{\rule{0.2em}{0ex}}%$. This agrees with predictions but is less than the only previous measurement. We find a $^{4}\mathrm{He}$ kinetic energy ${K}_{4}$ for pure $^{4}\mathrm{He}$ that agrees with previous determinations. ${K}_{4}$ decreases somewhat with increasing $^{3}\mathrm{He}$ concentration, less than observed previously and found in early calculations but in agreement with a more recent Monte Carlo calculation. The $^{3}\mathrm{He}$ response is not well reproduced by a Fermi-gas momentum distribution, $n(\mathbf{k})$. Rather an $n(\mathbf{k})$ having a small step height at the Fermi surface and a substantial high-momentum tail characteristic of a strongly interacting Fermi liquid provides a good fit. This $n(\mathbf{k})$ is consistent with calculated $n(\mathbf{k})$. Thus agreement between theory and experiment is obtained comparing $n(\mathbf{k})$ in contrast to earlier findings based on comparing calculated and observed $^{3}\mathrm{He}$ kinetic energies.

Fusion reactions in plasmas as probe of the high-momentum tail of particle distributions

In fusion reactions, the Coulomb barrier selects particles from the high-momentum part of the distribution. Therefore, small variations of the high-momentum tail of the velocity distribution can produce strong effects on fusion rates. In plasmas several potential mechanisms exist that can produce deviations from the standard Maxwell-Boltzmann distribution. Quantum broadening of the energy-momentum dispersion relation of the plasma quasi-particles modifies the high-momentum tail and could explain the fusion-rate enhancement observed in low-energy nuclear reaction experiments.

Quantum-tail effect in low-energy d+d reaction in deuterated metals

The Bochum experimental enhancement of the d+d fusion rate in a deuterated metal matrix at low incident energies is explained by the quantum broadening of the momentum–energy dispersion relation and consequent modification of the high-momentum tail of the distribution function from an exponential to a power-law.

High-momentum tail in the Tonks gas under harmonic confinement

We use boson–fermion mapping to show that the single-particle momentum distribution in a one-dimensional gas of hard point-like bosons (Tonks gas) inside a harmonic trap decays as p −4 at large momentum p. The relevant integrals expressing the one-body density matrix are evaluated for small numbers of particles in a simple Monte Carlo approach to test the extent of the asymptotic law and to illustrate the slow decay of correlations between the matter–wave field at different points.

Q2-dependence of backward pion multiplicity in neutrino–nucleus interactions

The production of pions emitted backward in inelastic neutrino-nucleus interactions is analyzed within the impulse approximation in the framework of the dual parton model. We focus on the $Q^2$-dependence of the multiplicity of negative pions, normalized to the total cross section of the reaction $\nu + A \to \mu + X$. The inclusion of planar (one-Reggeon exchange) and cylindrical (one-Pomeron exchange) graphs leads to a multiplicity that decreases as $Q^2$ increases, in agreement with recent measurements carried out at CERN by the NOMAD collaboration. A realistic treatment of the high momentum tail of the nucleon distribution in a nucleus also allows for a satisfactory description of the semi-inclusive spectrum of backward pions.

First-principles calculation of coincidence Doppler broadening of positron annihilation radiation

We report a first-principles method for calculating the momentum density of positron-electron pairs in materials, which can be accurately measured, in a wide momentum range, by means of coincidence Doppler broadening (CDB) of positron annihilation radiation. The calculation is based on the two-component density-functional theory within the local-density approximation. The electron and positron wave functions are calculated by means of the full-potential linearized-augmented-plane-wave method with use of semicore orbitals and of the pure plane-wave method, respectively. This hybrid basis set accurately determines the wave functions of core and valence electrons and is free from any shape or symmetry assumption for the positron wave function. The method is applied to two typical systems. i.e., Al and graphite having isotropic and anisotropic positron densities, respectively. The calculations agree well with experiments over the entire measurable momentum region. Especially, the calculations well reproduce the anisotropic high-momentum CDB tails of graphite, which originate from the quasi-two-dimensionally distributed positron. This reproduction suggests that the present method is applicable for a variety of materials.

Apparent tunneling in chemical reactions

A necessary condition for tunneling in a chemical reaction is that the probability of crossing a barrier is non-zero, when the energy of the reactants is below the potential energy of the barrier. Due to the non-classical nature (i.e, momentum uncertainty) of vibrational states this is, however, not a sufficient condition in order to establish genuine tunneling as a result of quantum dynamics. This proposition is illustrated for a two-dimensional model potential describing dissociative sticking of N 2 on Ru(s). It is suggested that the remarkable heavy atom tunneling, found in this system, is related to the high momentum tail of the initial vibrational state of nitrogen, allowing for amplitude to cross over the barrier.

Semiclassical transport of hadrons with dynamical spectral functions in [formula omitted] collisions at SIS/AGS energies

The transport of hadrons with dynamical spectral functions A h(X, P,M 2) is studied for nucleus–nucleus collisions at SIS and AGS energies in comparison to the conventional quasiparticle limit and the available experimental data within the recently developed off-shell HSD transport approach. Similar to reactions at GANIL energies the off-shell effects show up in high momentum tails of the particle spectra, however, at SIS and AGS energies these modifications are found to be less pronounced than at lower energies due to the high lying excitations of the nucleons in the collision zone.

Relativistic nuclear collisions at10AGeV energies fromp+Beto Au+Au with the hadronic cascade model

A hadronic cascade model based on resonances and strings is used to study mass dependence of relativistic nuclear collisions from p+Be to Au+Au at AGS energies ($\sim 10\AGeV$) systematically. Hadron transverse momentum and rapidity distributions obtained with both cascade calculations and Glauber type calculations are compared with experimental data to perform detailed discussion about the importance of rescattering among hadrons. We find good agreement with the experimental data without any change of model parameters with the cascade model. It is found that rescattering is of importance both for the explanation of high transverse momentum tail and for the multiplicity of produced particles.

Momentum distribution of confined bosons: Temperature dependence

The momentum distribution function of a parabolically confined gas of bosons with harmonic interparticle interactions is derived. In the Bose-Einstein condensation region, this momentum distribution substantially deviates from a Maxwell-Boltzmann distribution. It is argued that the determination of the temperature of the boson gas from the Bose-Einstein momentum distribution function is more appropriate than the currently used fitting to the high-momentum tail of the Maxwell-Boltzmann distribution.

Diffractive heavy quarkonium photoproduction and electroproduction in QCD

Hard diffractive photo- and electroproduction of heavy vector mesons ($J/\psi$ and $\Upsilon$) is evaluated within the leading $\alpha_s\ln{Q^2 \over\Lambda_{QCD}^2}$ approximation of QCD. In difference from our earlier work on that subject, also the production of transversely polarized vector mesons is calculated. Special emphasis is placed on the role of the vector meson's $q\bar q$ light-cone wave function. In that context, conventional non-relativistic quarkonium models and a light-front QCD bound state calculation are critically examined and confronted with QCD expectations. Our numerical analysis finds a significant high momentum tail in the latter wave functions and a deviation from the expected asymptotic behavior of $\phi_V(z,b=0)\propto z(1-z)$. We then design an interpolation to match the quarkonium models at large inter-quark separations with QCD expectations at small distances. We use these results to compare our predictions for the forward differential cross section of $J/\psi$ photo- and electroproduction with recent experimental results from HERA. In addition, our earlier discussion of $\rho^o$ electroproduction is updated in light of recent experimental and theoretical enhancements.

Beyond the Dirac-Brueckner-Hartree-Fock model: Equation of state and occupation probabilities of the Bonn potential.

We calculate nuclear matter observables for the Bonn-C potential in a relativistic conserving approach. This amounts to extending the Dirac-Brueckner-Hartree-Fock model by including hole-hole propagating diagrams to all orders, which also allows us to calculate the momentum distribution using a spectral function. The trends we find upon including hole-hole propagation are very similar to what we found performing the same calculation for the Groningen potential. One particular finding is that the high momentum tail of the momentum distribution is the same for both potentials. \textcopyright{} 1996 The American Physical Society.

Hard diffractive electroproduction of vector mesons in QCD.

Hard diffractive electroproduction of longitudinally polarized vector mesons is calculated within the leading $\alpha_s\ln{Q^2\over\Lambda_{QCD}^2}$ approximation of QCD using the leading order parton densities within the nucleon. Novel QCD features of the production of excited states and of the restoration of flavor symmetry are analyzed. At the onset of the asymptotic regime, our analysis finds an important role of quark Fermi motion within the diffractively produced vector mesons, and we suggest to use this effect to measure the high momentum tail of the wave function of the vector mesons. We deduce a kinematical boundary for the region of applicability of the decomposition of the hard amplitudes over powers of $Q^2$ and/or a limit on the increase of the cross sections of hard processes at small $x$, and briefly analyze its consequences. We also estimate the nuclear attenuation of the diffractive electroproduction of vector mesons and compare with estimates of the shadowing of the longitudinal structure function.

Atomic alchemy: Weak decays of muonic and pionic atoms into other atoms.

We consider the transitions between electromagnetic bound states, such as the exclusive weak decay of a muonic atom into an electronic atom: $(\mu^- Z) \to (e^- Z) {\bar \nu_e }\nu_\mu . $ We show that relativistic effects in the atomic wavefunctions are crucial for determining the rate. In the case of heavy atoms, the exclusive channel branching ratios exceed $10^{-6},$ possibly bringing the study of these rare decays within experimental reach. Such processes thus provide a detailed laboratory for studying the high momentum tail of wavefunctions in atomic physics; in addition, they provide a simple toy model for investigating analogous exclusive heavy hadronic decays in quantum chromodynamics such as $B \to \pi e \nu.$

Nucleon and pion electromagnetic form factors in a light-front constituent quark model

Nucleon and pion electromagnetic form factors are evaluated in the spacelike region within a light-front constituent quark model, where eigenfunctions of a mass operator, reproducing a large set of hadron energy levels, are adopted and quark form factors are considered in the one-body current. The hadron form factors are sharply affected by the high momentum tail generated in the wave function by the one-gluon-exchange interaction. Useful information on the electromagnetic structure of light constituent quarks can be obtained from the comparison with nucleon and pion experimental data.

Electromagnetic form factors of the ϱ meson in a light-front constituent quark model

The electromagnetic form factors of the ϱ meson are evaluated adopting a relativistic constituent quark model based on the light-front formalism, and using a meson wave function with the high-momentum tail generated by the one-gluon-exchange interaction. The breakdown of the rotational covariance for the one-body component of the current operator is investigated and the sensitivity of the ratio of the ϱ-meson form factors to the pion (charge) form factor to the spin-dependent component of the effective q q interaction is illustrated.

Charge form factors of pseudoscalar mesons.

The elastic charge form factors of the pion, kaon, D, and B mesons are calculated within a relativistic constituent quark model formulated on the light cone. Our parameter-free predictions agree well with the available data. The results are approximately independent of the assumed form of the light-cone wave function; in particular, they do not depend on the high momentum tail of the wave function for energies accessible to present experiments.