Momentum Distribution In Nuclei Research Articles

ALPHA PARTICLE MOMENTUM DISTRIBUTION IN NUCLEI WITHIN THE COHERENT DENSITY FLUCTUATION MODEL

The alpha particle centre of mass momentum distribution in nuclei is determined on the basis of the four-body density matrix obtained within the coherent density fluctuation model. The calculations are carried out for a number of nuclei. The results are compared with those deduced from analyses of experimental data on alpha-particle knockout reactions induced by electrons,protons and alpha-particles which provide information on the alpha-particle momentum distribution.

An analytical formula for proton momentum distribution in nuclei with A>4

A successful analytical formula for the proton momentum distribution in all nuclei with A>4 accounting for nucleon-nucleon correlation effects, is presented. In this formula the Isomorphic Shell Model wave functions are employed, which are readily available for all nuclei all the way up to 2 0 8Pb. However, other wave functions (e.g., shell model or Hartree-Fock) could be used with almost equivalent results. Available experimental data for 4He, 1 2C and 5 6Fe and predictions of other theories, e.g., for 4 0Ca, are used for comparison of the predictions of the present formula. A reservation is kept concerning the validity of this formula for the momentum distribution of exotic nuclei.

Isospin-sensitive observables as a probe of proton transition momentum in the HMT * * Partially supported by the National Natural Science Foundation of China (11875152, 11675066, U1867207, 11505085)

Based on the IBUU transport model, the effect of proton transition momentum on collective flows is studied in 40Ca + 40Ca,112Sn + 112Sn, and 197Au + 197Au collisions at an incident beam energy of 400 MeV/A with impact parameter . It is found that in a neutron rich system, the difference between neutron and proton elliptic flow is largely affected by the proton transition momentum. At beam energies around (and particularly below) the pion production threshold, the ratio is greatly sensitive to proton transition momentum in asymmetric nuclear matter. This study may help us to understand the nucleon momentum distribution in nuclei, which is important for the equation of state of asymmetric nuclear matter, such as neutron stars.

Isospin dependence of nucleon effective masses in neutron-rich matter

In this talk, we first briefly review the isospin dependence of the total nucleon effective mass $M^{\ast}_{J}$ inferred from analyzing nucleon-nucleus scattering data within an isospin dependent non-relativistic optical potential model, and the isospin dependence of the nucleon E-mass $M^{\ast,\rm{E}}_{J}$ obtained from applying the Migdal-Luttinger theorem to a phenomenological single-nucleon momentum distribution in nuclei constrained by recent electron-nucleus scattering experiments. Combining information about the isospin dependence of both the nucleon total effective mass and E-mass, we then infer the isospin dependence of nucleon k-mass using the well-known relation $M^{\ast}_{J}=M^{\ast,\rm{E}}_{J}\cdot M^{\ast,\rm{k}}_{J}$. Implications of the results on the nucleon mean free path (MFP) in neutron-rich matter are discussed.

19aAC-1 原子核の運動量分布と多核子相関

19aAC-1 原子核の運動量分布と多核子相関

Effects of the HMT on Nucleon Collective Flows within BUU Transport Model**Supported by the Fundamental Research Funds for the Central Universities under Grant No lzujbky-2014-170, the Research Fund for the Doctoral Program of Higher Education of China under Grant No 20120211120002, and the National Natural Science Foundation of China under Grant Nos 11205075 and 11375076.

Within the framework of a semiclassical Boltzmann–Uehling–Uhlenbeck (BUU) transport model, the high momentum tail (HMT) effects of nucleon momentum distribution in the nucleus on the nucleon collective flows are studied in semicentral Au+Au collisions. The HMT due to the isospin-dependent short-range correlations causes a smaller value of the collective flows. We find that the HMT effects on the nucleon collective flows are remarkable at beam energy of 300 MeV/nucleon and become weak as the incident beam energy increases. The results indicate that for the collective flow studies at intermediate energies, the HMT of nucleon momentum distribution in nucleus should be taken into account in transport models.

MULTI-CHAIN MODEL WITH SUCCESSIVE COLLISION AND HIGH-ENERGY NUCLEUS–NUCLEUS COLLISIONS

High-energy nucleus–nucleus collisions are studied in the multi-chain model with successive collision. Analytic forms for the longitudinal momentum distribution of the inclusive reaction are discussed. It is shown that the longitudinal momentum distribution in nucleus–nucleus collisions is expressed in the Glauber probability with the hypergeometric distribution.

Efficient First-Principles Calculation of the Quantum Kinetic Energy and Momentum Distribution of Nuclei

Light nuclei at room temperature and below exhibit a kinetic energy which significantly deviates from the predictions of classical statistical mechanics. This quantum kinetic energy is responsible for a wide variety of isotope effects of interest in fields ranging from chemistry to climatology. It also furnishes the second moment of the nuclear momentum distribution, which contains subtle information about the chemical environment and has recently become accessible to deep inelastic neutron scattering experiments. Here, we show how, by combining imaginary time path integral dynamics with a carefully designed generalized Langevin equation, it is possible to dramatically reduce the expense of computing the quantum kinetic energy. We also introduce a transient anisotropic Gaussian approximation to the nuclear momentum distribution which can be calculated with negligible additional effort. As an example, we evaluate the structural properties, the quantum kinetic energy, and the nuclear momentum distribution for a first-principles simulation of liquid water.

Scaling function, spectral function, and nucleon momentum distribution in nuclei

The link between the scaling function extracted from the analysis of $(e,{e}^{'})$ cross sections and the spectral function/momentum distribution in nuclei is revisited. Several descriptions of the spectral function based on the independent particle model are employed, together with the inclusion of nucleon correlations, and effects of the energy dependence arising from the width of the hole states are investigated. Although some of these approaches provide rough overall agreement with data, they are not found to be capable of reproducing one of the distinctive features of the experimental scaling function, namely its asymmetry. However, the addition of final-state interactions, incorporated in the present study using either relativistic mean-field theory or via a complex optical potential, does lead to asymmetric scaling functions in accordance with data. The present analysis seems to indicate that final-state interactions constitute an essential ingredient and are required to provide a proper description of the experimental scaling function.

Scaling function and nucleon momentum distribution

Scaling studies of inclusive quasielastic electron scattering reactions have been used in the past as a basic tool to obtain information on the nucleon momentum distribution in nuclei. However, the connection between the scaling function, extracted from the analysis of cross section data, and the spectral function only exists assuming very restricted approximations. We revisit the basic expressions involved in scaling studies and how they can be linked to the nucleon momentum distribution. In particular, the analysis applied in the past to the so-called scaling region, {\it i.e.,} negative values of the scaling variable $y$, is extended here to positive $y$, since a "universal" superscaling function has been extracted from the analysis of the separated longitudinal data. This leads to results that clearly differ from the ones based solely on the negative-$y$ scaling region, providing new information on how the energy and momentum are distributed in the spectral function.

Superscaling in a dilute Fermi gas and the nucleon momentum distribution in nuclei

The superscaling observed in inclusive electron scattering is described within the dilute Fermi gas model with interaction between the particles. The comparison with the relativistic Fermi gas (RFG) model without interaction shows an improvement in the explanation of the scaling function $f({\ensuremath{\psi}}^{\ensuremath{'}})$ in the region ${\ensuremath{\psi}}^{\ensuremath{'}}l\ensuremath{-}1$, where the RFG result is $f({\ensuremath{\psi}}^{\ensuremath{'}})=0$. It is found that the behavior of $f({\ensuremath{\psi}}^{\ensuremath{'}})$ for ${\ensuremath{\psi}}^{\ensuremath{'}}l\ensuremath{-}1$ depends on the particular form of the general power-law asymptotics of the momentum distribution $n(k)\ensuremath{\sim}1/{k}^{4+m}$ at large $k$. The best agreement with the empirical scaling function is found for $m\ensuremath{\simeq}4.5$ in agreement with the asymptotics of $n(k)$ in the coherent density fluctuation model where $m=4$. Thus, superscaling gives information about the asymptotics of $n(k)$ and the $\mathit{NN}$ forces.

Superscaling, scaling functions, and nucleon momentum distributions in nuclei

The scaling functions $f({\ensuremath{\psi}}^{'})$ and $F(y)$ from the ${\ensuremath{\psi}}^{'}$- and $y$-scaling analyses of inclusive electron scattering from nuclei are explored within the coherent density fluctuation model (CDFM). In addition to the CDFM formulation in which the local density distribution is used, we introduce a new equivalent formulation of the CDFM based on the one-body nucleon momentum distribution (NMD). Special attention is paid to the different ways in which the excitation energy of the residual system is taken into account in $y$ and ${\ensuremath{\psi}}^{'}$ scaling. Both functions, $f({\ensuremath{\psi}}^{'})$ and $F(y)$, are calculated using different NMDs and compared with the experimental data for a wide range of nuclei. The good description of the data for $y<0$ and ${\ensuremath{\psi}}^{'}<0$ (including ${\ensuremath{\psi}}^{'}<\ensuremath{-}1$) makes it possible to show the sensitivity of the calculated scaling functions to the peculiarities of the NMDs in different regions of momenta. It is concluded that the existing data on ${\ensuremath{\psi}}^{'}$ and $y$ scaling are informative for NMDs at momenta not larger than $2.0--2.5\phantom{\rule{0.3em}{0ex}}{\text{fm}}^{\ensuremath{-}1}$. The CDFM allows us to study simultaneously and on the same footing the role of both basic quantities---the momentum and density distributions---for the description of scaling and superscaling phenomena in nuclei.

Two nucleon correlations measured with 3He(e,e’pp)n

Despite tremendous progress in recent years in measuring single nucleon momentum distributions in nuclei, two-nucleon momentum distributions remain largely unmeasured. Here we report on a measurement of 3He(e,e’pp)n that is primarily sensitive to the two-nucleon momentum distribution and relatively uncontaminated by final state rescattering or by two-body currents.

Interplay between angular momentum transfer and nuclear structure in the production of isomers at intermediate energies

Isomeric ratios and momentum distributions of nuclei produced in the fragmentation of a 60A MeV ${}^{92}\mathrm{Mo}$ beam on a thin ${}^{27}\mathrm{Al}$ target have been studied in detail. A strong dependence of the isomeric ratio on the structure of the isomer and on the reaction mechanism has been observed for the first time at intermediate energies. The results are quantitatively reproduced in a framework of kinematical and statistical models of nuclear reactions.

Long-range correlations and the momentum distribution in nuclei

The influence of correlations on the momentum distribution of nucleons in nuclei is evaluated starting from a realistic nucleon-nucleon interaction. The calculations are performed directly for the finite nucleus $\,^{16}$O making use of the Green's function approach. The emphasis is focused on the correlations induced by the excitation modes at low energies described within a model-space of shell-model configurations including states up to the sdg shell. Our analysis demonstrates that these long-range correlations do not produce any significant enhancement of the momentum distribution at high missing momenta and low missing energies. This is in agreement with high resolution $(e,e'p)$ experiments for this nucleus. We also try to simulate the corresponding effects in large nuclei by quenching the energy-spacing between single-particle orbits. This yields a sizable enhancement of the spectral function at large momenta and small energy. Such behavior could explain the deviation of the momentum distribution from the mean field prediction, which has been observed in $(e,e'p)$ experiments on heavy nuclei like $^{208}$Pb.

Universal pattern in ( e, e′ p) at large missing momenta: quasi-deuteron or diffractive final state interactions?

The intrinsic single particle momentum distributions in nuclei are supposed to show a universal behavior at large momenta, dominated by short-range correlated pairs, or quasi-deuterons. We discuss whether the quasi-deuteron universality survives the final state interaction effects, which are present in the missing momentum spectra measured in A( e, e′ p) experiments at GeV energies. We demonstrate that in the observed missing momentum spectra an approximate universality is present, but originating from the universal pattern of diffractive final state interactions of the struck proton independent of the target nucleus.

Deep inelastic neutron scattering off D2 and H2 and momentum distributions of nuclei in diatomic molecules.

A quantum-mechanical calculation for the description of neutron scattering at very high momentum transfer off both homonuclear and heteronuclear diatomic molecules at T=0 K in terms of the nuclear momentum distribution, n(k), of the nuclei in these molecules is proposed. The results of this calculation compare well with neutron-scattering measurements on liquid ${\mathrm{D}}_{2}$ at T=20 K in the momentum transfer range 55q80 A${\mathrm{\r{}}}^{\mathrm{\ensuremath{-}}1}$ and with previous measurements on solid ${\mathrm{H}}_{2}$ at T=4 K and liquid ${\mathrm{H}}_{2}$ at T=20 K at high momentum transfer (q\ensuremath{\sim}100 A${\mathrm{\r{}}}^{\mathrm{\ensuremath{-}}1}$), showing that high-energy neutrons can be a sensitive probe to investigate the momentum distribution of the nuclei in these molecules.

Asymptotic behaviour of the scaling function in deep inelastic neutron scattering

A new method is proposed to obtain the atomic momentum distribution from deep inelastic neutron scattering in the framework of y scaling. The analysis is based on a model independent extrapolation to obtain the asymptotic scaling function at infinite momentum transfer (q→∞) from the experimental cross sections at finite momentum transfer, even if the data are affected by final state interactions. This method is an extension of an approach to y scaling already adopted to obtain the nuclear momentum distribution in nuclei. An application to polycrystalline D2O at 20 K shows that the momentum distribution of deuterium obtained with the asymptotic scaling function strongly differs from the results corresponding to the scaling function at finite momentum transfer.

Momentum distribution of nuclei in a one-dimensional nuclear model

The momentum distributions of finite nuclei are calculated using Monte Carlo techniques for a one-dimensional model having a two-body potential with a repulsive core and a long-range attraction. The results obtained in mean-field using a density-dependent effective interaction are compared to the exact solution.

Precocious y-scaling and nucleon momentum distributions in nuclei

Recent quasi-elastic electron scattering data on 56Fe are compared with an impulse approximation calculation based on a theoretical nuclear matter spectral function. A y-scaling analysis of the data shows that the scaling limit is approached at lower Q 2 than the theoretical calculation. A new y-scaling analysis based on the properties of the theoretical spectral function is introduced which allows direct comparison of the momentum distribution with the experimental scaling function.