Nucleon Momentum Distribution In Nuclei Research Articles

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.

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.

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.

Properties of nucleon momentum distributions in nuclei at finite temperatures

The nucleon momentum distributionn(k) in nuclei is investigated in the framework of the coherent density fluctuation model extended to finite temperatures. It is shown that the well-known zero-temperature mean-field approximation fails to explain the high-momentum region ofn(k) where short-range and tensor correlations are important. The temperature dependence of the deep hole nuclear state spectral functions is also considered in the model.

Nuclear structure studies at medium energies

Abstract Reactions initiated by electrons, nucleons, pions and kaons in the energy region 100–600 mev are discussed. It is shown that valuable information on nuclear structure can be obtained from these reactions, although precise determination of the nucleon momentum distribution in nuclei requires a combined study of a range of reactions and elastic scattering. It is suggested that attempts to determine the nucelon pair correlation function may be premature.

Effect of the Optical Potential on the Nucleon Momentum Distribution in Nuclei. The Pickup Reaction

The effect of the optical potential on the nucleon momentum distribution in nuclei is discussed in this work. The idea of McCarthy et al., that the refraction and localization effects caused by the real and imaginary parts of the optical potential smears the single-particle momentum distribution, is amplified and applied to nucleon momentum distribution experiments. The assertion is made here that it seems impossible to directly measure in any manner the momentum distribution of nucleons in nuclei. Further it is proposed that much or all of the large discrepancy between the experimental momentum determinations and the shell-model predictions is due to the neglect of these important sources of high-momentum components. The high-energy ${\mathrm{C}}^{12}(p, d){\mathrm{C}}^{11}$ pickup reaction data are re-analyzed in the light of these considerations. It is shown that for $\frac{{q}^{2}}{{\ensuremath{\beta}}^{2}}\ensuremath{\lesssim}8$, the $1p$-shell harmonic oscillator distribution, $(\frac{{q}^{2}}{{\ensuremath{\beta}}^{2}})\mathrm{exp}(\ensuremath{-}\frac{{q}^{2}}{{\ensuremath{\beta}}^{2}})$, has sufficient high-momentum components to fit the data. The lack of agreement for $\frac{{q}^{2}}{{\ensuremath{\beta}}^{2}}g8$ is possibly due more to a failure in the distorted-wave approximation calculation used here than to lack of high-momentum components in the wave function.

Quasi-Deuteron Model of Atomic Nuclei. I

Quasi-deuteron model is investigated, taking account of pair correlation functions in the ground state wave function of atomic nuclei. The formalism of this type makes it possible to use the cluster development method conveniently for the calculations of the expectation values or matrix elements by the model wave functions. Pair nucleon correlation functions are determined phenomenologically but self-consistently, by making use of partly the experimental information about two nucleon systems and partly the theoretical considerations for multiple scattering problem developed by Brueckner, Bethe and their collaborators. In this paper the properties of nuclear matter are investigated as the preliminary discussion. Two nucleon correlation functions are investigated in detail for every possible spin and isospin states of the nucleon pairs. The effect of the exclusion principle on these correlation functions is given in explicit form and it is shown that on the one band the exclusion principle plays the most important role for the appearance of the shell structure, and on the other hand it may have some relationships with alpha particle formation on the nuclear surface. With the use of our ground state wave function, the saturation of nuclear volume energy and that of nuclear density are discussed quantitatively and the velocity dependent one particle potential is constructed self-consistently. High energy nuclear reactions, which the independent particle model without correlation fails to explain, are discussed and it is shown that the nucleon momentum distribution in nuclei is given correctly by our model.