Nucleon Momentum Distribution Research Articles

Y-scaling analysis of quasielastic electron scattering and nucleon momentum distributions in few-body systems, complex nuclei, and nuclear matter.

The approach to y scaling previously adopted to obtain the nucleon momentum distribution in the two- and three-nucleon systems is extended to the case of complex nuclei and nuclear matter. The basic elements of this approach, which takes properly into account nucleon binding and momentum, are reviewed. A new method of analysis, which allows one to obtain the experimental asymptotic scaling function from inclusive cross sections even if these data are affected by final-state interactions, is proposed and illustrated. By such a method, the asymptotic scaling functions of $^{3}\mathrm{He}$, $^{4}\mathrm{He}$, $^{12}\mathrm{C}$, $^{56}\mathrm{Fe}$, and nuclear matter are obtained from recent experimental data and it is demonstrated that, particularly at high negative values of the scaling variable, the available data points at the highest value of the momentum transfer are affected by final-state interaction and cannot therefore be considered to represent the asymptotic scaling function. It is shown that, unlike what is commonly stated, the nucleon momentum distribution is not simply defined in terms of the derivative of the asymptotic scaling function, but as a sum of such a derivative plus the derivative of a quantity, the binding correction, generated by the removal energy distribution of nucleons embedded in the nuclear medium.The binding correction and its derivative are evaluated with various types of spectral functions, and the nucleon momentum distributions in $^{3}\mathrm{He}$, $^{4}\mathrm{He}$, $^{12}\mathrm{C}$, $^{56}\mathrm{Fe}$, and nuclear matter are obtained up to nucleon momenta k\ensuremath{\approxeq}500 MeV/c. For few-body systems the obtained momentum distributions satisfactorily agree with the ones extracted from (e,e'p) reactions and with theoretical calculations performed within Faddeev or variational approaches, whereas for complex nuclei they qualitatively agree with predictions of theoretical many-body approaches which take nucleon-nucleon correlations into account and, at the same time, at k\ensuremath{\ge}350 MeV/c they are larger by orders of magnitude than the ones predicted by mean field approaches. Such a result does represent unambiguous evidence of correlation effects in nuclei.

Momentum distribution in heavy nuclei

The nucleon momentum distribution is studied with particular emphasis on heavy nuclei. The effects of both the mean-field and short-range correlations are discussed. The latter are included using a method based on the local density approximation. A systematic comparison with the predictions of other theoretical approaches is presented.

Nucleon momentum distribution in colliding nuclei and potential between excited nuclei studied with the Vlasov equation.

The momentum distribution of nucleons in colliding $^{16}\mathrm{O}$${+}^{16}$O system is studied with the Vlasov equation in the incident energy region of 20--100 MeV/nucleon. A shift of the momentum distribution to higher momenta is observed until the time of full overlap of two nuclei. It is attributed to the acceleration of the colliding nuclei, and discussed in terms of the newly defined potentials acting between two excited nuclei. The acceleration of colliding excited nuclei is even larger than that in the elastic channel at 40--100 MeV/nucleon. This is due to the dynamical change of the density distribution avoiding high density.

Description of the nuclear stopping process within anisotropic thermo-hydrodynamics

Abstract A generalized hydrodynamics is presented, which takes into account the anisotropy of the nucleon momentum distribution. The dynamics of the nuclear stopping process is studied in this framework.

Asymptotic scaling function and nucleon momentum distribution in few nucleon systems

The nucleon momentum distributions in 3He and 4He are extracted from the inclusive (e,e') cross sections analyzed in terms of y-scaling. The method is based upon a model independent extrapolation to q → ∞ of the experimental scaling function and upon a careful consideration of binding effects. The obtained momentum distributions are in good agreement with the ones extracted from exclusive (e,e'p) cross sections.

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.

Occupation probabilities and hole-state strengths in nuclear matter.

The interpretation of the nucleon spectral function P(k,E) in terms of two parts, associated with one- and many-particle emission processes, is discussed in connection with the analytical structure of the nucleon momentum distribution n(k). The integrals over E of the one-particle emission part of P(k,E) yield the one-hole strengths. The estimated strengths in the lead region agree fairly well with recent (e,e'p) data.

Natural orbitals and occupation numbers in the coherent density fluctuation model

The natural orbitals and occupation numbers are evaluated in the framework of the coherent, density fluctuation model (CDFM) by diagonalizing of the one-body density matrix given by the model. They are consistent with the experimental data concerning both the nucleon momentum and density distribution. The short-rangeNN correlations included in the CDFM affect not only the occupation numbers but also the natural orbitals. The results are compared with the wave functions of the single-particle potential model and with available experimental data for the occupation numbers.

The nuclear spectral function and the mass dependence of the EMC effect

We examine the properties of the nuclear spectral function and point out that the mass dependence of the EMC effect can be reproduced within the conventional nuclear theory by using the appropriate experimental data for the momentum and energy distribution of nucleons in nuclei.

A single-particle model momentum distribution for 4He

The nucleon momentum distribution for 4He is obtained analytically by means of a single particle (SP) potential which contains both an attractive and a repulsive part. It is shown that the values of the momentum distribution eta sp(k) derived in this way deviate considerably at large values of the momentum k from those predicted by the harmonic oscillator model and behave like a negative power of k, becoming closer to the values obtained with many-body techniques.

Y-scaling analysis of inclusive electron scattering and the nucleon momentum distribution in few-body systems and complex nuclei

The basic assumptions underlying the y-scaling analysis of inclusive electron scattering by nuclei are summarized, and the nucleon momentum distribution in 2H, 3He, 4He and 12C obtained from available experimental data are presented and compared with the results of (e,e′p) reactions.

Collisional width of giant resonances and interplay with Landau damping.

We present a semiclassical method to calculate the widths of giant resonances. We solve a mean-field kinetic equation (Vlasov equation) with collision terms treated within the relaxation time approximation to construct a damped strength distribution for collective motions. The relaxation time is evaluated from the time evolution of distortions in the nucleon momentum distribution using a test-particle approach. The importance of an energy dependent nucleon-nucleon cross section is stressed. Results are shown for isoscalar giant quadrupole and octupole motions. A quite important interplay between self-consistent (Landau) and collisional damping is revealed.

Nucleons in nuclei (I)

A summary and a critical discussion of the working session Nucleons in Nuclei are presented focussing the attention on present and future investigations of the free nucleon form factor, the medium modifications of nucleon properties and the extraction of nucleon momentum distributions from exclusive and inclusive (y-scaling) scattering.

Electron-inclusive threshold electroproduction calculations and subthreshold kaon electroproduction from nuclei.

A technique for calculating electron-inclusive threshold electroproduction cross sections on the nucleon in the case of positive kaons is detailed. The study is extended to the analogous calculation of subthreshold kaon electroproduction on nuclei using several models of the nucleon momentum distribution. In anticipation of the forthcoming analysis of an experiment, results for positive kaon electroproduction on Cu for incident electrons of 700 MeV are given for both Gaussian and modified Chew-Goldberger momentum distributions.

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.

Dynamical deformations in nucleon momentum distributions of colliding ions

We analyze the effects of nucleon momentum distributions of colliding ions arising from excitation of collective vibrational motions. Phonon states are described in RPA and are excited through the action of the mean field of the partner nucleus. The 40Ca + 40Ca system is considered at E A =10 and 44 MeV, around a grazing trajectory. With increasing energy we have clear transition in the dominant collective states, from low-lying modes to the giant quadrupole resonance. Correspondingly we have a noticeable enhancement of dynamical distortions in momentum space, particularly around the Fermi momentum. The importance of nonlinear terms, describing the coupling of different phonon states, is stressed. Some clear effect on energetic particle production is expected.

How useful is the concept of y scaling?

We analyze the deep inelastic electron-deuteron inclusive data in the y⩽0 (Bjorken x⩾1) region to examine how reliably one can extract the nucleon momentum distribution from the data. The Q 2 dependence of the scaling function reveals a non-trivial behaviour in the measured range of Q 2. In particular, we do not observe an approach to scaling in the variable y.

Yscaling, binding effects, and the nucleon momentum distribution inHe3

The method, previously used to obtain the nucleon momentum distribution in $^{2}\mathrm{H}$ from the y-scaling analysis of inclusive electron scattering data, is extended to $^{3}\mathrm{He}$. It is shown that the binding correction which has to be handled in this case does not hinder the extraction of the momentum distribution from the scaling function. The obtained momentum distribution satisfactorily agrees with the one extracted from exclusive (e,e'p) reactions.

Nuclear stopping at intermediate beam energies.

We perform an analysis of exclusive heavy-ion reactions around 100 MeV/nucleon in terms of multipole moments of the momentum distribution of nucleons. Numerical calculations based on the Boltzmann-Uehling-Uhlenbeck theory are presented and compared to an approximate scaling function. We find that nuclei completely stop each other even at 100 MeV/nucleon, if ${A}_{P}+{A}_{T}g200$ in symmetrical central collisions. We propose that the mass dependence of the quadrupole momentum tensor can be used to determine the nuclear compressibility.

Generator coordinate calculations of nucleon momentum and density distributions in4He,16O and40Ca

An approach within the generator coordinate method with square-well construction potential and Skyrme-like forces, recently proposed and applied to calculate the nucleon momentum and density distributions as well as energies and r.m.s. radii of the ground and first monopole excited states of4He and16O, is extended to the case of40Ca. The nucleon momentum and the density distributions have a correct behaviour which is related to the account of both monople vibrations and short-range\({\mathcal{N}} - {\mathcal{N}}\) correlations. The results are compared with the predictions of other theoretical correlation methods and with experimental data for the nucleon momentum distribution of4He up to momenta ≈3 fm−1 now available.