I. Zh. Petkov

Nucleon momentum and density distributions of nuclei

In the framework of recently suggested density coherent fluctuations model the nucleon momentum and density distributions are examined. Nucleon momentum and density distributions are expressed in terms of the fluctuations function, experimentally obtainable from the elastic electron-nuclei scattering.

Spectral functions and hole nuclear states

An explicit expression for the spectral function of hole nuclear states is given in the framework of the coherent fluctuation model. It is shown that the spectral function and single-particle width, centroid energy, quasiparticle effective mass, etc., are functionals of the ground-state nucleon density distribution. Calculation of the spectral functions for58Ni,40Ca,28Si is carried out and the results are compared with the experimental data.

Natural orbital calculations of nucleon momentum distributions

SummaryThe natural orbital representation in the single-particle potential method is applied to calculate the proton momentum distribution in40Ca. The dependence of the momentum and density distributions on different sets of occupation numbers is examined, and the results are compared with calculations using other theoretical models including nucleon-nucleon correlations.RiassuntoSi applica la rappresentazione orbitale naturale al metodo del potenziale a particella singola, per calcolare la distribuzione dell’impulso del protone in40Ca. Si esamina la dipendenza delle distribuzioni dell’impulso e della densità da diversi insiemi di numeri di occupazione e i risultati sono confrontati con i calcoli usando altri modelli teorici, comprese le correlazioni nucleone-nucleone.

Natural orbitals and occupation numbers in the coherent density fluctuation model

SummaryThe 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.RiassuntoSi valutano gli orbitali naturali e i numeri di occupazione nell’ambito del modello di fluttuazione di densità coerente (CDFM) diagnonalizzando la matrice di densità a un corpo data dal modello. Essi sono coerenti con i dati sperimentali sia riguardo, all’impulso dei nucleoni che alla distribuzione di densità. Le correlazioniN-N incluse nel CDFM influenzano non solo i numeri, di occupazione ma anche gli orbitali naturali. Si confrontano i risultati con le funzioni d’onda del modello del potenziale a particella singola e con i dati sperimentali disponibili per i numeri di occupazione.

General functional relation between nucleon momentum and density distributions in nuclei

SummaryIt is shown on the basis of the Hohenberg-Kohn theorem that the nucleon momentum distribution is an unique functional of the local density distribution. A theoretical scheme in which density and momentum distributions enter equivalently as fundamental variables of the theory is suggested. The form of the momentum distribution proposed in the coherent density fluctuation model as a functional of the local density and its relation with the suggested theoretical scheme are discussed.RiassuntoSi mostra sulla base del teorema di Hohenberg-Kohn che la distribuzione dei momenti nucleonici è un funzionale unico della distribuzione di densità locale. Si suggerisce uno schema teorico in cui le distribuzioni di densità e impulso entrano equivalentemente come variabili fondamentali della teoria. Si discute la forma della distribuzione degli impulsi proposta nel modello di fluttuazione coerente di densità come funzionale della densità locale e la sua relazione con lo schema teorico suggerito.РезюмеНа основе теоремы Ноенберга-Коона показано, что импульсное распределение нуклонов является единственным функционалом локального плотностного распределения. Предложена теоретическая схема, в которой импульсное и плотно-стное распределения входят в теорию еквивалентным образом в качестве фундаментальных переменных. Обсуждается предложенная в модели когерентных флуктуации плотности форма импульсного распределения как функционал локальной плотности и ее связь с предложенной теоретической схемой.

Generator coordinate method calculations of natural orbitals and single-particle occupation numbers in4He,16O and40Ca

SummarySingle-particle occupation numbers and natural orbitals in4He,16O and40Ca are calculated diagonalizing the one-body density matrix obtained in an approach within the generator coordinate method. Square-well and harmonic-oscillator construction potentials and Skyrme-like forces are used. The natural orbitals (single-particle wave functions) are presented in both coordinate and momentum spaces. Together with the nucleon momentum distributionn(k) they are compared with results of Hartree-Fock as well as of correlation methods and with available experimental data forn(k) in4He. The realistic high-momentum behaviour ofn(k) and of the natural orbitals in the case of square-well construction potential shows that the nucleon-nucleon correlations at small distances are taken into account. It is pointed out that the correlations strongly affect the natural orbitals but not the occupation numbers.

Zero-motion correlations in high-energy proton elastic scattering on40Ca with noneikonal nucleon-nucleon amplitude

Using a noneikonal expression for the two-body scattering amplitude, consistent with the proton-nucleon scattering data, the cross-section of the 1.04 GeV-proton elastic scattering on40Ca is calculated by the Glauber-Sitenko theoretical scheme in the framework of the coherent density fluctuation model (CDFM) as well as of the independent-particle model (IPM). It is shown that the use of the noneikonal amplitude in the CDFM calculation improves the agreement with the experimental data especially at larger scattering angles in contrast to the case of the independent-particle model. To that end a decisive role play the zero-motion flucton correlations taken into account in the CDFM.

Scaling- and antiscaling-type oscillations in isoscalar and isovector nuclear monopole vibrations

Abstract Isoscalar (T = 0) and isovector (T = 1) giant monopole resonances are studied using a localscale version of the ATDHF theory developed on the basis of a rigorous energy-density functional approach. Due to the strong coupling between the bulk and surface density vibrations, the monopole collective motion is split into four normal modes. Two of them, lower in energy, correspond to scaling-type density vibrations. The other two are of antiscaling-type in which the nuclear surface oscillates opposite in phase to the scaling-type vibrations. Excitation energies, transition densities, T = 0 and T = 1 energy weighted sum rules and other properties of breathing even-even nuclei are calculated using different Skyrme-type effective forces. The strong sensitivity of the antiscaling-type vibrations to the particular form of the approximate energy-density functionals is demonstrated.

Optimal monopole dynamics in nuclei

SummaryA generator coordinate method with variationally determined generating functions is used in order to investigate the optimal ground-state correlations and monopole collective excitations in nuclei4He,16O and40Ca with Skyrme-type effective interaction. Simulating collective deformations by generalized scaling ansatz, we look for the optimal collective paths in terms of velocity fields. It is found that nuclear characteristics as the binding energy and the ground-state root-mean-square (r.m.s.) radius are not very sensitive to the choice of the path. On the contrary, radial density oscillations, ground-state nucleon momentum distributions, monopole excitation energies and the corresponding energy-weighted sum rules are sensitive to this choice.

A study of short-range correlation effects on nuclear spatial and momentum distribution

The relation between the nuclear spatial and momentum densities is studied by means of their integral representations in terms of uniform distributions. Examples of this approach are given for the harmonic oscillator model of4He and16O, with and without Jastrow correlations, and for the single-particle potential model of40Ca.