Inelastic sum rule for high-energy hadron scattering and nucleon-nucleon correlations

We have considered the influence of short-range dynamical and statistical correlations on the elastic and summed inelastic scattering of high-energy hadrons from light nuclei. Our calculations are based on the complete multiple scattering series of Glauber. The correlation effects are discussed on the example of the inelastic sum rule for p-¹⁶O scattering.     

Short-range correlations with pseudopotentials. IV

Using a unitary model operator, the short-range correlations between nucleons in nuclei have been considered. To achieve healing in the wave functions, short-range pseudopotentials are required to be added to the nucleon-nucleon potential. With the introduction of the pseudopotentials, the matrix element for the effective interaction in nuclei is developed with correlated basis wave functions. The tensor forces and the short-range pseudopotentials are renormalized in second-order perturbation theory. Hartree-Fock calculations are carried out for the two finite closed-shell spherical nuclei¹⁶O and⁴⁰Ca. The calculations of the resulting effective Hamiltonian are carried out with an effective interaction derived from the Tabakin potential. The present calculations of the binding energies per particle for the¹⁶O and⁴⁰Ca nuclei are in agreement with the experimental measurements.     

Energy-weighted M1 sum rule with explicit δ degrees of freedom

The influence of Δ degrees of freedom on the energy-weighted M1 sum rule is investigated and applied to ²H and ⁴He. Using π- and ρ-exchange potentials a reduction of the potential contribution of the order of 50% is obtained. The absolute value of the sum rule is strongly dependent on the short-range behaviour of the nuclear wave function. Furthermore, the contribution of c.m. effects is evaluated and found to be of the order of 5–10%.     

The problem of determining short-range order parameters in interpreting a M?ssbauer spectrum

We develop a procedure to interpret the model M?ssbauer spectra (MS) of resonant nuclei in a two-component crystal with short-range order. The procedure is describable not only by pair correlations but also by multiparticle correlations of the atomic distribution. The results of the interpretation are used to find M?ssbauer parameters for subspectra and for certain correlation moments that describe the short-range order. The developed approach was used to interpret the actual spectra of ⁵⁷Fe in iron-chromium alloys.     

On the investigation of nucleon-nucleon correlations by means of high-energy scattering

The possible effects of short-range dynamical nucleon-nucleon correlations on high-energy hadron scattering on ⁴He are examined. The Glauber theory of multiple scattering is used as the basis for the computations. The conclusion is that very small effects are to be expected for elastic and sum total inelastic scattering of commonly available projectiles.     

Multiple diffractive analysis of elastic and inelastic scattering by 1 GeV protons on 12C, 58Ni,and 208Pb

Recent elastic and inelastic scattering experiments of 1 GeV protons on ¹²C, ⁵⁸Ni, and ²⁰⁸Pb have been analyzed using multiple diffractive scattering theory.Elastic angular distributions have been calculated, including pair correlations in many-particle densities. There is evidence from the Ni and Pb data for the presence of correlations, but some evaluated correlation corrections do not produce detailed agreement.It is shown that the Glauber series for coherent inelastic scattering can be approximately summed to yield an eikonal form of the DWIA. In particular the smaller angle parts of the inelastic distributions are well described in this approximation.The expression for the summed incoherent inelastic cross section is considered as a sum rule. It is found that for ¹²C the excitation of the three lowest excited states exhaust ? 25 % of the sum rule up to ?t ? 1 fm^?2. For larger t quasi-elastic knock-out largely exhausts the sum rule.     

Structure of unstable nuclei near proton drip line

Gamov-Teller (GT) states in nuclei near the proton drip line are studied by using a microscopic Hartree-Fock (H-F) + Tamm-Dancoff approximation (TDA) (or random phase approximation (RPA)). The calculations predict that giant Gamow-Teller (GT) β-decays are possible for N=Z nuclei heavier than ₂₈⁵⁶Ni₂₈, carrying most of the sum rule strength. The amplitude of isospin T=1 admixed to the T=0 ground state in N=Z nuclei is also discussed in relation with Fermi β-decay sum rule. Finally, the shapes of unstable nuclei near the proton drip line are studied by using the finite-range droplet model (FRDM).     

Pole and quark-counting model for form factors of light nuclei

The dispersion relation approach is applied to form factors of light nuclei. The form factor is approximated by a sum of poles. The asymptotic behaviour of form factor is assumed to be determined by quark-counting rule. Examples of³He,⁴He and⁶Li are considered. Data on form factors of these nuclei have been fitted with smaller number of parameters than usual, and corresponding charge distributions have been found which differ from conventional ones in central regions of nuclei.     

11Li,14Be和17B核的软偶极共振模式

假定¹¹Li,¹⁴Be和¹⁷B核是由核芯和两个外层中子所组成,用Sum Rule探讨这类核的巨偶极共振,给出软偶极共振的能量和强度。结果与其它理论计算进行了比较。 关键词：     

Do we understand the electric quadrupole strength distributions in magic nuclei?

A comparison between the electric quadrupole (E2) strength distributions in ^{40, 48}Ca with new results from ⁵²Cr is presented. The deduced E2 strength distributions and the exhaustion of the isoscalar energy-weighted E2 sum rule are very different. Microscopic approaches fail to reproduce these differences. A survey of the available data shows that the exhaustion of the energy-weighted isoscalar E2 sum rule in doubly magic nuclei below the isoscalar giant quadrupole resonance is typically more than two times larger than in semi-magic nuclei. On the other hand, the E2 strength in this energy region exhausts about 50% of the total E2 strength, independent from shell closures.     

Structure of light neutron-rich nuclei through coulomb dissociation

Coulomb breakup of neutron-rich nuclei around mass A ∼ 20 has been studied experimentally using secondary beams (∼ 500–600 MeV/u) of unstable nuclei produced at GSI. The spectroscopic factor deduced for the neutron occupying s _1/2 level in ¹⁵C ground state is consistent with the earlier reported value. The data analysis for Coulomb breakup of ¹⁷C shows that most of the cross section yields the ¹⁶C core in its excited state. For ^17–22O, the low-lying E1 strength amounts up to about 12% of the energy weighted dipole sum rule strength depending on neutron excess. The cluster sum rule limit with ¹⁶O as a core is almost exhausted for ^17,18O, while for more neutron rich isotopes the strength with respect to that limit decreases.     

Green’s function calculations of light nuclei

The influence of short-range correlations in nuclei was investigated with realistic nuclear force. The nucleon-nucleon interaction was renormalized with V_lowk technique and applied to the Green’s function calculations. The Dyson equation was reformulated with algebraic diagrammatic constructions. We also analyzed the binding energy of ⁴He, calculated with chiral potential and CD-Bonn potential. The properties of Green’s function with realistic nuclear forces are also discussed.     

Electroinduced two-nucleon knockout and correlations in nuclei

A model to calculate cross sections for electroinduced two-nucleon emission from finite nuclei is presented. Short-range correlations in the wave functions and meson-exchange contributions to the photoabsorption process are implemented. Effects of the short-range correlations are studied with the aid of a perturbation expansion method with various choices of the Jastrow correlation function. The model is used to investigate the relative importance of the different reaction mechanisms contributing to the A(e,e′pn) and A(e,e′pp) process. Representative examples for the target nuclei ¹²C and ¹⁶O and for kinematical conditions accessible with contemporary high-duty cycle electron accelerators are presented. A procedure is outlined to calculate the two-nucleon knockout contribution to the semi-exclusive (e,e′p) cross section. Using this technique we investigate to what extent far semi-exclusive (e,e′p) reactions can be used to detect high-momentum components in the nuclear spectral function.     

Electric-dipole sum rule in nuclear matter

The enhancement factor K in the electric-dipole sum rule for some realistic models of symmetrical nuclear matter is calculated using variational theory. The nuclear-matter wave function used contains central, spin, isospin, tensor and spin-orbit pair correlations. The non-central correlations, particularly the tensor one, give the major contribution to K. At experimental equilibrium density K. turns out to be ≈ 1.8, of which 65% comes from OPEP and 30% from the short-range part of the interaction. The two-pion-exchange three-nucleon interaction contributes ≈ 0.2% and is cancelled, to a large extent, by the contribution due to the intermediate-range two-body potential. The relationship of the summed oscillator strength with the effective mass is also discussed.     

Cumulative production of nucleons and extremely light nuclei in 4Hep interactions at an incident momentum of 5 GeV/c

The invariant cross sections for the cumulative production of protons, neutrons, and extremely light nuclei (d, ³H, and ³He) are determined on the basis of experimental data obtained by exposing the 2-m liquid-hydrogen bubble chamber of the Institute of Theoretical and Experimental Physics (ITEP, Moscow) to a 5-GeV/c α-particle beam, the kinetic energy of primary protons in the rest frame of the nucleus involved being T _p = 620 MeV. The results obtained in this way are compared with the predictions of the Frankfurt-Strikman model, which takes into account short-range few-nucleon correlations, and with the predictions of the nuclear coalescence model.     

Isobar configurations in closed shell nuclei

Explicit expressions for one- and two-N¹ isobar configurations in closed shell nuclei have been derived in the impulse approximation and applied to ⁴He and ¹⁶O. Conventional transition potentials with π- and ?-exchange have been used and the influence of potential regularization and short-range correlations have been studied. The dominant isobar configurations are found to be the one- and two-Δ components and originate from two-nucleon pairs in a relative S-state. The probability for finding a nucleon as a Δ-isobar is about 4.5% in ⁴He and about 3.2% in ¹⁶O. These numbers should be considered as upper limits due to uncertainties in off-shell effects of the transition potentials.     

Brink model with tetrahedral alpha-particle clusters for three-particle forces

Three-particle interaction is introduced in the Brink model modification that takes into account an arbitrary localization of nucleons within alpha-particle clusters. Simultaneously, the class of single-particle variational functions is substantially extended by replacing the traditionally employed Gaussian function by the sum of Gaussian functions. In the case of the Bonche-Koonin-Negele (BKN) interaction, three Gaussian functions provide a good upper bound on the results of solving the Hartree-Fock equation for the ⁴He nucleus. It is shown that the BKN three-particle interaction simulates to some extent the effect of short-range correlations in the multiparticle wave function.     

New Data on Photoneutron Reaction Cross Sections for 76,78,80,82Se Nuclei

The problem of reliability of the cross section data obtained for partial photoneutron reactions on ^76,78,80,82Se nuclei in beams of quasimonoenergetic annihilation photons by means of neutron multiplicity sorting is discussed by employing objective physical criteria. It is shown that, because of substantial systematic uncertainties, experimental data on the (γ, 1n) and (γ, 2n) cross sections are unreliable. New data satisfying the reliability criteria are obtained for the partial photoneutron reaction cross sections for ^76,78,82Se nuclei by an experimental—theoretical method for evaluating such cross sections and are compared with experimental data and with data evaluated earlier for the isotope ⁸⁰Se. The evaluated integrated cross sections for the total photoneutron reactions on ^76,78,80,82Se nuclei are compared with the predictions of the Thomas-Reiche-Kuhn classical dipole sum rule.

     

Euclidian response of light nuclei

We discuss the longitudinal and transverse quasi-elastic cross-sections for ³He and ⁴He in terms of the Euclidian response, which can be directly calculated from the ground-state wave function. We find that the main open problem in quasi-elastic scattering, the excess of transverse strength, can be understood as a consequence of meson exchange currents, once the n-p short-range and tensor correlations in both initial and final state are included.Received: 1 November 2002, Published online: 15 July 2003PACS: 21.10.-k Properties of nuclei; nuclear energy levels - 25.30.-c Lepton-induced reactions