Continuum RPA correlations in quasielastic electron scattering from 12C decay on (e,e'p) and (e,e'n) reaction channels

We investigate the rôle of RPA correlations in longitudinal and transverse response functions for inelastic electron scattering from ¹²C at momentum transfers ranging between 200 MeV/c and 550 MeV/c. We refer to a continuum self-consistent RPA theory with a SK3 interaction. Electromagnetic operators are taken for uncorrelated nucléons. The partial response on (e, e'p) and (e, e'n) reaction channels is also calculated. Since energy-weighted sum rules are conserved, we can control the effect of the Hartree-Fock non-locality expressed by the SK3 nucleon effective mass as well as the action of creation and descruction of 1p 1h pairs on the true ground state induced by the RPA residual interaction.     

Vacuum insertion and nonperturbative effects for exclusive nonleptonic decays of charmed mesons and kaons

We re-examine QCD sum rules forS-wave charmonium. Dimension 6, 8 contributions for both³ S ₁,¹ S ₀ waves are taken into account using the factorisation model and found to be reasonably small. A good fit to the data requires the confinement parameterφto be much bigger than the generally accepted value.     

Analysis of the QCD sum rules for the heavy quarkonium

We study phenomenologically the QCD sum rules given by Shifman et al. for the heavy quarkonium. In the charmonium sum rules, we find that the contribution of the physical continuum to the moment ?_n is consistent with that of the effective one. As for the bottonium, the sum rules corrected by the Coulomb-like interaction are saturated very well by the four resonances observed at CESR. It is predicted that the³S₁ ground state of the toponium must exist in the range of \(M_{t\bar t} \) =30–44GeV, if the sum rules for the top quark are assumed.     

RPA calculations with Gaussian expansion method

The Gaussian expansion method (GEM) is applied to calculations of the nuclear excitations in the random-phase approximation (RPA). We adopt the mass-independent basis-set that is successful in the mean-field calculations. The RPA results obtained by the GEM are compared with those obtained by several other available methods in Ca isotopes, by using a density-dependent contact interaction along with the Woods–Saxon single-particle states. It is confirmed that energies, transition strengths and widths of their distribution are described by the GEM with good precision, for the 1⁻, 2⁺ and 3⁻ collective states. The GEM is then applied to the self-consistent RPA calculations with the finite-range Gogny D1S interaction. The spurious center-of-mass motion is well separated from the physical states in the E1 response, and the energy-weighted sum rules for the isoscalar transitions are fulfilled reasonably well. Properties of low-energy transitions in ⁶⁰Ca are investigated in some detail.     

Isotopic sum rules and compliance scheme

It is known that compliance scheme does not provide simple linear isotopic sum rules in λ^?1 similar to the ones in λ in the force constant scheme. The advantage of not having such sum rules in the compliance scheme is discussed in relation to the uniqueness problem of the molecular force field.Incidentally, for the molecules H₂O, D₂O, and HDO, two quadratic relations in terms of the inverse frequency parameters λ^?1 are obtained. These supplement the three obvious product rule relations.     

Collective excitations in neutron-rich nuclei within the model of a Fermi liquid drop

We discuss a new mechanism of splitting of giant multipole resonances (GMR) in spherical neutron-rich nuclei. This mechanism is associated with the basic properties of an asymmetric drop of nuclear Fermi liquid. In addition to well-known isospin shell-model predictions, our approach can be used to describe the GMR splitting phenomenon in the wide nuclear-mass region A ～ 40–240. For the dipole isovector modes, the splitting energy, the relative strength of resonance peaks, and the contribution to the energy-weighted sum rules are in agreement with experimental data for the integrated cross sections for photonuclear (γ, n) and (γ, p) reactions.     

Sum rules for the decays of the c-even charmonium states

Sum rules for the decays of the C-even charmonium levels (¹S₀, ³P₀, ³P₂, ¹D₂) are derived. These rules are based on the asymptotic freedom of the quantum chromodynamics at small distances and on the analyticity. They refer to the various vacuum amplitudes involving products of charmed quark currents: electromagnetic current as well as currents with quantum numbers J^PC=0^?+,0⁺⁺,2⁺⁺,2^?+. The contribution of the continuum to some of the sum rules is small, and they are saturated by the contribution of the lowest charmonium levels. In this way we predict the widths of the two-photon decays of the charmonium states and estimate their total hadronic widths.     

Effects of c.m. motion in nuclear electron scattering

We study the effect of nuclear c.m. recoil on the Coulomb dynamic structure factor and on its energy-weighted moments (sum rules). For the oscillator shell model it is possible to express the structure factor as a folding of an intrinsic structure factor with a c.m. response function. By exploiting this result we give a simple method for separating spurious from intrinsic excitation for all transitions. The resulting correction can be large even for heavy nuclei. In particular for the first energy-weighted sum rule the c.m. correction is of the same order as the exchange contribution. We explicitly evaluate the exchange effects for a few phenomenological interactions.     

What QCD sum rules tell about the rho meson — A new answer to an old question

First, a historical overview is presented concerning the use of QCD sum rules to learn about the p-meson properties at finite nuclear densities. Second, it is shown that the combination of the sum rule technique with the large-N _c expansion provides new insight. Especially it is possible to determine from the in-medium sum rules a vacuum(!) quantity which is an important ingredient for hadronic in-medium calculations of the p-meson spectral function. This quantity is the coupling strength of the p-nucleon system to the baryonic resonance N^*(1520).     

Strength distributions and statistical spectroscopy II. Shell-model comparisons

The theory of the preceding paper is applied to a number of M1, E2, and E4 electro-magnetic excitations in the (ds)⁶ space. Comparisons are made in detail with shell-model results for the pth energy-weighted sum rules, with p = 0, 1, 2 and starting states spanning the entire spectra, as well as with the exothermic-endothermic decomposition of the non-energy weighted sum rule, and the RMS fluctuations in, and correlations between, the sum-rule quantities. Further comparisons are made for the strength distributions themselves. In all cases the agreements are good, for the sum rules remarkably so, so that the statistical theory describes very well the essential features of the strength distribution. The only (partial) exception is with the usual low-lying quadrupole collectivity found microscopically for two of the starting states (for which most of the strength goes to a single final state) and predicted, though not in such detail, via a statistical calculation of the effective number of final states available for the quadrupole transitions. We are seeing here a real coexistence of collective and statistical phenomena. At higher excitations, where concentration of much of the strength into a single state is not to be expected, all the essential features should be statistically describable. As a result of the comparisons, we expect that the statistical theory, supplemented by further methods for the evaluation of the necessary input traces, should give an almost complete account of the essential features of the strength distributions, even in model spaces of arbitrarily large dimensionality.     

A sum rule description of giant resonances at finite temperature

A generalization of the sum rule approach to collective motion at finite temperature is presented. The m₁ and m_?1 sum rules for the isovector dipole and the isoscalar monopole electric modes have been evaluated with the modified SkM force for the ²⁰⁸Pb nucleus. The variation of the resulting giant resonance energies with temperature is discussed.     

Isotopic dependence of giant multipole resonances

A procedure is presented which allows the application of linear response theory and the random phase approximation to an open shell. The procedure is applied to Ca isotopes. The general features of giant multipole resonances are found to vary smoothly with the mass. The resonances exhibit more structure in the open 1f_{$\text{7}\text{2}$} shell nuclei. While the energy-weighted dipole sum is practically constant in all isotopes, the isoscalar quadrupole and octupole energy weighted sums increase continuously by ~ 30 % from ⁴⁰Ca to ⁴⁸Ca.     

Momentum and density dependence of the ph interaction in continuum RPA calculations with Skyrme forces

We analyse the momentum and density dependence of the ph interaction in self-consistent RPA calculations of electromagnetic reactions with Skyrme forces. First, we calculate the V⁰⁰_ph and V⁰¹_ph spin-isospin components in nuclear matter for an SK3 interaction. At the nuclear surface, they have decreasing values with increasing q-values up to momenta q=3 fm⁻¹. As a second point, we show that the predictions of the ¹²C(e, e') charge response at 400 MeV/c remain practically unchanged when the zero-range quadratic momentum dependence of the SK3 interaction is replaced by the momentum dependence associated with a Yukawa short-ranged force.     

Gamow-Teller strength with realistic nucleon-nucleon interactions

Two realistic nucleon-nucleon interactions are used to calculate the energy-weighted sum rules for the Gamow-Teller operators. There are no free parameters in our calculations. The two interactions give similar results for ⁴⁸Ca and ⁹⁰Zr.     

QCD sum rules for heavy quark systems

In this paper we present in a detailed and coherent fashion our work on QCD sum rules for equal mass heavy quark meson states. We discuss the technical procedures used to calculate the perturbative and non-perturbative contributions to the vacuum polarization, which have been calculated for all currents up to and including spin 2⁺⁺. Using dispersion relations, sum rules are derived. Extensive applications are made to the lowest lying states of the charmonium and upsilon systems. The masses of the S- and P-wave charmonium levels are reproduced to a high degree of accuracy, and the mass of the ¹P₁ level is predicted at 3.51 GeV. For the upsilon system it only appears to be possible to predict the γ-η_b splitting which gives 60 MeV. Very accurate values are given for the current quark masses at p² = ?m_q²: m_c = 1.28 GeV and m_b = 4.25 GeV.     

On the largeN c limit of theSU(N c ) colour quark-gluon partition function

Using Shifman-Vainshtein-Zakharov sum rules applied to three-point Green functions we obtain mass differences betweenSU _F (3) isomultiplets for the 1/2⁺ baryons. We also give some results for theg _A /g _V ratio.     

Electromagnetic response and breakup of light weakly bound nuclei in a dicluster model

The light weakly bound nucleus ⁷Li is studied within a dicluster α + t picture. Different observables obtained within our simple model are compared with previous calculations and experiments showing good agreement. In particular, we calculate dipole and quadrupole electromagnetic response to the continuum. The energy distribution of B(Eλ) values are consistent with the energy-weighted molecular sum rule and display a sizable contribution of non-resonant character arising from the weak binding property. The corresponding form factors for excitations to the continuum are used in a semiclassical coupled-channel scheme to get estimates for the breakup cross-section in a heavy-ion reaction. The nuclear contribution is found to play an important role in the process for bombarding energies around the Coulomb barrier. The masses and charges ratios of the two clusters are shown to lead to features of the cluster halo that may significantly differ from the one usually associated with one-nucleon haloes.     

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%.     

Chiral-limit theorems and corrections to PCAC in a model for the scalar Kℓ3 divergence form factor

Three sum rules on vertex functions are derived by applying a model on two-particle Kπ channels. SU(3) × SU(3) breaking is introduced by corrections to the PCAC forms of the axial currents. Taking the m_π → 0 limit the sum rules reduce to the Callan-Treiman theorem, a recent theorem by Dashen, Li, Pagels and Weinstein (DLPW) and a third relation. We encounter non-analytic correction terms in the two first sum rules. In the DLPW theorem we find, contrary to a previous suggestion, non-negligible ε and ε²ln ε terms which are due to the large K-mass. These terms are responsible for a curvature of the scalar K_?3 form factor, however negative values of the slope at the origin require also substantial SU(2) × SU(2) violations. The numerical results taking into account physical masses compare favourably with K_?3 decay and also with s-wave Kπ scattring data.