Meson fields, exchange currents and progenitor sum rules

The theory of the integrated photoabsorption cross section and the dipole sum rule is reviewed. A new progenitor sum rule, in which meson fields appear explicitly, is derived from a field theory of interacting pions and nucleons. The relation of this sum rule to previous results obtained in a potential theory is elucidated, and the role of neutron-proton correlations in nuclear ground states is discussed in terms of their effect on the dipole sum rule. The inclusion of ρ-mesons (again in an oversimplified theory) and their contribution to progenitor sum rules is also mentioned.     

Electric polarizability of nuclei from a longitudinal sum rule

The nuclear electric polarizability is theoretically analyzed using a sum rule derived from the longitudinal part of the forward Compton amplitude. Beyond the leading dipole contribution, this approach leads to the presence of potential-dependent terms that do not show up in previous analyses. The significance of these new contributions is illustrated by performing an explicit calculation for a proton-neutron system interacting via a separable potential.     

Analog giant dipole excitation in Si(n,p) at 59.6 MeV

The parent analog of the giant dipole resonance in ²⁸Si is studied by means of the (n, p) reaction. The continuum contribution to the giant dipole region was estimated by a phenomenological parameterization. The observed cross section exhausts 31% of the SJ sum rule; 88% of the GT sum rule or 67% of the Myers-Swiatecki prediction. A comparison is made to the giant resonance region observed in the ²⁸Si(p, p') reaction which was recently used, via comparison to ²⁸Si(α, α'), to infer that the GDR in ²⁸Si is not excited or at least not seen in (p, p').     

Electric and magnetic response to the continuum for A = 7 isobars in a dicluster model

The mirror isobars ⁷Li and ⁷Be are investigated in a dicluster model. The magnetic dipole moments and the magnetic dipole response to the continuum are calculated in this framework. The magnetic contribution is found to be small with respect to electric dipole and quadrupole excitations even at astrophysical energies, at a variance with the case of the deuteron. Energy-weighted molecular sum rules are evaluated and a formula for the molecular magnetic dipole sum rule is found which matches the numerical calculations. Cross-sections for photo-dissociation and radiative capture as well as the S -factor for reactions of astrophysical significance are calculated with good agreement with known experimental data.     

Isovector magnetic dipole sum rules in (d s)- shell

Linear-energy weighted sum-rules (LEWSR) are calculated for isovector magnetic dipole transitions from the ground state in some (d s)-shell nuclei. It is found that the well-known Kurath sum rule is inadequate to explain the experimental transition strengths in these nuclei. A significant contribution to the sum-rule is seen to arise from the two-body part of the Hamiltonian. The calculations are made using the spectral distribution methods.     

Isoscalar dipole resonances

The question of electromagnetic isoscalar dipole transitions is briefly reviewed. An energy weighted sum rule (corrected for c.m. effects) is applied and used with a doorway dominance approximation to predict inelastic form factors. Questions concerning the nature of the excited state are seen to be answerable with the sum rule.     

Photo-absorption sum rules σ<Subscript>–1</Subscript> in different environments (Atoms,nuclei, nucleons)

Combining the spin-dependent dispersion GDH-sum rule, the isotopic-spin-dependent Cabibbo-Radicati sum rule, and the relativistic dipole-moment-fluctuation (i.e. generalized Gottfried) sum rule with the three valence quark configuration of nucleons taken into account for the composition of the ground and the excited states of the nucleon, the relevant moments of the distribution and correlation functions of the quark electric dipole moment operators in the nucleon ground state are expressed via the experimentally measurable nucleon resonance photo-excitation amplitudes.These functions are of interest for checking detailed quark-configuration structure of the nucleon state vector. Within the non-relativistic approach to photo-absorption sum rules for the 3N-nuclei a new σ_–1 sum rule proposed which is based on general charge-symmetry (CS) consequences for the “CS-conjugated” triton and ³He.     

Comment on the analysis of angle-dependent X-ray magnetic circular dichroism in systems with reduced dimensionality

The magnetic dipole term T appearing in the X-ray magnetic circular dichroism (XMCD) spin sum rule can be eliminated from the analysis within the spin sum rule by angle-dependent XMCD spectroscopy if the effects of spin–orbit coupling are small so that T_x+T_y+T_z≈0. It is shown by the ab initio electron theory for the extreme case of a low-dimensional system, i.e., for a free-standing monatomic Co wire that this relation is strongly violated, indicating that the determination of T by the angle-dependent XMCD is possibly not very reliable for low-dimensional magnetic systems.     

RPA correlation effects in radiative pion capture

A sum rule approach to radiative pion capture is given in terms of the energy-weighted and inverse-energy weighted sum rules. They are evaluated with RPA accuracy for Skyrme-like interactions. The static polarizabilities of the dipole, quadrupole and octupole isovector modes turn out to be the relevant quantities to determine the total branching ratios and mean photon energies.     

Self-consistent mean-field theory,progenitor sum rules,and the giant dipole resonance

Self-consistent mean-field theory gives an expression for the giant dipole resonance energy which depends on κ (the enhancement of the dipole sum rule by exchange currents). The value of κ needed to fit the GDR is much smaller than that obtained from the integrated photoabsorption cross section, in Suzuki's treatment. A corrected treatment which resolves this discrepancy is given here.     

Conservation issue of pairwise quantum discord and entanglement of two coupled qubits in a two-mode vacuum cavity

The conservation issues of pairwise quantum discord and entanglement of two qubits coupled to a two-mode vacuum cavity are investigated by considering the dipole-dipole interaction between two qubits.It is found that the sum of the square of the pairwise quantum discords and the sum of the square of the pairwise concurrences are both conserved in the strong dipole-dipole interaction limit.However,in the middle dipole-dipole and weak dipole-dipole interaction limits,the sum of the square of the pairwise concurrences is still conserved while the sum of the square of the pairwise discords is not.The crucial reason for this is that the quantum discords are not equivalent if the measurements are performed on different subsystems in a general situation.So it is very important for quantum computation depending on the quantum discord to select the target performed by the measurements.     

Broad sub-continuum resonances and the case for finite-energy sum-rules

There is a need to go beyond the narrow resonance approximation for QCD sum-rule channels which are likely to exhibit sensitivity to broad resonance structures. We discuss how the first two Laplace sum rules are altered when one goes beyond the narrow resonance approximation to include possible subcontinuum resonances with nonzero widths. We show that the corresponding first two finite energy sum rules are insensitive to the widths of such resonances, provided their peaks are symmetric and entirely below the continuum threshold. We also discuss the reduced sensitivity of the first two finite energy sum rules to higher dimensional condensates, and show these sum rules to be insensitive to dimension condensates containing at least one pair. We extract the direct single-instanton contribution to the sum rule for the longitudinal component of the axial-vector correlation function from the known single-instanton contribution to the lowest Laplace sum rule for the pseudoscalar channel. Finally, we demonstrate how inclusion of this instanton contribution to the finite-energy sum rule leads to both a lighter quark mass and to more phenomenologically reasonable higher-mass-resonance contributions within the pseudoscalar channel. Received: 15 September 1997 / Revised version: 15 November 1997 / Published online: 26 February 1998     

A numerical study of resonance contributions to nuclear sum rules

The modified form of the nuclear sum rule which was proposed by Berggren is applied to a simple solvable problem and it is demonstrated, within the confines of that problem, that the continuum contribution to the sum rule is often dominated by the contribution from a few resonances, just as Berggren had anticipated. It is further shown that the bound, virtual and resonant states of the Hamiltonian considered form a complete set of states in terms of which the internal region of space can be expanded.     

Description of the 2νββ decay within a fully renormalised RPA approach

The RPA treatment of a many body Hamiltonian describing the states of even-even nuclei involved in a 2νββ decay is revisited. One shows that renormalizing the dipole two quasiparticle operators by accounting for new correlations in the ground state requires a simillar renormalization for the dipole density operators which results in activating new boson degress of freedom. Possible consequences on Ikeda sum rule and Gamow-Teller transition amplitude are suggested. A numerical application for a two levels model is presented     

Evidence for pygmy and giant dipole resonances in 130Sn and 132Sn

The dipole strength distribution above the one-neutron separation energy was measured in the unstable 130Sn and the double-magic 132Sn isotopes. The results were deduced from Coulomb dissociation of secondary Sn beams with energies around 500 MeV/nucleon, produced by in-flight fission of a primary 238U beam. In addition to the giant dipole resonance, a resonancelike structure ("pygmy resonance") is observed at a lower excitation energy around 10 MeV exhausting a few percent of the isovector E1 energy-weighted sum rule. The results are discussed in the context of a predicted new dipole mode of excess neutrons oscillating out of phase with the core nucleons.     

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.     

Sum rule for bremsstrahlung cross section for 6Li in the resonating-group method

In the method of resonating-group structure, the wave function of ⁶Li is assumed to have a single channel of alpha and deuteron substructures in the ground state. It is shown that the intercluster exchange of nucleons is an important effect which causes significant change in the root mean square radius and the dipole transition cross section. Due to the lack of symmetry in space coordinates of ⁶Li, the dipole operator is not identical to the mean square radius operator for this sum rule calculation and is expected to display like behavior in similar systems. It is also shown that the deuteron substructure in this nucleus is substantially larger than the alpha substructure.     

Retardation of E1 transitions and the neutron effective charge in 29Si

The effect of the giant dipole resonance on E1 transition rates is investigated, and an expression is derived which allows E1 effective charges to be calculated using the γ-absorption cross section of the neighbouring even-mass core. It is shown how this expression can be approximated using a sum rule in cases where the absorption cross section is not adequately known. Application is made to ²⁹Si; using wave functions from a particle-core model, calculated E1 transition rates are in excellent agreement with experiment.     

The Bertlmann–Martin Inequality and Spin Degrees of Freedom

The Bertlmann–Martin inequality based on the dipole sum rule is revisited taking into account the spin degrees of freedom. We consider 1 and 2 particles of spin 1/2 in a mean field, adding a spin dependent interaction. The derivation of the inequality relies on the closure relation. We discuss the effect of the Pauli principle, and the restrictions it imposes on the use of the closure relation. The problem is exemplified by a simple model based on harmonic forces. Moreover, in the 2 particle case, the model we use is separable in the relative and centre of mass coordinates. In this case, we show that for operators connecting only singlet states, their sum rule can be calculated in the usual way, i.e. via the double commutator of this operator with the Hamiltonian. An upper bound can also be obtained by using the Bertlmann–Martin technique. This is not possible for operators involving a transition between singlet and triplet states.     

Effect of the nuclear magnetic susceptibility on the evaluation of the electric dipole polarizability

The σ_?2 photonuclear sum rule together with recently determined magnetic susceptibilities is used to evaluate the corrections to the static electric dipole polarizability of nuclei. Those corrections are sizeable in the realm of very light nuclei.