Class Of Sum Rules Research Articles

Distribution ofE2strength inSi28below 50 MeV excitation energy

Inelastic electron scattering in $^{28}\mathrm{Si}$ between 4 and 50 MeV excitation energy reveals two concentrations of $E2$ strength in the continuum. One is between 15 and 20 MeV, with a peak at 17 MeV, and can be identified with the giant quadrupole resonance in the ground state oblate well. A broad distribution of $E2$ strength between 22 and 42 MeV is predominatly isovector in nature. In addition, a small but persistent $E2$ peak at 24 MeV was found, which may be interpreted as being the corresponding state in the prolate well to the 17 MeV resonance. It is shown that 50% or more of the photon cross section in excess of the classical dipole sum rule between 10 MeV and the pion threshold may be due to $E2$ absorption.NUCLEAR REACTIONS $^{28}\mathrm{Si}$($e$,${e}^{\ensuremath{'}}$), ${E}_{0}=92$ MeV. Measured $\frac{{d}^{2}\ensuremath{\sigma}}{d\ensuremath{\Omega}d{E}_{x}}$, bound and continuum states. Deduced multipolarity $\ensuremath{\lambda}$, reduced matrix element $B(E\ensuremath{\lambda})$, sum rule exhaustion.

The TRK-sum rule in 4He including isobar effects

The TRK-sum rule has been reevaluated for 4He and an enhancement of about 90 per cent has been found confirming the earlier evaluation of Weng et al. It is not so sensitively dependent on details of the correlation functions. One- and two-Δ isobar configurations in 4He contribute about one additional classical sum rule.

A model study on the nuclear photoeffect

In a simple model of a spinless particle moving in a finite square well potential influences of final state Born approximation and of various approximations in the electromagnetic operators on photoabsorption differential, total and integrated cross sections are investigated. While the Born approximation is very poor in all respects, the long wave length approximation turns out to be the best and reproduces the total cross section quite well. However, appreciable deviations occur in the differential cross section at intermediate energies. The integrated cross section slightly exceeds the classical sum rule resulting from nonanalyticity of the forward compton scattering amplitude, as is discussed in the limiting case of theδ-potential.

Photonuclear sum rules and interaction effects in the deuteron

The photonuclear sum rules σ o , σ −1, and σ −2 are evaluated for the deuteron by direct integration of the theoretical cross section up to the π-threshold. Effects of isobar configurations and mesonexchange currents are included. The integrated cross section is also determined from the double commutator of the dipole operator with the Hamiltonian. The usual potentials increase the classical sum rule σ 0 by about 50 % while isobar configurations contribute an additional 20 % which is in reasonable agreement with the experimental integrated cross section above the Δ-resonance up to 540 MeV. The energy weighted sum rules σ −1 and σ −2 are little affected by interaction effects. Electric polarizability and paramagnetic susceptibility are also calculated.

Hadron electromagnetic mass differences

Mass differences between members of isotopic-spin multiplets of hadrons are calculated in the MIT bag model. All low-mass SU(4) multiplets of spin 0, 1/2, 1, and 3/2 particles are considered. Both Coulomb and magnetic contributions to mass differences are evaluated without the assumption of SU(6)-degenerate intermediate states. The mass difference between the "up" and the "down" quarks inside the bag is not (necessarily) taken to be a constant; we propose a parameterization for it that works well for its contribution to known hadron electromagnetic mass differences. Based on the parametrization we present a class of sum rules for charmed-particle electromagnetic mass differences.

Sum rule for the transition current density

We derive a mode-independent sum rule for the space-like component of the nuclear four-vector current. The energy-weighted sum rule for the time-like component is also obtained as a result of the conservation of electric charge. Furthermore, in the long wave-length limit, it reduces to the classical energy-weighted sum rule for photoexcitation. The four-vector current density of the Tassie model is obtained as a special case.

Giant resonance region ofN15studied by polarized and unpolarized proton capture measurements

We have measured the cross sections and the analyzing powers for the $^{14}\mathrm{C}(\stackrel{\ensuremath{\rightarrow}}{p}, \ensuremath{\gamma})^{15}\mathrm{N}$ reaction for proton energies from 4.0 to 16.2 MeV. The corresponding range in excitation energies, 13.94 to 25.33 MeV, covers the region of the giant dipole resonance in $^{15}\mathrm{N}$. The five-angle angular distributions measured with unpolarized and with polarized beams at eight energies over this region were analyzed to determine the magnitudes and relative phases of the transition matrix elements. The analysis included $E1$, $M1$, and $E2$ transitions. The observed $E1$ strength exhausts only about 6% of the classical dipole sum rule. The dominant $E1$ strength is compared to a shell-model calculation which includes 3p-3h excitations. A fairly uniform distribution of $E2$ strength is observed which exhausts about 7% of the total energy-weighted sum rule. Although large uncertainties on this result could allow the existence of a giant $E2$ resonance, the most probable values indicate that no appreciable concentration of $E2$ strength is observed.

ρππRegge Residue Function from a New Class of Sum Rules, and a New Representation forππAmplitudes

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Sum rules for the structure parameters of the nucleon

Based on the parton model and some commonly used assumptions, a class of sum rules is obtained which relates the structure parameters of the nucleon such as the proton charge radius with the quantities which can be most directly connected with the experimental observables in the hard massive photon limit, that is, the deep inelastic nucleon structure functions.

Nuclear photon scattering between 10 and 80 MeV

Dipole oscillator strengths for light elements have been measured in a photon scattering experiment. The summed dipole strength up to 80 MeV photon energy was found to be 1.4 times the value given by the classical sum rules for all elements investigated.

Finite-Energy Sum Rules and Their Application toπNScattering at Fixedu

The finite-energy sum rule, and a class of sum rules which can be used to probe the existence of fixed poles, are obtained for amplitudes whose left- and right-hand cuts are not related by crossing symmetry. The finite-energy sum rule is evaluated for each of four independent $\ensuremath{\pi}N$ amplitudes with $u$ fixed at ${(1236\phantom{\rule{0ex}{0ex}}\mathrm{M}\mathrm{e}\mathrm{V})}^{2}$, both sides of the resultant four sum rules being obtained from the properties of the low-energy $\ensuremath{\pi}N$ resonances. Results are presented for three choices of end point: ${(1356\phantom{\rule{0ex}{0ex}}\mathrm{M}\mathrm{e}\mathrm{V})}^{2}$, ${(1808\phantom{\rule{0ex}{0ex}}\mathrm{M}\mathrm{e}\mathrm{V})}^{2}$, and ${(2313\phantom{\rule{0ex}{0ex}}\mathrm{M}\mathrm{e}\mathrm{V})}^{2}$. For the intermediate end point, all four sum rules work. For the highest one, however, they all fail. These results, while pointing to a failure of the resonance dominance approximation above 1800 MeV, give us a new confirmation of Regge high-energy behavior on the basis of low-energy data alone. In particular, they verify in some detail the relation predicted by Reggeism between the high-energy, fixed-$u$ behavior of the amplitudes and the low-energy $u$-channel resonances. They also show that for $u={(1236 \mathrm{MeV})}^{2}$, all the $\ensuremath{\pi}N$ amplitudes have Regge behavior on the average (duality) above 1800 MeV. The finite-energy sum rules are shown to be violated in a fictitious universe where the lowest particle on each of the leading $\ensuremath{\pi}N$ Regge trajectories is accompanied by a degenerate partner of opposite parity.

The use of photonuclear sum rules in the study of light nuclei

The method of multipole sum rules is applied to the photodisintegration of3He,4He,12C,14N,16O. A comparison is made with the classical Levinger-Bethe and Migdal sum rules, and the totalE2 photoabsorption is calculated.

New Type of Dispersion-Theory Sum Rule

We show that a new class of sum rules can be obtained by comparing, for example, fixed-$t$ and fixed-$u$ dispersion relations. In particular, if an amplitude obeys both fixed-$t$ and fixed-$u$ dispersion relations at ${t}^{*}$ and ${u}^{*}$, respectively, we obtain a sum rule by equating the two dispersion relations for the amplitude evaluated at ${t}^{*}$ and ${u}^{*}$. Under special circumstances the no-subtraction requirement can be lifted. We apply our procedure to the ${A}^{(\ensuremath{-}1)}$ and ${B}^{(\ensuremath{-})}\ensuremath{\pi}N$ amplitudes to derive new sum rules, and we show that these sum rules are reasonably well satisfied with only $\ensuremath{\rho}$, $N$, and ${N}^{*}$ contributions for the choice ${t}^{*}={u}^{*}=0$.

Superconvergence Condition and Okubo's Ansatz

Recently a class of sum rules) for strong interactions has been derived on the basis of a dispersion theoretic approach. In such a derivation, one makes assumptions*) related to the high energy bounds for scattering amplitudes, which specify the convergence properties of the relevant dispersion relations. If the dispersion integral is approximated by a sum consisting of intermediate particles, the masses and cou piing constants of different particles are related. Thus AFRF considered. the p-n forward scattering and obtained some relations connecting coupling constants and masses, where they made the approximation of keeping only n, w, q; as intermediate states. This approximation leads to inconsistent results.**) This suggests that, in order to obtain consistent results, one should include other higher resonant states in addition to n, w and q; as intermediate states. In view of this situation we consider pseudoscalar-meson-vector-meson scattering within the framework of SU(3) symmetry and investigate possible strong interaction sum rules for the scattering. Our approximation for the dispersion integrals of the sum rules includes as intermediate states the pseudoscalar-meson octet (P), the vector-meson nonet (V) the axial-vector-meson nonet (U) and the tensor-meson nonet (T) .***) In this note we are particular-

Sum-Rule Calculation of the Isovector Form Factor

A class of sum rules due to Fubini is rederived from a point of view which clarifies the assumptions made about the singularities of field operators. A calculation of the isovector magnetic moment is performed in the isobar approximation. The result $F_{1}^{}{}_{}{}^{V}(0)=\frac{1}{2}$ emerges as a model-independent consistency condition, but the calculated value $F_{2}^{}{}_{}{}^{V}(0)=3.64$ is in disagreement with the experimental value.

The12C (γ, n)11C cross-section above the giant resonance

The cross-section for the reaction12C(γ, n)11C above the giant resonance has been measured up to 70 MeV of γ-ray energy. The Penfold and Leiss analysis gives a value of the integrated cross-section of (88 ± 7) mb MeV in agreement with the classical dipole sum rule; the contribution between 35 and 70 MeV is about 30 mb MeV,i.e. 34% of the measured integrated (γ, n) cross-section. A wide resonance at about 35 MeV mainly corresponding to 1s12/−11p1/2 transition predicted by the particle-hole calculations has been observed. There is also some evidence of structure at about 53 MeV.

Total Photonuclear Cross Sections for Low Atomic Number Elements

Total photonuclear cross sections have been measured in an attenuation experiment using a scintillation pair spectrometer and an x-ray spectrum with a fixed maximum energy of 90 MeV. The cross sections as a function of x-ray photon energy for beryllium, carbon, oxygen, sodium, magnesium, aluminum, silicon, sulfur, calcium, nickel, cobalt, copper, and silver show detailed structure in many cases at x-ray energies of 15-30 MeV and display a consistent trend in shapes and magnitudes. The integrated cross sections up to 35 MeV relative to the classical dipole sum rule show a monotonic increase with atomic weight. Other analyses of the total photonuclear cross sections in terms of mean energies and of the ratios of the total cross sections to photoneutron cross sections are also presented.

Symmetry theory of the Aharonov-Bohm effect: Quantum mechanics in a multiply connected region: Lindsay J. Tassie and Murray Peshkin

We derive a mode-independent sum rule for the space-like component of the nuclear four-vector current. The energy-weighted sum rule for the time-like component is also obtained as a result of the conservation of electric charge. Furthermore, in the long wave-length limit, it reduces to the classical energy-weighted sum rule for photoexcitation. The four-vector current density of the Tassie model is obtained as a special case.