Kinematic effective charges in photonuclear reactions

It is shown that the Gartenhaus-Schwartz-transformation of the electric multipole operator Ω^[L], i.e. expressing it in lab frame coordinates, not only leads to the well known concept of kinematic effective charges but in addition gives 2-, 3-,...,N-particle operator contributions whereN=min(A, L). In particular forE2 transitions the electric quadrupole operator contains one- and two-particle operators which contribute to the single particle transition rate and which will lead to two particle transitions.     

Functional averages in the theory of superconductivity

The grand canonical partition function of a superconductor described byGorkov's model Hamiltonian is represented as a functional integral with Gaussian measure. The integrand can be regarded as the partition function of a free Fermi system which interacts with a fluctuating external source potential. Perturbation-theoretic techniques are applied to the latter partition function. TheGibbs' potential proves to be stationary with respect to the energy gap parameterΔ. From the stationarity condition an equation forΔ is obtained which is a generalization of the usual Bardeen-Cooper-Schrieffer (BCS) equation. For the evaluation of the functional integral a variational procedure is employed. It leads to an expression for theGibbs' potential which shows a further remarkable stationarity property. As its simplest approximation this expression contains a result that was firstly derived by Thouless in the ladder graph approximation.     

Resonant and nonresonant contributions from unphysical regions in dispersion relations

Unphysical regions on the right hand cut in partial wave dispersion relations for a two-particle processA+B→A′+B′ are expressed by measurable quantities, under the assumption that there is only one important 2-particle channel in the unphysical region. The solution is unique, if the phase shiftδ _l for the elastic scattering in the channel responsible for the appearance of the unphysical region takes a value between 0 andπ at the physical threshold forA+B→A′+B′. The difference between non resonant (δ_l≠π/2 in the unphysical region) and resonant contributions is shortly discussed.     

Quantum electrodynamics with “two-particle” unitarity: Charged spin-0 bosons

The spin-0 propagator in quantum electrodynamics of charged spinless bosons (“pions”) is investigated in detail via the closest approximation to the Schwinger-Dyson equation in the two-particle unitarity approximation proposed initially by Salam by replacing the photon propagator by its zero order result. The high-energy behavior (in spacelike directions) of the (renormalized) spin-0 propagator Δ(p²) is explicitly derived and a finite electromagnetic mass excitation for the “pion” is obtained. The latter follows as a result of the derived asymptotic behavior of Δ^?1(p²) (p² → ∞) that the unrenormalized mass m₀ ≡ 0. This brings us into contact with earlier work of Johnson, Landau and their collaborators. The fact that m₀² ≡ 0 and that Δ^?1(p²)/_p²=?m² = 0 (m ≠ 0) (in Nambu's sense) gives us an eigenvalue equation for the fine structure constant which may be then computed in terms of no other parameters. This eigenvalue equation is expanded in powers of the coupling constant with all the expansion coefficients being finite. The latter is computed to sixth order in the charge.     

InclusiveΔ ++ inpp interactions at ISR energies

Inclusive cross sections forΔ ⁺⁺ production inpp interactions at different ISR energies are presented. The differential cross sectiondσ/dx forΔ ⁺⁺ production is found to be approximately independent of Feynmanx. No strong energy dependence is seen over the ISR energy range. The topological cross sections ofΔ ⁺⁺ at \(\sqrt s = 62\) GeV show an appreciable contribution from non-diffractive production mechanisms. An upper limit for theΔ ⁰ production cross section is determined.     

Coulomb energies and nuclear radii in the energy density formalism

The relation between Coulomb displacement energies,ΔE _c , andΔr=r _n -r _p , the difference between the rms radii of neutrons and protons in nuclei, is investigated within the energy density formalism (EDF). The variational equation, obtained by minimizing the Coulomb plus symmetry energies, is solved assuming the symmetry interaction is a simple functional of the local nuclear matter density. Varying parameters of the model, rather unique relation betweenΔE _c andΔr is obtained (within ±50 keV).ΔE _c isindependent ofr _ex, the rms radius of the excess neutrons distribution. Using the experimental values ofr _p and adjusting the model to reproduce the recent data onΔr (Δr∽~0.05 fm for⁴⁸Ca and²⁰⁸Pb), which are significantly smaller than those obtained from current Hartree-Fock calculations, the calculatedΔE _c agree with the experimental results. Using the value ofΔr～0.05 fm and the experimental values ofr _ex, a small compression (<0.02 fm) of the proton core in the analogue state relative to its parent state emerges, thus contributing an additional electrostatic term to the Coulomb displacement energy. The size of this relative core-compression effect depends on the values assumed forΔr andr _ex, it increases with the decreasing ofΔr and the increasing ofr _ex. IfΔr～0.05 fm the effect is large enough to remove the long standing Coulomb energy anomaly. The main result of the present work is the correlation betweenΔE _c andΔr, suggesting that the difficulties of current Hartree-Fock calculations in reproducing isotope shifts ofr _p , the small value ofr _n ?r _p and the values ofΔE _c may all be different manifestations of some missing residualp n effective interaction.     

Second and third virial coefficient of a quantum gas from two-particle scattering amplitude

Starting from the cluster expansion of the partition function the second and third virial coefficient of a quantum gas is expressed in terms of the two-particle scattering amplitude. In the case of spherically symmetric interaction the result forB(T) agrees with the well known expression ofBeth andUhlenbeck, but the method given here is also valid for non-spherically symmetric and even for non-local potentials. For the third virial coefficientC(T) an expression is derived in lowest order in the two-particle scattering amplitude which is suitable for numerical calculations.     

Microscopic calculation of the surface absorption in the optical potential

We calculated the contributions of the two-particle one-hole (2p-1h) and the one-particle two-hole (1p-1h) excitations to the imaginary partW(E, R) of then-⁴⁰Ca optical potential. The bound single particle states and energies of the⁴⁰Ca nucleus are calculated quantum mechanically by solving the Schrödinger equation with a Woods-Saxon potential. For the excited states in the continuum we use the Thomas-Fermi approximation. Different forms of contact residual interactions have been tested. A combination of aδ-force and a smeared SDI can fit the phenomenologicalW(E, R).     

Vergleich zweier Methoden zur Berechnung des dynamischen Strukturfaktors für klassische Systeme

Starting from the equation of motion of the one-particle distribution function as given in the BBGKY-hierarchy Nelkin and Ranganathan and Singwiet al., respectivly, have developped two different methods of calculating the dynamic structure factor. We show, that both methods are equivalent, if one uses the same approximation for the two-particle distribution function.     

Parity violating pion electroproduction off the nucleon

Parity violating (PV) contributions due to interference betweenγ and Z⁰ exchange are calculated for pion electroproduction off the nucleon. A phenomenological model with effective Lagrangians is used to determine the resulting asymmetry for the energy region between threshold andΔ(1232) resonance. TheΔ resonance is treated as a Rarita-Schwinger field with phenomenological NΔ transition currents. The background contributions are given by the usual Born terms using the pseudovectorπN Lagrangian. Numerical results for the asymmetry are presented.     

Nonleptonic Cabibbo favouredB-decays andCP-asymmetries for charmed final hadron states in Isgur and Wise theory

The Cabibbo allowed non-leptonicB-decays in two hadrons are studied, within the factorization hypothesis, in the framework of Isgur and Wise theory for the matrix elements of the ΔB=?ΔC=±1 weak currents. TheSU(2) _HF symmetry relates |ΔB|=1 to |ΔC|=1 currents, which have been measured in the semileptonic strange decays of charmed particles. By assuming colour screening and allowing forSU(3) invariant contributions from the annihilation terms with charmed final states one is able to comply with the present experimental knowledge. TheCP violating asymmetries in neutralB decays are given charmed final states in terms of theK-M angles. With the central values found for the annihilation parameters there is a destructive (constructive) interference between the direct and annihilation terms in the Cabibbo allowed (doubly forbidden) amplitudes for the decays intoD ⁰(D ^*0)π⁰ and {D ⁰ρ⁰ so that they may be of the same order. This would imply large asymmetries, for which however our present knowledge on the amplitudes does not allow to predict even their sign. We have better confidence in our predictions for the charged final states than the neutral ones and can draw the conclusion that the detection of the corresponding asymmetries requires, at least, 10⁶ tagged neutralB-particles.     

Complete fusion of7Li+16O in the region of the Coulomb threshold

Excitation functions of the one- and two-particle evaporation reactions¹⁶O(⁷Li,xγ) and¹⁶O(⁷Li,xyγ), x, y=n, p, d, t andα have been measured in steps of 100–160 keV forE _Li=4–10 MeV. All yield curves were rather smooth and could well be described by statistical model calculations taking into account one- and two-particle decays. No significant deviations of the total fusion cross section from the reaction cross section as given by the optical model were observed. A critical comparison is performed with earlier data of the same reaction taken at slightly higher energies where drastically reduced fusion cross sections were reported.     

Collective bands in doubly even Sn nuclei

Starting from a simplified picture treating proton two-particle two-hole excitations coupled with spherical quadrupole vibrations, in interaction with the low-lying quadrupole vibrational states in the doubly even Sn nuclei, we are able to account for a regular ΔJ = 2 band structure on top of excited J^π = 0⁺ states. We compare in some detail results for ¹¹⁶Sn concering energy spectra and E2 transition rates.     

Correlation with large transverse momentum photons and the gluon structure function

The inclusive two-particle cross section for the production of largep _T photons and opposite side charged hadrons in proton-proton collisions is examined in detail in the framework of QCD. The model, with the parametrization as in our previous work, agrees with the measured single photon spectra. Quantitative predictions are made for two-particle distributions to be measured at the ISR. The contributions due to the photon bremsstrahlung and the effects coming from the intrinsic constituent motion are estimated. It is shown that indeed the direct subprocess gluon+quark→photon+quark gives the dominant contribution in the experimentally relevant region of phase space, and that direct information about the gluon structure function can be obtained from such measurements.     

πd Backward scattering via isobars in the deuteron

Pion-deuteron elastic backward scattering atp _π ^lab ～ 0.2–1.0 GeV/c is analyzed in terms of a two-particle exchange mechanism. Inclusion of isobarsΔ (1236) in the intermediate states, such that the initial or final deuteron is in aΔΔ configuration, produces qualitative agreement with the observed structure of the excitation function. IntermediateN′(1520) andN′(1535) states are found to be negligible.     

Local-potential approximation for the Brueckner G matrix and problem of optimally choosing model subspace

The validity of the local-potential approximation, which was proposed previously for the singlet-pairing problem in semi-infinite nuclear matter, is investigated in the Bethe-Goldstone equation for the Brueckner G matrix. For this purpose, use is made of the method developed earlier for solving this equation for a planar slab of nuclear matter in the case of a separable form of NN interaction. The ¹ S ₀ singlet and the ³ S ₁+³ D ₁ triplet channel are considered. The complete two-particle Hilbert space is split into a model and the complementary subspace that are separated by an energy E ₀. The two-particle propagator is calculated precisely in the first subspace, and the local-potential approximation is used in the second subspace. With an eye to subsequently employing the G matrix to calculate the Landau-Migdal amplitude, the total two-particle energy is fixed at E=2μ, where μ is the chemical potential of the system under consideration. Specific numerical calculations are performed at μ=?8 MeV. The applicability of the local-potential approximation is investigated versus the cutoff energy E ₀. It is shown that, in either channel being considered, the accuracy of the local-potential approximation is rather high for E ₀≥10 MeV.     

Relativistic entropy and related Boltzmann kinetics

It is well known that the particular form of the two-particle correlation function, in the collisional integral of the classical Boltzmman equation, fixes univocally the entropy of the system, which turns out to be the Boltzmann-Gibbs-Shannon entropy. In the ordinary relativistic Boltzmann equation, some standard generalizations, with respect to its classical version, imposed by the special relativity, are customarily performed. The only ingredient of the equation, which tacitly remains in its original classical form, is the two-particle correlation function, and this fact imposes that also the relativistic kinetics is governed by the Boltzmann-Gibbs-Shannon entropy. Indeed the ordinary relativistic Boltzmann equation admits as stationary stable distribution, the exponential Juttner distribution. Here, we show that the special relativity laws and the maximum entropy principle suggest a relativistic generalization also of the two-particle correlation function and then of the entropy. The so obtained, fully relativistic Boltzmann equation, obeys the H-theorem and predicts a stationary stable distribution, presenting power law tails in the high-energy region. The ensued relativistic kinetic theory preserves the main features of the classical kinetics, which recovers in the c \( \rightarrow\) ∞ limit.