Singular integral equations for meson spectra are obtained by making a Fock space expansion of the quantum chromodynamics (QCD) mass eigenstate followed with a partial wave decomposition. The expansions are truncated and approximate equations for the mass eigenvalues and eigenvectors are derived variationally. Using values for the QCD coupling constant and the quark rest masses obtained from a relativistic two-constituent quark model as starting values, the resulting singular integral equations for the heavy mesons are then solved by iteration to convergence in momentum space using an expansion in cubic B splines. In these initial variational calculations we restrict ourselves to configurations having a maximum of one qq¯ pair and 20 gluons. However, we do not introduce any phenomenological confinement interaction. Nevertheless these variational results compare favorably with the results of the phenomenological two-constituent quark model and with experiment. Remarkably, we find no evidence for any continuum. There is no parameter adjustment in these initial variational calculations. In a second set of variational calculations the quark masses and QCD coupling constant are determined by a fit to the heavy meson spectrum again without employing a phenomenological confining potential. We then obtain an improved description of the heavy meson spectrum compared with experiment.

The reaction sequences governing the reaction flow in the rp process are important for the understanding of the energy generation and nucleosynthesis of heavy elements in hot and explosive stellar hydrogen burning. Of considerable interest are (p,α) reactions along the process path which lead to the formation of reaction cycles rather than to chains of proton capture processes and β decays. Previous direct attempts to measure the low-energy reaction cross sections for ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$(p,α${)}^{28}$Si and ${}_{}{}^{35}{}_{}{}^{}\mathrm{Cl}$(p,α${)}^{32}$S resulted only in upper limits for the strengths of possible low-energy resonances which may dominate the reaction rates. In this paper an indirect experimental approach is presented to study the structure of the low-energy unbound states in the compound nuclei ${}_{}{}^{32}{}_{}{}^{}$ S and ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$. The results allow a more accurate determination of the contributions of these low-energy levels in the (p,α) reaction channel.

High-spin states have been identified in doubly odd ${}_{}{}^{114}{}_{}{}^{}\mathrm{I}$ produced in the ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$${(}^{58}$Ni,3pnγ) reaction. Two rotational band structures have been observed. One band exhibits no signature splitting, while the second exhibits a large signature splitting. These bands are interpreted in terms of π${\mathit{g}}_{9/2}$⊗ν${\mathit{h}}_{11/2}$ and π${\mathit{g}}_{7/2}$⊗ν${\mathit{h}}_{11/2}$ quasiparticle configurations, respectively.

The reaction ${}_{}{}^{168}{}_{}{}^{}\mathrm{Er}$(d,2nγ) and conventional in-beam γ-ray spectroscopy have been used to assign, for the first time, many γ-ray transitions to ${}_{}{}^{168}{}_{}{}^{}\mathrm{Tm}$. On the basis of γ-γ coincidence data, some of these observed γ rays are identified as transitions between the low-spin members of rotational bands in ${}_{}{}^{168}{}_{}{}^{}\mathrm{Tm}$, specifically, those with ${\mathit{K}}^{\mathrm{\pi }}$=$3^{+}$, ($3^{\mathrm{-}}$), and ($4^{\pm }$).

As a follow-up on our earlier paper we calculate the ${\mathrm{\chi }}^2$ of various NN potential models with respect to the np scattering data. We find that only the most recent potential models give a reasonably good description of these data. Almost none of the potentials is truly an NN potential in the sense that it gives a good description of both pp and np scattering simultaneously.

Published n${\mathrm{-}}^{209}$Bi elastic differential cross-section, analyzing power, and total cross-section data in the energy range from 1.5 to 14 MeV were analyzed via a phase-shift analysis in order to find out whether these data show similar, unexplained resonance structures as observed recently for n${\mathrm{-}}^{208}$Pb scattering. Although the n${\mathrm{-}}^{209}$Bi and n${\mathrm{-}}^{208}$Pb data are very similar, some of the phase shifts are quite different for the two systems. Only one resonancelike structure was observed for n${\mathrm{-}}^{209}$Bi scattering in the excitation energy range from 9 to 18 MeV compared to eleven in the n${\mathrm{-}}^{208}$Pb system, implying that n${\mathrm{-}}^{209}$Bi data are probably more suitable than the classical n${\mathrm{-}}^{208}$Pb system for detailed mean-field analyses approached through dispersion-relation optical models.

The E2 cross section calculated by Langanke and Shoppa for the RIKEN experiment on the Coulomb dissociation of ${}_{}{}^8{}_{}{}^{}\mathrm{B}$ uses E2 nuclear matrix element from one specific model. Other nuclear models predict a considerably smaller E2 cross section (by approximately a factor of 3 to 4), and Langanke and Shoppa appear to assume the most optimistic scenario, predicting a large E2 cross section. We also note that Barker has already criticized the nuclear model used by Langanke and Shoppa. A model independent chi-square analysis of the RIKEN data suggest the best fit for the current RIKEN data is obtained with E1 amplitudes only. The upper limit (90% confidence) on the E2 component derived from our chi-square analysis is considerably smaller than that used by Langanke and Shoppa. The model dependent analysis of Langanke and Shoppa should not be considered as a correction to the RIKEN result, as claimed, and their quoted ${\mathit{S}}_{17}$(0) is not substantiated.

This is a reply to the preceding Comment.

The hypothesis of a large weak matrix element between single-particle states in heavy nuclei, ∼100 eV, contradicts the results of atomic parity nonconserving correlation (PNC) experiments.

We reply to the preceding comment.

The first measurement of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(γ,${\mathit{K}}^{+}$) has been performed in a photon energy range of 0.8≤${\mathit{E}}_{\gamma }$≤1.1 GeV. The differential cross sections are compared with a calculation which assumes a quasi-free Λ-producing ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(γ,${\mathit{K}}^{+}$) process. The deviation of experimental values from the calculation is explained in terms of bound Λ residual states. The differential cross section ratio of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(γ,${\mathit{K}}^{+}$) to p(γ,${\mathit{K}}^{+}$)Λ is 4.2±0.6, which is in good agreement with a calculation using a semiclassical model.

We have measured cross sections for (d${,}^2$He) induced reactions on the p-shell nuclei ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, and ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ and the sd-shell nucleus ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ at an energy of ${\mathit{E}}_{\mathit{d}}$=125.2 MeV. The measured excitation energy spectra are very similar to those from (p,n), (n,p), and (d${,}^2$He) reactions at higher energies. The measured 0° (d${,}^2$He) cross sections show a remarkably well-defined linear relation with the Gamow-Teller strengths deduced either from β decay or from (p,n) reactions. Our results demonstrate that the (d${,}^2$He) reaction can be used as a powerful tool to study Gamow-Teller strengths in the ${\mathrm{\beta }}^{+}$ direction at energies as low as ${\mathit{E}}_{\mathit{d}}$=125.2 MeV.

Total reaction cross sections ${\mathrm{\sigma }}_{\mathit{R}}$ for ${}_{}{}^8{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, and ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ on ${}_{}{}^{\mathrm{nat}}{}_{}{}^{}\mathrm{Si}$ were measured from about 20 to 60 MeV/nucleon. The ${\mathrm{\sigma }}_{\mathit{R}}$ for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ compared reasonably well with conventional strong absorption and microscopic calculations. Measured ${\mathrm{\sigma }}_{\mathit{R}}$ for ${}_{}{}^8{}_{}{}^{}\mathrm{B}$ were slightly larger than those for the two heavier nuclei, and notably larger than the conventional calculations. The ${}_{}{}^8{}_{}{}^{}\mathrm{B}$ data were well reproduced by microscopic calculations using the same matter distribution used to explain the ${}_{}{}^8{}_{}{}^{}\mathrm{B}$ quadrupole moment data, and therefore provide new evidence for the existence of a proton halo in ${}_{}{}^8{}_{}{}^{}\mathrm{B}$.

A superdeformed (SD) band consisting of 13 γ-ray transitions has been observed in ${}_{}{}^{154}{}_{}{}^{}\mathrm{Er}$, an isotone of ${}_{66}{}^{152}{}_{}{}^{}\mathrm{Dy}$. The experiment was performed using the ${}_{}{}^{118}{}_{}{}^{}\mathrm{Sn}$${(}^{40}$Ar,4n) reaction at E${(}^{40}$Ar)=185 MeV and the early implementation of GAMMASPHERE. This is an observation of a SD band in the A≊150 region with a proton number greater than 66. The ${\mathcal{J}}^{\mathrm{}\left(2\right)\mathrm{}}$ moment of inertia of the band is constant above ħω=0.45 MeV and shows a sharp rise below this value suggesting a paired band crossing. These results suggest that total Routhian surface calculations fail to accurately predict the deformation of the band.

Estimates of isospin mixing in proton-rich medium-heavy nuclei in the region of mass numbers A=80 and 100 are made with the use of Hartree-Fock (HF) calculations with Skyrme forces. An isospin mixing probability of 4–5 % is predicted in the ground state of ${}_{}{}^{100}{}_{}{}^{}\mathrm{Sn}$ and about 3–4 % in ${}_{}{}^{80}{}_{}{}^{}\mathrm{Zr}$. These are about a factor of 2 larger than the estimates given by Bohr and Mottelson who directly evaluate the isospin mixing with a collective model description of the isovector giant monopole resonance (IVGMR). We show that if we use the energy-weighted sum rule together with the energies of the IVGMR given by Bohr and Mottelson, the predicted isospin admixtures are close to those of HF calculations. More realistic estimates of isospin mixing with random-phase approximation are also presented in the case of ${}_{}{}^{100}{}_{}{}^{}\mathrm{Sn}$.

The effect of an axially symmetric hexadecapole term is investigated in a strongly deformed quadrupole potential. While the system is nonintegrable and shows significant chaotic behavior classically, the quantum mechanical treatment not only produces a general smoothing effect with regard to chaos but even yields a pronounced shell structure at certain hexadecapole strength parameter values for oblate and prolate deformation.

We calculate the finite-temperature corrections in the dilated chiral quark model using the effective potential formalism. Assuming that the dilaton limit is applicable at some short length scale, we interpret the results to represent the behavior of hadrons in dense and hot matter. We obtain the scaling law, ${\mathit{f}}_{\mathrm{\pi }}$(T)/${\mathit{f}}_{\mathrm{\pi }}$ =${\mathit{m}}_{\mathit{Q}}$(T)/${\mathit{m}}_{\mathit{Q}}$≃${\mathit{m}}_{\mathrm{\sigma }}$(T)/${\mathit{m}}_{\mathrm{\sigma }}$ while we argue, using partial conservation of axial-vector current, that pion mass does not scale within the temperature range involved in our Lagrangian. It is found that the hadron masses and the pion decay constant drop faster with temperature in the dilated chiral quark model than in the conventional linear σ model that does not take into account the QCD scale anomaly. We attribute the difference in scaling in heat bath to the effect of baryonic medium on thermal properties of the hadrons. Our finding would imply that the alternating-gradient synchrotron experiments (dense and hot matter) and the RHIC experiments (hot and dilute matter) will ‘‘see’’ different hadron properties in the hadronization phase.

The differential cross section of inelastic coherent diffractive dissociation off nuclei p${+}^4$He →X${+}^4$He is expressed in terms of the relative cumulants of the cross-section distribution ${\mathit{P}}_{\mathit{N}}$(σ). The theoretical result for the ratio r=(d${\mathrm{\sigma }}_{\mathrm{diff}}$/dt${)}_{\mathit{t}=0\mathrm{}}^{\mathit{p}\mathrm{He}}$/(d${\mathrm{\sigma }}_{\mathrm{diff}}$/dt ${}_{\mathit{t}=0\mathrm{}}{}^{\mathit{pp}}{}_{}{}^{}$=6.8–7.6 is close to the value r=7.1±0.7 which we extracted from the FNAL data. These are the only A≳2 data of this kind. The comparison provides the first confirmation of the color/cross-section fluctuation approach to the description of the absolute value of the inelastic diffraction cross section off nuclei. It provides also a new constraint on the first four cumulants of the cross-section distribution.

We show how pion-nucleus scattering data can be used to constrain four-quark in-medium matrix elements, whose uncertainty is currently the most important problem inhibiting the use of QCD sum rules to study hadrons in nuclear matter, a problem related to early-universe phase transitions. We take an important step towards determining the matrix elements by extracting a value for a particular linear combination using the Isobar-Doorway model propagator of the in-medium Δ(1232) and a QCD sum rule analysis of both the free and in-medium Δ.