Showing papers in "Physical Review C in 1986"
TL;DR: The present calculations indicate that super-deformed rotating ground states,more, which are predicted in the liquid-drop model, would not survive fission long enough to undergo electromagnetic decay.
Abstract: I present a macroscopic model for the energy of rotating nuclei which has several refinements relative to the rotating-liquid-drop model. Of most importance are the inclusion of finite-range effects in the nuclear surface energy by means of a Yukawa-plus-exponential potential, finite surface diffuseness effects in the Coulomb energy and in the rotational moments of inertia, and an improved specification of nuclear shapes. With this model I calculate the properties of points of equilibrium corresponding to nuclear ground states and fission saddle points. The results are qualitatively similar to those of the rotating-liquid-drop model, but there are significant quantitative differences in fission-barrier heights and moments of inertia. Fission barriers for nonrotating nuclei are calculated for nuclei with atomic numbers varying from 14 to 117. For rotating nuclei, detailed results are given for the entire range of angular momentum for which a fission barrier exists, for nuclei with atomic numbers from 20 to 100, and for mass numbers which exceed the range of known nuclei. The calculated barriers are lower than liquid-drop-model barriers for lighter nuclei and are consistent with those deduced from experimental fission-fusion data over a wide range of nuclear species. The present calculations indicate that super-deformed rotating ground states, which are predicted in the liquid-drop model, would not survive fission long enough to undergo electromagnetic decay. Multiparameter functions which approximately reproduce the calculated results for barrier heights and moments of inertia are described.
527 citations
TL;DR: This investigation investigates systematically the possibilities and the limits of the Skyrme force for reproducing nuclear ground-state properties in a spherical Hartree-Fock calculation by means of least-squares fits of the force parameters to the measured binding energy, diffraction radius, and surface width of eight selected nuclei.
Abstract: We investigate systematically the possibilities and the limits of the Skyrme force for reproducing nuclear ground-state properties in a spherical Hartree-Fock calculation. This investigation is performed by means of least-squares fits of the force parameters to the measured binding energy, diffraction radius, and surface width of eight selected nuclei. Particular emphasis is put on the density dependence of the interaction, which turns out to be determined mainly by the surface width. The least-squares fitting procedure yields the best-fit parameters together with uncertainties on them, and it also allows one to estimate the uncertainties of an extrapolation to other fields, e.g., nuclear matter properties. We also study the contribution of random-phase-approximation correlations to the ground-state properties and their influence on the parameters of the effective interaction. Here, we also compare to giant dipole resonance energies.
199 citations
TL;DR: Calculations verify the validity of the equal a priori probabilities assumption underlying exciton model calculations and demonstrate that the one- and two-component models produce very similar results when similar assumptions are made about the relative probabilities of exciting proton and neutron degrees of freedom.
Abstract: A closed form version of the two-component exciton model is derived. Discussions of corrections for the Pauli exclusion principle, of the expected behavior of the residual two-body matrix elements, and of the relative merits of different types of reaction calculations within the exciton model are presented. Calculations verify the validity of the equal a priori probabilities assumption underlying exciton model calculations and demonstrate that the one- and two-component models produce very similar results when similar assumptions are made about the relative probabilities of exciting proton and neutron degrees of freedom.
174 citations
TL;DR: From the numerical analysis, it is concluded that the production of high-energy gamma rays is limited to the very early stage of the collision.
Abstract: The cross section for emitting high energy gamma rays in heavy-ion collisions is calculated in a model based on the Boltzmann-Uehling-Uhlenbeck equation. The elementary production cross section is assumed to be neutron-proton bremsstrahlung. Comparison is made with experimental data at bombarding energies from 20 to 84 MeV/nucleon. The calculations are found to roughly reproduce the energy spectrum, bombarding energy dependence, and angular distribution. From the numerical analysis we conclude that the production of high-energy \ensuremath{\gamma} rays is limited to the very early stage of the collision.
105 citations
TL;DR: It is shown that strongly-bound eta-nucleus systems, which were previously shown to be able to form between an eta meson and nuclei of mass number A>10, can be formed between an and p nuclei.
Abstract: It is shown that strongly-bound \ensuremath{\eta}-nucleus systems, which we term \ensuremath{\eta}-mesic nuclei, can be formed between an \ensuremath{\eta} meson and nuclei of mass number Ag10. We show that a distinct experimental signature for the formation of the \ensuremath{\eta}-mesic nucleus can be observed in (${\ensuremath{\pi}}^{+}$,p) reactions. The formation cross sections are predicted. Effects of higher order dynamics on the predicted width of the \ensuremath{\eta}-mesic nucleus are also estimated.
77 citations
65 citations
TL;DR: The excitation energies and widths of the monopole and dipole are in good agreement with random-phase-approximation calculations and for the dipole they are also in agreement with other data.
Abstract: We measured the energies, widths, and cross sections of the isovector monopole and dipole resonances in various nuclei between $^{40}\mathrm{Ca}$ and $^{208}\mathrm{Pb}$ with the reactions (${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$,${\ensuremath{\pi}}^{0}$). Both resonances exhaust approximately the same substantial fraction of the cross section calculated in a random-phase-approximation--distorted-wave-impulse-approximation model. The excitation energies and widths of the monopole and dipole are in good agreement with random-phase-approximation calculations and for the dipole they are also in agreement with other data. No isovector quadrupole resonance was observed, and the upper limits for the cross sections for the light elements are well below the sum rule strength for the isovector monopole and giant dipole resonance.
65 citations
TL;DR: These results show that shell effects are strong near threshold at E-italic/sub n/ = 0.80 MeV, but decrease significantly at the higher excitation energy, in qualitative agreement with the model of Wilkins, Chasman, and Steinberg, however, the observed increase in the number of prompt fission neutrons cannot be explained by this model.
Abstract: We report on a four-parameter measurement of the kinetic energies E-italic and the velocities v-italic of correlated fragments in fast-neutron-induced fission of /sup 237/Np. The influence of excitation energy on the important fragment properties such as mass, kinetic energy, and prompt neutron emission have been investigated experimentally at 0.80 and 5.55 MeV neutron energy. Our results include mean values of fragment properties before and after neutron evaporation, e.g., of fragment velocities and masses, total kinetic energies, and the respective variances. Also given are the distributions of fragment mass, of E-italic/sub k-italic//sub ,tot/, the variance of E-italic/sub k-italic//sub ,tot/, as well as the number of prompt fission neutrons as a function of fragment mass. These results show that shell effects are strong near threshold at E-italic/sub n/ = 0.80 MeV, but decrease significantly at the higher excitation energy, in qualitative agreement with the model of Wilkins, Chasman, and Steinberg. However, the observed increase in the number of prompt fission neutrons, which appears only in the heavy fragment, cannot be explained by this model.
62 citations
TL;DR: Cross sections for the production of nuclides in the region 91 ~ Z ~ 100 were determined radiochemically from bombardments with 18o, 86Kr and 136xe ions, indicating that the use of heavy-ion transfer reactions to produce new neutron-rich above-target species is limited.
Abstract: Transfer reactions of heavy ions with $^{248}$Cm targets are evaluated for their usefulness in producing unknown neutron-rich actinide nuclides. Cross sections for the production of nuclides in the region 91\ensuremath{\le}Z\ensuremath{\le}100 were determined radiochemically from bombardments with $^{18}$O, ${\mathrm{}}^{86}$Kr, and $^{136}$Xe ions. The systematic trends in the cross sections for these reactions can be understood in terms of the Coulomb potential and the stabilizing effect of the reaction Q values, which tend to favor the production of nuclei with Zg${Z}_{\mathrm{target}}$ with low excitation energies. Extrapolation of the product yields into unknown regions of charge and mass indicates that the use of heavy-ion transfer reactions to produce new neutron-rich above-target species is limited. Substantial production of unknown neutron-rich below-target species is expected in reactions with heavy projectiles like $^{136}$Xe and $^{238}$U.
61 citations
TL;DR: In this article, the fusion-fission, transfer, and elastic angular distributions were measured for all four systems and the experimental sub-barrier fusion cross sections were underpredicted by the one-dimensional barrier penetration model in all cases.
Abstract: The fusion of the heavy asymmetric systems of $^{16}$O,${\mathrm{}}^{18}$O${+\mathrm{}}^{208}$Pb and $^{15}$N,${\mathrm{}}^{16}$O${+\mathrm{}}^{209}$Bi was studied at bombarding energies near and below the Coulomb barrier. The fusion-fission, transfer, and elastic angular distributions were measured for all four systems. The evaporation residue component of the fusion was measured for only the $^{16}$O${+\mathrm{}}^{208}$Pb\ensuremath{\rightarrow}${\mathrm{}}^{224}$Th reaction; in agreement with statistical model calculations, the cross section for the evaporation residues was found to be negligible compared to the fission, and hence can be ignored in all the systems. The shapes of the fission fragment angular distributions are then a direct measure of the entrance channel spins which lead to fusion. The experimental sub-barrier fusion cross sections are underpredicted by the one-dimensional barrier penetration model in all cases. However, if the zero point motion of the targets is included in the barrier penetration model, the energy dependence of both the total fusion and the fission angular distributions can be explained for the $^{15}$N${+\mathrm{}}^{209}$Bi system alone. To fit the low-energy fusion of the oxygen reactions requires considerably more zero point motion---this being inconsistent with the fact that this effect should be the same in all the reactions. Also, the cross sections measured for the transfer channels were found to exhibit the same trend as the fusion at the lower energies. This correlation suggests that some of the sub-barrier fusion in the oxygen-induced reactions may be due to transfer-related processes.
59 citations
TL;DR: In this paper, the authors measured the photonuclear cross sections for /sup 233/U, /sup 234/U and /sup 237/Np from threshold up to 18 MeV, and found that the integrated photofission cross sections are large, accounting for 60% to 80% of the total photonuclear absorption strength.
Abstract: The photonuclear cross sections for /sup 233/U, /sup 234/U, /sup 237/Np, and /sup 239/Pu have been measured from threshold up to 18 MeV. The source of radiation was the monoenergetic photon beam from the annihilation in flight of fast positrons. The branching among the neutron-producing reaction channels was determined by measuring the photofission prompt neutron multiplicities nu-bar/sub p/. One interesting result is the complete absence of any (..gamma..,2n) cross section for /sup 233/U and /sup 234/U. The values of nu-bar/sub p/(E) for /sup 234/U agree with those measured with neutrons incident on /sup 233/U. The parameters of the giant dipole resonance deduced from the total photonuclear cross sections show that these nuclei have large static deformations, as expected. The integrated photofission cross sections are large (as are the absolute fission probabilities), and account for 60% to 80% of the total photonuclear absorption strength.
TL;DR: Yields for isotopes of Rn through Pu have been measured in the reaction /sup 48/Ca+/sup 248/Cm and there is evidence that these nuclides are produced with little excitation energy.
Abstract: Yields for isotopes of Rn through Pu have been measured in the reaction /sup 48/Ca+/sup 248/Cm at an energy of 248--263 MeV (1.04--1.10 times the Coulomb barrier). Despite the low bombarding energy, high and essentially constant integral yields of about 1 to 2 mb for the elements Rn through U were observed. There is evidence that these nuclides are produced with little excitation energy.
TL;DR: The three-body absorption cross sections for ..pi../sup +/ and ..Pi../sup -/ are found to be comparable to each other and show no strong energy dependence.
Abstract: Pion absorption in /sup 3/He was studied at T/sub ..pi../ = 62.5 and 82.8 MeV using nucleon-nucleon coincidences. For ..pi../sup +/ absorption on proton-neutron pairs the differential cross section is the same as that for ..pi../sup +/+d..-->..p+p except for an increase by a factor of about 1.5. For ..pi../sup -/ absorption on the proton-proton pair, the differential cross section is asymmetric about 90/sup 0/, indicating possible isospin mixing. The total cross sections sigma/sub pn/(..pi../sup +/) are 10.2 +- 0.9 mb and 13.5 +- 1.3 mb at 62.5 and 82.8 MeV and for sigma/sub pp/(..pi../sup -/) are 0.70 +- 0.07 mb and 0.92 +- 0.10 mb at 62.5 and 82.8 MeV. The three-body absorption cross sections for ..pi../sup +/ and ..pi../sup -/ are found to be comparable to each other and show no strong energy dependence. The three-body absorption cross section sigma/sub 3/(..pi../sup +/) is 6.7 +- 2.5 mb and 5.7 +- 2.3 mb and for ..pi../sup -/, sigma/sub 3/(..pi../sup -/) is 8.7 +- 1.4 mb and 6.5 +- 2.0 mb at 62.5 and 82.8 MeV, respectively.
TL;DR: The general question of the analysis of beta-delayed particle emission is discussed and it is found that satisfactory fits are obtained without introducing intruder states below 26-MeV excitation.
Abstract: The general question of the analysis of beta-delayed particle emission is discussed. It is emphasized that neither an integrated Fermi function nor a beta branching ratio is, in general, rigorously defined for beta decay to a specific level (resonance). As an example, spectra of breakup \ensuremath{\alpha} particles observed following $^{8}\mathrm{Li}$(${\ensuremath{\beta}}^{\mathrm{\ensuremath{-}}}$${)}^{8}$Be and $^{8}\mathrm{B}$(${\ensuremath{\beta}}^{+}$${)}^{8}$Be are analyzed by the many-level one-channel approximation of R-matrix theory. In addition, the L=2 \ensuremath{\alpha}-\ensuremath{\alpha} elastic scattering phase shifts are analyzed up to ${E}_{\ensuremath{\alpha}}$=34 MeV. It is found that satisfactory fits are obtained without introducing intruder states below 26-MeV excitation. Gamow-Teller matrix elements are extracted for decay to the 3.0-MeV first-excited state of $^{8}\mathrm{Be}$ and for the doublet near 16 MeV. The width and location of the $^{8}\mathrm{Be}$ 3.0-MeV state are also obtained. The results are compared to shell-model predictions.
TL;DR: The formalism for the treatment of pionic atoms level widths and shifts using the Kemmer-Duffin-Petiau equation is laid down and an analytical transformation is shown that connects between different sets of interactions.
Abstract: We lay down the formalism for the treatment of pionic atoms level widths and shifts using the Kemmer-Duffin-Petiau equation. Interactions are introduced in a Lorentz invariant way. An analytical transformation is shown that connects between different sets of interactions. The Kisslinger potential is obtained as a special case of a scalar-tensor optical potential. Results are shown in the accompanying paper.
TL;DR: A formalism for calculating three effects of nuclear dissipation on neutron emission prior to fission is presented: Kramers's modification of the Bohr-Wheeler statistical-model result for the fission width; the transient time required to build up the quasistationary probability flow over the barrier; and the mean time required for the system to descend from the saddle point to scission.
Abstract: We present a formalism for calculating three effects of nuclear dissipation on neutron emission prior to fission: (1) Kramers's modification of the Bohr-Wheeler statistical-model result for the fission width; (2) the transient time required to build up the quasistationary probability flow over the barrier; and (3) the mean time required for the system to descend from the saddle point to scission. Each of these effects increases the average multiplicity of neutrons emitted prior to fission relative to that calculated with a standard statistical model. The multiplicity calculation includes the dependence of the ratio ${a}_{f}$/${a}_{\mathrm{n}}$ of level-density parameters for fission and neutron emission upon dissipation that is imposed by the low-energy fission probability. We use this formalism to analyze recent experimental results of Gavron et al. for the reaction $^{16}\mathrm{O}$${+}^{142}$Nd\ensuremath{\rightarrow}${\mathrm{}}^{158}$Er at 207 MeV, where 2.7\ifmmode\pm\else\textpm\fi{}0.4 neutrons are emitted prior to fission compared to 1.6 neutrons calculated with a standard statistical model. This determines the limit \ensuremath{\beta}\ensuremath{\lesssim}5\ifmmode\times\else\texttimes\fi{}${10}^{21}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ for the reduced nuclear dissipation coefficient \ensuremath{\beta} defined as the ratio of the dissipation coefficient to the inertia.
TL;DR: Rosenbluth separations of electron scattering response functions for uranium targets were made with data using measurements from five laboratory angles (60/sup 0/, 90/Sup 0), 134.5/sup 1, 140/sup 2, and 160/sup 3) at three-momentum transfers ranging from 280 to 500 MeV/c as mentioned in this paper.
Abstract: Rosenbluth separations of electron scattering response functions for uranium targets were made with data using measurements from five laboratory angles (60/sup 0/, 90/sup 0/, 134.5/sup 0/, 140/sup 0/, and 160/sup 0/) at three-momentum transfers ranging from 280 to 500 MeV/c. The separations were made to determine if previously reported quenching of the longitudinal response function persisted in targets with large atomic number. The results are compared to relativistic Fermi gas calculations and calculations following the formalism of Rosenfelder. The measured transverse response functions agree quite well with the Rosenfelder-type calculations and almost as well with the relativistic Fermi gas calculations. The measured longitudinal response functions show significant quenching at low q. This quenching diminishes with increasing q but is never quite overcome.
TL;DR: Using the conservation law for the current, the lifetime of the event is defined in terms of the probability of finding the nuclear system in the potential well corresponding to the ground-state deformation using the time-integrated escape rate across the collective potential barrier.
Abstract: Induced nuclear fission is described as a transport process of the fission degree of freedom over the fission barrier. The lifetime of the event is defined in terms of the probability of finding the nuclear system in the potential well corresponding to the ground-state deformation. This definition appears as a natural generalization to nonstationary transport processes of the usual expression for the lifetime. Using the conservation law for the current we relate the lifetime to the time-integrated escape rate across the collective potential barrier.
TL;DR: The expectation value of the relativistic energy operator with the nonrelativistic wave function is a fairly good approximation, but approximate expressions involving expansions in powers of the momentum are shown to be quite unreliable.
Abstract: We formulate relativistic and nonrelativistic two-particle dynamics in such a manner that the two-body binding energies are the same for both We then formulate and solve the relativistic Faddeev equations for a simple s-wave potential (Malfliet-Tjon V) The relativistic effects are small (about 3%) and reduce the three-body binding energy The expectation value of the relativistic energy operator with the nonrelativistic wave function is a fairly good approximation, but approximate expressions involving expansions in powers of the momentum are shown to be quite unreliable
TL;DR: Differential cross sections for proton elastic scattering from /sup 42,44,48/Ca have been measured and the optical potential parameters were used to calculate nuclear matter radius information for the calcium isotopic series, which is compared to previous results.
Abstract: Differential cross sections for proton elastic scattering from $^{42}$,44,48Ca have been measured at seven energies in the laboratory energy range from 21.0 to 48.4 MeV, and for $^{40}\mathrm{Ca}$ at six energies between 25.0 and 45.0 MeV. Measurements were made at 2.5\ifmmode^\circ\else\textdegree\fi{} intervals from 10\ifmmode^\circ\else\textdegree\fi{} to 90\ifmmode^\circ\else\textdegree\fi{} (laboratory angles), and at 5.0\ifmmode^\circ\else\textdegree\fi{} intervals between 90\ifmmode^\circ\else\textdegree\fi{} and 170\ifmmode^\circ\else\textdegree\fi{}. Relative errors in the data are typically between 3% and 4%; the scale errors are also 3%. The data have been analyzed by both nonrelativistic and relativistic optical models. The optical potential parameters were used to calculate nuclear matter radius information for the calcium isotopic series, which is compared to previous results.
TL;DR: In this paper, deep inelastic scattering cross sections have been measured for /sup 40/Ca and /sup 48/Ca at electron energies between 100 and 375 MeV at scattering angles of 90/sup 0/ and 140 /sup 0/.
Abstract: Deep inelastic scattering cross sections have been measured for /sup 40/Ca and /sup 48/Ca at electron energies between 100 and 375 MeV at scattering angles of 90/sup 0/ and 140/sup 0/. Longitudinal and transverse response functions at three-momentum transfers between 250 and 410 MeV/c have been extracted using a Rosenbluth separation. The response functions are compared to calculations modeling the nucleus as a noninteracting relativistic Fermi gas. The model is found to agree with the observed transverse response function in the region of expected quasi-free nucleon knockout, but the model overestimates the observed longitudinal response. Comparisons of the response functions of the two isotopes are made, and differences between /sup 40/Ca and /sup 48/Ca are seen.
TL;DR: The mean-square spin value of the compound nucleus /sup 248/Cf has been determined from fission fragment angular distributions for the /sup 12/C+ /Sup 236/U and /sup 16/O+ /sup 232/Th reactions at sub-barrier bombarding energies, suggesting that quasifission processes are not playing a significant role.
Abstract: The mean-square spin value of the compound nucleus /sup 248/Cf has been determined from fission fragment angular distributions for the /sup 12/C+ /sup 236/U and /sup 16/O+ /sup 232/Th reactions at sub-barrier bombarding energies. The anisotropy and hence the mean-square spin values are much larger than predicted by models which reproduce the cross section enhancement observed in the sub-barrier fusion excitation functions. A similar experiment with the spherical target /sup 208/Pb also leads to larger anisotropies and mean-square spin values than predicted by various fusion models, including an especially complete coupled channels calculation. Supplementary fragment-fragment coincidence experiments have been performed with the heavier targets to confirm that the observed fission is associated with full momentum transfer. The mass distribution for the /sup 12/C+ /sup 236/U reaction has been measured at two angles and found to be independent of angle. This last result suggests that quasifission processes are not playing a significant role.
TL;DR: The spin observables in quasielastic proton scattering are calculated in a simple relativistic model where the NN interaction is assumed to depend on the enhancement of the lower components of nucleon wave functions (because of strong nuclear potentials).
Abstract: The spin observables in quasielastic proton scattering are calculated in a simple relativistic model where the NN interaction is assumed to depend on the enhancement of the lower components of nucleon wave functions (because of strong nuclear potentials). This enhancement is characterized by an average effective mass M( of (0.8--0.9)M which is calculated in an eikonal model. The M( dependence of the NN interaction is taken from relativistic impulse approximation calculations. The polarization is found to decrease by 40 percent compared to the free NN value at 500 MeV. Next, simple formulas are provided to estimate the effects of spin-orbit potential distortions on spin observables. At 500 MeV and 18.5/sup 0/ in /sup 208/Pb, the polarization is decreased by 5 percent while D/sub l/'l and D/sub s/'s are decreased by 15 percent and D/sub n/n is almost unchanged.
TL;DR: A systematic study of the radioactive background in materials used in Ge-detector fabrication was conducted prior to the construction of an ultralow-background, 135 cm/sup 3/ prototype detector.
Abstract: A systematic study of the radioactive background in materials used in Ge-detector fabrication was conducted prior to the construction of an ultralow-background, 135 cm/sup 3/ prototype detector. The background from primordial radioactivities in the new system was lower by factors of between 1.5 x 10/sup 3/ and 2.5 x 10/sup 4/ when compared to commercial low-background detectors. Data were collected for 8089 h with the detector located 1438 m underground, resulting in improved lower limits for the half-lives for both two-neutrino and neutrinoless ..beta beta.. decay of /sup 76/Ge to the ground state of /sup 76/Se and for the neutrinoless ..beta beta.. decay to the first excited state of /sup 76/Se. The results of four recent theoretical calculations are compared in detail and used to extract limits on , the Majorana mass of ..nu../sub e-italic/, and on the amplitudes of the couplings of right-handed Majorana neutrinos. The best combination of the lowest background data from recent experiments results in a new limit T-italic/sub 1/2//sup 0//sup ..nu../approx. >3 x 10/sup 23/ yr, corresponding to <2.4 eV neglecting right-handed couplings or 2.8 eV including both right-handed neutrino couplings.
TL;DR: The resulting three-nucleon force differs from the original Tucson-Melbourne potential only in the presence of several new nonlocal terms, and in the specification of the choice of ambiguity parameters in the latter potential.
Abstract: Those two-pion-exchange three-nucleon forces which arise from nuclear processes that involve only pions and nucleons are calculated. Among the processes which contribute are pion seagulls (e.g., nucleon-antinucleon pair terms) and overlapping, retarded pion exchanges. The resulting potential is shown to be a (v-italic/c-italic)/sup 2/ relativistic correction, and satisfies nontrivial constraints from special relativity. The relativistic ambiguities found before in treatments of relativistic corrections to the one-pion-exchange nuclear charge operator and two-body potential are also present in the three-nucleon potential. The resulting three-nucleon force differs from the original Tucson-Melbourne potential only in the presence of several new nonlocal terms, and in the specification of the choice of ambiguity parameters in the latter potential.
TL;DR: A remedy to this problem is presented that has the added advantage of improving the fit to the phase shifts in the P-italic/sub 11/ channel by using physical values of the coupling constant in the crossed diagram which reduces the repulsion rather than adds attraction.
Abstract: Most applications of the cloudy bag model to ..pi..N scattering involve unitarizing the bare diagrams arising from the Lagrangian by iterating in a Lippmann-Schwinger equation. However, analyses of the renormalization of the coupling constant proceed by iterating the Lagrangian to a given order in the bare coupling constant. These two different approaches means there is an inconsistency between the calculation of phase shifts and the calculation of renormalization. A remedy to this problem is presented that has the added advantage of improving the fit to the phase shifts in the P-italic/sub 11/ channel. This is achieved by using physical values of the coupling constant in the crossed diagram which reduces the repulsion rather than adds attraction. This approach can be justified by examining equations for the ..pi pi..N system that incorporate three-body unitarity.
TL;DR: It is found that a multidimensional model is necessary to describe the enhanced fusion cross sections in oxygen and the two-dimensional incoming wave boundary condition model suggests that a complete description of the fusion, inelastic, and elastic cross sections is possible.
Abstract: We have measured the sub-barrier fusion cross sections for 16,17,18O on 16O and we present the data and the experimental method in detail. The data were analyzed with a one-dimensional potential barrier inversion model, a two-dimensional incoming wave boundary condition model, and a two-dimensional Wentzel-Kramers-Brillouin model. We find that a multidimensional model is necessary to describe the enhanced fusion cross sections in oxygen and the two-dimensional incoming wave boundary condition model suggests that a complete description of the fusion, inelastic, and elastic cross sections is possible.
TL;DR: It is shown that the finite basis results can be obtained from the classical model results using the Gaussian quadrature to evaluate the former and Hermite quadratures for the latter.
Abstract: The relation between the finite basis adiabatic model and the classical adiabatic model (corresponding to a complete set of degenerate states) is elucidated when the internal system is rotational or vibrational. It is shown that the finite basis results can be obtained from the classical model results using the Gaussian quadrature to evaluate the former and Hermite quadrature for the latter.
TL;DR: The Glauber model comparison suggests that the nucleus-nucleus total reaction cross section at intermediate and high energies is governed by the nucleon-n nucleon cross section.
Abstract: Elastic scattering angular distributions for $^{12}\mathrm{C}$ on $^{12}\mathrm{C}$, $^{40}\mathrm{Ca}$, $^{90}\mathrm{Zr}$, and $^{208}\mathrm{Pb}$ were measured for projectile energies between 10 and 35 MeV/nucleon Total reaction cross sections were extracted by an optical model analysis and compared to the prediction of the Glauber model This comparison suggests that the nucleus-nucleus total reaction cross section at intermediate and high energies is governed by the nucleon-nucleon cross section
TL;DR: A detailed study of pion production in inelastic and central nucleus-nucleus collisions was carried out using a 2 m streamer spectrometer in this paper, where nuclear targets mounted inside the streamer chamber were exposed to nuclear beams of 4.5 GeV/c/nucleon momentum.
Abstract: A detailed study of pion production in inelastic and central nucleus-nucleus collisions was carried out using a 2 m streamer spectrometer. Nuclear targets mounted inside the streamer chamber were exposed to nuclear beams of 4.5 GeV/c/nucleon momentum. A systematic study of the influence of the central trigger on observed data is performed. The data on multiplicities, rapidities, transverse momenta, and emission angles of negative pions are presented for various pairs of colliding nuclei. Intercorrelations between various characteristics are studied and discussed. The results are compared with predictions of some theoretical models. It is shown that the main features of the pion production in nuclear collisions can be satisfactorily described by a model assuming independent nucleon-nucleon collisions with subsequent cascading process. However, the observed correlation between \ensuremath{\Lambda} and pion characteristics seems to be unexplained by this picture.