Showing papers in "Physical Review C in 1979"
TL;DR: In this article, a unified nuclear potential for the description of large-scale nuclear collective motion was developed by generalizing the modified liquid-drop model so that two semi-infinite slabs of constant-density nuclear matter have minimum energy at zero separation, this potential is given in terms of a double volume integral of a Yukawa-plusexponential folding function.
Abstract: We develop a unified nuclear potential for the description of large-scale nuclear collective motion and find that it satisfactorily reproduces experimental data for heavy-ion elastic scattering, fusion, fission, and ground-state masses. Obtained by generalizing the modified liquid-drop model so that two semi-infinite slabs of constant-density nuclear matter have minimum energy at zero separation, this potential is given in terms of a double volume integral of a Yukawa-plus-exponential folding function. For heavy nuclear systems the resulting heavy-ion interaction potential is similar to the proximity potential of Swiatecki and co-workers. However, for light nuclear systems our potential lies slightly below the proximity potential at all nuclear separations. For heavy nuclei fission barriers calculated with our Yukawa-plus-exponential model are similar to those calculated with the liquid-drop model. However, for light nuclei the finite range of the nuclear force and the diffuse nuclear surface lower the fission barriers relative to those calculated with the liquid-drop model. Use of a Wigner term proportional to $\frac{|N\ensuremath{-}Z|}{A}$ in the nuclear mass formula resolves the major part of the anomaly between nuclear radii derived from elastic electron scattering on the one hand and from ground-state masses and fission-barrier heights on the other.NUCLEAR REACTIONS $^{4}\mathrm{He}$+$^{12}\mathrm{C}$, $^{16}\mathrm{O}$+$^{28}\mathrm{Si}$, $^{84}\mathrm{Kr}$+$^{208}\mathrm{Pb}$; calculated heavy-ion interaction potential. $^{16}\mathrm{O}$+$^{28}\mathrm{Si}$, $E=37.7, 81.0, 215.2$ MeV; calculated elastic-scattering angular distribution. $^{32}\mathrm{S}$+$^{27}\mathrm{Al}$, $^{35}\mathrm{Cl}$+$^{62}\mathrm{Ni}$, $^{16}\mathrm{O}$+$^{208}\mathrm{Pb}$; calculated compound-nucleus cross section. Calculated fission-barrier heights and ground-state masses for nuclei throughout Periodic Table. Nuclear potential energy of deformation, liquid-drop model, droplet model, modified liquid-drop model, Yukawa-plus-exponential model, proximity potential, Woods-Saxon potential, double-folding potential, optical model, ingoing-wave boundary condition, single-particle corrections, Strutinsky's method.
439 citations
TL;DR: In this article, the authors analyzed the effect of Bose-Einstein symmetrization on pion interferometry in the context of relativistic nuclear collisions and derived expressions for the degree of coherence of the produced pion field and the geometric structure of the chaotic field component.
Abstract: The topic of pion interferometry (identical pion correlations) is analyzed in detail in the context of relativistic nuclear collisions. Through an exactly solvable field theoretic model specified by an ensemble of classical pion source currents, ${J}_{i}(x)$, we calculate the ${\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}$ correlation function $R({\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{k}}_{1},{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{k}}_{2})$ for chaotic, coherent, and partially coherent pion fields. We analyze how $R$ can be used to determine the degree of coherence of the produced pion field as well as the geometric structure of the source of the chaotic field component. With this model we are able to distinguish between those correlations due to Bose-Einstein symmetrization (the Hanbury-Brown and Twiss or Goldhaber effect) and those due to specific multiparticle production dynamics. In particular we show that Bose-Einstein symmetrization dominates the form of $R({\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{k}}_{1},{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{k}}_{2})$ only for chaotic pion fields produced over a time scale large compared to ${{m}_{\ensuremath{\pi}}}^{\ensuremath{-}1}$. If, due to collective phenomena, there is some coherence of the pion field, then the intercept $R(\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{k},\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{k})=2\ensuremath{-}{D}^{2}(\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{k})$ is shown to measure mode by mode that degree of coherence $D(\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{k})$. Geometric information about the source of the chaotic field component may be extracted from $R({\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{k}}_{1},{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{k}}_{2})$ only after $D(\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{k})$ has been determined. Expressions are also derived that incorporate distortions of $R$ due to one-body and two-body final state interactions. These expressions will be numerically evaluated in a subsequent paper. Relative ${\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}$ interactions lead to a penetration factor $G({\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{k}}_{1},{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{k}}_{2})$ that modulates the form of $R({\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{k}}_{1},{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{k}}_{2})$. An expression for $G$ is obtained to all orders in the one-body optical potential but to first order in the two-body potential. This penetration factor must be evaluated before data for $R$ can be used to determine $D(\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{k})$.NUCLEAR REACTIONS Relativistic nuclear collisions, multipion inclusive cross sections, ${\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}$ correlations, Hanbury-Brown-Twiss effect, partially coherent fields, final state interactions.
287 citations
TL;DR: In this paper, the intranuclear cascade model of Chen et al. was extended to high-energy reactions between two heavy ions, and the results of the calculations were compared with experimental results for the inclusive proton and pion cross sections, two-particle correlations, particle multiplicity distributions, and spallation cross section distributions.
Abstract: We have extended the intranuclear cascade model of Chen et al. to high-energy reactions between two heavy ions. The results of the calculations are compared with experimental results for the inclusive proton and pion cross sections, two-particle correlations, particle multiplicity distributions, and spallation cross section distributions from light (/sup 12/C + /sup 12/C) to heavy (/sup 40/Ar + /sup 238/U) projectile-target systems in the laboratory bombarding energy range E/A = 250--1000 MeV. The comparison shows that the model is fairly successful in reproducing the various aspects of high-energy reactions between heavy ions. The discrepancies between the calculations and the experimental results are probably due to shortcomings of the present calculation, particularly the neglect of interactions between cascade particles, and do not provide strong evidence for cooperative phenomena in high-energy heavy-ion reactions. We also show that the assumption that high particle multiplicities are indicative of central (small impact parameter) collisions is well founded for heavy projectile-target systems.
262 citations
TL;DR: In this paper, the antineutrino and electron spectra associated with various nuclear fuels are calculated and the sources of uncertainties in the spectrum are identified and analyzed in detail.
Abstract: The antineutrino and electron spectra associated with various nuclear fuels are calculated. While there are substantial differences between the spectra of different uranium and plutonium isotopes, the dependence on the energy and flux of the fission-inducing neutrons is very weak. The resulting spectra can be used for the calculation of the antineutrino and electron spectra of an arbitrary nuclear reactor at various stages of its refueling cycle. The sources of uncertainties in the spectrum are identified and analyzed in detail. The exposure time dependence of the spectrum is also discussed. The averaged cross sections of the inverse neutron β decay, weak charged and neutral-current-induced deuteron disintegration, and the antineutrino-electron scattering are then evaluated using the resulting ν_e spectra.
[RADIOACTIVITY, FISSION 235U, 238U, (^239)Pu, (^240)Pu, (^241)Pu, antineutrino and electron spectra calculated. σ for ν induced reactions analyzed.]
198 citations
TL;DR: In this article, a unified shell-model description of nuclear deformation valid throughout the periodic table is presented, and it is shown that deformation is produced by the isoscalar component of the neutron-proton interaction in this region, as in the lighter ($2s,$1d$)-shell region.
Abstract: A unified shell-model description of nuclear deformation valid throughout the periodic table is presented. Microscopic calculations for the Zr and Mo isotopes are carried out in the frameworks of the shell model and the Hartree-Fock-Bogoliubov method, respectively, to study the shape transition in these nuclei. It is shown that deformation is produced by the isoscalar component of the neutron-proton ($n\ensuremath{-}p$) interaction in this region, as in the lighter ($2s$,$1d$)-shell region. Deformation sets in when the $T=0$ $n\ensuremath{-}p$ interaction dominates over the sphericity-favoring pairing interaction between $T=1$ pairs of nucleons. When shell effects are important, as for the light and medium-weight regions mentioned above, the simultaneous occupation of neutrons and protons of spin-orbit "partner" orbitals plays a crucial role in determining the onset of deformation. However, their effect is probably less important in the rare-earth and transuranic regions due to the rapid accumulation of single-particle orbitals.NUCLEAR STRUCTURE Microscopic description of nuclear deformation; shell-model calculations of $^{96}\mathrm{Zr}$, $^{98}\mathrm{Zr}$, and $^{100}\mathrm{Zr}$; HFB calculations of $^{98}\mathrm{Mo}$-$^{110}\mathrm{Mo}$; discussion of light and heavy deformed nuclei; relation to interacting boson approximation.
177 citations
TL;DR: In this article, the half-lives of the Na isotopes up to /sup 32/Na were determined, in most cases, in absolute value, by measuring the branching ratio P/sub n/ for /sup 29/Na, /sup 30/Na and /sup 31/Mg.
Abstract: The ..gamma.. activities from the ..beta.. decay of Na isotopes up to /sup 32/Na, which are formed in high-energy fragmentation and analyzed through mass spectrometry techniques, are observed, as well as those from their Mg or Al descendants. Their intensities are measured, in most cases, in absolute value. The radioactive half-lives of /sup 29/Mg, /sup 30/Mg, and /sup 31/Mg are determined. Delayed-neutron branching ratios P/sub n/ are measured for /sup 29/Na, /sup 30/Na, and /sup 32/Na. In some cases, partial branching ratios to excited states of the daughter nucleus are also measured. The most prominent ..gamma.. ray in the ..beta.. decay of even Na isotopes is assigned to 2/sup +/ ..-->.. 0/sup +/ transition in the daughter Mg isotopes. The position of the first excited 2/sup +/ level is therefore deduced for /sup 30/Mg and /sup 32/Mg. For /sup 32/Mg, the excitation energy drops markedly. It is taken as an indication of a stronger deformation for that isotope.
172 citations
TL;DR: In this paper, the fragmentation of /sup 56/Fe at 1.88 GeV/nucleon has been studied on H, Li, Be, C, S, Cu, Ag, Ta, Pb, and U targets.
Abstract: The fragmentation of /sup 56/Fe at 1.88 GeV/nucleon has been studied on H, Li, Be, C, S, Cu, Ag, Ta, Pb, and U targets. The detection apparatus consisted of a simple transmission detector. A method is presented which eliminates the effects of multiple interactions in the targets which were typically half an interaction-length thick. Elemental production cross sections, sigma (Z), were measured for Z = 13 to 25. Measured charge-changing cross sections, sigma/sub DeltaZ/ > or = 1, and derived mass-changing cross sections, sigma/sub DeltaA/ > or = 1, are presented for each target. The sigma (Z) factor into a term which depends only on the target and a term which depends only on the fragment observed. The sigma/sub DeltaZ/ > or = 1 and sigma/sub DeltaA/ > or = 1 follow a simple geometric behavior. The cross section for the removal of one proton from the /sup 56/Fe projectile is enhanced for the heavier targets. This effect is described by a model assuming Coulomb dissociation. The sigma (Z) for /sup 56/Fe on the H target are compared to the semiempirical formulas of Silberberg and Tsao.
133 citations
TL;DR: In this paper, Kerman, McManus, and Thaler optical potential formalism and the impulse approximation are used to compute the total and reaction cross sections for a number of target nuclei at energies ranging from 100 to 2200 MeV.
Abstract: Proton-nucleus total and reaction cross sections are computed for a number of target nuclei at energies ranging from 100 to 2200 MeV using the Kerman, McManus, and Thaler optical potential formalism and the impulse approximation. Corrections due to Pauli, short-range dynamical, and center-of-mass correlations are included in the calculations. In addition, the electric form factor of the neutron and the nucleon magnetic moments are included in deriving the necessary proton densities from available empirical charge distributions. The proton-nucleon scattering amplitudes are obtained from phase shift solutions or directly from the published $N\ensuremath{-}N$ data. The proton and neutron point densities are deduced where possible from analyses of electron and proton scattering or from Hartree-Fock predictions if the appropriate elastic angular distribution data are unavailable. An estimate of the uncertainty in the calculated total cross sections is given. The total and reaction cross sections computed in this way are shown to be in very good agreement with the data above 400 MeV but overestimate the data by 15-25% at lower energies, indicating that the approximate multiple scattering calculations generally performed near 1 GeV are inadequate when applied at energies below 400 MeV. Several theoretical improvements are suggested for this lower energy range and some numerical estimates are given. Analysis of total cross section data is also shown to be an unsuitable method for obtaining accurate measurements of neutron matter densities.NUCLEAR REACTIONS proton-nucleus scattering; total and reaction cross sections; ${E}_{p}=100 \mathrm{to} 2200$ MeV; targets $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{27}\mathrm{A}1$, $^{56}\mathrm{Fe}$, $^{63,65}\mathrm{Cu}$, $^{72,74}\mathrm{Ge}$, $^{127}\mathrm{I}$, and $^{208}\mathrm{Pb}$; Kerman, McManus, and Thaler optical potential; target nucleon correlations.
119 citations
TL;DR: In this paper, the authors measured the total fusion cross sections for three different fusion systems over the energy range from 1.5 to 3 times the Coulomb barrier energy, and deduced fusion barrier parameters.
Abstract: Measurements of the total fusion cross sections for $^{12}\mathrm{C}$ + $^{12}\mathrm{C}$, $^{13}\mathrm{C}$, $^{14}\mathrm{N}$, $^{15}\mathrm{N}$, $^{16}\mathrm{O}$, $^{18}\mathrm{O}$, and $^{19}\mathrm{F}$ and $^{16}\mathrm{O}$ + $^{16}\mathrm{O}$ have been performed over the energy range from 1.5 to 3 times the Coulomb barrier energy. Fusion barrier parameters were extracted for each system. Three systems, $^{12}\mathrm{C}$ + $^{12}\mathrm{C}$, $^{12}\mathrm{C}$ + $^{16}\mathrm{O}$, and $^{16}\mathrm{O}$ + $^{16}\mathrm{O}$, show rather pronounced oscillatory structure in the energy dependence of the fusion cross sections. The maximum fusion cross sections for the systems studied vary by as much as 10-20%, depending on the particular entrance channel. The specific structure of the interacting nuclei clearly does have an effect; the fusion process is not entirely dominated by the macroscopic features of the ion-ion interaction.NUCLEAR REACTIONS, fusion, measured ${\ensuremath{\sigma}}_{\mathrm{fusion}}(E)$; $^{12}\mathrm{C}$ + $^{12}\mathrm{C}$, $7.4l~{E}_{\mathrm{c}.\mathrm{m}.}l~31.2$ MeV; $^{12}\mathrm{C}$ + $^{13}\mathrm{C}$, $7.6l~{E}_{\mathrm{c}.\mathrm{m}.}l~24.9$ MeV; $^{12}\mathrm{C}$ + $^{14}\mathrm{N}$, $15.1l~{E}_{\mathrm{c}.\mathrm{m}.}l~24.0$ MeV; $^{12}\mathrm{C}$ + $^{15}\mathrm{N}$, $8.9l~{E}_{\mathrm{c}.\mathrm{m}.}l~26.7$ MeV; $^{12}\mathrm{C}$ + $^{16}\mathrm{O}$, $12.9l~{E}_{\mathrm{c}.\mathrm{m}.}l~27.0$ MeV; $^{12}\mathrm{C}$ + $^{18}\mathrm{O}$, $11.9l~{E}_{\mathrm{c}.\mathrm{m}.}l~28.0$ MeV; $^{12}\mathrm{C}$ + $^{19}\mathrm{F}$, $11.6l~{E}_{\mathrm{c}.\mathrm{m}.}l~27.1$ MeV; $^{16}\mathrm{O}$ + $^{16}\mathrm{O}$, $14.9l~{E}_{\mathrm{c}.\mathrm{m}.}l~36.0$ MeV; deduced fusion barrier parameters.
107 citations
TL;DR: The microscopic spin-independent proton-nucleus optical potential defined by Kerman, McManus, and Thaler as mentioned in this paper was used to analyze recent 0.8 GeV polarized proton elastic scattering data from $^{40,48}\mathrm{Ca}, $^{58,64}\mathm{Ni} and $^{116,124}\math mn{Sn}, and $€ 208}.
Abstract: The microscopic spin-independent proton-nucleus optical potential defined by Kerman, McManus, and Thaler is used to analyze recent 0.8 GeV polarized proton elastic scattering data from $^{40,48}\mathrm{Ca}$, $^{58,64}\mathrm{Ni}$, $^{116,124}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$. Second-order effects due to target nucleon correlations are included in both the central and spin-orbit parts of the proton-nucleus optical potential. Electromagnetic corrections to the proton density which arise from the electric and magnetic form factors of the neutron, and from the magnetic form factor of the proton, are also calculated. A discussion is presented regarding uncertainties in the nucleon-nucleon amplitudes used in construction of the potential, and also discrete ambiguities which arise from fitting the limited set of nucleon-nucleon data available near 1 GeV are examined. Approximately model-independent forms are assumed for the target neutron density distributions, thereby allowing the statistical and model-dependence errors to be estimated. Neutron density and rms radii are deduced and compared to Hartree-Fock predictions, with good agreement found for most of the seven nuclei studied. Because of the uncertainty in the proton-nucleon amplitudes, neutron density and radius differences are considered more reliable than individual absolute values. Owing to the inclusion of certain second-o\ifmmode \acute{r}\else \'{r}\fi{}der terms discussed here, an accurate determination of these differences is obtained.
90 citations
TL;DR: In this article, cross sections and spectra were measured for the emission of protons, deuterons, and alpha particles for 15-MeV neutrons on natural iron, nickel, and chromium.
Abstract: Cross sections have been measured for the emission of protons, deuterons, and alpha particles for 15-MeV neutrons on $^{54,56}\mathrm{Fe}$, $^{58,60}\mathrm{Ni}$, $^{50,52}\mathrm{Cr}$, and $^{63,65}\mathrm{Cu}$, as well as on natural iron, nickel, and chromium. A quadrupole spectrometer served to detect particles with energies as low as 1 MeV. For some of the targets, a substantial fraction of the charged-particle spectrum is at energies below the Coulomb barrier. Cross sections and spectra are compared with statistical and pre-equilibrium model predictions.NUCLEAR REACTIONS $^{50,52}\mathrm{Cr}$, Cr, $^{54,56}\mathrm{Fe}$, Fe, $^{58,60}\mathrm{Ni}$, Ni, $^{63,65}\mathrm{Cu}$, ($n$,$p$), ($n$,$d$), ($n$,$\ensuremath{\alpha}$), $E=14.8$ MeV; measured $\ensuremath{\sigma}({E}_{p},\ensuremath{\theta})$, (${E}_{d}$, $\ensuremath{\theta}$), (${E}_{\ensuremath{\alpha}}$, $\ensuremath{\theta}$), enriched and natural targets. Hauser-Feshbach analysis, deduced reaction mechanism.
TL;DR: The shape of the low energy elastic scattering cross section for light elements is particularly sensitive to the relative strength of the repulsive and velocity-dependent attractive parts of the optical potential, and is well reproduced by pionic atom parameters.
Abstract: We have estimated the parameters of the optical potential for low energy pion-nucleus scattering from the values obtained empirically in the analysis of pionic atom data. The ambiguities in these parameters are discussed. The shape of the low energy elastic scattering cross section for light elements is particularly sensitive to the relative strength of the repulsive and velocity-dependent attractive parts of the optical potential, and is well reproduced by pionic atom parameters. Absorption is the dominant reaction channel at low energies. Pion nucleon phase shifts are used to extrapolate optical model parameters to higher energies. The behavior of the elastic and inelastic angular distributions and of various partial cross sections is discussed, and compared with experiment.NUCLEAR REACTIONS Calculated pion-nucleus optical potential, elastic scattering, inelastic scattering and partial cross sections. 30, 40, 50 MeV on various targets. 116-220 MeV on individual targets.
TL;DR: In this article, the experimental results were analyzed within the framework of the pre-equilibrium exciton model together with the evaporation theory for complete charged light-particle (Z or = 140/sup 0/) spectra.
Abstract: Complete charged light-particle (Z or = 140/sup 0/) the spectra exhibit characteristic evaporation behavior with approximately the same slope for each target nucleus for a given observed particle. The slopes of the evaporation peaks (corresponding to a temperature of 2--3 MeV) for the different particle type are also rather similar. The experimental results were analyzed within the framework of the pre-equilibrium exciton model together with the evaporation theory. The pre-equilibrium exciton model usingmore » a 2p-1h initial configuration generally reproduces the experimental angle-integrated energy spectra reasonably well in shape, but underestimates especially the proton yield in the region of high-energy continuums« less
TL;DR: In this article, the energy spectra and angular distributions of charged light particles were measured for the bombardment of 80 MeV deuterons on two triple-counter telescopes using combinations of EDE and time-of-flight techniques for particle identification.
Abstract: Complete energy spectra and angular distributions of charged light particles ($Z\ensuremath{\le}2$ and $A\ensuremath{\le}4$) were measured for the bombardment of 80 MeV deuterons on $^{27}\mathrm{Al}$ and $^{58}\mathrm{Ni}$ and 70 MeV deuterons on $^{90}\mathrm{Zr}$, $^{208}\mathrm{Pb}$, and $^{232}\mathrm{Th}$. The charged particles were detected by two triple-counter telescopes using combinations of $\ensuremath{\Delta}E\ensuremath{-}E$ and time-of-flight techniques for particle identification. The experimental results are presented in cross sections doubly differential in energy and angle, as well as in angle- and energy-integrated cross sections. For all the nuclei studied, the proton energy spectra show large deuteron-breakup peaks centered at approximately half of the incident deuteron energy at forward angles. The energy spectra for the same type of emitted particle are similar in shape for all nuclei at a given angle except in the region of the low-energy evaporation peak. The magnitude of evaporation peak varies rapidly with target mass. The total nonequilibrium yield of charged light particles is approximately $(300\ifmmode\pm\else\textpm\fi{}50){A}^{\frac{1}{3}}$ mb. The angular distributions for the high-energy particles are strongly forward peaked and are nearly isotropic for the low-energy particles. The deuteron and triton yields increase with $A$; while those for $p$, $^{3}\mathrm{He}$, and $\ensuremath{\alpha}$ particles decrease with $A$. The total charged light-particle yield is found to be roughly two times the total reaction cross section (${\ensuremath{\sigma}}_{R}$) for light- and medium-mass nuclei; while it is less than ${\ensuremath{\sigma}}_{R}$ for heavy nuclei. The experimental results were analyzed within the framework of the pre-equilibrium exciton model together with evaporation theory. The pre-equilibrium exciton model using a 3p-1h initial configuration reproduces the experimental angle-integrated energy spectra for all target nuclei studied both in spectral shapes and in magnitudes for all emitted particles except protons. The deuteron-breakup yield in the proton spectra was compared with the Serber model. When the breakup yield is added to the pre-equilibrium yield, agreement is obtained for the proton spectra.NUCLEAR REACTIONS $^{27}\mathrm{Al}$, $^{58}\mathrm{Ni}$, $^{90}\mathrm{Zr}$, $^{208}\mathrm{Pb}$, $^{232}\mathrm{Th}$ ($d$,$\mathrm{xp}$), ($d$,$\mathrm{xd}$), ($d$, $\mathrm{xt}$), ($d$, $x^{3}\mathrm{He}$), ($d$,$x\ensuremath{\alpha}$), $E=80, 70$ MeV $\ensuremath{\theta}=20\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}150\ifmmode^\circ\else\textdegree\fi{}$, measured $\frac{{d}^{2}\ensuremath{\sigma}}{d\ensuremath{\Omega}d\ensuremath{\epsilon}}$, deduced $\frac{d\ensuremath{\sigma}}{d\ensuremath{\epsilon}}$ and $\ensuremath{\sigma}(E)$. Comparisons with pre-equilibrium exciton, compound nuclear evaporation and deuteron-breakup models.
TL;DR: In this paper, the production cross sections for the production of approximately 100 radionuclides in the interaction of silver with 25.2 GeV ions and 300 GeV protons have been determined.
Abstract: Cross sections for the production of approximately 100 radionuclides in the interaction of silver with 25.2 GeV $^{12}\mathrm{C}$ ions and 300 GeV protons have been determined. The results have been parametrized in terms of a 10-parameter equation which accurately reproduces the measured isobaric- and mass-yield curves. The cross sections of products in the $A=40\ensuremath{-}106$ mass range are consistent with the factorization hypothesis. At lower mass numbers, the yields of products formed in reactions induced by $^{12}\mathrm{C}$ ions are enhanced by over a factor-of-2 relative to the ratio of total reaction cross sections. The results are compared with Monte Carlo cascade-evaporation calculations and with the abrasion-ablation model.NUCLEAR REACTIONS Ag($^{12}\mathrm{C}$, spallation) and Ag($p$, spallation) ${E}_{^{12}\mathrm{C}}=25.2$ GeV, ${E}_{P}=300$ GeV. Production cross sections for \ensuremath{\sim} 100 radionuclides; deduced charge dispersions and mass-yield curves. Comparison with cascade-evaporation and abrasion-ablation calculations.
TL;DR: In this article, a clean-cut fireball model is used to calculate the number of participant nucleons in the abrasion stage and the excitation energy of the spectators (primary residues).
Abstract: Calculations of large mass fragment yields from high-energy heavy-ion reactions are performed based on the abrasion-ablation model. The geometrical picture of the clean-cut fireball model is used to calculate the number of participant nucleons in the abrasion stage and the excitation energy of the spectators (primary residues). A standard statistical evaporation code is used to calculate the ablation stage. Results from this model show an overall agreement with experimental data, although some systematic discrepancies are found and discussed. A frictional spectator interaction is introduced which increases the average excitation energy of primary fragments and improves the results considerably.NUCLEAR REACTIONS Relativistic Heavy-ions, abrasion-ablation model, peripheral reactions, calculated fragmentation cross sections.
TL;DR: In this paper, the photofission of mass chains with 12-, 15-, 20-, 30-, 30, and 70-MeV bremsstrahlung was investigated.
Abstract: Cumulative yields for about 40 mass chains and fractional independent yields of $^{128}\mathrm{Sn}$, $^{128}\mathrm{Sb}^{g}$, $^{131}\mathrm{Te}^{g}$, $^{131}\mathrm{Te}^{m}$, $^{132}\mathrm{I}^{g}$, $^{132}\mathrm{I}^{m}$, $^{134}\mathrm{I}$, $^{134}\mathrm{Cs}$, $^{135}\mathrm{Xe}$, and $^{136}\mathrm{Cs}$ were determined for the photofission of $^{238}\mathrm{U}$ with 12-, 15-, 20-, 30-, and 70-MeV bremsstrahlung. Changes in the characteristics of the mass distribution are studied. An enhanced yield in the mass region 133-134, decreasing with increasing end-point energy of the bremsstrahlung (${E}_{e}$), is observed. From the determined independent yields the most probable charges ${Z}_{p}({E}_{e})$ are calculated using the value 0.85 for the width parameter $c$ of the charge distribution as deduced from our results for mass chain 134. The determined ${Z}_{p}({E}_{e})$ values are very well described by the empirical relation of Nethaway except for the mass chain 136. This discrepancy for mass chain 136, which decreases with increasing end-point energy of the bremsstrahlung, is attributed to an abnormal low yield of $^{136}\mathrm{Cs}$. Fragment shell effects are discussed. From the isomeric ratios for $^{131}\mathrm{Te}^{g}\ensuremath{-}^{131}\mathrm{Te}^{m}$ and $^{132}\mathrm{I}^{g}\ensuremath{-}^{132}\mathrm{I}^{m}$ average initial fragment spins are calculated using a statistical model analysis.NUCLEAR REACTIONS, FISSION $^{238}\mathrm{U}$($\ensuremath{\gamma}$,$F$), ${E}_{\ensuremath{\gamma}max}=12, 15, 20, 30, 70$ MeV; measured: fragment $\ensuremath{\gamma}$-ray spectra; deduced: mass distributions, most probable charges, isomeric ratios, average initial fragment spins.
TL;DR: In this paper, the properties of high-spin states in Sb reactions were studied using Ge(Li) and Si(Li)-detector in-beam measurements of the excitation function of a single-particle plus core-excitation states.
Abstract: Properties of high-spin states in $^{113,115,117,119}\mathrm{Sb}$ have been studied via the $^{A}\mathrm{Cd}(^{6}\mathrm{Li},3n)^{A+3}\mathrm{Sb}$ reactions. Using Ge(Li) and Si(Li) detectors, in-beam measurements of $\ensuremath{\gamma}$-ray excitation functions, $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ coincidences, $\ensuremath{\gamma}$-ray angular distributions, and pulsed beam-$\ensuremath{\gamma}$ timing spectra were made to determine level energies, decay schemes, $\ensuremath{\gamma}$-ray multipolarities, ${J}^{\ensuremath{\pi}}$ assignments, isomeric lifetimes, and a $g$ factor. Systematic $\ensuremath{\Delta}J=1$ bands built on low-lying $\frac{9}{{2}^{+}}$ proton-hole (2p-1h) states were observed in these nuclei. The bandheads that involve the excitation of a $1{g}_{\frac{9}{2}}$ proton across the $Z=50$ shell achieve an energy minimum near the middle of the neutron shell. The observed properties of these bands are consistent with significant prolate deformations; the band spacings imply a deformation asymmetry of $\ensuremath{\gamma}=20$ in a triaxial rotor model. In addition, single-particle and single-particle plus core-excitation states were observed in these Sb nuclei. Two isomers were identified, a $\frac{19}{{2}^{(\ensuremath{-})}}$ state at 2796 keV in $^{115}\mathrm{Sb}$ ($\ensuremath{\tau}=230\ifmmode\pm\else\textpm\fi{}4$ ns and $g=+0.290\ifmmode\pm\else\textpm\fi{}0.005$) and a ($\frac{27}{{2}^{+}}$) state in $^{119}\mathrm{Sb}$ ($\ensuremath{\tau}=1.23\ifmmode\pm\else\textpm\fi{}0.13$ s).NUCLEAR REACTIONS $^{110\ensuremath{-}116}\mathrm{Cd}$ ($^{6}\mathrm{Li}$,$3n$)$^{113\ensuremath{-}119}\mathrm{Sb}$; measured $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ coincidences, $\ensuremath{\gamma}(E,\ensuremath{\theta},t)$, spin rotation in $B=10.3$ kG; deduced level schemes in odd-mass $^{113\ensuremath{-}119}\mathrm{Sb}$, $\ensuremath{\gamma}$ multipolarities, ${J}^{\ensuremath{\pi}}$, ${T}_{\frac{1}{2}}$, $g$-factor. Enriched targets, Ge(Li) detectors.
TL;DR: In this article, complete energy spectra and angular distributions of the light charged particles were measured for the bombardment of the particles and the experimental results were analyzed using the pre-equilibrium exciton model, the compound nuclear evaporation model and a Serber type of model for the particle breakup.
Abstract: Complete energy spectra and angular distributions of the light charged particles ($A\ensuremath{\le}4$) were measured for the bombardment of $^{27}\mathrm{Al}$, $^{58}\mathrm{Ni}$, $^{90}\mathrm{Zr}$, $^{209}\mathrm{Bi}$, and $^{232}\mathrm{Th}$ with 140 MeV $\ensuremath{\alpha}$ particles. The spectral shapes of a given emitted particle are very similar for all target nuclei except in the region of the evaporation peak. The slopes of the energy spectra in the forward direction become steeper as the mass of the observed particle decreases and vary very rapidly with angles. The experimental data can be characterized by compound nuclear evaporation processes at low energies, or at backward angles, and by direct reactions, nonequilibrium components and projectile breakup processes at high energies and forward angles. The breakup cross section for $\ensuremath{\alpha}$ particles is found to be appreciable. The total yield of light charged particles is approximately a factor \ensuremath{\sim} 2 to 3 larger than the total reaction cross section for $^{27}\mathrm{Al}$, $^{58}\mathrm{Ni}$, and $^{90}\mathrm{Zr}$ and is \ensuremath{\sim} 0.7 of reaction cross section for $^{209}\mathrm{Bi}$ and $^{232}\mathrm{Th}$. The nonequilibrium light charged particle yield is of the order of 1000-1800 mb. The experimental results were analyzed using the pre-equilibrium exciton model, the compound nuclear evaporation model and a Serber type of model for the $\ensuremath{\alpha}$ particle breakup. The pre-equilibrium model calculations using a 5p-1h initial configuration reproduced the experimental angle-integrated energy spectra rather well.NUCLEAR REACTION $^{27}\mathrm{Al}$, $^{58}\mathrm{Ni}$, $^{90}\mathrm{Zr}$, $^{209}\mathrm{Bi}$, $^{232}\mathrm{Th}$ ($\ensuremath{\alpha}$,$\mathrm{xp}$), ($\ensuremath{\alpha}$,$\mathrm{xd}$), ($\ensuremath{\alpha}$,$\mathrm{xt}$), ($\ensuremath{\alpha}$,$x^{3}\mathrm{He}$), ($\ensuremath{\alpha}$,$x\ensuremath{\alpha}$), ${E}_{\ensuremath{\alpha}}=140$ MeV; $\ensuremath{\theta}=20\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}140\ifmmode^\circ\else\textdegree\fi{}$, measured $\frac{{d}^{2}\ensuremath{\sigma}}{d\ensuremath{\Omega}d\ensuremath{\epsilon}}$, deduced $\frac{d\ensuremath{\sigma}}{d\ensuremath{\epsilon}}$ and $\ensuremath{\sigma}(E)$. Comparisons with preequilibrium exciton, evaporation and projectile breakup models.
TL;DR: In this article, the validity of the Pauli exclusion principle for nucleons has been investigated and the mean life against p-shell nucleons in /sup 12/C falling into the fully occupied 1s/sub 1/2/ shell has been shown to be > 6 x 10/sup 27/sec (99.7% confidence limit).
Abstract: The validity of the Pauli exclusion principle for nucleons has been investigated. The mean life against p-shell nucleons in /sup 12/C falling into the fully occupied 1s/sub 1/2/ shell has been shown to be > 6 x 10/sup 27/ sec (99.7% confidence limit). A limit has also been obtained for the relative amplitude of symmetric components in the wave functions of nucleons.
CERN1
TL;DR: The masses of neutron-deficient and neutron-rich isotopes of rubidium and cesium were determined by direct on-line mass spectrometry as discussed by the authors, and the measured masses were compared to current mass predictions.
Abstract: The masses of neutron-deficient and neutron-rich isotopes of rubidium (/sup 74en-dash79/Rb, /sup 90en-dash99/Rb) and of cesium (/sup 117en-dash124,126/Cs, /sup 138,140en-dash147/Cs) have been determined by direct on-line mass spectrometry. The measured masses are compared to current mass predictions. From the trend of neutron separation energies, experimental neutron pairing energies are deduced and evidence is found for the onset of a deformation at N = 60 in the neutron-rich rubidium isotopes.
TL;DR: In this article, an extended time-dependent Hartree-fock approximation with collision-free limit is proposed, which is obtained by a truncation of the Martin-Schwinger hierarchy at the second level and by using a simple representation of the one-body Green's function in terms of timedependent occupation numbers.
Abstract: In the time-dependent Hartree-Fock approximation, the fermions are assumed to interact only through the mean field and the collisions between particles are neglected. We formulate an extended time-dependent Hartree-Fock approximation which incorporates particle collisions due to the residual interaction, with the usual time-dependent Hartree-Fock approximation as the collisionless limit. It is obtained by a truncation of the Martin-Schwinger hierarchy at the second level and by using a simple representation of the one-body Green's function in terms of time-dependent occupation numbers. The final set of coupled equations consists of a modified time-dependent Hartree-Fock equation and a master equation for the occupation numbers. These results are physically transparent and describe properly the physics of the collision process. They may also be simple enough to be of practical use to study heavy-ion collisions or the dynamics of other fermion systems. Furthermore, as the configuration-space analog of the quantum Boltzmann equation, many important results concerning statistical dynamics are obtained. Concepts such as entropy, temperature, and local and thermal equilibrium can be quantitatively introduced. The well-known $H$ theorem that entropy never decreases can be readily recovered. With the collision term explicitly exhibited, the macroscopic equations (equations of continuity, momentum flux, and energy) and their associated conservation theorems can also be derived. Analytic solutions for the master equation for simple cases lead to new "level crossing" formulas having characteristics distinctly different from the Landau-Zener level-crossing formula and illuminate the salient features as to how a nonequilibrium fermion system approaches thermal equilibrium.NUCLEAR REACTIONS Extension of time-dependent Hartree-Fock approximation. Collisions between particles. Master equation for occupation probabilities. Entropy, temperature, and thermal equilibrium. $H$ theorem. Analytic solution of the master equation. New types of level crossing formula.
TL;DR: In this paper, the damped collision and fusion-fission components of the /sup 165/Ho + /sup 56/Fe reaction at a bombarding energy of 8.5 MeV/u were measured.
Abstract: Neutron emission and ..cap alpha..-particle emission in the /sup 165/Ho + /sup 56/Fe reaction have been measured for the damped-collision and fusion-fission components of this reaction at a bombarding energy of 8.5 MeV/u. The c.m. neutron energy spectra for damped collisions indicate equal temperatures for the light and heavy fragments, a result consistent with the equilibration of the excitation energy during the interaction time. Pre-equilibrium neutron emission is found to contribute less than 5%. An out-of-plane neutron anisotropy A/sub 2/ = 0.2 +- 0.1 is found. The measured ratios of the neutron multiplicities for the light and heavy fragments suggest a rapid approach of the fragment N/Z ratios during the collision to that corresponding to minimum potential energy of the composite system.
TL;DR: In this article, the results of an optical model analysis of medium energy p-/sup 4/He elastic scattering cross section and analyzing power measurements are reported based on the use of the Dirac equation with a mixture of a Lorentz scalar potential and the timelike component of a four-vector potential.
Abstract: The results of an optical model analysis of medium energy p-/sup 4/He elastic scattering cross section and analyzing power measurements are reported. The analysis is based on the use of the Dirac equation with a mixture of a Lorentz scalar potential and the timelike component of a four-vector potential.
TL;DR: The measurement of invariant cross sections for the production of protons by 400 GeV protons from a variety of nuclear targets is described in this paper, where some angular distributions are given over a wider selection of angles.
Abstract: The measurement of invariant cross sections for the production of protons by 400 GeV protons from a variety of nuclear targets is described. Results are given for Li6, Be, C, A1, Cu, and Ta at 70°, 90°, 118°, 137° and 160° for detected protons from 0.4 to 1.4 GeV/c. Some angular distributions are given over a wider selection of angles. Comparisons are made with observed experimental results at other energies.
NUCLEAR REACTIONS Inclusive cross section, 400 GeV, Li6, Be, C, A1, Cu, and Ta.
TL;DR: In this article, absolute differential and total (integrated) cross sections for the reaction at proton energies between 0.14 and 3 MeV are presented, and compared with previous measurements.
Abstract: Absolute differential and total (integrated) cross sections for the $^{6}\mathrm{Li}$($p$,$^{3}\mathrm{He}$)$^{4}\mathrm{He}$ reaction at proton energies between \ensuremath{\sim}0.14 and 3 MeV are presented, and compared with previous measurements. The results comprise a consistent set of data over much of the energy range of interest to a number of applications. Thermonuclear reaction rate parameters and astrophysical $S$ factors are calculated. The measured angular distributions are compared to predictions of a preliminary $R$-matrix analysis based on the nuclear properties of energy levels in the mass-7 system.NUCLEAR REACTIONS $^{6}\mathrm{Li}$($p$,$^{3}\mathrm{He}$)$^{4}\mathrm{He}$, ${E}_{p}=0.14\ensuremath{-}3$ MeV; enriched target; measured $\ensuremath{\sigma}({E}_{p},\ensuremath{\theta})$, $\ensuremath{\sigma}({E}_{p})$; calculated $〈\ensuremath{\sigma}v〉$, astrophysical $S$ factor.
TL;DR: In this article, the energy levels, mixing ratios, branching ratios, and lifetimes in the positive-parity band were derived using a particle-plus-rotor model at a small, symmetric deformation.
Abstract: Levels in $^{105,107}\mathrm{Ag}$ have been studied using heavy-ion reactions. The experiments included $\ensuremath{\gamma}$-ray yields as a function of bombarding energy, $\ensuremath{\gamma}$-ray angular distributions, and three-detector $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ coincidence measurements. The positive-parity band based on the unique-parity ${g}_{\frac{9}{2}}$ orbital in both nuclei exhibits a $\ensuremath{\Delta}I=1$ character, unlike its counterpart ${h}_{\frac{11}{2}}$ band in Pd nuclei. The energy levels, $\ensuremath{\gamma}$-ray mixing ratios, branching ratios, and lifetimes in this band as well as in the ground-state negative-parity band are shown to be in good agreement with calculations using a particle-plus-rotor model at a small, symmetric deformation ($\ensuremath{\delta}=0.12$). The Coriolis and recoil effects are explicitly included and a variable moment of inertia is used. The low-lying "anomalous" $\frac{7}{{2}^{+}}$ state is also readily reproduced by this model. The calculation also shows that the $\ensuremath{\Delta}I=1$ nature of the positive-parity band results primarily from the fact that the Fermi surface is far from the $K=\frac{1}{2}$ state, whereas the transition properties are governed by the Coriolis mixing of the strong-coupled bands. Two bands built on the $\frac{17}{{2}^{\ensuremath{-}}}$ and $\frac{21}{{2}^{+}}$ states with high bandhead energies are thought to have three-quasiparticle configurations.NUCLEAR STRUCTURE $^{92}\mathrm{Zr}$($^{16}\mathrm{O}$,$p2n$)$^{105}\mathrm{Ag}$ at 60 MeV, $^{96}\mathrm{Zr}$($^{14}\mathrm{N}$, $3n$)$^{107}\mathrm{Ag}$ at 49 MeV: measured ${I}_{\ensuremath{\gamma}}(E(^{16}\mathrm{O}))$, ${I}_{\ensuremath{\gamma}}(E(^{14}\mathrm{N}))$, ${I}_{\ensuremath{\gamma}}(\ensuremath{\theta})$, $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ coin $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ DCOQ. $^{105,107}\mathrm{Ag}$ deduced levels, $J$, $\ensuremath{\pi}$, $\ensuremath{\gamma}$ mixing ratios. Rotational model calculations, Coriolis, calculated levels, mixing ratios, branching ratios, lifetimes. Ge(Li) detectors.
TL;DR: In this paper, a phase transition from a statically deformed prolate nucleus to a γ-unstable one, in general (but not detailed) agreement with the prediction of a dynamic-collective-model calculation, was detected.
Abstract: Photoneutron cross sections, including $\ensuremath{\sigma}[(\ensuremath{\gamma},n)+(\ensuremath{\gamma},pn)]$, $\ensuremath{\sigma}[(\ensuremath{\gamma},2n)+(\ensuremath{\gamma},p2n)]$, and $\ensuremath{\sigma}(\ensuremath{\gamma},3n)$, were measured for $^{188}\mathrm{Os}$, $^{189}\mathrm{Os}$, $^{190}\mathrm{Os}$, and $^{192}\mathrm{Os}$ from 7 to 30 MeV and for $^{186}\mathrm{Os}$ from 11 to 20 MeV, with a photon energy resolution of about 300 keV. The source of radiation was the monoenergetic photon beam obtained from the annihilation in flight of fast positrons. The partial photoneutron cross sections were determined by neutron multiplicity counting, and the average neutron energies for each multiplicity were determined simultaneously with the cross-section data by the ring-ratio technique. Nuclear information extracted from the data includes parameters of the giant dipole and giant quadrupole resonances, integrated cross sections and their moments, nuclear symmetry energies, and nuclear deformation parameters and intrinsic quadrupole moments. No fewer than eight kinds of evidence point to a sudden change of behavior between $^{189}\mathrm{Os}$ and $^{190}\mathrm{Os}$, which could be interpreted as a phase transition from a statically deformed prolate nucleus to a $\ensuremath{\gamma}$-unstable one, in general (but not detailed) agreement with the prediction of a dynamic-collective-model calculation.
TL;DR: The existence of a virtual state of the three nucleon system was established on the basis of three different analyses as mentioned in this paper, including a fit to the experimental data, from partial wave dispersion relations, and from an exact three-particle, separable potential calculation.
Abstract: The existence of a virtual state of the three nucleon system is established on the basis of three different analyses. Values for its pole position and residue in the doublet, $s$-wave, $n\ensuremath{-}d$ elastic scattering amplitude, are obtained from a fit to the experimental data, from partial wave dispersion relations, and from an exact three-particle, separable potential calculation. The calculations indicate that these parameters are determined mainly by the one-nucleon exchange mechanism and the doublet scattering length ${a}_{2}$. For ${a}_{2}=0.65$ fm our best calculation gives an energy of 0.482 MeV below the elastic threshold, on the second Riemann sheet, and a residue parameter ${{C}_{\ensuremath{
u}}}^{2}=0.0504$, where ${{C}_{\ensuremath{
u}}}^{2}$ is defined in analogy to the triton asymptotic normalization parameter.NUCLEAR REACTIONS Three-nucleon virtual state; fits to data; dispersion relations; separable potential calculations.