Showing papers in "Physical Review C in 1984"

Boltzmann equation for heavy ion collisions

Abstract: The sensitivity of inclusive observables in heavy ion collisions to the nuclear equation of state can be tested with the Boltzmann equation. We solve the Boltzmann equation, including mean field and Pauli blocking effects, by a method that follows closely the cascade model. We find that the inclusive pion production is insensitive to the nuclear equation of state, contrary to recent claims.

Experimental results from high energy proton-nucleus interactions, critical phenomena, and the thermal liquid drop model of fragment production

Abstract: In an inclusive experiment, isotopically resolved fragments, $3\ensuremath{\le}Z\ensuremath{\le}13$, produced in high-energy proton-nucleus collisions have been studied using a low mass time-of-flight, gas $\ensuremath{\Delta}E$-silicon $E$ spectrometer and an internal gas jet. Measurement of the kinetic energy spectra from 5 to 100 MeV enabled an accurate determination of fragment cross sections from both xenon and krypton targets. Fragment spectra showed no significant dependence on beam energy for protons between 80 and 350 GeV/c. The observed isobaric yield is given by $Y\ensuremath{\alpha}{A}_{f}^{\ensuremath{-}\ensuremath{\tau}}$, where $\ensuremath{\tau}\ensuremath{\sim}2.6$ for both targets; this also holds for correlated fragment data. The power law is the signature for the fragment formation mechanism. We treat the formation of fragments as a liquid-gas transition at the critical point. The critical temperature ${T}_{c}$ can be determined from the fragment isotopic yields, provided one can set an energy scale for the fragment free energy. The high energy tails of the kinetic energy spectra provide evidence that the fragments originate from a common remnant system somewhat lighter than the target which disassembles simultaneously via Coulomb repulsion into a multibody final state. Fragment Coulomb energies are about $\frac{1}{10}$ of the tangent sphere values. The remnant is characterized by a parameter $T$, obtained from the high energy tails of the kinetic energy distributions. $T$ is interpreted as reflecting the Fermi momentum of a nucleon in this system. Since $T\ensuremath{\gg}{T}_{c}$, and $T$ is approximately that value expected for a cold nucleus, we conclude that the kinetic energy spectra are dominated by this nonthermal contribution.[NUCLEAR REACTIONS $\mathrm{Xe}(\mathrm{p},X)$, $\mathrm{Kr}(\mathrm{p},X)$, $80\ensuremath{\le}{E}_{q}\ensuremath{\le}350$ GeV; measured $\ensuremath{\sigma}(E,\ensuremath{\theta})$, $X=\mathrm{Li} \mathrm{to} \mathrm{Al}$, $\ensuremath{\theta}={34}^{\ensuremath{\circ}}$. Fragmentation.]

Liquid-gas phase transitions in finite nuclear matter

Abstract: A procedure is developed to calculate the chemical potential of a system of fermions at high temperatures in the independent particle model. This is then used to investigate the occurrence of liquid-gas phase transitions in finite nuclei employing various zero-range nuclear effective interactions. Finite size effects and the Coulomb force are found to lead to a sizeable reduction (\ensuremath{\sim}8 MeV) in the "critical" temperature as compared to the case of infinite nuclear matter.

Liquid-gas phase instabilities and droplet formation in nuclear reactions

Abstract: The thermodynamics and critical exponents of nuclear matter near the critical point of a liquid-gas phase transition are studied. We then investigate fluctuations near the critical point. One effect of a finite number of nucleons, as in nuclear reactions, is to wash out the first-order phase transition for several MeV below the critical temperature. This is manifested in the fact that there is a finite probability for the system to exist in the metastable or unstable regions of infinite matter. The phenomenological droplet model is applied to a wide range of recent data on fragment yields in the range $6lAl52$, and good fits are obtained. Heavy ion reactions are consistent with droplet formation in a supersaturated vapor, with supersaturation ratios up to 3.25. Proton-nucleus reactions are consistent with droplet formation in a saturated vapor.

Two pion correlations in heavy ion collisions

Abstract: An application of intensity interferometry to relativistic heavy ion collisions is reported. The correlation between two like-charged pions is used to study the reactions Ar+KC1..-->..2..pi../sup + -/+X and Ne+NaF..-->..2..pi../sup -/+X, both at an incident beam energy of 1.8A GeV. Source sizes and lifetimes are measured and compared to the predictions of simple geometric models and of Monte Carlo cascade calculations. There appears to be a substantial coherent component of the pion source, although measurement is complicated by the presence of final state interactions. A detailed discussion of the techniques of intensity interferometry is also presented. The generation of uncorrelated background events is discussed, along with the influence of the correlation on the background and the prescription for its removal. The statistical errors in the background spectrum are examined and found to have nontrivial implications for the analysis. The effect of the mutual Coulomb repulsion of the two pions, and of the pion-nuclear Coulomb interaction, on the two-pion correlation function is analyzed. The impact parameter bias resulting from a two-pion trigger is calculated and found to be substantial. Finally, a simple model for the interpretation of Gaussian source parameters is presented and compared to the predictions of Monte Carlo cascade calculations.

Triaxial shapes in the interacting boson model

Abstract: We suggest the use of cubic terms in the interacting boson model. It is shown that, examining the classical limit, such cubic terms can give rise to stable, triaxial shapes. Energy spectra are studied in the U(5), O(6), and SU(3) limits. Also, a more realistic case is studied in $^{104}\mathrm{Ru}$.

Fragment velocities, energies, and masses from fast neutron induced fission of U 235

Abstract: We report on a complete ($2E,2v$) experiment for fast neutron induced fission on $^{235}\mathrm{U}$. The energy dependence of fragment properties so far known only for thermal neutron induced fission is studied. Experimental problems as well as difficulties in data analysis are considered in detail in order to obtain clean and unbiased results. In particular, a self-consistent determination of the fragment total kinetic energy (${E}_{K,\mathrm{tot}}$) was achieved by comparing the results obtained via the respective velocities and pulse heights. We find systematic discrepancies of 2 MeV if ${E}_{K,\mathrm{tot}}$ is determined from the observed pulse heights with the calibration scheme of Schmitt et al. Therefore, refined calibration constants were deduced by comparison with accurate radiochemical mass yields. Measurements were performed at neutron energies of 0.50 and 5.55 MeV. 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. We also show the distributions of fragment mass, of ${E}_{K,\mathrm{tot}}$, and of the variance of ${E}_{K,\mathrm{tot}}$. In addition, the number of prompt fission neutrons $\ensuremath{ u}$ is given as a function of fragment mass. Our resolution of 2.1 mass units reveals fine structure not only in the fragment mass distribution but also in ${E}_{K,\mathrm{tot}}({A}^{*})$ and $\ensuremath{ u}({A}^{*})$. For the lower neutron energy of 0.50 MeV the present results compare reasonably well with similar measurements performed with thermal neutrons. Apparently the 0.5 MeV increase in saddle point excitation does not alter the results significantly. The improved accuracy of this measurement is demonstrated by comparison of our neutron emission data with direct measurements of fission neutrons. At the higher neutron energy of 5.55 MeV we observe the expected decrease of shell and pairing effects which indicates an increase in nuclear temperature. These results are in qualitative agreement with the model of Wilkins, Chasman, and Steinberg. However, a striking discrepancy exists for the number of fission neutrons, where we find that the increase in the total number of fission neutrons is totally accounted for by heavy fragments alone.

Separable representation of the Bonn nucleon-nucleon potential

Abstract: A separable representation of a boson-exchange nucleon-nucleon potential is constructed via the Ernst-Shakin-Thaler method. The resulting separable interactions provide for a satisfactory approximation of the on-shell as well as off-shell properties of the Bonn potential. Their form factors are composed of rational functions suitable for today's computer codes for few-body systems. First results obtained with these separable potentials for elastic nucleon-deuteron scattering are presented.

Quasi-elastic scattering of polarized electrons on polarized He 3

Abstract: Cross sections and asymmetries for quasi-elastic scattering of longitudinally polarized electrons on polarized $^{3}\mathrm{He}$ are calculated. The model used consists of impulse approximation plus closure approximation to sum over final states. At the quasi-elastic peak the asymmetry is found to be dominated by scattering from the neutron, and judicious choice of target polarization allows sensitivity to either the neutron's electric or magnetic form factor to be maximized. Away from the quasielastic peak, the protons contribute to the asymmetry. The proton's contribution is mainly owing to two partial wave channels, one mixed symmetry $S$ state and one $D$ state which have small total probability in the $^{3}\mathrm{He}$ wave function.

Alpha cluster model and the spectrum of O 16

Abstract: The structure of $^{16}\mathrm{O}$ is studied in the alpha cluster model with parity and angular-momentum projection for several nucleon-nucleon interactions. The method differs from previous studies in that the states of positive and negative parity are determined without the customary restriction of the variational space to cluster positions with certain assumed symmetries. It turns out that a number of variational results in the literature are spurious under unrestricted variations. We demonstrate that the alpha cluster model of $^{16}\mathrm{O}$ is capable of explaining most of the experimental $T=0$ levels up to about 15 MeV excitation. In particular, the 6.05 MeV rotational band is reproduced remarkably well. A shell-model analysis of the excited cluster-model states shows the necessity of including a very large number of shells. The evidence for the recently proposed tetrahedral symmetry of some excited states is also discussed.

Comparison of the energy and mass characteristics of the /sup 239/Pu(n/sub th/,f) and the /sup 240/Pu(sf) fragments

Abstract: The energy and mass distributions and their correlations have been studied for the spontaneous fission of $^{240}\mathrm{Pu}$ and the thermal neutron induced fission of $^{239}\mathrm{Pu}$. A comparison of the $^{240}\mathrm{Pu}$(sf) and the $^{239}\mathrm{Pu}({\mathrm{n}}_{\mathrm{th}},f)$ results shows a narrower mass distribution, a much higher peak yield, a much lower symmetric fission yield, and a more pronounced fine structure for the spontaneous fission than for the neutron induced fission. The average total kinetic energy is 1.3 MeV higher for $^{240}\mathrm{Pu}$(sf) than for $^{239}\mathrm{Pu}({\mathrm{n}}_{\mathrm{th}},f)$, and also the energy-mass correlations behave differently in both cases. All these results are discussed and interpreted in the framework of the scission point model of Wilkins et al. Finally, the damping of the $^{240}\mathrm{Pu}$ fission mode below the barrier is demonstrated.

Isotopic effects in the fusion of Ca 40 with Ca 4 0 , 4 4 , 4 8

Abstract: Excitation functions for fusion of $^{40}\mathrm{Ca}$+$^{40,44,48}\mathrm{Ca}$ have been measured over a range of energies from below to well above the classical fusion barrier. Strong isotopic effects are observed in both the sub- and above-barrier cross sections, which are qualitatively consistent with suggestions of the importance of transfer reactions in the fusion process.

Nonmesonic decay of heavy Λ hypernuclei

Abstract: We have calculated the ratio of the rate for nonmesonic decay of the $\ensuremath{\Lambda}$ in nuclear matter to that of the free $\ensuremath{\Lambda}$ decay rate using a pion and rho meson exchange model Including tensor force effects and a final-state correlation function generated from the Reid-soft-core potential, we estimate $\frac{{\ensuremath{\Gamma}}_{\mathrm{nm}}}{{\ensuremath{\Gamma}}_{\mathrm{free}}}$ to be of order 1 A discrepancy with respect to the prior estimate of Adams is resolved

Cold breakup of spectator residues in nucleus-nucleus collisions at high energy

Abstract: Inclusive data from fragmentation reactions of the type ${A}_{P}+{A}_{T}\ensuremath{\rightarrow}Z+X$ are analyzed and a reaction mechanism is proposed. A projectile ${A}_{P} (\mathrm{p}, \mathrm{He}, \ensuremath{\alpha}, or \mathrm{Ne})$ collides with a target nucleus ${A}_{T}$ (Au) and one fragment with charge $Z$ and energy $E$ is observed at a solid angle $\ensuremath{\Omega}$. Projectile energies vary between $84A$ MeV and several $A$ GeV. We propose a parametrization for the triple differential cross section $\frac{{d}^{3}\ensuremath{\sigma}}{d\ensuremath{\Omega}}\mathrm{dE}\mathrm{dZ}$ with six free parameters. The parametrization generalizes the two-vector model which is often used to describe spallation products in proton-nucleus collisions. By fitting data from various experiments we establish a systematics of the six parameters. The experimental values of the parameters can be quantitatively understood in a model where the target nucleus breaks into several fragments similar to the shattering of glass.

Binding energies of hypernuclei and three-body. lambda. NN forces

Abstract: Binding energies of hypernuclei are calculated with use of accurate variational methods for $A=3,5$, with effective interaction calculations for $A=5,9,13,\ensuremath{\infty}$, and with Fermi hypernetted-chain variational calculations for $A=\ensuremath{\infty}$. Effective interactions and variational results agree within a few percent. For $\ensuremath{\Lambda}N$ forces consistent with $\ensuremath{\Lambda}\mathrm{p}$ scattering, agreement with the experimental energies is obtained with strongly repulsive Wigner type $\ensuremath{\Lambda}\mathrm{NN}$ forces, and for $Ag5$ also with a weakened $p$-state $\ensuremath{\Lambda}\mathrm{N}$ strength about half that of the $s$-state strength.

Statistical fluctuations in the i/sub 13/2/ model

Abstract: The finite-temperature Hartree-Fock-Bogoliubov cranking equations are solved for the ${i}_{\frac{13}{2}}$ model. For any temperature below $k{T}_{c}=0.2$ MeV, rotations induce a sharp first-order phase transition. When statistical fluctuations in the pair gap $\ensuremath{\Delta}$ are included, the phase transition is smoothed out for $\frac{1}{2}{T}_{c}lTl{T}_{c}$. The rotation-aligned ${i}_{\frac{13}{2}}$ pair is unaffected by temperatures up to 0.5 MeV. The finite-temperature violation of the zero-temperature Hartree-Fock-Bogoliubov relation ${R}^{2}=R$ is given by the quasiparticle number fluctuation.

Neutron capture cross sections and solar abundances of /sup 160,161/Dy, /sup 170,171/Yb, /sup 175,176/Lu, and /sup 176,177/Hf have been measured

Abstract: The neutron capture cross sections and solar abundances of $^{160,\phantom{\rule{0ex}{0ex}}161}\mathrm{Dy}$, $^{170,\phantom{\rule{0ex}{0ex}}171}\mathrm{Yb}$, $^{175,\phantom{\rule{0ex}{0ex}}176}\mathrm{Lu}$, and $^{176,\phantom{\rule{0ex}{0ex}}177}\mathrm{Hf}$ have been measured. With this data base $s$-process studies have been carried out to determine the $s$-process neutron density and temperature and to investigate the $s$-process nucleosynthesis of the $^{176}\mathrm{Lu}$ clock. From various branchings the neutron density was found to be (0.8-1.8)\ifmmode\times\else\texttimes\fi{}${10}^{8}$ neutrons per ${\mathrm{cm}}^{3}$ and the temperature $\mathrm{kT}$ to be 18---28 keV. On the basis of the present data, $^{176}\mathrm{Lu}$ proved not to be applicable as a cosmic clock because of the temperature sensitivity of the $^{176}\mathrm{Lu}$ half-life but can be used instead as a stellar thermometer. Constraints for the $s$-process temperature ($kT=20\ensuremath{-}28$ keV) were found to be in good agreement with the investigated branchings.

Complete and incomplete fusion in C 12 + V 51 at E ( C 12 ) = 36 − 100 MeV from analysis of recoil range and light particle measurements

Abstract: Excitation functions and detailed differential recoil range distributions for radioisotope products of the reactions of $^{12}\mathrm{C}$ on $^{51}\mathrm{V}$, together with inclusive proton and $\ensuremath{\alpha}$ particle spectra, have been measured at energies up to 157 MeV. The range distributions clearly show three separable components, which are attributed to complete fusion of $^{12}\mathrm{C}$, incomplete fusion of $^{8}\mathrm{Be}$, and incomplete fusion of $^{4}\mathrm{He}$, respectively, with the target. Detailed Monte Carlo modeling of the shapes of the recoil range distributions for these processes, using information on the breakup process derived from the measured $\ensuremath{\alpha}$ particle spectra, has enabled the separate contribution of each fusion process to the formation of each product studied to be deduced as a function of energy up to 100 MeV. The partitioning amongst the observed products is consistent with statistical model predictions for the subsequent evaporation; this allows the total cross section for each process to be estimated as a function of energy. For projectile energies up to 100 MeV, the observed yield of "breakup" $\ensuremath{\alpha}$ particles is exhausted by incomplete fusion. The results suggest that incomplete fusion is occurring principally for partial waves near or even outside the hard grazing value, and that the total cross section for the various fusion processes exceeds the hard-grazing cross section.

Fusion-energy reaction H 2 ( t , α ) n from E t = 12.5 to 117 keV

Abstract: We have measured the cross section for the important fusion-energy reaction $^{2}\mathrm{H}(\mathrm{t},\ensuremath{\alpha})\mathrm{n}$ at 17 energies over the triton bombarding energy range of 12.5-117 keV. This corresponds to an equivalent deuteron bombarding energy range of 8.3-78.1 keV and to a plasma temperature ($\mathrm{kT}$) range of 0.7-18.8 keV. The cross section is accurate to 1.4% over most of the energy range, with the error rising to 4.8% at the lowest energy. These data are considerably more accurate than the previous d + t measurements in this energy range. We compare our data with those of other measurements and with an existing $R$-matrix analysis of the mass-5 system. We have also performed a single-level $R$-matrix analysis of a restricted data base that contains our data and have used that analysis to compute Maxwellian reactivities up to a plasma temperature of 20 keV. In addition, for calibration purposes, we measured to better than 1% absolute error the $^{2}\mathrm{H}$(p,p)$^{2}\mathrm{H}$ elastic differential cross section at six laboratory angles at a proton bombarding energy of 10.04 MeV.

K + N phase shifts from 600 to 1500 MeV/c

Abstract: K/sup +/-nucleon phase shifts are presented in the region 600--1500 MeV/c laboratory kaon momentum. They are obtained by a single-energy phase-shift analysis for the KN I = 1 and I = 0 states using world data including recently measured P(K/sup +/n..-->..K/sup +/n) and P(K/sup +/n..-->..K/sup 0/p). The result supports the resonances in the P/sub 13/ and D/sub 03/ waves. Other resonancelike structures have also been found in the P/sub 11/ and D/sub 05/ states, which could be interpreted as new candidates for Z( resonances. In this paper numerical phase shifts are demonstrated as well as their accuracy. These values could be used for future studies on kaon-induced nuclear reactions.

Inclusive Production of Isotopically Resolved Li Through Mg Fragments by 480-{MeV} $p$ Ag Reactions

Abstract: Energy spectra and angular distributions have been measured for 46 isotopically separated Li through Mg fragments produced in reactions of 480 MeV protons with Ag. Thin silicon solid state detectors have been used with time-of-flight techniques to extend measured fragment energies as low as 1 MeV per nucleon, well below the most probable fragment energies. Reasonable fits to the relatively small evaporative components of the spectra are obtained using a self-consistent calculation previously developed. An analysis of the remaining nonevaporative components using contours of relativistically invariant cross section in the plane of rapidity and perpendicular momentum indicates that these components can be described in terms of isotropic emission from moving sources if the source velocity is allowed to be a function of the fragment's radial velocity in the source frame. The relationship between these velocities is essentially independent of fragment Z and A. Coupled with the evaporation calculation, this relationship allows all spectra to be reasonably fit at all angles by use of a simple (four parameters per fragment) phenomenological form for the isotropic nonevaporative component in the moving source frame. While such a form might suggest a statistical origin for the nonevaporative components, detailed consideration of the parameters requiredmore » suggests difficulties with such an interpretation. Implications of these data for other models are discussed. Energy integrated and total cross sections are calculated.« less

Relation between pairing correlations and two-particle space correlations

Abstract: We study the spatial correlations between two particles (or two holes) around a closed shell core in terms of the probability distribution expressed as a function of the c.m. coordinate $R$ of the two particles and of their relative coordinate $r$. We find that the mixing of configurations induced by the pairing force leads to a probability distribution centered in regions corresponding to larger values of $R$ and smaller values of $r$, as compared to the case of a pure ${(j)}_{0}^{2}$ configuration. This tendency to a "surface clustering" is mainly due to the interference of the contributions coming from levels with different parity. However, even with the inclusion of a large number of configurations, the size of the localized "cluster" is much larger than that of a free dinucleon system.[NUCLEAR STRUCTURE Pairing correlations, correlation in space, two-particle transfer reactions.]

Half-life of Al 26

Abstract: We have measured the half-life of $^{26}\mathrm{Al}$ because data on $^{21}\mathrm{Ne}$ production rates in meteorites has indicated that the half-life may have been too low by 30---40%. We produced $^{26}\mathrm{Al}$ using the $^{26}\mathrm{Mg}(p,n)^{26}\mathrm{Al}$ reaction on thick natural Mg, the yield being calculated from cross section data. The activity of two such samples was measured with a Ge(Li) detector and the calculated half-life is ${t}_{\frac{1}{2}}=(7.8\ifmmode\pm\else\textpm\fi{}0.5)\ifmmode\times\else\texttimes\fi{}{10}^{5}$ years, in agreement with the accepted half-life of $^{26}\mathrm{Al}:{t}_{\frac{1}{2}}=(7.16\ifmmode\pm\else\textpm\fi{}0.32)\ifmmode\times\else\texttimes\fi{}{10}^{5}$ years. Therefore, another explanation must be found for the anomalous $^{21}\mathrm{Ne}$ production rate based on $^{26}\mathrm{Al}$ ages in meteorites.

Meson theory of nucleon-nucleon scattering up to 2 GeV

Abstract: We show that it is possible to construct a meson-exchange Hamiltonian for $\mathrm{N},\ensuremath{\pi},\ensuremath{\Delta}$, and ${\mathrm{N}}^{*}$ (1470 MeV) to describe NN scattering up to 2 GeV. The model consists of: (a) vertex interactions $\ensuremath{\pi}\mathrm{N}\ensuremath{\leftrightarrow}\ensuremath{\Delta} or {\mathrm{N}}^{*}$, and $\ensuremath{\pi}\ensuremath{\Delta}\ensuremath{\leftrightarrow}\ensuremath{\Delta} or {\mathrm{N}}^{*}$ with which an isobar model is constructed to describe the ${P}_{33}$ and ${P}_{11}\ensuremath{\pi}\mathrm{N}$ scattering phase shifts up to 1 GeV; (b) the transition interactions from $\mathrm{NN}\mathrm{to}\mathrm{N}\ensuremath{\Delta},\ensuremath{\Delta}\ensuremath{\Delta},\mathrm{N}{\mathrm{N}}^{*}, \mathrm{and} {\mathrm{N}}^{*}{\mathrm{N}}^{*}$ are determined from one-pion and one-rho exchange mechanisms; (c) the $\mathrm{NN}\ensuremath{\rightarrow}\mathrm{NN}$ interaction is directly derived from the Paris potential by using a momentum-dependent procedure to subtract the contributions from intermediate states involving $\ensuremath{\Delta}$ or ${\mathrm{N}}^{*}$. The $\mathrm{NN}\ensuremath{\rightarrow}\mathrm{NN}$ scattering equation is cast into the familiar coupled-channel form, but with a highly nonlocal isobar self-energy $\ensuremath{\Sigma}(E,p)$ calculated from the vertex interactions $\ensuremath{\pi}\mathrm{N}\ensuremath{\leftrightarrow}\ensuremath{\Delta} or {\mathrm{N}}^{*}$ in a dynamical three-body approach. Both the isospin $T=1$ and $T=0$ NN scattering phase shifts of Arndt et al. up to 1 GeV can be described to a very large extent by the model. The fits are, on the average, better than most of the previous NN calculations. The model also describes reasonably well both the magnitudes and signs of the NN total cross sections ${\ensuremath{\sigma}}^{\mathrm{tot}}$, $\ensuremath{\Delta}{\ensuremath{\sigma}}_{T}^{\mathrm{tot}}$, and $\ensuremath{\Delta}{\ensuremath{\sigma}}_{L}^{\mathrm{tot}}$ up to 2 GeV, except the strong energy dependences in the region near 800 MeV. We discuss the origin of this problem in connection with future necessary improvements of the model and the questions about the dibaryon resonances. The model can be used for a unified approach to study the isobar-nucleus dynamics at both low and intermediate energies.[NUCLEAR REACTIONS Isobar model for $\ensuremath{\Delta}$ and ${\mathrm{N}}^{*}$ excitation, mesonexchange theory of NN scattering from 0 to 2 GeV.]

Alpha-particle spectroscopic strengths using the ( p , p α ) reaction at 101.5 MeV

Abstract: Proton-alpha particle coincidence spectra from 101.5 MeV ($\mathrm{p},\mathrm{p}\ensuremath{\alpha}$) reactions on $^{16}\mathrm{O}$, $^{20}\mathrm{Ne}$, $^{24}\mathrm{Mg}$, $^{28}\mathrm{Si}$, $^{32}\mathrm{S}$, $^{40}\mathrm{Ca}$, $^{48}\mathrm{Ti}$, $^{54}\mathrm{Fe}$, and $^{66}\mathrm{Zn}$ have been obtained in a coplanar geometry at quasifree angle pairs for each target. A missing energy resolution of $\ensuremath{\lesssim}450$ keV was sufficient to separate the lowlying states of the residual nuclides. Data for ground-state transitions, and for eight excited states were obtained and compared with distorted-wave impulse approximation calculations. The targetmass dependence of the resultant relative ground-state spectroscopic factors is reasonably consistent with that obtained from ($^{6}\mathrm{Li}$,d) reactions. The corresponding absolute spectroscopic factors are larger than shell-model predictions, but sensitive to the bound-state parametrization. However, the spectral shapes do constrain the range of possible bound-state rms radii. The fits to the excited states are less satisfactory.

Deuteron and entropy production and the nuclear liquid-gas phase transition

Abstract: The entropy of hot matter produced in medium energy nuclear collisions is inferred from recent data on light fragment cross sections. A previously suggested model is used to fit the abundances of both the deuterons, and the deuteronlike pairings contained in higher mass clusters, with a single parameter. The model takes into account finite density effects in six-dimensional phase space. The entropy rises monotonically with energy, as expected, but remains rather high even at the lower energies. Surprisingly the measured entropy always lies above the theoretically expected value (about 3.3) at the critical point of the liquid-gas phase transition which, it is argued, depends only upon the gross features of the nuclear matter equation of state.

Coupled-channels fusion calculations for 58 Ni+ 58 Ni

Abstract: Fusion calculations are carried out for /sup 58/Ni+ /sup 58/Ni using the coupled-channels scattering formalism with an ingoing-wave boundary condition. The enhancement of the sub-barrier cross section due to couplings to inelastic excitation channels is studied and compared to simple, analytical estimates. At energies above the barrier the combined Coulomb-nuclear interaction significantly alters the distribution of angular momentum absorbed by the compound nucleus.

Angular momentum projection on a mesh of cranked Hartree-Fock wave functions

Abstract: A method for projecting on angular momentum wave functions discretized on a three-dimensional Cartesian mesh is presented. The method is based on a matrix representation of the rotation operator. It is applied to cranked Hartree-Fock wave functions calculated for $^{24}\mathrm{Mg}$ with a simple interaction. In this case, the accuracy of the projected matrix elements is estimated to be of the order of 0.1%. An extensive comparison of the projected and cranking energies is made. The validity of the cranking method as an approximation to a variation-after-projection calculation seems to be wider than usually expected. The study of the fission barrier of $^{24}\mathrm{Mg}$ for the channel $^{4}\mathrm{He}$-$^{16}\mathrm{O}$-$^{4}\mathrm{He}$ shows that the cranking predictions for these very deformed states are quite reliable.

Systematics of ground-state quadrupole moments of odd-A deformed nuclei determined with muonic M x rays

Abstract: The ground-state quadrupole moments of $^{151}\mathrm{Eu}$, $^{153}\mathrm{Eu}$, $^{159}\mathrm{Tb}$, $^{163}\mathrm{Dy}$, $^{167}\mathrm{Er}$, $^{177}\mathrm{Hf}$, $^{179}\mathrm{Hf}$, $^{191}\mathrm{Ir}$, and $^{193}\mathrm{Ir}$ were determined by measuring the quadrupole hyperfine-splitting energies of muonic $M$ x rays. The results are $Q=0.903(10)e$ b for $^{151}\mathrm{Eu}$, $Q=2.412(21) e$ b for $^{153}\mathrm{Eu}$, $Q=1.432(8) e$ b for $^{159}\mathrm{Tb}$, $Q=2.648(21) e$ b for $^{163}\mathrm{Dy}$, $Q=3,565(29) e$ b for $^{167}\mathrm{Er}$, $Q=3.365(29) e$ b for $^{177}\mathrm{Hf}$, $Q=3.793(33) e$ b for $^{179}\mathrm{Hf}$, $Q=0.816(9) e$ b for $^{191}\mathrm{Ir}$, and $Q=0.751(9) e$ b for $^{193}\mathrm{Ir}$. The present quadrupole moments, compared with values obtained from electronic-atom hyperfine measurements, show that the Sternheimer correction factors used in the rare-earth electronic-atom analysis are unreliable. Systematics of deformation parameters ${\ensuremath{\beta}}_{2}$ calculated from the present quadrupole moments for odd-$A$ nuclei, and from $B(E2)$ values of Coulomb excitation measurements for even-$A$ nuclei, also indicate that the largest deformation change so far known exists between $^{151}\mathrm{Eu}$ and $^{153}\mathrm{Eu}$. Except at the onset of nuclear deformation, the deformation parameters of the odd-$A$ nuclei are quite consistent with those of the even-$A$ neighbors.