Showing papers in "Physical Review C in 1974"

Effect of deuteron breakup on elastic deuteron - nucleus scattering

Abstract: The properties of the transition matrix elements ${V}_{\mathrm{ab}}(R)$ of the breakup potential ${V}_{N}$ taken between states ${\ensuremath{\varphi}}_{a}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ and ${\ensuremath{\varphi}}_{b}(r)$ are examined. Here ${\ensuremath{\varphi}}_{a}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ are eigenstates of the neutron-proton relative-motion Hamiltonian, and the eigenvalues of the energy ${\ensuremath{\epsilon}}_{a}$ are positive (continuum states) or negative (bound deuteron); ${V}_{N}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},\stackrel{\ensuremath{\rightarrow}}{\mathrm{R}})$ is the sum of the phenomenological proton nucleus ${V}_{p\ensuremath{-}A}(|\stackrel{\ensuremath{\rightarrow}}{\mathrm{R}}\ensuremath{-}\frac{1}{2}\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}|)$ and neutron nucleus ${V}_{n\ensuremath{-}A}(|\stackrel{\ensuremath{\rightarrow}}{\mathrm{R}}+\frac{1}{2}\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}|)$ optical potentials evaluated for nucleon energies equal to half the incident deuteron energy. The bound-to-continuum transition matrix element for relative neutron-proton angular momenta $l=2$ are found to be comparable in magnitude to the ones for $l=0$ for values of ${\ensuremath{\epsilon}}_{a}$ larger than about 3 MeV, and both decrease only slowly with ${\ensuremath{\epsilon}}_{a}$, suggesting that a large breakup spectrum is involved in deuteron-nucleus collisions. The effect of the various breakup transitions on the elastic phase shifts is estimated by numerically solving a set of coupled equations. These equations couple the functions ${\ensuremath{\chi}}_{a}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{R}})$ which are the coefficients of the expansion of the neutron-proton-nucleus wave function in a set of the ${\ensuremath{\varphi}}_{a}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$'s. The equations are rendered manageable by performing a (rather crude) discretization in the neutron-proton relative-momentum variable ${k}_{a}$. Numerical results for 21.6-MeV deuterons incident on Ni and Ca which include only the first momentum bin (${\ensuremath{\epsilon}}_{a}\ensuremath{\le}10$ MeV) and $l=0 \mathrm{and} 2$ show that the effects on the elastic phase shifts are similar in several respects to those found by Johnson and Soper.[NUCLEAR REACTIONS Elastic deuteron-nucleus scattering theory. Effect of deuteron breakup. Numerical applications to $E=21.6$ MeV $d\ensuremath{-}\mathrm{Ca}$ and $d\ensuremath{-}\mathrm{Ni}$.]

High-momentum-transfer electron scattering from 24 Mg, 27 Al, 28 Si, and 32 S

Abstract: High-momentum-transfer elastic electron scattering data ($0.76\ensuremath{\le}q\ensuremath{\le}3.74 {\mathrm{fm}}^{\ensuremath{-}1}$) from $^{24}\mathrm{Mg}$, $^{27}\mathrm{Al}$, $^{28}\mathrm{Si}$, and $^{32}\mathrm{S}$ are presented and analyzed using phenomenological charge distributions; the oscillation in $\ensuremath{\rho}(r)$ due to the shell-model structure is obtained. An analysis in terms of a Woods-Saxon nuclear potential is described and the $\frac{2s}{1d}$ occupation numbers are deduced. The cross sections for certain strongly excited or well isolated inelastic levels are also given, but not analyzed.[NUCLEAR REACTIONS $^{24}\mathrm{Mg}$, $^{27}\mathrm{Al}$, $^{28}\mathrm{Si}$, $^{32}\mathrm{S}(e,e)$, ($e,{e}^{\ensuremath{'}}$), $E=250$, 500 MeV; measured $\ensuremath{\sigma}(E,\ensuremath{\theta})$, deduced phenomenological $\ensuremath{\rho}$; shell-model calculations; deduced $\frac{2s}{1d}$ occupation numbers.]

Interaction of alpha particles in the lead region near the Coulomb barrier

Abstract: The ($\ensuremath{\alpha},n$) cross section on $^{208}\mathrm{Pb}$ and $^{209}\mathrm{Bi}$ has been measured between 16 and 24 MeV by observing the $\ensuremath{\alpha}$ activity of the residual nuclei $^{211}\mathrm{Po}$ and $^{212}\mathrm{At}$. The relative yields to both the ground and metastable states of each residual nucleus were obtained and new half-life determinations have been made for these states. The absolute yield was measured at 20 and 22 MeV to normalize the relative data. Below the ($\ensuremath{\alpha},2n$) threshold, $\ensuremath{\sigma}(\ensuremath{\alpha},n)$ constitutes most of the total reaction cross section, and the ($\ensuremath{\alpha},n$) data, together with accurate elastic scattering measurements at 19, 20, and 22 MeV are reproduced well by a six-parameter optical model. The fits are sensitive to the reaction cross-section data, and serve to define the magnitude and shape of the real potential at a radial distance of about 11 fm. The real potential in this region dominates the interaction at the present energies. The imaginary potential is relatively small; it is not well determined and serves only to absorb those waves which penetrate the real potential. The real potential obtained is interpreted in terms of an $\ensuremath{\alpha}$-folding model using a free $\ensuremath{\alpha}$-nucleon two-body force. The potential near the peak of the Coulomb barrier is determined primarily by the target matter density near 9 fm, where it is approximately 1% of its value at the center of the nucleus. Implications concerning the relative distributions of target neutron and protons are discussed.

Accurate momentum-space method for scattering by nuclear and Coulomb potentials

Abstract: A coordinate-space boundary-matching method is used to solve the problem of including the long-range Coulomb interaction in momentum-space calculations of elastic scattering

Proton form factor from 0.15 to 0.79 fm-2

Abstract: The absolute electron-proton elastic scattering cross section has been measured by detecting the recoil protons. The proton charge form factor has been extracted for values of the square of the momentum transfer between 0.15 and 0.79 fm−2. The rms charge radius determined from these measurements is 0.81±0.04 fm. [NUCLEAR REACTIONS H1(e,p), E=55−130 MeV, measured σ(E;Ep,θ); deduced charge form factor, rms charge radius.]

Fission of odd-A and doubly odd actinide nuclei induced by direct reactions

Abstract: Fission probability distributions have been measured using ($d,pf$), ($t,pf$), ($^{3}\mathrm{He},df$), ($^{3}\mathrm{He},\ensuremath{\alpha}f$), and ($t,\ensuremath{\alpha}f$) reactions to excite a variety of odd-$A$ and odd-odd actinide nuclei. Fission of the residual nuclei $^{229,231}\mathrm{Th}$, $^{231,232,233}\mathrm{Pa}$, $^{234,235,236,237,238,239}\mathrm{Np}$, $^{241}\mathrm{Pu}$, $^{240,241,243,245,247}\mathrm{Am}$, $^{249}\mathrm{Cm}$, and $^{249}\mathrm{Bk}$ was studied. These results and other data available from previous ($d,pf$), ($t,pf$), and ($n,f$) studies are analyzed with a statistical model to obtain estimates of the heights and curvatures of one or both peaks of the double humped fission barrier. Estimates of barrier parameters are obtained for the above nuclei and for $^{233}\mathrm{Th}$, $^{235,237,239}\mathrm{U}$, $^{239,243,245}\mathrm{Pu}$, $^{242,244}\mathrm{Am}$, $^{245,247}\mathrm{Cm}$, and $^{253}\mathrm{Cf}$. Systematic variations of the barrier parameters are discussed.NUCLEAR REACTIONS, FISSION Measured fission probabilities, ${E}^{*}\ensuremath{\le}7.5$ MeV for $^{229,231}\mathrm{Th}$, $^{231,232,233}\mathrm{Pa}$, $^{234,235,236,237,238,239}\mathrm{Np}$, $^{241}\mathrm{Pu}$, $^{240,241,243,245,247}\mathrm{Am}$, $^{249}\mathrm{Cm}$, and $^{249}\mathrm{Bk}$ using ($d,pf$), ($t,pf$), ($^{3}\mathrm{He},df$), ($^{3}\mathrm{He},\ensuremath{\alpha}f$), and ($t,\ensuremath{\alpha}f$) reactions. Deduced properties of the double peaked fission barrier for these nuclei and for $^{233}\mathrm{Th}$, $^{235,237,239}\mathrm{U}$, $^{239,243,245}\mathrm{Pu}$, $^{242,244}\mathrm{Am}$, $^{245,247}\mathrm{Cm}$, and $^{253}\mathrm{Cf}$.

Optical-model potential in nuclear matter from Reid's hard core interaction

Abstract: We describe a method for the calculation of the leading term of a previously proposed low-density expansion for the self-energy of nucleons in nuclear matter. We compute the single-particle complex potential energy, the average binding energy per nucleon, the complex symmetry potential, and the symmetry energy. We use Reid's hard core nucleon-nucleon interaction and take a Fermi momentum ${k}_{F}=1.4$ ${\mathrm{fm}}^{\ensuremath{-}1}$. The calculated single-particle potential energy is compared with the phenomenological values of the optical-model potential in the inner region of a nucleus. The real part of our theoretical value is given by $56\ensuremath{-}0.3E$ (MeV) below $E=150$ MeV, and changes sign at 200 MeV. The imaginary part rises from 2 MeV at low energy to about 20 MeV at $E=200$ MeV. These features are in good agreement with experimental evidence. The average binding energy $B$ per nucleon calculated with a self-consistent potential energy for the particle states above ${k}_{F}$ is equal to -11 MeV. In the standard approach, with no potential energy for intermediate particle states above ${k}_{F}$, one finds -8.65 MeV. We also calculate the symmetry potential. At low energy, its real part is equal to $14 \frac{(N\ensuremath{-}Z)}{A}$ (MeV); it changes sign at 110 MeV. Its imaginary part is equal to $3.5\frac{(N\ensuremath{-}Z)}{A}$ (MeV) at low energy, and rises to $8.5\frac{(N\ensuremath{-}Z)}{A}$ (MeV) at 200 MeV. The symmetry energy is equal to 27.8 MeV.NUCLEAR REACTIONS Calculated complex optical-model potential, symmetry potential, average binding energy and symmetry energy for nucleons in nuclear matter, for a Fermi momentum equal to 1.4 ${\mathrm{fm}}^{\ensuremath{-}1}$, from Reid's hard core nucleon-nucleon interaction, in the frame of Brueckner's theory.

Optical-model analysis of p pb-208 elastic scattering from 15-1000 mev

Abstract: Measurements have been made of the differential cross sections for $p+^{208}\mathrm{Pb}$ elastic scattering at mean proton energies of 21.0, 24.1, 26.3, 30.5, 35.0, 45.0, and 47.3 MeV. Measurements have also been made of the differential cross sections and polarizations at 185 MeV. These data together with the data in the energy range 15-1000 MeV available in the literature have been analyzed in terms of a standard 11-parameter optical model. Relativistic corrections to the optical-model analysis were introduced. The energy dependence of the real central potential (as indicated by the volume integral per nucleon and by the strength parameter) can be represented by a linear relation if a limited energy range is chosen. This linear energy relation cannot be extrapolated to higher energies since it makes the real central potential repulsive at too low an energy as indicated by the results of optical-model analyses of proton scattering data above 200 MeV. A logarithmic energy dependence gives a reasonable presentation of the volume integral per nucleon of the real central potential for energies up to 1 GeV.NUCLEAR SCATTERING $^{208}\mathrm{Pb}(p,p)$, $T=21.0, 24.1, 26.3, 30.5, 35.0, 45.0, \mathrm{and} 47.3$ MeV, measured $\ensuremath{\sigma}(\ensuremath{\theta})$, $\ensuremath{\theta}=15\ensuremath{-}167.5\ifmmode^\circ\else\textdegree\fi{}$; $T=185$ MeV measured $\ensuremath{\sigma}(\ensuremath{\theta})$, $P(\ensuremath{\theta})$, $\ensuremath{\theta}=4\ensuremath{-}38\ifmmode^\circ\else\textdegree\fi{}$; optical-model analysis, previous data $\ensuremath{\sigma}(\ensuremath{\theta})$, $P(\ensuremath{\theta})$, ${\ensuremath{\sigma}}^{R}$ included.

Nuclear magnetic moments of very short-lived states via the transient-field implantation perturbed-angular-correlation technique

Abstract: The Lindhard and Winther equations for the transient magnetic field effect have been numerically integrated with the inclusion of a decays-in-flight correction and using the best available stopping power formulas. The calculations are carried out for an iron host and curves are generated from which the transient-field angular shift may be predicted for any $Zg12$ to an accuracy of \ensuremath{\sim} 20%. The transient-field calculations are employed in the analysis of angular shift data for the first ${2}^{+}$ states of $^{104}\mathrm{Pd}$, $^{106}\mathrm{Pd}$, $^{108}\mathrm{Pd}$, and $^{110}\mathrm{Pd}$ isotopes implanted into an ${\mathrm{Fe}}_{0.8}$-${\mathrm{Co}}_{0.2}$ alloy and for $^{54}\mathrm{Fe}$ and $^{56}\mathrm{Fe}$ implanted into iron. The $g$ factors of the six isotopes are obtained and the hyperfine field of Pd in the alloy is determined. Evidence is presented which suggests that the hyperfine fields measured in oxygen beam implantation perturbed-angular-correlation experiments for Ru, Pd, Cd, and Te in Fe are consistently reduced from the hyperfine fields measured by other methods. In light of these results and the decays-in-flight corrections to the transient-field theory, angular shift data of previous workers on even-even isotopes of Ge, Ru, Pd, Cd, and Te have been reanalyzed. With the exception of $^{70}\mathrm{Ge}$, all the $g$ factors are in agreement with a collective model.[NUCLEAR REACTIONS ce, transient-field IMPAC technique. Measured $\ensuremath{\gamma}(\ensuremath{\theta})$, deduced hyperfine fields, $g({2}^{+})$ for $^{104,106,108,110}\mathrm{Pd}$ in ${\mathrm{Fe}}_{0.8}$-${\mathrm{Co}}_{0.2}$, for $^{54,56}\mathrm{Fe}$ in Fe. Reanalysis of previous $g({2}^{+})$ for $^{70,72,74,76}\mathrm{Ge}$, $^{98,100,102,104}\mathrm{Ru}$, $^{104,106,108,110}\mathrm{Pd}$, $^{110,112,114,116}\mathrm{Cd}$, $^{120,122,124,126,128,130}\mathrm{Te}$.]

Quasielastic electron scattering

Abstract: Data and interpretation are presented for inelastic electron scattering in the quasielastic region from nine target nuclei ranging from lithium to lead at an incident energy of 500 MeV and a scattering angle of 60\ifmmode^\circ\else\textdegree\fi{}. The average kinetic and separation energies of nucleons in these nuclei are deduced. Results of and comments on the radiative correction procedures used in the data analysis are also discussed.[NUCLEAR REACTIONS $^{6}\mathrm{Li}(e,{e}^{\ensuremath{'}})$, $^{12}\mathrm{C}(e,{e}^{\ensuremath{'}})$, $^{24}\mathrm{Mg}(e,{e}^{\ensuremath{'}})$, $^{40}\mathrm{Ca}(e,{e}^{\ensuremath{'}})$, $^{58.7}\mathrm{Ni}(e,{e}^{\ensuremath{'}})$, $^{89}\mathrm{Y}(e,{e}^{\ensuremath{'}})$, $^{118.7}\mathrm{Sn}(e,{e}^{\ensuremath{'}})$, $^{181}\mathrm{Ta}(e,{e}^{\ensuremath{'}})$, $^{208}\mathrm{Pb}(e,{e}^{\ensuremath{'}})$, $E=500$ MeV, $\ensuremath{\theta}={60}^{\ensuremath{\circ}}$; measured $\ensuremath{\sigma}(E)$; deduced nucleon separation and kinetic energies in Fermi gas model.]

Refractive behavior in intermediate-energy alpha scattering

Abstract: We report on recent $\ensuremath{\alpha}$-scattering experiments at 141.7 MeV using $^{40}\mathrm{Ca}$ and $^{90}\mathrm{Zr}$ targets. The results are compared with previous experiments on other nuclides at approximately the same energy and are used to illustrate phenomena occurring in intermediate-energy $\ensuremath{\alpha}$ scattering to which we have given the name "refractive behavior." All the elastic scattering differential cross sections exhibit the exponential-like falloff at large angles characteristic of nuclear rainbow scattering. The variation in the rainbow angle with $A$ is found to be approximately linear. In each instance it is shown that, consistent with earlier predictions, it is the data beyond the rainbow angle which make possible the elimination of the discrete ambiguities in the optical potential: For each nucleus studied, only a single family of Woods-Saxon optical potentials is found to fit the data. The real parts of the extracted potentials are characterized by well depths ranging from 108 to 118 MeV and volume integrals $\frac{J}{4A}$ ranging from 297 to 352 MeV ${\mathrm{fm}}^{3}$; hence they are more nearly three times the strength of nucleon-nucleus potentials at 1/4 the incident energy, rather than 4 times, as is frequently assumed. Systematic variations of the optical potentials with $A$ occur primarily in the imaginary part of the potential and are greatest for the lighter nuclei; as $A$ decreases, $W$ and ${a}^{\ensuremath{'}}$ decrease, $r_{0}^{}{}_{}{}^{\ensuremath{'}}$ increases, and the volume integral of the real part of the potential increases.NUCLEAR REACTIONS $^{40}\mathrm{Ca}$, $^{90}\mathrm{Zr}(\ensuremath{\alpha},\ensuremath{\alpha})$, $E=141.7$; enriched targets; measured $\ensuremath{\sigma}(\ensuremath{\theta})$; deduced optical-model parameters, nuclear rainbow angles; results compared with those from $^{58}\mathrm{Ni}$, $^{12}\mathrm{C}$.

Faddeev approach to pion production and pion-deuteron scattering

Abstract: Some consequences of a new approach to pion production are explored in the threshold region. We treat the $\ensuremath{\pi}\mathrm{NN}$ system as a three-body system, with absorption (or production) occurring because of the existence of a $\ensuremath{\pi}N$ bound state in the ${P}_{11}$ (nucleon) channel. This description of the $\mathrm{NN}\ensuremath{\pi}$ vertex is justified by successfully using the model to calculate the long range part of the $N\ensuremath{-}N$ scattering amplitude. The results of the pion production calculation confirm a sensitivity to the short range behavior of the deuteron wave function and its $D$-state probability reported earlier. We also find a stronger variation of the production amplitude with energy than has previously been reported. This may resolve the apparent incompatibility of some experimental results. Finally, we also discuss the implications of the model for pion-deuteron elastic scattering.NUCLEAR REACTIONS $\mathrm{pp}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}d$, ${E}_{\ensuremath{\pi}}=0\ensuremath{-}30$ MeV; $s$-wave pions, calculated $\ensuremath{\sigma}$ as function of ${E}_{\ensuremath{\pi}}$, also dependence on $N\ensuremath{-}N$ interaction. $d(\ensuremath{\pi}, \ensuremath{\pi})$; calculated scattering length, including absorption. Faddeev calculation, separable interactions.

Spallation of Cu by 3.9-GeV N 14 ions and 3.9-GeV protons

Abstract: Relative yields of 35 products extending from $^{3}\mathrm{H}$ to $^{76}\mathrm{Br}$ have been measurd for the interaction of 3.9-GeV (278-MeV/amu) $^{14}\mathrm{N}$ ions with copper. For purposes of comparison, cross sections of 54 nuclides produced by the irradiation of Cu with 3.9-GeV protons are also reported. Although the over-all patterns of yields for $^{14}\mathrm{N}$ ions and protons are qualitatively similar, there are significant differences. In the mass region $37\ensuremath{\le}A\ensuremath{\le}64$, the mass yield curve for $^{14}\mathrm{N}$ ions decreases more rapidly with decreasing $A$ than does the proton curve. No difference could be detected in the shapes of the charge dispersion curves. However, the data indicate a small shift ($l0.1Z$ unit) favoring neutron-deficient products near the target in the case of $^{14}\mathrm{N}$ ions. The mass yield curves appear to have similar shapes from $A\ensuremath{\approx}40$ down to $A\ensuremath{\approx}24$, but formation of the still lighter products, $^{7}\mathrm{Be}$ and particularly $^{3}\mathrm{H}$, is favored in the $^{14}\mathrm{N}$ irradiation. An observed enhancement of products such as $^{62}\mathrm{Zn}$, $^{66}\mathrm{Ga}$, and $^{69}\mathrm{Ge}$ is interpreted as arising largely from secondary reactions rather than from primary processes which add charge or mass from the $^{14}\mathrm{N}$ to the target nuclei. Some discussion of results from this and other experiments with high-energy protons and heavy ions with complex nuclei is presented in terms of the concepts of limiting fragmentation and factorization.NUCLEAR REACTIONS Cu($^{14}\mathrm{N}$, spallation), $E=3.9$ GeV; measured relative $\ensuremath{\sigma}(A,Z)$, 35 products $^{3}\mathrm{H}$-$^{76}\mathrm{Br}$. $\mathrm{Cu}(p, \mathrm{spallation})$, $E=3.9$ GeV; measured $\ensuremath{\sigma}(A,Z)$, 54 products $^{3}\mathrm{H}$-$^{69}\mathrm{Ge}$. Natural targets, Ge(Li), $\ensuremath{\beta}$ counting, radiochemistry.

Study of charged particles emitted from 117 Te compound nuclei. II. Comparison between 40 Ar + 77 Se and 14 N + 103 Rh reactions and determination of critical angular momenta

Abstract: The compound nucleus $^{117}\mathrm{Te}$ was formed with $^{14}\mathrm{N}$ + $^{103}\mathrm{Rh}$ at 71- and 107-MeV excitation energies. The deexcitation by protons, deuterons, tritons, and $\ensuremath{\alpha}$ particles was studied and compared to the deexcitation of the same compound nucleus $^{117}\mathrm{Te}$ issued from $^{40}\mathrm{Ar}$ + $^{77}\mathrm{Se}$ at the same excitation energies. The influence of angular momentum on the evaporation mechanism (angular distributions and cross sections of charged particles) have allowed to determine different values of critical angular momenta limiting compound-nucleus formation. These values are discussed with respect to different models.[NUCLEAR REACTIONS $^{103}\mathrm{Rh}$($^{14}\mathrm{N}$, $^{14}\mathrm{N}$); $E=81,121$ MeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$; optical-model analysis $^{103}\mathrm{Rh}(^{14}\mathrm{N},p)$, ($^{14}\mathrm{N},d$), ($^{14}\mathrm{N},t$), ($^{14}\mathrm{N},\ensuremath{\alpha}$); $E=81,121$ MeV measured $\ensuremath{\sigma}(E,{E}_{\mathrm{particle}})$, $\ensuremath{\sigma}({E}_{\mathrm{particle}},\ensuremath{\theta})$, ${\ensuremath{\sigma}}_{\mathrm{particle}}$; discussion with regard to statistical model; comparison with Ar-induced reactions; deduced critical angular momenta.]

Theory of mean removal energies for single particles in nuclei.

Abstract: A useful way to characterize the hole-energy spectrum excited in a direct particle-removal reaction like ($p,2p$) or ($e,{e}^{\ensuremath{'}}p$) is through the centroid or mean removal energy. We derive the rules for computing this quantity in a linked-cluster expansion, and give some examples. We demonstrate the close relation of the mean removal energy to Brandow's self-consistent orbital energy, and discuss briefly the connection with Green's function theory.[NUCLEAR STRUCTURE Linked-cluster theory of mean or centroid removal energies measured in ($p,2p$) or ($e,{e}^{\ensuremath{'}}p$); applications and relation to other hole energies.]

New integral equations for the transition operators of many-body systems

Abstract: A new set of coupled integral equations for the transition operators of a nonrelativistic quantum-mechanical $n$- body system is presented. These equations are a generalization to the many-body system of a special case of a set suggested for the three-body problem by Kouri, Baer, and Levin. The Kouri-Baer-Levin formalism effectively couples together the Lippmann-Schwinger integral equations for the transition operators for all open channels thus simultaneously imposing all asymptotic boundary conditions. The effect of our specialization of these equations is to make the kernel of the integral equations connected so that the resulting equations appear to be a suitable basis for many-body calculations.

Limitation on complete fusion during heavy-ion collisions

Abstract: In a recent paper Lefort and collaborators have extracted a critical distance of approach as the mechanism limiting fusion of two heavy ions In this comment it is shown that this analysis does not depend on the specific model used for the calculation of the ion-ion potential Furthermore an expression is derived to analyze both high- and low-energy fusion data on the same basis It is concluded that all existing data are compatible with the existence of a critical distance However, data spanning a larger range of energies and being more accurate at high energies are needed for a final check of the critical distance hypothesisNUCLEAR REACTIONS Heavy-ion complete fusion; critical distance of approach

Study of the α+α system below 15 MeV (c.m.)

Abstract: Differential cross sections for $\ensuremath{\alpha}+\ensuremath{\alpha}$ elastic scattering have been measured at lab energies of 18.00, 21.12, 24.11, 25.50, 26.99, 28.50, and 29.50 MeV. The majority of the data have relative errors less than 1%, and the additional error in absolute scale is 0.30%. A phase-shift analysis of the data has been performed, and most of the phase shifts have been determined to within $\ifmmode\pm\else\textpm\fi{}\frac{1}{3}\ifmmode^\circ\else\textdegree\fi{}$. These phase shifts and others from the literature were used to study properties of the $\ensuremath{\alpha}+\ensuremath{\alpha}$ system in the center of mass energy range 1.50 to 14.74 MeV. First, an $R$-matrix analysis was made of the $l=4$ phase shifts; this analysis yields a resonance energy of 11.7 \ifmmode\pm\else\textpm\fi{} 0.4 MeV and a level width at resonance of 4.0 \ifmmode\pm\else\textpm\fi{} 0.4 MeV. Second, comparison was made of the $\ensuremath{\alpha}+\ensuremath{\alpha}$ phase shifts with results of previous resonating-group calculations, and this comparison shows good agreement with a calculation which includes one inelastic channel and a nucleon-nucleon repulsive core. Third, an $\ensuremath{\alpha}+\ensuremath{\alpha}$ potential model was constructed. This model contains an attractive potential obtained by folding Gaussian $\ensuremath{\alpha}$-particle densities together with a Yukawa-shaped direct part of a nucleon-nucleon potential and, in addition, contains phenomenological short-range repulsive components in the $l=0$ and $l=2$ states. The model reproduces the experimental phase shifts quite well when the Yukawa potential is taken to have a range corresponding to a two-pion mass.NUCLEAR REACTIONS $^{4}\mathrm{He}(\ensuremath{\alpha},\ensuremath{\alpha})^{4}\mathrm{He}$, $E=18.00\ensuremath{-}29.50$ MeV; measured $\ensuremath{\sigma}(E; \ensuremath{\theta})$; deduced phase shifts $l=0,2,4,6$. $R$-matrix analysis $l=4$. Comparison with resonating-group calculations. Potential-model analysis.

New neutron-deficient Pb and Bi nuclides produced in cross bombardments with heavy ions

Abstract: New $\ensuremath{\alpha}$ -emitting bismuth nuclides ranging in mass number from 189 to 197 and lead nuclides ranging from 186 to 192 have been produced in the following reactions: $^{203}\mathrm{Tl}{(^{3}\mathrm{He},xn)}^{206\ensuremath{-}x}\mathrm{Bi}$, $^{187}\mathrm{Re}{(^{16}\mathrm{O},xn)}^{205\ensuremath{-}x}\mathrm{Bi}$, $^{185}\mathrm{Re}{(^{16}\mathrm{O},xn)}^{203\ensuremath{-}x}\mathrm{Bi}$, $^{181}\mathrm{Ta}{(^{20}\mathrm{Ne},xn)}^{201\ensuremath{-}x}\mathrm{Bi}$, $^{159}\mathrm{Tb}{(^{40}\mathrm{Ar},xn)}^{199\ensuremath{-}x}\mathrm{Bi}$, $^{181}\mathrm{Ta}{(^{19}\mathrm{F},xn)}^{200\ensuremath{-}x}\mathrm{Pb}$, $^{182}\mathrm{W}{(^{16}\mathrm{O},xn)}^{198\ensuremath{-}x}\mathrm{Pb}$ and $^{155}\mathrm{Gd}{(^{40}\mathrm{Ar},xn)}^{195\ensuremath{-}x}\mathrm{Pb}$. Assignments were made on the basis of excitation function measurements and comparison with similar reactions leading to the formation of the analogous well-known Po nuclides. The following assignments were made, where for each nuclide the two listed numbers are the $\ensuremath{\alpha}$-ray energy in MeV and half-life: $^{197}\mathrm{Bi}^{m}$\char22{}5.77, 10 min; $^{195}\mathrm{Bi}$-5.43, 170 sec; $^{195}\mathrm{Bi}^{m}$\char22{}6.11, 90 sec; $^{194}\mathrm{Bi}$-5.61, 105 sec; $^{193}\mathrm{Bi}$-5.90, 64 sec; $^{193}\mathrm{Bi}^{m}$\char22{}6.18; $^{192}\mathrm{Bi}$-6.06, 42 sec; $^{191}\mathrm{Bi}$-6.32, 13 sec; $^{191}\mathrm{Bi}^{m}$\char22{}6.63; $^{191}\mathrm{Bi}^{m}$\char22{}6.86; $^{190}\mathrm{Bi}$-6.45, 5.4 sec; $^{189}\mathrm{Bi}$-6.67, 2 sec; $^{192}\mathrm{Pb}$-5.06, 2.3 min; $^{191}\mathrm{Pb}$-5.29, 1.3 min; $^{190}\mathrm{Pb}$-5.58, 1.2 min; $^{189}\mathrm{Pb}$-5.72, 51 sec; $^{188}\mathrm{Pb}$-5.98, 26 sec; $^{187}\mathrm{Pb}$-6.08, 17 sec; and $^{186}\mathrm{Pb}$-6.32, 8 sec. Estimates of $\ensuremath{\alpha}$ branching ratios are also presented.

Decay properties of the neutron-rich isotopes, Li 11 and Na 2 7 − 3 1

Abstract: Using an on-line mass spectrometer the decay properties of the ${T}_{z}\ensuremath{\ge}\frac{5}{2}$ nuclei $^{11}\mathrm{Li}$, $^{27\ensuremath{-}31}\mathrm{Na}$, $^{29,30}\mathrm{Mg}$ were studied. The new isotope $^{30}\mathrm{Mg}$ (${T}_{\frac{1}{2}}=1200\ifmmode\pm\else\textpm\fi{}500$ msec) identified by $\ensuremath{\beta}$ counting. For the other isotopes the half-lives were remeasured by three independent methods with improved precision. By recording $\ensuremath{\beta}$-coincident $\ensuremath{\gamma}$ spectra, the decays of $^{27\ensuremath{-}29}\mathrm{Na}$ were studied, leading to a ${1}^{+}$ assignment for the $^{28}\mathrm{Na}$ ground state. By simultaneous $\ensuremath{\beta}$ and neutron multiscaling the delayed neutron emission probabilities ${P}_{n}$ were determined for $^{11}\mathrm{Li}$ and $^{27\ensuremath{-}31}\mathrm{Na}$. The following half-lives (msec) and ${P}_{n}$ values (%) were found (errors see text): $^{11}\mathrm{Li}$ (8.5/60.8), $^{27}\mathrm{Na}$ (304/0.08), $^{28}\mathrm{Na}$ (30.5/0.58), $^{29}\mathrm{Na}$ (42.9/15.1), $^{30}\mathrm{Na}$ (53.0/33.1), $^{31}\mathrm{Na}$ (16.9/30).

Nuclear muon-capture sum rules and mean nuclear excitation energies

Abstract: A discussion is given of non-energy-weighted and of energy-weighted sum rules in nuclear muon capture. It is argued that the mean nuclear excitation energy in muon capture does not vary appreciably as $A$ and $Z$ vary. A combined non-energy-weighted and energy-weighted sum rule which constitutes a three-parameter fit to the experimental data on total muon-capture rates is presented.