Showing papers in "Physical Review C in 1973"

Hartree-Fock Calculations with Skyrme's Interaction. II. Axially Deformed Nuclei

Abstract: Skyrme's interaction is used in deformed Hartree-Fock calculations of some light and rare-earth nuclei. A method of solution is presented, which exploits as much as possible the simple features of the Skyrme force in order to allow calculations of heavy deformed nuclei. In the rare-earth region pairing correlations are taken into account in a simplified but self-consistent way by considering energy functionals depending also on occupation probabilities. Calculations have been made for the two parameter sets which were used in a previous study of double-closed-shell nuclei. The set providing the best fit to ground-state properties of spherical nuclei is also found to give a satisfactory description of nuclear deformations. Comparison is made with other available Hartree-Fock calculations in the case of light nuclei, and a discussion of the importance of various terms in the effective force upon nuclear deformations is given.

Complete Hydrogen and Helium Particle Spectra from 30- to 60-MeV Proton Bombardment of Nuclei with A = 12 to 209 and Comparison with the Intranuclear Cascade Model

Abstract: Differential cross sections for the production of proton, deuteron, triton, helium-3, and $\ensuremath{\alpha}$ particles from as many as 10 targets ($A=12\ensuremath{-}209$) were measured using 29-, 39-, and 62-MeV incident protons. The particles were detected, with $\ensuremath{\approx}0.2$-MeV [full width at half maximum (FWHM)] energy resolution for protons, over a secondary energy range of $\ensuremath{\approx}2\ensuremath{-}6 \mathrm{to} 62$ MeV in a total absorption telescope composed of three solid-state detectors. Representative results are shown for cross sections differential in energy and angle, as well as for angle-and energy-integrated cross sections. For incident 60-MeV protons the integral magnitude of the nonevaporation charged-particle production is found to be $\ensuremath{\sim}{10}^{2}{A}^{\frac{1}{3}}$ mb. Fewer protons but more complex particles were measured for carbon and oxygen targets than expected from an ${A}^{\frac{1}{3}}$ dependence for either component alone. The continuum cross sections for $z=1$ particles at a given angle (mb ${\mathrm{sr}}^{\ensuremath{-}1}$ Me${\mathrm{V}}^{\ensuremath{-}1}$) are nearly independent of incident energy when measured with incident protons in the 30- to 60- MeV energy range. Nonevaporation production of complex particles ($A\ensuremath{\ge}2$) is 25-40% of that for protons. The proton spectra have been compared with predictions from the intranuclear cascade model. Differential spectral predictions compare well with the measured spectra for angles in the range \ensuremath{\sim}25-60\ifmmode^\circ\else\textdegree\fi{}, and relatively poor predictions for small and large angles are more favorable when reflection and refraction by the potential well are included. Evidence is given that predictions for backward angles are greatly improved by allowing proton scattering from nucleon pairs within the model nucleus, but the $A$-dependent underprediction at extreme forward angles is not understood at all. The calculated angle-integrated spectra reproduce the measured spectral shape but consistently predict $\ensuremath{\approx}30%$ too few nonevaporation protons for targets with $A\ensuremath{\ge}27$.[NUCLEAR REACTIONS $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{27}\mathrm{Al}$, $^{54}\mathrm{Fe}$, $^{56}\mathrm{Fe}$, $^{60}\mathrm{Ni}$, $^{89}\mathrm{Y}$, $^{120}\mathrm{Sn}$, $^{197}\mathrm{Au}$, $^{209}\mathrm{Bi}$, ($p,{p}^{\ensuremath{'}}X$), ($p,dX$), ($p,tX$), ($p,^{3}\mathrm{He}X$), ($p,\ensuremath{\alpha}X$), $E=62,39,29$ MeV; semi; measured $\ensuremath{\sigma}(E;{E}_{{p}^{\ensuremath{'}}},{E}_{d},{E}_{{3}_{\mathrm{He}}},{E}_{\ensuremath{\alpha}},\ensuremath{\theta})$; deduced $\ensuremath{\sigma}(E)$. $2\ensuremath{\lesssim}{E}_{{p}^{\ensuremath{'}}},{E}_{d},{E}_{t},{E}_{{3}_{\mathrm{He}}},{E}_{\ensuremath{\alpha}}\ensuremath{\lesssim}70$ MeV. Comparisons with intranuclear cascade model.]

Prompt Gamma Rays from 235 U(n,f), 239 Pu(n,f), and Spontaneous Fission of 252 Cf

Abstract: The spectra of prompt $\ensuremath{\gamma}$ rays from $^{235}\mathrm{U}(n,f)$, $^{239}\mathrm{Pu}(n,f)$, and $^{252}\mathrm{Cf}$(s.f.) emitted at 0-10 nsec after fission were measured with 4-nsec time resolution. A $\ensuremath{\gamma}$-ray spectrometer with a near-Gaussian response was used over the entire energy region, and the prompt neutrons from fission were positively rejected by time of flight. The measured $\ensuremath{\gamma}$-ray spectra show a systematic softening with increasing mass number for $^{235}\mathrm{U}$, $^{239}\mathrm{Pu}$, and $^{252}\mathrm{Cf}$. The average photon energy above 0.14 MeV is 0.97 \ifmmode\pm\else\textpm\fi{} 0.05, 0.94 \ifmmode\pm\else\textpm\fi{} 0.05, and 0.88 \ifmmode\pm\else\textpm\fi{} 0.04 MeV/photon for thermal-neutron fission of $^{235}\mathrm{U}$ and $^{239}\mathrm{Pu}$, and spontaneous fission of $^{252}\mathrm{Cf}$, respectively. This behavior is discussed in terms of nearness of $Z$ and $N$ of the average fission fragment to closed-shell values, of the corresponding changes in level density expected, and of corroborative evidence from x-ray measurements. The total $\ensuremath{\gamma}$-ray energy released, ${\overline{E}}_{\ensuremath{\gamma},\mathrm{tot}}$, is 6.51, 6.81, and 6.84 MeV/fission for $^{235}\mathrm{U}(n,f)$, $^{239}\mathrm{Pu}(n,f)$, and $^{252}\mathrm{Cf}$ (s.f.), respectively, for photons above 0.14 MeV and for 0-10 nsec after fission. The calculations of Thomas and Grover are seen to be in agreement with these data in that they predict the correct partition of fission-fragment deexcitation energy between neutron and photon emission. This partition is related to the separation energy required to emit an additional neutron, to the pairing energy, and to the spin barrier for neutron emission. Two theoretical $\ensuremath{\gamma}$-ray spectra were compared to the measured spectrum for $^{235}\mathrm{U}(n,f)$, and each was found to fit the measured spectrum well over only a limited portion of the total energy range.

E2 and E4 Transition Moments and Equilibrium Deformations in the Actinide Nuclei

Abstract: Precision Coulomb-excitation experiments using $^{4}\mathrm{He}$ ions have been performed in the actinide region ($230\ensuremath{\le}A\ensuremath{\le}248$) by the observation of elastic and inelastically scattered projectiles using a split-pole magnetic spectrometer equipped with a position-sensitive proportional detector. 12 even-$A$ targets from $^{230}\mathrm{Th}$ to $^{248}\mathrm{Cm}$ have been investigated and the reduced quadrupole matrix element, $〈2\ensuremath{\parallel}\mathfrak{M}(E2)\ensuremath{\parallel}0〉$, and the reduced hexadecapole matrix element, $〈4\ensuremath{\parallel}\mathfrak{M}(E4)\ensuremath{\parallel}0〉$, have been determined from the experimental excitation probabilities of the ${0}^{+}$, ${2}^{+}$, and ${4}^{+}$ states in the ground-state rotational bands. The values of $B(E4,0\ensuremath{\rightarrow}4)$ range from 167 single-particle units for $^{234}\mathrm{U}$ to essentially zero single-particle units for $^{244,246,248}\mathrm{Cm}$. Model-dependent deformation parameters, ${\ensuremath{\beta}}_{20}$ and ${\ensuremath{\beta}}_{40}$, are extracted from the measured $E2$ and $E4$ transition moments for distributions of nuclear charge represented by deformed Fermi distributions and by a deformed homogeneous distribution.

Rules for Spin and Parity Assignments Based on Log ft Values

Abstract: A survey was made of $log\mathrm{ft}$ values for forbidden $\ensuremath{\beta}$ transitions. Three cases, $^{90m}\mathrm{Y}$, $^{65}\mathrm{Ni}$, and $^{144}\mathrm{Pm}$ decays, were examined experimentally. A number of low $log\mathrm{ft}$ values reported in the literature are superseded by more recent larger values. Empirical rules for making spin and parity assignments from $log\mathrm{ft}$ values are proposed.

Experimental Measurements of the C 12 + C 12 Nuclear Reactions at Low Energies

Abstract: The nuclear reactions $^{12}\mathrm{C}(^{12}\mathrm{C}, \ensuremath{\alpha})^{20}\mathrm{Ne}$ and $^{12}\mathrm{C}(^{12}\mathrm{C}, p)^{23}\mathrm{Na}$ have been observed from 5-MeV down to 2.45-MeV center-of-mass energy. Angular distributions and energy distributions of the protons and $\ensuremath{\alpha}$ particles were analyzed to obtain the total cross sections and other nuclear information. The Coulomb and angular momentum barrier penetrability was factored out to elucidate the intermediate resonance structure in the nuclear factor $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{S}$. The observed rise in the nuclear factor at the lowest energies may be interpreted as "absorption under the barrier" as proposed by Michaud and Vogt. The importance of these reactions for the carbon burning era of nucleosynthesis and energy generation in the later evolution of stars is mentioned and reaction rates are estimated for various burning temperatures.

Hauser-Feshbach Theory and Ericson Fluctuations in the Presence of Direct Reactions

Abstract: Neglecting level-level correlations, we show that consistency conditions derived from general properties of the $S$ matrix determine the distribution of resonance parameters. This is also true in the presence of direct reactions. Formulas are given for average cross sections, autocorrelation, and cross-correlation functions.

Total Neutron Yield from the Reactions C-13 (alpha , n) O-16 and O-17, O-18 (alpha , n) Ne-20, Ne-21

Abstract: Compound states of high excitation in $^{17}\mathrm{O}$ and $^{21,22}\mathrm{Ne}$ have been observed, with good resolution, in the total neutron yield from the reactions $^{13}\mathrm{C}(\ensuremath{\alpha}, n)^{16}\mathrm{O}$ and $^{17,18}\mathrm{O}(\ensuremath{\alpha}, n)^{20,21}\mathrm{Ne}$. Bombarding $\ensuremath{\alpha}$-particle energies were approximately from 1 to 5 MeV. Analysis of the area under the excitation curves gives $\ensuremath{\alpha}$-particle strength functions of ${S}_{\ensuremath{\alpha}}=0.029\ifmmode\pm\else\textpm\fi{}0.030$ for $^{13}\mathrm{C}$+$\ensuremath{\alpha}$, 0.030\ifmmode\pm\else\textpm\fi{}0.023 for $^{13}\mathrm{C}$+$\ensuremath{\alpha}$, and 0.022\ifmmode\pm\else\textpm\fi{}0.010 for $^{18}\mathrm{O}$+$\ensuremath{\alpha}$. For astrophysical purposes these strength functions are used to extrapolate the average cross sections to lower energies.

Variational method for dense systems

Abstract: The variational method for calculating energy of quantum fluids, and its applications to the Bose liquid He4, Fermi neutron gas, and liquid He3 are discussed. The correlation functions are parametrized by their healing distance, and can depend on the states occupied by the correlated particles in the model wave function. They are calculated by constrained variation of the lowest-order contributions. The healing distance has a prescribed value in lowest-order calculations, whereas it is sufficiently large in hopefully exact energy calculations. The many-body cluster contributions in Bose fluids are summed with successive approximations of an integral equation due to van Leeuwen et al. A simple diagrammatic cluster expansion is presented for Fermi liquids, and its direct diagrams are summed with the integral equation. The contribution of exchange diagrams is shown to decrease rapidly with the number of exchanges, and their sums are truncated after the energy has converged to within a few percent.

Separable Representations of Two-Body Interactions

Abstract: Consideration is given to the approximation in which an arbitrary potential is replaced by a separable potential. A method is presented which permits the construction of a rank-$N$ separable potential which has the property that the resulting $T$ matrix is exact on the energy shell and half off the energy shell at $N$ selected bound state and/or continuum energies. This construction yields a $T$ matrix that is correct off the energy shell in the vicinity of the $N$ on-shell points.

Renormalization of the Axial-Vector Coupling Constant in Nuclear β Decay

Abstract: The isoscalar magnetic moments and Gamow-Teller $\ensuremath{\beta}$ decay of the systems $A=11,13,15,17,19, \mathrm{and} 21$ are analyzed in an attempt to extract, in a largely model-independent way, the effective nuclear renormalization of the axial coupling constant: ${g}_{A}\ensuremath{\rightarrow}{g}_{\mathrm{Ae}}$. We find: $\frac{{g}_{\mathrm{Ae}}}{{g}_{A}}=0.920\ifmmode\pm\else\textpm\fi{}0.047$.

X-Ray Isotope Shifts and Variations of Nuclear Charge Radii in Isotopes of Nd, Sm, Dy, Yb, and Pb

Abstract: Isotope shifts of electronic $K\ensuremath{\alpha}$ x-ray transitions have been measured in isotopes of Nd, Sm, Dy, Yb, and Pb using a curved crystal spectrometer. The $\ensuremath{\delta}〈{r}^{2}〉$ values of the nuclear charge distribution, as derived from the data, are presented. A combination with results from optical isotope shifts yields an improved accuracy for $\ensuremath{\delta}〈{r}^{2}〉$. The optical mass shifts and the electronic coefficients can also be obtained. A comparison with muonic x-ray isotope shifts is presented for Nd and Pb. Consistancy between electronic and muonic data is noted.

Alpha-Structure Amplitudes for the 1p Shell

Abstract: Structure amplitudes for transfer of a ${(1p)}^{4}$ group with spatial symmetry [4] are given for $1p$-shell targets with initial and final states represented by intermediate-coupling wave functions. The strength is fragmented, a feature likely to be even stronger in heavy nuclei as is shown for the ($2p, 1f$) region.

Recoil Effects in Single-Nucleon-Transfer Heavy-Ion Reactions

Abstract: The effect of recoil in single-nucleon-transfer heavy-ion reactions is found to be twofold: Extra transfer angular momenta are introduced and the radial integrals are changed Comparison of an exact recoil distorted-wave Born-approximation program with experimental data from heavy-ion reactions induced on $^{11}\mathrm{B}$ and $^{12}\mathrm{C}$ gives excellent quantitative agreement Recoil effects on other targets and energies are considered

Studies of mendelevium isotopes with mass numbers 248 through 252.

Abstract: Five isotopes of mendelevium, with mass numbers 248 through 252, were studied by means of $\ensuremath{\alpha}$-particle spectroscopy. The isotopes were produced by bombarding $^{241}\mathrm{Am}$ and $^{243}\mathrm{Am}$ targets with $^{12}\mathrm{C}$ and $^{13}\mathrm{C}$ ions accelerated by the Berkeley heavy-ion linear accelerator. The half-lives of the nuclides and the energies of the main $\ensuremath{\alpha}$-particle groups, respectively, were observed to be: $^{248}\mathrm{Md}$: 7 \ifmmode\pm\else\textpm\fi{} 3 sec, 8.32 \ifmmode\pm\else\textpm\fi{} 0.02 MeV; $^{249}\mathrm{Md}$: 24 \ifmmode\pm\else\textpm\fi{} 4 sec, 8.03 \ifmmode\pm\else\textpm\fi{} 0.02 MeV; $^{250}\mathrm{Md}$: 52 \ifmmode\pm\else\textpm\fi{} 6 sec, 7.75 \ifmmode\pm\else\textpm\fi{} 0.02 MeV; $^{251}\mathrm{Md}$: 4.0 \ifmmode\pm\else\textpm\fi{} 0.5 min, 7.55 \ifmmode\pm\else\textpm\fi{} 0.02 MeV; $^{252}\mathrm{Md}$: 2.3 \ifmmode\pm\else\textpm\fi{} 0.8 min, no $\ensuremath{\alpha}$ decay. The $\ensuremath{\alpha}$-particle energies of $^{245}\mathrm{Es}$, $^{246}\mathrm{Es}$, and $^{247}\mathrm{Es}$, produced mainly by ($\mathrm{HI},\ensuremath{\alpha}\mathrm{xn}$) reactions, were measured to be 7.73 \ifmmode\pm\else\textpm\fi{} 0.02, 7.36 \ifmmode\pm\else\textpm\fi{} 0.03, and 7.31 \ifmmode\pm\else\textpm\fi{} 0.03 MeV, respectively, and the half-life of $^{247}\mathrm{Es}$ was found to be 4.7\ifmmode\pm\else\textpm\fi{}0.3 min. Excitation curves for producing the Md isotopes and some other activities are presented. Estimates for the electron-capture branching of the Md isotopes are given. $\ensuremath{\alpha}$-decay hindrance factors were calculated using the spin-independent equations of Preston. The $\ensuremath{\alpha}$-decay energy systematics of the mendelevium isotopes is discussed.

Proton Capture by Be 7 and the Solar Neutrino Problem

Abstract: It is shown theoretically that the $^{7}\mathrm{Be}(p,\ensuremath{\gamma})^{8}\mathrm{B}$ reaction cross section contains substantial contributions from $p$ and $d$ partial waves at laboratory energies, and extrapolations to stellar energies based on the assumption of pure $s$-wave capture are therefore erroneous. However, there is no change in the predicted solar neutrino flux, because the calculated low-energy cross-section factor, 31 eVb, is essentially the same as the empirical value in current use.

Generalization of the Jost Function and Its Application to Off-Shell Scattering

Abstract: An off-shell generalization of the Jost function is developed within the framework of the differential-equation approach to the off-shell $T$ matrix. Irregular solutions of the inhomogeneous Schr\"odinger-like equation that occurs in this approach are introduced, and their behavior at the origin is used to define an off-shell Jost function. The half-off-shell $T$ matrix is expressed directly in terms of the off-shell Jost function. It is shown how the fully off-shell $T$ matrix for a particular partial wave can be expressed simply in terms of a single integral involving the irregular solution for that partial wave. An integral equation for the irregular solution is developed, and used to derive an integral representation for the off-shell Jost function. Iteration of the integral equation leads to a series of successive approximations to the $T$ matrix. The formalism is applied to several examples, including a boundary-condition model.

Isomeric States in Fm-250 and No-254

Abstract: A preliminary report on the discovery of isomeric states in $^{250}\mathrm{Fm}$ and $^{254}\mathrm{No}$ was included in a recent article on $\ensuremath{\alpha}$-emitting isotopes of element 104. The existence and assignments of the 1.8 \ifmmode\pm\else\textpm\fi{} 0.1-sec isomer to $^{250}\mathrm{Fm}$ and the 0.28 \ifmmode\pm\else\textpm\fi{} 0.04-sec isomer to $^{254}\mathrm{No}$ have now been confirmed by cross-bombardment techniques. Isomeric ratios based on measurements of collection efficiency of recoil atoms from the decay of isomeric states are given. An interpretation of the even-even isomers as high-spin two-quasiparticle states is discussed.

Neutron-nucleus total and inelastic cross-sections - 900 to 2600 mev/c

Abstract: Total cross sections have been measured for neutrons on 16 targets: 12 selected elements, muscle-tissue-equivalent plastic, water, shielding concrete, and plastic scintillator. The momenta of the incident neutrons 900 to 2600 $\frac{\mathrm{MeV}}{c}$ were determined by time of flight. Over-all uncertainties are of the order of 5%. The dependence of the total cross sections on the atomic weight of the targets can be approximated by an ${A}^{\ensuremath{\beta}}$ law, where $\ensuremath{\beta}$ varies with momentum from 0.72 to 0.84. The momentum dependence of the cross sections is found to be similar to that of neutron-proton cross sections. Results and similar analyses are also presented for total inelastic cross sections.

Fragment-mass and kinetic-energy distributions from the spontaneous fission of $sup 246$Cm

Abstract: Pre-neutron-emission fragment-mass and total-kinetic-energy distributions and the mass-energy correlations in the spontaneous-fission decay of 2.30-sec $^{252}\mathrm{No}$ have been deduced from measured energies of coincident fragment pairs using silicon surface-barrier detectors. The $^{252}\mathrm{No}$ for these measurements was produced in the $^{241}\mathrm{Am}(^{15}\mathrm{N}, 4n)$ reaction and deposited on 40-\ensuremath{\mu}g ${\mathrm{cm}}^{\ensuremath{-}2}$ carbon foils using a He-jet technique. From an analysis of 154 correlated fission events, the average pre-neutron-emission total-kinetic energy, $〈\mathrm{TKE}〉$, was found to be 202.4\ifmmode\pm\else\textpm\fi{}1.2 MeV. The mass distribution is decidedly asymmetric, similar to that observed for $^{252}\mathrm{Cf}$ spontaneous fission, although a maximum in the $〈\mathrm{TKE}〉$ curve as a function of fragment mass occurs for near-symmetric mass divisions as it does for the heavier isotopes of fermium. The measured spontaneous-fission-decay branching fraction for $^{252}\mathrm{No}$ is 26.9\ifmmode\pm\else\textpm\fi{}1.9% and the measured total half-life is 2.30\ifmmode\pm\else\textpm\fi{}0.22 sec. The measured and deduced fission char\`acteristics for $^{252}\mathrm{No}$ are compared with those for the Cm, Cf, and Fm nuclides as well as with recent theoretical predictions.RADIOACTIVITY, FISSION $^{252}\mathrm{No}(\ensuremath{\alpha}, \mathrm{sf})$ measured fragment-fragment coin $E$, ${T}_{\frac{1}{2}}$, $E\ensuremath{\alpha}$, $\frac{\ensuremath{\alpha}}{\mathrm{sf}}$, $\ensuremath{\sigma}$ for $^{241}\mathrm{Am}(^{15}\mathrm{N}, 4n)$ reaction; deduced pre-neutron fragment masses, energies, and total kinetic $E$ distribution. Enriched target.

Decay energies of gaseous fission products and their daughters for A = 88 to 93

Abstract: The $\ensuremath{\beta}$-decay energies for several mass-separated Xe fission products and their daughters have been measured at the TRISTAN on-line separator facility at the Ames Laboratory research reactor. A well-type plastic scintillator was used in coincidence with a Ge(Li) $\ensuremath{\gamma}$ detector to determine $\ensuremath{\beta}$-group end-point energies and deduce $Q$ values. The following $\ensuremath{\beta}$-decay energies have been determined: $^{138}\mathrm{Xe}$, 2.83 \ifmmode\pm\else\textpm\fi{} 0.08 MeV; $^{138}\mathrm{Cs}$, 5.29 \ifmmode\pm\else\textpm\fi{} 0.07 MeV; $^{139}\mathrm{Xe}$, 4.88 \ifmmode\pm\else\textpm\fi{} 0.06 MeV; $^{139}\mathrm{Cs}$, 4.29 \ifmmode\pm\else\textpm\fi{} 0.07 MeV; $^{140}\mathrm{Xe}$, 4.06 \ifmmode\pm\else\textpm\fi{} 0.06 MeV; $^{140}\mathrm{Cs}$, 5.8 \ifmmode\pm\else\textpm\fi{} 0.1 MeV; $^{141}\mathrm{Xe}$, 6.0 \ifmmode\pm\else\textpm\fi{} 0.1 MeV; $^{141}\mathrm{Cs}$, 4.98 \ifmmode\pm\else\textpm\fi{} 0.08 MeV; $^{141}\mathrm{Ba}$, 3.01 \ifmmode\pm\else\textpm\fi{} 0.06 MeV; $^{142}\mathrm{Xe}$, 4.9 \ifmmode\pm\else\textpm\fi{} 0.1 MeV; and $^{142}\mathrm{Cs}$, 6.89 \ifmmode\pm\else\textpm\fi{} 0.06 MeV. The decay energies are compared with previous measurements, systematics predictions, and two currently accepted mass relations. The energies are also used to predict the $\ensuremath{\beta}$-decay energies for seven additional nuclei by means of systematics.

Asymmetry in nuclear fission

Abstract: The two-center shell model for fission has been generalized to include asymmetric deformations. The calculation of the potential energy involves four independent shape variables, where only two were required in the symmetric calculations. Potential energy calculations have been carried out for $^{202}\mathrm{Pb}$, $^{210}\mathrm{Po}$, $^{236}\mathrm{U}$, $^{248}\mathrm{Cm}$, $^{252}\mathrm{Fm}$, and $^{264}\mathrm{Fm}$. Asymmetric fission is found to be energetically preferred in $^{236}\mathrm{U}$, $^{248}\mathrm{Cm}$, and $^{252}\mathrm{Fm}$; and symmetric fission is preferred in $^{202}\mathrm{Pb}$, $^{210}\mathrm{Po}$, $^{258}\mathrm{Fm}$, and $^{264}\mathrm{Fm}$. Two of these nuclei, namely $^{236}\mathrm{U}$ and $^{210}\mathrm{Po}$, have been studied in detail. It is seen that the asymmetry in $^{236}\mathrm{U}$ remains almost constant from the second saddle to scission, whereas in $^{210}\mathrm{Po}$ (and also in $^{202}\mathrm{Pb}$), the preferred shape changes from asymmetry in the region of the second saddle to symmetry in the region of scission. The results for Fm isotopes indicate that there is a transition from asymmetric fission in the lighter Fm isotopes to symmetric fission in the heavier Fm isotopes. The preference for symmetric mass division in $^{264}\mathrm{Fm}$ is very strong, since two double-magic $_{50}^{132}\mathrm{Sn}_{82}$ fragments are formed at symmetry. In general, the structures which appear in the potential energy surfaces are the results of an interplay between compound-nucleus shell structure, fragment shell structures, and liquid-drop-model energies. Comparisons of our results with experimental observations indicate that the observed mass distribution is correlated with the potential energy surface in the neighborhood of scission.

Study of the (p,t) reaction on the even gadolinium nuclei

Abstract: The ($p,t$) reaction has been studied at 18 MeV on all the stable even-even Gd targets. A strong population of both ${0}^{+}$ and ${2}^{+}$ excited states has been found; the ${0}^{+}$ ($\ensuremath{\beta}$ vibrations) in the deformed nuclei are all $\ensuremath{\approx}15%$ of the ground-state cross sections. The shape transition at $\mathbf{N}=88$ is observed in the $^{154}\mathrm{Gd}(p,t)^{152}\mathrm{Gd}$ reaction: Two excited ${0}^{+}$ states are strongly populated. In the deformed Gd nuclei, a distinction between $K=0$ and $K=2 {2}^{+}$ states can be made on the basis of the shapes of their angular distributions. The spectrum observed in the $^{152}\mathrm{Gd}(p,t)^{150}\mathrm{Gd}$ reaction is characteristic of that expected on spherical nuclei, with a relatively strong population of an excited ${0}^{+}$ state. Distorted-wave Born-approximation calculations are highly successful in fitting the ${0}^{+}$ transitions but, generally, not the ${2}^{+}$ and higher spin states.

Nuclear Charge Distributions of Isotone Pairs. 2. K-39 and Ca-40

Abstract: Cross sections for electron elastic scattering from $_{19}^{39}\mathrm{K}$ and $_{20}^{40}\mathrm{Ca}$ are given for the momentum-transfer range from 0.6 to 3.4 ${\mathrm{fm}}^{\ensuremath{-}1}$. The data were analyzed by means of a phase-shift code using phenomenological Fermi charge distributions modified with small undulations. The difference of the $^{39}\mathrm{K}$ and $^{40}\mathrm{Ca}$ distributions has been compared with a $1{d}_{\frac{3}{2}}$ proton distribution and with other nuclear models.

Convergence Rate of Intermediate-State Summations in the Effective Shell-Model Interaction

Abstract: We examine the convergence rate of the sum over intermediate-particle states in the second-order core-polarization diagram of the effective shell-model interaction. For a $G$ matrix resulting from the Reid soft-core interaction, convergence is achieved in an oscillator basis only after the intermediate particle is summed over five or six major-shell excitations ($10\ensuremath{\hbar}\ensuremath{\Omega}$ to $12\ensuremath{\hbar}\ensuremath{\Omega}$ excitations). The total effect of this diagram on the shell-model spectra of $^{18}\mathrm{O}$ is markedly altered from the results of Kuo and Brown and others who only include oscillator excitations of one major shell ($2\ensuremath{\hbar}\ensuremath{\Omega}$) in the second-order diagram. We further demonstrate that slow convergence is attributed to strong components of the effective tensor force in the $G$ matrix.