Medium-weight Nuclei Research Articles

States of intermediate charge symmetry as low-lying, 0 + collective excitations of medium weight nuclei

A method for calculating the states of the charge-independent pairing hamiltonian that have intermediate charge symmetry is presented. The states are shown to be collective 0 + excitations with energies that fall well within the gap in the single-particle spectrum.

Nuclear-State Widths of Medium-Weight Nuclei in the Continuum

The technique of fluctuation averaging has been utilized with ($p,\ensuremath{\alpha}$) reactions to measure subkilovolt average widths $\ensuremath{\Gamma}$ of excited states for six medium-weight nuclei. The following compound-nucleus widths were determined: 386 \ifmmode\pm\else\textpm\fi{} 80, 465 \ifmmode\pm\else\textpm\fi{} 111, and 390 \ifmmode\pm\else\textpm\fi{} 100 eV at excitations of 15.24, 17.02, and 17.00 MeV, respectively, for the $^{76}\mathrm{Se}$ compound nucleus; 114 \ifmmode\pm\else\textpm\fi{} 40, 150 \ifmmode\pm\else\textpm\fi{} 66, 206 \ifmmode\pm\else\textpm\fi{} 34, and 190 \ifmmode\pm\else\textpm\fi{} 65 eV at excitations of 17.36, 18.80, 18.90, and 20.85 MeV, respectively, for $^{90}\mathrm{Zr}$; 111 \ifmmode\pm\else\textpm\fi{} 46 and 312 \ifmmode\pm\else\textpm\fi{} 85 eV at excitations of 15.50 and 17.72 MeV, respectively, for $^{104}\mathrm{Pd}$; 36 \ifmmode\pm\else\textpm\fi{} 30 and 101 \ifmmode\pm\else\textpm\fi{} 30 eV at excitations of 15.06 and 16.27 MeV, respectively, for $^{108}\mathrm{Cd}$; 128 \ifmmode\pm\else\textpm\fi{} 64 eV at an excitation of 15.98 MeV for $^{110}\mathrm{Cd}$; and ${58}_{\ensuremath{-}58}^{+120}$ eV at an excitation of 19.29 MeV for $^{116}\mathrm{Sn}$. In all these measurements, excitation functions were measured over a span of several hundred keV in steps of 5- to 15-keV proton energy. The accurately known instrumental resolutions required by the method were primarily determined from the target thicknesses, which were about 10 keV. The required dominance of compound-nucleus reactions was obtained by the use of sufficiently low incident energies and by observations at backward angles. Excitation functions over a span of several MeV and angular distributions were measured in order to select regions of negligible direct reactions.Comparison of these measurements with widths calculated from the statistical model of the nucleus suggests the need for reduced level densities. The measured widths show no evidence for shell effects.

ReactionQValues from Near-Threshold Neutron Spectra

A thick-target time-of-flight technique has been employed to measure neutron energies for ($p,n$) resonance levels near threshold in medium-weight nuclei. Combining the results with proton energy measurements of these resonances, the following ground state $(p,n) Q$ values have been deduced: $^{41}\mathrm{K}$, -1203.8\ifmmode\pm\else\textpm\fi{}0.5 keV; $^{45}\mathrm{Sc}$, -2843.6\ifmmode\pm\else\textpm\fi{}4.0 keV; $^{51}\mathrm{V}$, -1533.7\ifmmode\pm\else\textpm\fi{}1.5 keV; and $^{57}\mathrm{Fe}$, -1618.2\ifmmode\pm\else\textpm\fi{}2.0 keV.

Cross sections for the production of nucleides from medium-weight elements by high-energy proton bombardment

Starting from a simplified and idealised model, an expression for the formation cross section of nucleides by the bombardment of high-energy protons on a medium-weight nucleus has been derived from a statistical approach which, with the help of a few reliable experimental data, could give the cross sections of the whole series of the nucleides that might be formed from such target. It is applied to the targets V, Mn, Fe, Co, Ga, As, Y and Nb. Considering the level of accuracy of the experimental cross sections, the calculated values agree fairly well with the experimental ones.

11-MeV Proton Inelastic Scattering from Even-Even Medium-Weight Nuclei

The analysis of inelastic scattering of 11-MeV protons from quadrupole and octupole collective levels of 14 even-even nuclei between $^{48}\mathrm{Ti}$ and $^{76}\mathrm{Ge}$ is reported. The distorted-wave Born approximation is used to calculate the cross sections using the collective-model generalization of the optical model for inelastic scattering. The analysis is performed using both real and complex form factors for the model. A satisfactory description of all the data is obtained when a contribution due to compound-nucleus decay for most of the octupole levels and a few of the quadrupole levels is included.

Further studies in the liquid-drop theory on nuclear fission

We study the properties of the division of an idealized nucleus using a simplified version of the liquid-drop model. The shape of the nuclear surface is specified by means of a parameterization that has six degrees of freedom, defined in terms of three smoothly joined portions of quadratic surfaces of revolution (e.g. two spheroids connected by a hyperboloidal neck). The system's Hamiltonian is treated in an approximation in which the potential energy is considered to be a sum of surface and Coulomb energies. The kinetic energy is calculated according to the method of Werner and Wheeler, which approximates the internal hydrodynamical flow by the flow of circular layers of fluid; this type of flow corresponds approximately to the irrotational flow of a non-viscous incompressible fluid. On the basis of this model, we calculate probability distributions for the masses and kinetic energies of the fragments at infinity. For nuclei throughout the periodic table, the calculated distributions are compared with experimental distributions as functions of the internal excitation energy of the compound nuclei undergoing fission. The comparisons indicate that this simplified version of the non-viscous irrotational liquid-drop model is not capable of accounting for the properties of the division of heavy nuclei at low excitation energies (e.g. for the observed mass asymmetry). However, it does reproduce approximately experimental fission-fragment mass and energy distributions for the fission of heavy nuclei at high excitation energies (energies above about 40 MeV) and medium-weight nuclei at all excitation energies. In all cases, the experimental kinetic energies and widths are larger than the calculated ones (for non-viscous irrotational flow), and this and other evidence suggest that in the fission process the flow of nuclear matter is either rotational or viscous.

Elastic scattering of 104 MeV alpha particles

Differential cross sections were measured for elastic scattering of 104 MeV alpha particles on 6Li, 9Be, 12C, 14N, 16O, 20Ne, 40Ar, 64Ni, 90Zr, 124Sn, 208Pb and 209Bi. All angular distributions show a pronounced diffraction pattern. For the lightest nuclei measured ( 6Li to 16O) the cross section exceeds the Rutherford cross section by a factor of up to 15 at angles around 45°. The cross section data were analysed in terms of parametrized phase-shift functions using 9 free parameters and in terms of the spinless optical model using up to 7 free parameters. Good fits were obtained. A strong absorption was found for the heavy nuclei, A ≧ 124. For these nuclei, only the outermost region of the nuclear surface contributes to the scattering. A potential radius cannot be extracted regardless of the pronounced diffraction pattern. The absorption is not so strong for the medium weight nuclei, A = 20–90. Information about the nuclear surface can be extracted from the differential cross section. The well known phase ambiguity in the optical model was found for these nuclei. For the light nuclei ( A ≦ 16) the inner region of the interaction potential contributes to the scattering. A repulsive core for small interaction distances explains the observed cross sections which indicates the nonlocal character of the true interaction. The phase shift analysis leads to good fits, but the phase shifts obtained differ significantly from those of the optical-model analysis. This indicates that the phase-shift analysis is ambiguous also.

Polarization in the elastic scattering of 12 MeV deuterons by 12C, 56Fe and 58Ni

Angular distributions are presented of the vector polarization of 12 MeV deuterons elastically scattered by 12C, 56Fe and 58Ni for lab scattering angles 20–160°. The vector polarized deuteron beam from the Birmingham Radial Ridge Cyclotron polarized deuteron source was used, and the experimental method involved frequent “on-off” switching of the polarization at the source. Asymmetries were measured, using semiconductor detector telescopes in the scattering plane, against simultaneous readings of a carbon polarimeter whose analysing power was calibrated by means of the d- 4He scattering. Large values of polarization were observed for 12C; the medium-weight nuclei 56Fe and 58Ni showed characteristic oscillatory patterns of lower amplitude. An attempt was made to explain the results in terms of optical-model predictions, and the calculations seem to favour a potential for deuterons approximating the sum of the proton and neutron optical model potentials.

Proton total reaction cross sections at 9.1 MeV

Proton total reaction cross sections have been measured at 9.1 MeV for Mg, Ti, 63Cu, 65Cu, natural Cu and Zr using a counter anti-coincidence technique. These and earlier results have been compared with the predictions of the nuclear optical model. Good agreement has been found in the case of medium-weight nuclei.

New parameters for scattering of 18.6 MeV polarized protons

Optical-model and coupled-channel calculations are presented for the scattering of 18.6 MeV polarized protons from medium-weight nuclei using parameters which are consistent with the analysis of higher-energy data. Reasonable elastic fits and improved inelastic fits are obtained by reducing the radius of the central real potential with respect to the radius of the imaginary potential which is increased from the previous Perey value. The diffuseness of the real potential is larger than has previously been inferred, while the diffuseness of the imaginary potential is unchanged. The elastic and inelastic data are analysed using a derivative spin-orbit form factor instead of the Thomas form factor usually used to describe the spin-orbit coupling. The fits obtained are in very good agreement with those found by using the usual 1 r dependence. The symmetry term or (N−Z) A dependence of the potential is derived either for the central real potential or for the imaginary potential and appears to give satisfactory agreement with other recent optical-model analyses, if the 54Fe data are not taken into account. It is shown that the symmetry terms corresponding to V s and W D do not depend on the geometrical parameters used for the analysis.

Observation of the ReactionK−+He4→Λ0+π−+p+d

This paper reports the observation of 164 definite and 20 ambiguous examples of the reaction ${K}^{\ensuremath{-}}+{\mathrm{He}}^{4}\ensuremath{\rightarrow}{\ensuremath{\Lambda}}^{0}+{\ensuremath{\pi}}^{\ensuremath{-}}+p+d$ produced by ${K}^{\ensuremath{-}}$-meson absorptions at rest in the Northwestern University 20-cm liquid-helium bubble chamber. We confirm that the reaction is dominated by the two-step process ${K}^{\ensuremath{-}}+{\mathrm{He}}^{4}\ensuremath{\rightarrow}(\ensuremath{\Sigma}+\mathrm{nucleus})+{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\Lambda}}^{0}+p+d+{\ensuremath{\pi}}^{\ensuremath{-}}$. The momentum distributions of the baryonic particles (for events with ${\ensuremath{\pi}}^{\ensuremath{-}}$-meson momentum below 180 $\frac{\mathrm{MeV}}{c}$ are compared with the predictions of an impulse-model calculation. In this calculation the $\ensuremath{\Sigma}$-hyperon-nucleus interaction in the intermediate state is approximated by an effective potential acting on the $\ensuremath{\Sigma}$ hyperon. It is found that very good fits are obtained with a potential of central depth around 37 MeV. This value implies that the $\ensuremath{\Lambda}$-and $\ensuremath{\Sigma}$-hyperon-nuclear potentials are of similar strengths. We show that such a result is consistent with the data on free (${\ensuremath{\Sigma}}^{\ifmmode\pm\else\textpm\fi{}},p$) and ($\ensuremath{\Lambda},p$) interactions at low energies, and data on hypernuclear binding energies. This potential depth is also consistent with the meager information on the effective potential felt by $\ensuremath{\Sigma}$ hyperons in medium-weight nuclei. There is therefore no evidence in the reaction observed for any final-state ($\ensuremath{\Lambda},p$) resonance as postulated by Bugg, Bhatt, and Cohn.

The (g, p) and (g, n) Reactions in Molybdenum

Measurements have been made of the cross sections for some of the (g,p) and (y, n) reactions in molybdenum using the technique of residual activation analysis. The gross structure of these cross sections is compared with previous measurements and the results are interpreted as evidence for the isospin splitting of the giant dipole resonance in medium weight nuclei.

(He4,t) Reaction on Medium-Weight Nuclei

A 26.7-MeV beam of ${\mathrm{He}}^{4}$ ions from the Los Alamos variable-energy cyclotron was used to study the (${\mathrm{He}}^{4},t$) reaction on ${\mathrm{Cr}}^{52}$, ${\mathrm{Fe}}^{54}$, ${\mathrm{Fe}}^{56}$, ${\mathrm{Fe}}^{58}$, ${\mathrm{Co}}^{59}$, ${\mathrm{Ni}}^{60}$, ${\mathrm{Ni}}^{62}$, and ${\mathrm{Ni}}^{64}$. Angular distributions of tritons from the more strongly excited states of the residual nuclei were obtained over the angular range of ${11}^{\ensuremath{\circ}}\ensuremath{\lesssim}{\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}\ensuremath{\lesssim}{48}^{\ensuremath{\circ}}$. There are marked differences between distributions from ${\frac{3}{2}}^{\ensuremath{-}}$ states and ${\mathrm{\textonehalf{}}}^{\ensuremath{-}}$ states, and between distributions from ${\frac{7}{2}}^{\ensuremath{-}}$ states and ${\frac{5}{2}}^{\ensuremath{-}}$ states. The behavior of the distributions also appears to depend strongly upon the $Q$ of the reaction. The experimental results are compared to the predictions of a spin-independent distorted-wave calculation. Although such a calculation cannot reproduce the $j$-dependent behavior of the distributions, the extracted spectroscopic factors are usually in acceptable agreement with those obtained from recent (${\mathrm{He}}^{3},d$) reaction studies on these nuclides, and thus a meaningful comparison of the results from the (${\mathrm{He}}^{4},t$) and (${\mathrm{He}}^{3},d$) reaction studies can be made. This provides evidence that under the conditions of the studies, core-excitation mechanisms are relatively unimportant.

The analysis of the low-lying 0 +′ states in the medium-weight nuclei

The low-lying spectra of some medium-weight nuclei are analysed in terms of the Davydov non-adiabatic model. It is shown that some critical data like B(E2;0 +′→2 +)/ B(E2;0 +→2 +) and the effective γ-deformation of nuclei as 70,72,74Ge, 76Se and perhaps other nuclei can be interpreted by means of the Davydov non-adiabatic model, where the 0 +′ states belong to the oblate shape ellipsoid.

On the average separation energy of strongly bound nucleons

The separation energy of a strongly bound nucleon from a light or medium-weight nucleus has been calculated in terms of a general two-body nucleon-nucleon interaction potential. It is assumed that the nuclear wave function can be approximated by a linear combination of a few Slater determinants. Single-particle wave functions are approximated by harmonic oscillator wave functions. Simple formulae, which contain only a few potential matrix elements, are derived for the separation energies and numerical results are presented for several choices of the nucleon-nucleon interaction potential.

A spectrometer for 14 MeV neutron capture spectroscopy

A telescopic scintillation pair spectrometer for the measurements of energy spectra of gamma rays from the radiative capture of 14 MeV neutrons is described. The main parts of the spectrometer are: a lead foil as a converter of gamma rays to electron-positron pairs, a 12.5 cm dia. × 12.5 cm long plastic scintillator in which the energy of pairs is absorbed and an arrangement of two thin plastic scintillators. Two thin scintillators, together with the appropriate electronics, form a coincidence-anticoincidence shield which appreciably reduces the background due to charged particles created in the main scintillator or coming into the spectrometer from outside. An average ratio of the net effect to the background of about 1:1 was achieved for medium weight nuclei like Fe. The meson background in the whole energy range of the spectrometer is reduced to about 0.5 cpm. The energy resolution of the spectrometer is 12.5%, 9.5% and 8.0% for gamma rays of 12.1 MeV, 16.5 MeV and 20.4 MeV, respectively. An average value of the spectrometer efficiency in this energy region is 0.5%. The spectrum of gamma rays from the capture of 14 MeV neutrons in 56Fe is shown as an example of the application of the spectrometer.

The reactions 63,65Cu(t, p) 65,67Cu

Angular distributions of the Cu(t, p) reactions leading to states of 65Cu and 67Cu have been measured at an incident energy of 12 MeV, using the Aldermaston multi-angle magnetic spectrograph. For 65Cu, 27 excited states were observed up to an excitation energy of 3.8 MeV; and for 67Cu, 17 excited states were observed up to 4.3 MeV. The shapes of the angular distributions of the stronger proton groups are similar to known L = 0, L = 2 and L = 3 (t, p) distributions in other medium-weight nuclei. The data for 65Cu are compared with the 64Ni( 3He, d) results of Blair and it is concluded that below 2.2 MeV the same levels are excited in the two experiments. The empirical L assignments for 65Cu are in the majority of the cases consistent with the spin and parity assignments of Blair. The (t, p) data for 67Cu show many similarities with the 65Cu data and this fact is used for tentative assignments of some levels in 67Cu.

Optical-model analysis of the scattering of 24.7 MeV alpha particles

The measured elastic scattering of 24.7 MeV alpha particles from the nuclei O, Mg, Al, Si, Ca, Ma, Ni, Co, Cu, Ge, Zr, Ag, In, Sn, Hf, W, Au, Bi and U has been analysed using the optical model. Fits were obtained using a four-parameter Woods-Saxon potential. No marked improvement was found by using a more general potential. The fits for medium and heavy nuclei are good, but those for the lighter nuclei are noticeably poorer. Potential ambiguities were studied in some detail for Ni and Mg, and potentials with depths of about 150 MeV and 200 MeV were obtained for all the nuclei in addition to a more shallow potential. The medium-weight nuclei show a preference for the deep potentials, the light nuclei for the shallow ones. The behaviour of the predicted scattering matrix elements is discussed also.

Kernreaktionen durch Deuteronen von 52 MeV

The nuclear reactions of 52 MeV deuterons have been studied at some medium weight and heavy nuclei. The angular distributions of elastically scattered deuterons show sharp structures which are smoothed out — similar to the results at lower deuteron energies — for target nuclei near A = 100. The optical model analysis gives good fits with parameters extrapolated from the best values at lower energies. The „Smoothed Cut-off“ models do not describe the results properly. The influence of the nuclear interior on the elastic scattering is important. The proton spectra from the (d, p) and (d, pn) reactions are dominated by a broad „break up“ maximum. From the width of the maximum and the A-dependence of the cross section it is concluded that nuclear break up is more frequent at 52 MeV than COULOMB break up. The spectra of deuterons and tritons from the (d, d′) and (d, t) reactions show maxima up to Q-values of — 15 MeV. With these reactions it should be possible to study collective excitation up to high excitation energies and to get information about inner shells. The intensity of low energy inelastic deuterons is surprisingly large.

Model for the origin and properties of the cosmic‐ray rigidity spectrum

We propose a model to explain a number of features of the differential rigidity spectra of the nuclear component of the primary cosmic radiation. A supernova explosion is assumed to result in the acceleration of nuclei to a pure power law rigidity spectrum and a composition relatively rich in heavy and medium weight nuclei. The supernova remnant into which these particles are injected is characterized as a large‐scale trapping region resulting from predominantly closed magnetic field lines that partially isolate the region from the surrounding galactic space. This feature of the supernova region is represented by a dipole‐like field. We assume that, superimposed on this field, magnetic irregularities produce a certain amount of distortion of the field lines in the interior of the source, and that irregularities along the periphery of the source lead to local distortions of the field and, hence, a mixing of galactic and source field lines in the neighborhood of these irregularities.The observed large‐scale regularity of the magnetic field in the Crab leads us to treat the particle motion within the source region in the guiding center approximation (except at very high rigidities), so that these particles are capable of guiding outward to the source boundary and returning inward to the interior along the source's predominantly closed magnetic lines of force. The well defined inward field gradient and field curvature, however, cause the particles to drift longitudinally as they spiral along the periphery of the source region, and accordingly they have a certain probability of drifting into a neighborhood of field mixing and onto a galactic field line which guides them out of the source region.During their confinement within the source region, the particles necessarily undergo nuclear interactions and ionization loss, and, therefore, the differential rigidity spectrum of particles escaping from the source boundary into the galaxy is jointly determined by their injection spectrum, their escape probability, and the extent to which they suffer loss processes. A continuity equation combining these various processes is constructed and then averaged over the entirety of active sources in the galaxy. The solutions of the averaged continuity equation for each charge group then give us the differential rigidity spectra with which the cosmic radiation is injected into the galactic medium.The additional effects of intragalactic motion on the cosmic‐ray spectrum are treated in the approximation that the particles escaping from source regions undergo magnetic diffusion in the galactic volume with a rigidity independent scattering mean free path. The differential rigidity spectra of the various charge groups incident on the solar system are thereby obtained. The effects of solar modulation on the galactic cosmic‐ray spectrum are treated in accordance with the solar wind theory. The resulting differential rigidity spectra are derived and compared with data taken near solar minimum, and it is found that the calculated spectra, as well as the rigidity dependence of various abundance ratios, are in reasonable agreement with the available data.