Shell-model Distribution Research Articles

The shell-model distribution of nuclear shapes

Nuclei have giant resonance and low-energy quadrupole shape-changing degrees of freedom. It is shown that the giant-resonance degrees of freedom can be factored out by restricting to states in which the nucleus is in its giant-resonance vibrational ground state. The set of possible nuclear shapes then becomes a discrete countable set and is in one-to-one correspondence with the set of irreducible sp(3, R) representations in the nuclear shell-model Hilbert space. The relationship between observable deformation parameters and the labels of sp(3, R) irreps is given. Methods are presented for classifying sp(3, R) irreps and ordering them such that the most relevant ones for the description of low-lying states can be selected. It is shown that high-lying shell-model configurations are needed to obtain the deformations observed in deformed nuclei and that such configurations are brought down into the low-energy arena by deformation and spin-orbit interactions.

Study of local environment in a series of amorphous ferric fluorides

Amorphous samples of Fe${\mathrm{F}}_{3}$, KFe${\mathrm{F}}_{4}$, and RbFe${\mathrm{F}}_{4}$ have been prepared by vapor deposition at liquid-nitrogen temperature, and room-temperature M\"ossbauer quadrupole spectra are reported for each. The spectra are broad and indicate the existence of a distribution of electric-field-gradient (EFG) magnitudes at the iron sites. Using a least-squares computer fit to the data determined from a Lorentz broadened EFG distribution function, we are able to make separate determinations of the Lorentz widths of the individual transitions and of the form of the EFG distribution. We find a natural Lorentz width of 0.20 mm/s and an EFG distribution function of asymmetric Gaussian form. The latter has the same shape for all three materials and is both significantly broader and more asymmetric about its peak than predicted by random-packing models using hard spheres and point-charge summations. An analytic shell-model distribution function is shown to be an accurate description of EFG histograms for random-packing models but is unable to provide a quantitative description of the measured quadrupole spectra.

Relaxation times and size distribution readjustments in micellar kinetics

The methods of relaxation kinetics have been applied to study processes occurring in micellization since 1965. Generally, these experiments have revealed kinetics taking place in two well-separated time domains. Mechanistic interpretation of these phenomena has involved considerable disagreement in the literature. The present effort at a detailed revaluation of at least the fast, initial relaxation process is based on a model for the distribution of all species present under the starting equilibrium conditions prior to perturbation. The shell model distribution function developed by the author in a recent publication is selected as the starting point.

Quasi-elastic electron scattering (e, e′p) and (e, e′d) from 6Li in a coincidence experiment

Coincidence cross sections for the reactions 6Li(e, e′p) and 6Li(e, e′d) have been measured in the region of quasi-elastic scattering. Using incident electrons of 2.5 and 2.7 GeV, the four-momentum transfers to the proton were 6.6 fm −2, 10.0 fm −2 and 11.6 fm −2. The proton coincidence data agree with shell-model distributions assuming a Woods-Saxon potential and including short-range nucleon-nucleon correlations. The best fit to the deuteron coincidence data is obtained with a cluster wave function for the p-nucleons and a harmonic oscillator wave function for the s-nucleons taking into account the deuteron yield from the s-shell. The ratio of the deuteron cross section from 6Li divided by the elastic e-d scattering cross section depends only slightly on the four-momentum transfer and has a value of ≈ 2.

Nuclear charge radii of Al and Si from elastic electron scattering between 25 and 60 MeV

Elastic electron scattering cross sections of27Al and Si (natural isotopic mixture) have been measured relative to carbon. The rms charge radiiR m , deduced with partial wave calculations, are (3.01±0.05) fm for27Al and (3.06±0.05) fm for Si, in good agreement with results from muonic X-ray energies. The values given are those for a Fermi charge distribution with skin thickness 2.5 fm; harmonic oscillator shell model distributions yield radii smaller by 0.03 fm. The ratioR m (27Al)/Rm(Si) is 0.984±0.016.

The density distribution of He 6

A two-parameter density distribution has been obtained for He 6 using an oscillator shell model distribution with different oscillator length parameters a s and a p for the s and p-nucleons respectively. One relation between a s and a p is obtained by equating the calculated Coulomb energy difference between He 6 and the lowest T = 1 state of Li 6 with the empirical value while a second relation has been obtained using a method due to Überall which gives good agreement for the form factor of Li 6 and which assumes that the s-nucleon distribution is due to a recoiling α-particle. One then obtains a s = 1.79±0.04 fm, a p = 2.60±0.06 fm and 〉r 2〉 1 2 = 2.78±0.05 fm for the r.m.s. radius of the point nucleon distribution. Compared with Li 6 the extension of the s-nucleons is only slightly greater. However, 〈r 2〉 1 2 and the extension of the p-nucleons is significantly greater, consistent with the smaller binding energy of the p-nucleons in He 6. The effect of the Coulomb interaction in extending the p-nucleons in the T = 1 state of Li 6 beyond those in He 6 is shown to be negligible.