Shape-excited states of28Si

The Hartree-Fock (HF) minima for the nucleus²⁸Si were obtained for the prolate, oblate and spherical shapes using the interaction obtained by Preedom and Wildenthal. The interaction gives rise to large energy separation between the prolate and the oblate shapes. The spherical solution is just 2 MeV above the lowest HF (oblate) minimum. The spectrum projected from the oblate HF state is in good agreement with the experimental spectrum. The transition probabilities for the different energy levels also agree reasonably well. The configuration mixing calculations performed on the basis of states projected from the three shapes indicate that there is no significant mixing of different projected states. The second 0 ₂ ⁺ state, thus obtained, corresponds to the third 0 ₃ ⁺ state in the experimental spectrum and stems dominantly from the spherical HF state. It is seen that the structure of the energy levels of²⁸Si, especially the second 0 ₂ ⁺ level is very sensitive to the two body interaction. The results are compared with those obtained using the renormalised interaction of Kuo.     

Search for missing predicted high-spin states in28Si

New shell model calculations have predicted several high-spin (I ^π=5⁺ and 6⁺) levels in²⁸Si near 10 MeV excitation energy which are missing from or ambiguous in existing experimental studies. Angular distributions, linear polarizations and Doppler-shifts ofγ-rays have been measured for theγ-decay of theE _p=1,911 and 2,073 KeV resonances of the²⁷Al(p, γ) reaction in an attempt to discover these missing states or confirm the discrepancies between experiment and theory. The excitation energies and spin-parities of the resonances were determined as 13,424.4±0.2 keV,I ^π=5⁺ and 13,582.3±0.5 keV,I ^π=6⁺. States populated in theγ-decay of these resonances were assigned spins and parities as follows: 11,777 keV,I ^π=5⁺; 11,331 keV,I ^π=6⁺; 10,417 keV,I ^π=5⁺; 9,417 keV,I ^π=4⁺ and 8,945 keV,I ^π=5⁺. On the basis ofγ-ray transition rates T=1 is assigned to the 13,424 keV level and T=0 to the 10,417 and 11,777 keV levels. With the new data excellent agreement is achieved between the experimental spectrum of²⁸Si and the new shell model predictions. These data provide evidence for aK ^π=3⁺ rotational band comprised by the 6,276, 6,889, 8,945 and 11,331 keV levels. This band emerges also from the shell model wave functions as do theK ^π=0⁺ bands based on the ground state and the 6,691 keV state.     

The 6− analog-antianalog states of 28Si

A resonance is observed in the ²⁷Al(p, γ)²⁸Si reaction at E_p=2876±2 keV, which corresponds to an excitation energy of 14356±2 keV. The 14.36 MeV level decays to a new level at 11577±2 keV, which is turn decays to the known level at 9701.8±0.5 keV. With previous information on the 9.70 MeV level and the present γ-ray angular distributions, obtained from singles spectra as recorded by a 40 cm³ Ge(Li) detector, the spins of the three levels can be limited to J=5, 6; J=6; and J=5, respectively. Transition strength arguments based on measurements of the strength of the 2876 keV resonance and the lifetime of the 11.58 MeV level indicate that the 14.36 MeV level has J^π=6^?, T=1 and that the 11.58 MeV level has J^π=6^?, T=0.     

Structure of28Si from the spectroscopy of high-spin states

A search for high-spin states in²⁸Si has been performed byn?y coincidence measurements in the²⁵Mg(α,nγy) reaction atE _α=14 and 15.5 MeV. Spin-parity assignments of the observed levels were obtained fromn?γ angular correlation and lifetime measurements atE _α=14.5 MeV. Theγ-decay of the 9,164 keV level was investigated separately with the²⁷Al(p, γ) reaction at theE _p=2,160 and 2,312 keV resonances. Rotational bands withK ^π=3^? (comprising levels atE _x=6,879, 8,413, 10,188 and 12,204 keV),K ^π =5^? (comprising levels atE _x=9,702, 11,577 and 13,741 keV) andK ^π=0⁺ (comprising levels atE _x=6,691, 7,381, 9,164 and 11,509 keV) were observed. The finding of the latter band supports the idea of coexisting oblate and prolate shapes in²⁸Si. A level at 14,643 keV excitation energy has the properties of theI ^π=8⁺ member of the ground state band. There are additional positive-parity high-spin states which do not fit into rotational bands. All types of positive-parity states are well accounted for by shell model calculations.     

Angular correlations in 28Si + 28Si resonances

Recent particle—particle—γ coincident measurements on a ²⁸Si+²⁸Si resonance have suggested “vanishing spin alignments”. New analyses of the spin alignments with a molecular model are presented. It is clarified that due to a triaxial deformation of the total system a wobbling mode (K-mixing) appears to give rise to spin disalignment.     

Alpha decay of isobaric analogue states in24Mg and28Si

Theα-decay of isobaric analogue states (which are forbidden by isospin selection rules) excited in²⁴Mg and²⁸Si through preton capture by²³Na atE _p=677 and 739 keV and by²⁷Al atE _p=295, 327 and 405 keV, respectively, have been studied using solid state track detectors. The ratio ofα-decay widths of the two resonance states in²⁴Mg to the state at 1.632 MeV (2⁺) in²⁰Ne yields the value 0.065 for the mixing parameterε and the value 4.01 keV for the Coulomb matrix element responsible for the isospin mixing in²⁴Mg. In²⁸Si the measurement of theα-decay widths of the three resonance states resulted in the determination of the proton, gamma and alpha partial widths which comprise the total width of the resonance states. Limits have been set for the value of the two mixing parameters involved in this case. Upper limits of 16 and 39 keV have been obtained for the Coulomb matrix elements responsible for the isospin mixing in²⁸Si.     

Deformation effects in the 28Si+12C and 28Si+28Si reactions

The possible occurrence of highly deformed configurations is investigated in the ⁴⁰Ca and ⁵⁶Ni di-nuclear systems as formed in the ²⁸Si + ¹²C, ²⁸Si reactions by using the properties of emitted light charged particles. Inclusive as well as exclusive data of the heavy fragments and their associated light charged particles have been collected by using the ICARE charged particle multidetector array. The data are analysed by Monte Carlo CASCADE statistical-model calculations using a consistent set of parameters with spin-dependent level densities. Significant deformation effects at high spin are observed as well as an unexpected large ⁸Be cluster emission of a binary nature.     

An application of the theory of Bi-determinantal intrinsic states to28Si

For some 4n nuclei in the 2s?1d shell, Hartree-Fock (HF) theory with most two-body interactions predicts nearly degenerate prolate and oblate Intrinsic states. The spectrum ofJ ^π states obtained from these Intrinsic states by projection is too compressed in relation to the observed levels. For such systems with a two-fold degeneracy of HF solutions, a Bi-Determinantal Intrinsic state (BDIS) is the more apt variational state. The equations of the theory of BDIS, which were first derived by B. Bremond, are here simplified and cast in a form suitable for numerical solution. The transformation operators introduced by Bremond are given a suitable representation, compatible with the symmetries of these 4n nuclei, and an independent definition is then given of self-consistent (SC) Hamiltonians. These equations are then iteratively solved in a tripyl-SC way, by the method of diagonalizing the SC Hamiltonions, for the problematic nucleus²⁸Si. By angular momentum projection from this BDIS, the low-lying spectrum is obtained. The discrepancy between this projected spectrum and the observed levels suggests that²⁸Si is not describable by a BDIS. The present results are in reasonable agreement with those of other Multi-Determinantal Theories for this nucleus.     

Mixed symmetry states and isospin excitation in the N =Z nucleus 28Si

The interacting boson model with isospin (IBM-3) has been used to study the isospin excitation states and mixed symmetry states at low spin for 28Si. The theoretical calculations are in agreement with experimental data. The theoretical results show that the 81+ energy is 14.73 MeV.     

Mixed symmetry states and electromagnetic transition in the N=Z nucleus ^28Si

The interacting boson model with isospin （IBM-3） has been used to study mixed symmetry states and electromagnetic transitions at low-lying states for a ^28Si nucleus. The theoretical calculations show that the 24^＋ state is the lowest mixed symmetry state in ^28Si and the 43＋ state is also a mixed symmetry state.     

Isobaric analogue states in28Si from (p, γ) reaction in27Al

Analogue states in²⁸Si are identified through (p, γ) reaction in²⁷Al in the energy rangeE _p =0.85–3.0 MeV. There appears hardly any indication of a mixing. Coulomb displacement energy ΔE _c for the isobaric pair²⁸Al-²⁸Si is obtained. A least squares analysis is also carried out on all the available experimental results of ΔE _c as a function of ¯Z/A ^1/3.     

A test of the collective correlations calculation of the dipole states of28Si

We solve a one band hopping model in the presence of a homogeneous static electric fieldF. In this case the exact eigenvalues do form a ladder:E _m =m e Fa, the corresponding eigenfunctions are localized within the “tilted” band.     

Towards 0.99999 28Si

A new approach for producing high-purity silicon with isotopic enrichment of ²⁸Si isotope is reported. The methods of centrifugal enrichment were modified to obtain the initial gaseous silicon tetrafluoride with a record-breaking enrichment of 0.99999664(11) with respect to ²⁸Si. The effective conversion of silicon tetrafluoride into elementary silicon with minimal isotopic dilution was achieved in an electron cyclotron resonance discharge plasma, sustained by gyrotron microwave radiation with a frequency of 24 GHz. We have experimentally demonstrated the deposition of the layers of microcrystalline ²⁸Si with enrichment of 0.999986 ± 0.000003, which is the best result at the present time.     

Mixed symmetry states and electromagnetic transition in the N=Z nucleus ~(28)Si

The interacting boson model with isospin (IBM-3) has been used to study mixed symmetry states and electromagnetic transitions at low-lying states for a ²⁸Si nucleus. The theoretical calculations show that the 2₄⁺ state is the lowest mixed symmetry state in ²⁸Si and the 4₃⁺ state is also a mixed symmetry state.     

Metastable states in Si:H

The results of ab initio LDF calculations applied to large clusters of Si atoms containing H in various positions are described. We find the bond centred (BC) defect to be most stable for neutral and positively charged H. H placed at an antibonding site is also stable with an energy 0.1 eV higher than the BC defect. The stability of H₂ and H^*₂ is also discussed. New results are reported for the conversion of BC defects into Si dangling bonds. It is found that H attached to vacancy-like defects is bi-stable: for Si-H-Si lengths less than ≈3.8 Å, the BC defect is stable, whereas for longer separations, the Si-H ··· Si dangling bond is stable. A discussion of the relevance of this to the Staebler-Wronski effect is given.     

On the difference between the effective charges used for bound states of29Si and for low-energy neutron radiative capture by28Si

The neutron effective charges used in the analysis of low-energy neutron radiative capture and in nuclear spectroscopy differ by several orders of magnitude. This is illustrated by a quantitative analysis of the²⁸Si(n, γ) reaction; this difference reflects the dominance of external capture.     

Analyses of electron and proton scattering to low-excitation isoscalar states in 20Ne, 24Mg and 28Si

The excitation of low-lying isoscalar 2⁺ and 4⁺ states in ²⁰Ne, ²⁴Mg and ²⁸Si by electron and proton scattering is studied. Large basis models of nuclear structure are used to determine both the electromagnetic and hadronic transition densities. The analyses of the longitudinal form factors obtained from electron scattering show that little or no effective charges are required with these nuclear structure models. Proton inelastic scattering to these states then is analysed to test effective forces based upon the Paris and Hamada-Johnston interactions. At intermediate energies (155 MeV) density-dependent t-matrices from both potentials were used with fits to data giving a clear preference for that based upon the Paris interaction. For lower energies only the Hamada-Johnston t-matrix is available and comparison of analyses of 24 and 49 MeV data made using this (complex) t-matrix with those in which the (real) Paris G-matrix is used as the effective force show a clear preference for the t-matrix. This is particularly the case with analyses of polarization data and suggests that the use of the G-matrix as an effective force in nuclear reaction calculations is inadequate even at low energies.