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.     

Structure of30Si from the spectroscopy of highly excited states

Highly excited states in³⁰Si were investigated using the²⁷Al(α, p γ) reaction. Proton-γ ray angular correlations were measured atE _α=12, 14.1 and 15MeV. At 15MeV linear polarizations ofγ-rays were measured in coincidence with protons using a five-crystal Compton-polarimeter. Lifetimes were measured atE _α=14.6 MeV using the Dopper-shift attenuation method. Unambigious spin-parity assignments were obtained for the levels at 6,865 (3⁺), 7,001 (5⁺), 7,079 (3⁺), 7,810 (4), 9,371 (6⁺), 7,613 (4^?), 8,196 (5^?), 8,596 (4^?), 8,963 (5^?), 9,111 (6^?), 9,350 (4^?), 9,507 (5^?), 9,777 (6^?), 10,188 (5^?), 10,305 (3^?), 10,561 (6^?), 10,725 (7^?), 11,477 (6^?) and 11,544 (7^?)keV excitation energy, respectively. The structure of³⁰Si is understood both in terms of the shell model and the collective model. The levels at 5,487, 6,505, 8,196, 9,777 and 11,544keV, respectively, are theI ^π=3^? through 7^? members of a well developedK ^π=3^? rotational band with intrinsic quadrupole moment |Q ₀|=350 _?70 ⁺²⁵⁰ mb. There is evidence of further rotational bands, among them aK ^π=3^? band with |Q ₀|=800 _?80 ⁺⁴²² mb.     

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.     

Proton-threshold states in 28Si

The ²⁷Al(³He, d)²⁸Si reaction has been used to locate candidates for resonances in the ²⁷Al + p system residing near the proton-capture threshold in the energy region characteristic of quiescent stellar hydrogen burning. Two such states are observed at excitation energies E_x = 11.658 MeV(J^π = 2⁺) and 11.671 MeV (J^π = 1⁻). A comparison of the cross sections for the ²⁷Al(³He, d)²⁸Si and the ²⁷Al(α, t)²⁸Si reactions implies angular-momentum transfers of l = 2 and l = 3, respectively, for the two states of interest. Using this result, an astrophysically significant upper limit on the thermonuclear reaction rate has been calculated for the ²⁷Al(p, γ)²⁸Si reaction which is found to be too slow to affect the ²⁷Al abundance in red giants.     

Structure change of 156Yb at high-spin states

High-spin states of 156Yb have been studied via the 144Sm(16O,4n)156Yb fusion-evaporation reaction at beam energy 102 MeV. The positive-parity yrast band and negative-parity cascade have been extended up to higher-spin states, respectively. The characteristics of the negative-parity sequence above the 25- state may related to the excitation from the nucleon in the Z = 64, N = 82 core. The E-GOS curve for the positive-parity yrast sequence in 156Yb indicate that this nucleus may undergo an evolution from quasivibrational to quasirotational structure with increasing angular momentum. The Cranked Woods-Saxon-Strutinsky calculations by means of Total-Routhian-Surface (TRS) methods has been made to understand this structure change.     

Shape coexistence and high-spin states in 28Si

The spectrum of ²⁸Si is investigated within the cranked Nilsson-Strutinsky model with all kinds of many-particle-many-hole excitations accounted for. Calculated excitation energies and quadropole moments are compared with experimental data. The recently observed backbend from 8⁺ to 10⁺ is suggested to be caused by the crossing of the oblate ground band with a prolate or slightly triaxial band having one proton and one neutron excited to the fp shell.     

Search for high-spin states in29Si using a neutron time-of-flight spectrometer

The²⁶Mg(α,nγ) reaction has been used in connection with a neutron time-of-flight spectrometer to search for high spin states in²⁹Si betweenE _x =8.4 and 11.4 MeV. The γ-decay of twenty levels has been observed. Nine levels have not been observed before. A candidate for theJ ^π=13/2^?,K=7/2 state has been located with theE _x =8761 keV level.     

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 of high-spin states in 143Pm

High-spin states of ¹⁴³Pm have been studied in the reactions ¹⁴¹Pr(α, 2n)¹⁴³Pm and ¹⁴³Nd(d, 2n)¹⁴³Pm by means of in-beam spectroscopy. The level scheme, spin and parity assignments are based on results obtained from singles γ-ray spectra, conversion electron spectra, prompt and delayed γ-γ coincidences, γ-ray angular distribution and linear polarization measurements. Positive- and negative-parity states with energies up to 4580 keV and spins up to $\text{25}\text{2}$ have been established including 22 new levels. For two nanosecond isomeric states the nuclear spin precession in an external magnetic field was observed providing the following g-factors:

$\text{g(}\text{11?}\text{2}\text{, 959.7 keV)=1.14(9), g(}\text{15+}\text{2}\text{, 1898.3 keV)=1.00(7).}$

The experimental results are well understood by calculations which have been performed in the framework of the shell model (for positive-parity states of 11 valence protons above a Z = 50, N = 82 core) and of the cluster-vibration model (for 3 holes in a Z = 64, N = 82 core). In the case of positive-parity states no evidence for particle-core coupling could be found, while the negative-parity states could qualitatively be understood within the particle-core coupling picture.     

On the ferromagnetism of high-spin states

It is established on the basis of the idea of strong interaction within the unit cell that ferromagnetic instability is possible in a system with hopping between d-electron states of atoms that are in high-spin states and form a bcc lattice. The phase diagram of the existence of ferromagnetic ordering as a function of the degree of filling of the d shell is constructed. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 4, 275–280 (25 August 1998)     

Structure change of 156Yb at high-spin states

High-spin states of ¹⁵⁶Yb have been studied via the ¹⁴⁴Sm(¹⁶O,4n)¹⁵⁶Yb fusion-evaporation reaction at beam energy 102~MeV. The positive-parity yrast band and negative-parity cascade have been extended up to higher-spin states, respectively. The characteristics of the negative-parity sequence above the 25^－ state may related to the excitation from the nucleon in the Z=64, N=82 core. The E-GOS curve for the positive-parity yrast sequence in ¹⁵⁶Yb indicate that this nucleus may undergo an evolution from quasivibrational to quasirotational structure with increasing angular momentum. The Cranked Woods-Saxon-Strutinsky calculations by means of Total-Routhian-Surface (TRS) methods has been made to understand this structure change.     

Properties of electromagnetic transitions from high-spin states in94Mo

The multipole mixing ratios of transitions from 6⁺ and 8⁺ states in⁹⁴Mo, following the decay of⁹⁴Tc, have been measured by means ofγγ angular correlations. The spin of the 2423.4 keV state, being important for the interpretation ofγ cascades feeding this level, has been firmly established as 6⁺ by a method in which the angular correlation data are utilized in a non-conventional way. Furthermore, properties of electromagnetic transitions in⁹⁴Mo have been calculated in the shell model framework and are compared with the corresponding experimental quantities.     

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.     

Structure of high-spin states in 232Th, 234U and 236U

Multiple Coulomb excitation of ²³²Th, ²³⁴U and ²³⁶U by 5.3 $\text{MeV}\text{u}$²⁰⁸Pb ions has been studied using γ-ray spectroscopy. Excitation of ground-band levels is observed up to spin I^π = 26⁺ (tentatively 28 ⁺) in ²³²Th and ²³⁴U and I^π = 28⁺ (tentatively 30⁺)in ²³⁶U. High-spin levels of the K^π = 0^? octupole-vibrational bands are also observed in these nuclei. The measured transition energies between ground-band levels suggest that at $\text{I≈ 28}\text{h}\text{?}$ several units of angular momentum are carried by single particles aligned with the rotation axis.This result can be understood in terms of a super band built on aligned two-quasiparticle configurations which crosses the ground-state rotational band at a rotational frequency of $\text{h}\text{?}\text{ω ? 0.25}\text{MeV}\text{(I ? 28}\text{h}\text{?}\text{)}$. The E2 transition-matrix elements deduced from the experimental γ-yields agree within their errors with the rigid-rotor predictions up to the highest spins observed.The experimental results are discussed using the concept of rotation alignment and are compared with predictions of the rotation-vibration model and the interacting-boson model.     

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.     

Spectroscopy of high-spin states in 211,212,213Fr

The level structures of ²¹¹Fr, ²¹²Fr and ²¹³Fr have been observed to high spins, ~ 28 /kh, (and excitation energies ~ 8 MeV) using a variety of γ-ray spectroscopic techniques. The structure of these nuclides is discussed in terms of couplings of single-particle states through empirical shell-model calculations. Good agreement with experiment is obtained. In ²¹²Fr and ²¹³Fr core-excited configurations are required to explain the properties of the highest states. A number of long-lived states were observed in each nucleus some of which decay by enhanced E3 transitions. The E3 transition strengths are discussed.     

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.     

g-Factors of high-spin states in the g- and s-bands

The phenomenon of the crossing of the g-band with the s-band is described by using the 0- and 2-quasiparticle cranked Hartree-Fock-Bogoliubov approximations with the number projection. The energy spectra and the gyromagnetic ratios of the g- and s-bands of¹⁶²Er are calculated.The author is also indebted to Dr. M. Wakai for his cooperative and stimulating discussions.