Comparison of neutron resonance spacings with microscopic theory for spherical nuclei

The nuclear level spacings determined from neutron resonance experiments for nuclei with 20 ≦ A ≦ 148 and 181 ≦ A ≦ 209 are compared with spacings calculated for spherical nuclei with a microscopic theory which includes the nuclear pairing interaction. Single particle levels of Seeger et al. and Nilsson et al. are used in the calculations. The gross features of the experimental data due to nuclear shells are reproduced with the microscopic theory. In addition, the absolute agreement between experiment and theory is reasonable (67 % of the 151 cases examined agree to within a factor of 2) in view of uncertainties in the experimental data, the theoretical single particle levels and the pairing strength. Values of the spin cutoff parameter σ²(E), calculated with a microscopic theory, are included also for several doubly even nuclei and discussed in terms of nuclear shells.     

Matrix elements of Yale potential and level properties of light nuclei

Shell model calculations using bare and renormalized matrix elements of the Yale potential are reported for the normal-parity states ofA=6–9 nuclei. Renormalization of the two-body matrix elements using second-order perturbation theory is not found to improve the agreements with the experimental data. Inclusion of the energy shifts of ground state rotational bands in⁸Be and⁹Be are, however, found to improve the agreements with the excitation energies of nuclear levels. The need for carrying out more calculations of these nuclei with realistic forces is pointed out.     

Level-density parameters in the back-shifted Fermi gas model

The parameters a and δ_eff appearing in the back-shifted Fermi gas model are determined for about 3000 nuclei on the basis of modern estimated experimental data and the proposed systematics. For 272 of these nuclei, the parameters are deduced from experimental data on the cumulative numbers of low-lying levels and on mean spacings between S-wave neutron resonances at the neutron binding energy in the nuclei. For 952 nuclei, the parameter δ_eff is calculated by using the cumulative numbers of low-lying levels and values of the parameter a that were obtained via an interpolation from the points corresponding to the aforementioned 272 nuclei. For the remaining nuclei, the parameters a and δ_eff are obtained on the basis of the proposed systematics. An expression is constructed for taking into account the damping of shell effects with increasing excitation energy of nuclei. The results are compared with those from other studies.     

Dynamic rotational characteristics of actinides on empirical approach

In the paper calculation of the moments of inertia for nuclei from the region 87 ≤ Z ≤ 100 and 130 ≤ N ≤ 156 was made in dependence on the angular momentum of their rotational states. The experimental values of the moments of inertia were calculated for rotational energy of the classic rotor in its quantum form, with the use of a simple formula. The moment of inertia term appearing in the formula was treated as a variable. The calculations were carried out on the basis of experimental data for the energies of the rotational levels for 51 bands built on ground states for even-even nuclei and for nuclei with odd mass number A. In addition, 30 rotational bands built on excited states were also analysed in the investigated region in case of even-even nuclei. For many bands and nuclei the considered dependence of the moment of inertia on angular momentum has been found in the analytical form by fitting polynomials to the experimental data. It turned out that obtained results for the moments of inertia made it possible to describe the energies of rotational levels with a relative deviation not greater or only slightly greater than 1%. In general, in the case of 12 bands of ground level the maximum relative deviation of obtained level energies is smaller than 1%.      

Anomalous moments of inertia for high-spin levels in the beta vibrational band of 154Gd

The levels of ¹⁵⁴Gd populated by the ¹⁵⁴Sm(α,4n) reaction have been studied with γ-γ coincidence techniques. The energy spacings of the β-band levels of spin > 8 are found to differ from the rotational picture in a manner similar to that recently observed in the ground-state bands of some other rare-earth nuclei. The ground-state band of ¹⁵⁴Gd does not show the anomaly;     

The Rotational Effects in E4 Transitions of Deformed Nuclei

By employing the 1/N expansion technique,the analytical expressions of the reduced E4 matrix elements are derived for deformed nuclei.The results of the strengths of E4 transitions show that the inclusion of the rotational effects in E4 transition improves greatly the agreement between the theory and the experimental data.     

Anomalous Rotational Resonance Spectra in Magic-Angle Spinning NMR

Magic-angle spinning NMR spectra of samples containing dilute spin-1/2 pairs display broadenings or splittings when a rotational resonance condition is satisfied, meaning that a small integer multiple of the spinning frequency matches the difference in the two isotropic shift frequencies. We show experimental rotational resonance NMR spectra of a 13C2-labeled retinal which are in qualitative disagreement with existing theory. We propose an explanation of these anomalous rotational spectra involving residual heteronuclear couplings between the 13C nuclei and the neighboring 1H nuclei. These couplings strongly influence the rotational resonance 13C spectrum, despite the presence of a strong radiofrequency decoupling field at the 1H Larmor frequency. We model the residual heteronuclear couplings by differential transverse relaxation of the 13C single-quantum coherences. We present a superoperator theory of the phenomenon and describe a numerical algorithm for rapid Liouville space simulations in periodic systems. Good agreement with experimental results is obtained by using a biexponential transverse relaxation model for each spin site.     

Hyperfine Structure in the Rotational Spectrum of GaF: A Comparison of Experimental and Calculated Spin-Rotation and Electric Field Gradient Tensors

The high-resolution pure rotational spectrum of GaF has been measured using a Balle-Flygare-type Fourier transform spectrometer. Improved nuclear quadrupolar coupling constants and rotational constants have been obtained along with the first reported fluorine spin-rotation constant for gallium fluoride, C(I) ((69)Ga(19)F, v = 0) = +32.0(21) kHz. Accurate spin-rotation tensors from microwave or molecular beam spectroscopy are particularly important to NMR spectroscopists and theoreticians because these data provide information about anisotropic nuclear magnetic shielding in the absence of intermolecular effects. For quadrupolar nuclei such as gallium, the quadrupolar interaction is sufficiently large that it is very difficult to characterize shielding tensors directly via NMR spectroscopy. The experimentally determined nuclear quadrupolar coupling constants and spin-rotation constants for GaF are compared with the results of a series of high-level ab initio calculations carried out at various levels of theory with a range of basis sets. Further calculations on BF and AlF, supplemented with available experimental data for InF and TlF, allow for the investigation of trends in nuclear magnetic shielding, spin-rotation, and electric field gradient tensors in the group-13 fluorides. Calculations at the MP2/6-311++G** and MP2/6-311G(2df, 2pd) levels provide the most consistently satisfactory results in comparison with the experimental data. Copyright 2000 Academic Press.     

Comparison between formulas of rotational band for axially symmetric deformed nuclei

The experimental rotational spectra of the deformed nuclei available in even-even and odd-A nuclei in the rare-earth and actinide regions are systematically analyzed with several rotational spectra formulas,including Bohr-Mottelson's I(I+l)-expansion,Harris'w2-expansion,ab and abc formulas.It is shown that the simple 2-parameter ab formula is much better than the widely used 2-parameter Bohr-Mottelson's AB formula and Harris'αβ formula.The available data of the rotational spectra of both ground-state band in even-even nuclei and one-quaasiparticle band in odd-A nuclei can be conveniently and rather accurately reproduced by ab formula and abc formula.The moment of inertia and the variation with rotational frequency of angular momentum can be satisfactorily reproduced by ab and abc formulas.     

An analysis of odd-mass rare-earth nuclei using angular momentum projection

A systematic analysis of positive-parity rotational states in odd-mass rare-earth nuclei is presented. The theory used is microscopic in the true sense and conserves both the angular momentum and the particle number as the projection technique is applied. The hamiltonian contains the quadrupole pairing interaction (in addition to the conventional (monopole) pairing and Q · Q forces) which plays an essential role in odd-mass as well as in doubly-even nuclei. Agreement between theory and experimental data is excellent.     

Semi-classical model of neutron rearrangement using quantum coupled-channel approach

A quantum coupled-channel approach with collective degrees of freedom (the rotation of deformed nuclei and/or their surface vibrations) is combined with an empirical coupled-channel model to add neutron rearrangement channels to vibrational and rotational excitations. The calculated fusion cross sections and the barrier distribution functions for several combinations of nuclei are in good agreement with experimental data.     

偶偶核基带的量子群U_（qp）（u_2）模型的理论分析

通过对锕系和稀土偶偶核基带转动谱实验数据的拟合和Ｍａｌｌｍａｎｎ图的研究，系统地分析了量子群Ｕｑｐ（ｕ２）模型对原子核转动谱的适用性．结果表明，Ｕｑｐ（ｕ２）模型的理论值与实验值比较接近，明显优于单参数形变量子代数ＳＵｑ（２）模型．此外，还建立了Ｕｑｐ（ｕ２）的形变参量ｑ、ｐ与核软度的关系．     

Triplet cooper pairing in nuclear matter and rotational states of superdeformed nuclei

One hundred and sixty-one rotational bands of superdeformed states in nuclei are considered on the basis of a model that admits triplet Cooper pairing in superfluid nuclear matter. The behavior of the dynamical moment of inertia for such states is investigated within this model, which is shown to comply well with available experimental data and to describe successfully the rotational spectra of superdeformed states.     

Level statistics of near-yrast states in rapidly rotating nuclei

The nearest neighbour level spacing distribution and the Δ₃ statistic of level fluctuations associated with very high spin states (I ≳ 30) in rare-earth deformed nuclei are analysed by means of a cranked shell model. The many particle-many hole configurations created in the rotating Nilsson potential are mixed by the surface-delta two-body residual interaction. The levels in the near-yrast region show a Poisson-like level spacing distribution. As the intrinsic excitation energy U increases, the level statistics shows a gradual transition from order to chaos, reaching at U ≳ 2 MeV the Wigner distribution typical-of the Gaussian orthogonal ensemble of random matrices. This transition is caused by the residual two-body interaction. On the other hand, the level spacings between the yrast and the first excited state show a peculiar behaviour, displaying a Wigner-like distribution instead of the Poisson-like distribution seen for the other near-yrast rotational states. The lowest spacings reflect the properties of the single-particle orbits in the mean-field, and are only weakly affected by the residual two-body interaction.     

α-decay Branching Ratios to Rotational Band of Heavy Even-even and Odd-A Nuclei

By using a simple barrier penetration approach,we predict the α-decay branching ratios to members of ground-state rotational band of heavy even-even No isotopes.We also extend our approach to calculate the α-decay branching ratios to the rotational band of heavy odd-A nuclei.The theoretical branching ratios of α-decays are found in good agreement with the available experimental data.     

Multidimensional Langevin approach to description of near-barrier heavy-ion fusion and deep-inelastic collisions

A six-dimensional Langevin approach is developed for the analysis of near-barrier heavy-ion fusion and deep-inelastic collisions. In its framework, vibrational and rotational degrees of freedom of both nuclei are taken into account explicitly. Calculated fusion cross sections, compound nuclei spin distributions, and angular and energy distributions of deep-inelastic products show satisfactory agreement with experimental data.     

Single-Proton states of159Ho studied with the (p,α) reaction spectroscopic evidence for the unusual coriolis strengths in159, 161, 163Ho nuclei

The proton-hole character of states in¹⁵⁹Ho has been studied using the^{162, 164}Er(p, α)^{159, 161}Ho reactions with 17 MeV protons. The shapes of angular distributions measured for both nuclei were compared, with good agreement in most cases, to tritoncluster-transfer DWBA calculations. The deviations obtained and the experimental normalization factors deduced for the¹⁶⁴Er(p, α)¹⁶¹Ho reaction by comparisons to (t, α) cross sections indicate a need for a revised treatment of the mechanism of the (p, α) reaction on deformed nuclei. By comparisons to the well-known states in¹⁶¹Ho, nuclear structure factors were obtained for many levels in¹⁵⁹Ho. The Nilsson assignments for the 3/2⁺[411], 5/2^?[532] and 5/2⁺[413] bands were confirmed and the lowest rotational members of these bands were established. The anomalous strengths of the strongly mixed positive parity states in^{159, 161, 163}Ho are discussed in the frame-work of the Nilsson model with the pairing and effective Coriolis strengths included. The Coriolis strengths giving best fits to excitation energies also improve the agreement of theory with the experimental nuclear structure factors. Rotational spacings of the 5/2⁺[413] and especially those of the 5/2^?[532] bands in^{159, 161, 163}Ho show mixmg effects unexplainable by the present calculations.     

Relation between signature splitting in rotational bands of odd nuclei and the amplitude of the Ω=1/2 component

The relation between signature splitting in the spectra of rotational bands of odd nuclei and the structure of wave functions of these states is investigated. Rotational bands are considered both in axisymmetric nuclei and in nuclei that do not possess axial symmetry. A simple formula is obtained that makes it possible to extract the amplitude of the Ω=1/2 wave-function component from experimental data on energy spectra.     

Magnetic rotation and chiral symmetry breaking

The deformed mean field of nuclei exhibits various geometrical and dynamical symmetries which manifest themselves as various types of rotational and decay patterns. Most of the symmetry operations considered so far have been defined for a situation wherein the angular momentum coincides with one of the principal axes and the principal axis cranking may be invoked. New possibilities arise with the observation of rotational features in weakly deformed nuclei and now interpreted as magnetic rotational bands. More than 120 MR bands have now been identified by filtering the existing data. We present a brief overview of these bands. The total angular momentum vector in such bands is tilted away from the principal axes. Such a situation gives rise to several new possibilities including breaking of chiral symmetry as discussed recently by Frauendorf. We present the outcome of such symmetries and their possible experimental verification. Some possible examples of chiral bands are presented.