Angular Momentum Cutoff Research Articles

Magnetic 3d impurities in Nb and Mo revisited

The authors re-examine the electronic structure of 3d impurities in niobium and molybdenum using local density functional theory and an improved version of the KKR-Green function method. The calculations reveal an extraordinary sensitivity of the local 3d moments with respect to the angular momentum cutoff lmax of the wavefunctions. Whereas previous calculations with lmax=2 yielded very large moments for Cr, Mn and Fe impurities in Nb, these moments are completely suppressed, if higher angular momenta (lmax=3 or 4) are added. A qualitatively similar trend is found for the Mo host; however the reduction of the local moments is more moderate. The present results are in good agreement with the experimental data.

Semiclassical calculation for 16O+16O elastic scattering at high energies.

A semiclassical method has been used to calculate terms of order ${\mathrm{\ensuremath{\Elzxh}}}^{2}$, the $^{16}\mathrm{O}$${+}^{16}$O elastic-scattering cross section for the c.m. energy range 35--90 MeV for various optical model potentials. We find that the calculated results with an energy-dependent absorptive part along with an angular momentum cutoff agree qualitatively with the experimental results.

Radiative capture in the light heavy-ion systems 6Li+ 6Li and 6Li+ 7Li at Ec.m. = 1–8 MeV

The heavy-ion radiative-capture reactions 6Li( 6Li, γ) 12C and 7Li( 6Li, γ) 13C have been studied. Utilizing a large-volume NaI(Tl) γ-spectrometer, the γ-transitions to the ground state and the three lowest excited states of 12C in the former case and the transitions γ 0, γ 1, γ 2 3 , γ 4 and γ 5 6 7 in the latter case could be resolved. The evaluation of absolute cross sections which range from 0.3 to 210 nb/sr relies on the thoroughly investigated response function of the spectrometer. Excitation functions at 125° as well as three-point angular distributions at several energies were measured. The results are compared with statistical model calculations. The latter make use of a smooth angular momentum cutoff in the entrance channel, isospin mixing in the compound nucleus, and giant resonances built upon excited states for γ-strenght distributions. All data are described by these model calculations. In addition to these statistical features a broad resonance ( gL ∼ 0.8 MeV) is observed for th γ 1-transition in 6Li( 6Li, γ) 12C at E x ∼ 30.3 MeV.

Green's function and a generalized Lloyd formula for the density of states in disordered muffin-tin alloys.

We consider the Korringa-Kohn-Rostoker coherent-potential-approximation Green's function for a disordered system of muffin-tin potentials and evaluate its integral over the Wigner-Seitz cell rigorously throughout the complex energy plane. The resulting expression is shown to possess a perfect derivative form, provided the angular-momentum summations are extended to infinity; for a finite angular-momentum cutoff this result is valid to a good approximation. For real energies our expression constitutes a generalization of the Lloyd formula for the density of states. The conventional Lloyd formula contains unphysical singularities that are not only unsatisfactory from a formal viewpoint, but also make its use increasingly cumbersome in multicomponent alloys as the number of atoms in the unit cell becomes larger. Our expression, on the other hand, is free from such singularities, and thus provides a useful basis for evaluating density of states and its energy integral in muffin-tin systems.

Limiting Angular Momenta for Light Heavy-Ion Fusion at High Energy

The shapes of angular distributions in reactions /sup 12/C(/sup 16/O,..cap alpha..) to the J/sup ..pi../ = O/sup +/ /sup 24/Mg ground state are studied from E(/sup 16/O) = 28.5 to 100 MeV. The position of the first minimum (and maximum) of these oscillatory angular distributions is expected to be sensitive to the presence of a low--angular-momentum cutoff in the compound-nucleus formation cross section. No evidence for a low-L cutoff is found even at energies well beyond the predicted threshold.

Energy dependence of fusion and reaction cross sections in the 9Be + 12C system

Angular distributions of protons, deuterons. tritons and α-particles were measured for the system 9Be + 12C at lab energies between 12 and 27 MeV. The compound nucleus model with level densities calculated according to the Gilbert-Cameron formula describes satisfactorily the measured proton, deuteron and triton data. In the α-particle spectra contributions from other processes seem to be present. In the analysis the fusion cut-off angular momentum was adjusted at each energy in order to reproduce correctly the proton, deuteron and triton channels. From this analysis the fusion cross section was determined as a function of the energy. The results were compared with fusion and total reaction cross section values calculated from a potential model with the real part of the interaction potential obtained from the double folding procedure of Satchler.

The energy dependence of fusion in the 9Be+ 28Si system

The angular distributions of the energy spectra of the light charged particles (p, d and α) from the 9Be + 28Si reaction have been measured in the energy range 12 ≦ E lab ≦ 30 MeV. The particle evaporation spectra and the angular distributions were analyzed with a spin dependent statistical model. Angular distributions of 9Be ions elastically scattered on 28Si have been measured at the energies 12 MeV, 17 MeV, 23 MeV and 30 MeV and were analysed, together with previously measured cross sections, with the optical model. The fusion cut-off angular momentum l fus( E), the fusion cross section σ fus( E) and the ratio σ fus/ σ R OM( E) were deduced. The excitation function for fusion was analyzed with the Glas and Mosel model. The parameters obtained from the fusion excitation function were compared with the corresponding ones from the 9Be + 28Si optical-model interaction potential.

Light charged-particle production in the 9Be + 12C reaction at 11.4 MeV c.m. energy

Angular distributions of protons, deuterons, tritons and α-particles have been measured for the 9Be + 12C system at a c.m. energy of 11.4 MeV. The dominant process is compound nucleus formation. The fusion cut-off angular momentum and the fusion cross section were estimated from an analysis of the proton, deuteron and triton data. Contributions from other reaction mechanisms, e.g. cluster transfer, are responsible for α-particle emission. Spin selectivity in the excitation of a few states of the residua] nuclei was observed mainly in the proton channel.

Effect of the critical angular momentum on the high spin selectivity of heavy-ion compound reactions

A drastic limitation of the high-spin selectivity of heavy-ion compound reactions is shown to be introduced by the angular momentum cutoff ${J}_{max}$ in the composite system. However, for final spins near ${J}_{max}$ a strong shape dependence of the angular distributions (being peaked at 90\ifmmode^\circ\else\textdegree\fi{}) arises as result of a strong decrease of the alignment of the final nucleus and can be used for high spin spectroscopy.NUCLEAR REACTIONS: Statistical model calculations-critical angular momentum effects.

Complete fusion of 16O with 26Mg and 19F with 23Na

Abstract Cross sections, σ c.n. ( E ), for complete fusion of 16 O + 26 Mg and 19 F + 23 Na, both forminf the compound nucleus 42 Ca, were measured for E c.n. between 25 and 70 MeV. The maximum cross section for the 19 F + 23 Na reaction is larger than that for 16 O + 26 Mg and an apparent angular momentum cutoff, well below the prediction of the liquid drop model, was observed for the 16 O + 26 Mg reaction only. A simple parameterization for σ c.n. ( E ) is used to compare the two reactions in terms of compound nucleus and entrance channel phenomena.

Two-body final states in thed+dinteraction in the 50-85 MeV incident energy range

Angular distributions of the $^{2}\mathrm{H}(d, d)^{2}\mathrm{H}$, $^{2}\mathrm{H}(d, p)^{3}\mathrm{H}$, and $^{2}\mathrm{H}(d, n)^{3}\mathrm{He}$ reactions at six incident energies in the 50-85 MeV range have been measured. The $^{2}\mathrm{H}(d, p)^{3}\mathrm{H}$ reaction data have been analyzed in terms of the plane-wave Born-approximation theory. A smooth cutoff in the partial wave expansion of the reaction matrix has been introduced to allow the suppression of the low angular momentum components. The calculated angular distributions obtained with a constant cutoff angular momentum ${l}_{\mathrm{co}}=3$ show reasonably good agreement with the experimental data in the whole 50-85 MeV energy range. This is consistent with the peripheral character of the reaction.NUCLEAR REACTIONS $^{2}\mathrm{H}(d, d)$, $^{2}\mathrm{H}(d, p)$, $^{2}\mathrm{H}(d, n)$, $E=50\ensuremath{-}85$ MeV; measured $\frac{d\ensuremath{\sigma}}{d\ensuremath{\Omega}}$; analysis in terms of PWBA with a smooth $l$ cutoff; deduced cutoff angular momenta.

Cross sections for 6Li production in the reactions 10B + 16O and 12C + 14N at low energies

Absolute cross sections have been measured for the reactions 10B( 16O, 6Li) 20Ne and 12C( 14N, 6Li) 20Ne at several energies in the range E c.m. = 7.5–16.2 MeV, and 13.8–16.6 MeV, respectively. The predictions of Hauser-Feshbach calculations show generally good agreement with the experimental data without parameter variation. The consequences of an angular momentum cutoff in the entrance channel and in the compound nucleus are discussed.

Comment on the existence of a lower angular momentum cutoff in the fusion of heavy ions

Gauvin et al. have suggested that one possible explanation for the high thresholds of the reactions $^{74}\mathrm{Ge}(^{84}\mathrm{Kr}, xn)^{158\ensuremath{-}x}\mathrm{Er}$ is the existence of a lower limit to the angular momentum of the compound system formed in the fusion step. We note that such lower limits have, in fact, previously been observed in the collisions of water droplets. Investigation of such lower limits may provide interesting new information on nuclear properties.NUCLEAR REACTIONS Heavy ion fusion.

Behavior of the Cross Sections for Polonium Production in Nuclear Reactions ofAr40withDy104

Excitation functions are reported for the reactions of $^{164}\mathrm{Dy}$ with $^{40}\mathrm{Ar}$ to produce $^{200}\mathrm{Po}$ and $^{199}\mathrm{Po}$. The cross sections are much smaller than the calculated values and it is concluded that this is due to an angular momentum cutoff and to a large fission width. The reaction threshold at a laboratory energy of 4.2 MeV per nucleon indicates a low Coulomb barrier (${r}_{0}=1.45$ fm).

Inelastic scattering of [formula omitted] particles in the Austern-Blair theory

The inelastic scattering of strongly absorbed spin- 1 2 particles by spin-0 targets is treated in the Austern-Blair theory for one-phonon excitations, suitably extended to include spin-orbit interactions. Closed formulae for the cross section and the polarisation are derived in the angular region ε ⪡ θ ⪡ π− ε, ε = L 2/ l 0 where L is the spin of the excited level and l 0 is the cut-off angular momentum. Comparison with the corresponding expressions for elastic scattering reveals that the Blair phase rule holds for both the cross section and the polarisation.

The Akhieser-Pomeranchuk-Blair model analysis of the elastic scattering of 24.7 MeV alpha-particles from heavy nuclei

The measured angular distributions of 24.7 MeV alpha-particles elastically scattered from the nuclei Ag, In, Sn, Hf, W, Au, Bi and U have been analysed in terms of the improved Akhieser-Pomeranchuk-Blair model. In these analyses, the parameterslA and ΔlA, respectively the cut-off angular momentum and the range of partial waves over which the transition from complete absorption to no absorption takes place, were found to be adequate and good agreement with experimental results could be obtained.

An Impact Parameter Formalism. III

In order to understand the physical meaning of an impact parameter amplitude, the formalism proposed by us is applied to various strong absorption models. A simple black disc model with a sharp boundary is not self-consistent; that is, the total elastic cross section derived from the angular distribution is not equal to what is calculated from the impact parameter amplitude. This inconsistency is expressed as the violation of the unitarity relation. It disappears in the high energy limit, where the semi-classical particle picture is applicable. A general rule is given for getting consistent results even in the finite energy region. It is observed that the model proposed by Fernbach, Serber and Taylor contains the same inconsistency. On the other hand, a sharp cutoff model with a sharp cutoff angular momentum involves no such difficulty. The strong interaction region expressed by this model has a diffuse edge with respect to the impact parameter. Thus, the concept of a radius of this region is introduced. It is pointed out that the so-called high energy approximation to the familiar partial-wave expansion of the scattering amplitude for large angular momenta does not include any limitation on the scattering angle.