Critical Angular Momentum Research Articles

Reaction cross sections forN14+N14

Excitation functions for the yields of eleven residual nuclei from the $^{14}\mathrm{N}$+ $^{14}\mathrm{N}$ reaction have been measured over the range ${E}_{\mathrm{c}.\mathrm{m}.}=7\ensuremath{-}25$ MeV in steps of \ensuremath{\sim} 250 keV with $\ensuremath{\gamma}$-ray techniques. The magnitude and energy dependence of the excitation functions for the partial yields are very different from those for the $^{12}\mathrm{C}$+ $^{16}\mathrm{O}$ system. The total fusion cross section is similar to that from $^{12}\mathrm{C}$+ $^{16}\mathrm{O}$ when compared at the same center of mass energy, but appears to saturate at an energy and magnitude which are lower than expected from previous systematics. Small, regular fluctuations can be seen in the fusion cross section at the 1-2% level.NUCLEAR REACTIONS $^{14}\mathrm{N}(^{14}\mathrm{N}, x)$; ${E}_{\mathrm{c}.\mathrm{m}.}=7\ensuremath{-}25$ MeV; measured excitation functions for production of $A=16\ensuremath{-}27$ reaction products, observed small structures at ${E}_{\mathrm{c}.\mathrm{m}.}=15.0, 17.1, 18.5, 20.4, \mathrm{and} 22.0$ MeV; deduced critical angular momentum for fusion.

Further experimental study of fast fission with the Cl + Au system

The onset of fast fission was investigated with the Cl + Au system. The mass distribution of the fragments and the fusion cross sections were determined at six different bombarding energies. It turns out that the width of the symmetric component of the mass distribution increases strongly with the critical angular momentum. This could be related with the disappearance of the fission barrier due to centrifugal effects. A semi-static model is developed and the results are compared with the experimental data. In this framework, the observed broadening of the mass distribution can be attributed to the presence of the fast fission phenomenon.

Pair correlations and the fission barrier at very high angular momenta

The influence of pair correlations on deformation energy surfaces and the shape of fission barriers are investigated for a symmetrically fissioning, rotating actinide nucleus. Ii is shown that the assumption thapair correlations break down in the spin region 20–30ħ is not justified. It is found that the critical angular momentum for the collapse of pairing is strongly deformation dependent. The height of the first barrier is lowered by pairing for spins I ≲ 60ħ and the height of the second barrier for even higher spins. The critical angular momentum for giant backbending may be lowered considerably by pairing correlations.

Gamma-ray studies of theO16+Ne20system

Excitation functions for the yields of eight residual nuclides from the $^{16}\mathrm{O}$ + $^{20}\mathrm{Ne}$ reaction have been measured over the range ${E}_{\mathrm{c}.\mathrm{m}.}=15\ensuremath{-}29$ MeV using $\ensuremath{\gamma}$-ray techniques. Weak oscillatory structure in the fusion-evaporation yield is observed, with maxima near ${E}_{\mathrm{c}.\mathrm{m}.}=20, 22, \mathrm{and} 23$ MeV. Two strong anomalies in the inelastic scattering and $\ensuremath{\alpha}$-transfer channels have been located at ${E}_{\mathrm{c}.\mathrm{m}.}=19.9 \mathrm{and} 25.4$ MeV. These structures have properties similar to those of characteristic resonances in other light systems. The ${E}_{\mathrm{c}.\mathrm{m}.}=19.9$ MeV resonance occurs at the same $^{36}\mathrm{Ar}$ excitation energy as a similar resonance previously observed in the $^{12}\mathrm{C}$ + $^{24}\mathrm{Mg}$ reaction yields.NUCLEAR REACTIONS $^{20}\mathrm{Ne}$($^{16}\mathrm{O}$,$x$); ${E}_{\mathrm{c}.\mathrm{m}.}=15\ensuremath{-}29$ MeV; measured excitation functions for the production of $A=20\ensuremath{-}34$ reaction products; observed structure at ${E}_{\mathrm{c}.\mathrm{m}.}=19.9, 22.0, 22.8, \mathrm{and} 25.4$ MeV; deduced critical angular momentum for fusion.

Binary l-matched reactions in 14N + 159Tb collisions

Various channels from the 14N + 159Tb reaction at 140 MeV were studied using γ-particle coincidences combined with γ-ray multiplicity measurements. A wide class of binary reactions ranging from typical incomplete fusion processes to few-nucleon capture reactions was selected and investigated. Energy spectra, absolute cross sections and average γ-ray multiplicities were measured for a large number of reaction channels. From a detailed kinematical analysis it was found that all the reactions quite precisely satisfy the “recoil formula” of Siemens et al. for hard-grazing collisions. It is attempted to describe this wealth of reaction data on the common footing of the sum-rule model that combines the idea of partial statistical equilibrium with a generalized concept of critical angular momentum. The experimental results seem to confirm the basic assumptions of the model.

Localizedlwindow from partial fusion reactions accompanied by proton, deuteron, and triton emission

A high and localized spin population associated with partial fusion reactions has been established through the measurement of $\ensuremath{\gamma}$-ray multiplicity in coincidence with fast forward $p$, $d$, or $t$ produced by 167-MeV $^{14}\mathrm{N}$ on $^{154}\mathrm{Sm}$. The average $\ensuremath{\gamma}$ multiplicities are constant (${M}_{\ensuremath{\gamma}}=31$) for all the yrast transitions up to spin $26\ensuremath{\hbar}$ in $^{158}\mathrm{Er}$, which implies that no spins up to $26\ensuremath{\hbar}$ were populated initially. The deduced average angular momentum transferred is $63\ensuremath{\hbar}$, which is comparable to the critical angular momentum ${l}_{\mathrm{cr}}$ predicted for the fusion of $^{13}\mathrm{C}$ and $^{154}\mathrm{Sm}$. The mass distribution of the residual nuclei is appreciably narrower than that for compound nuclear reactions, and this gives another indication of the narrow $l$ window.NUCLEAR REACTIONS Partial fusion $^{154}\mathrm{Sm}$ [$^{14}\mathrm{N}$, ($p$,$d$, or $t$) $\mathrm{xn}\ensuremath{\gamma}$] $^{156\ensuremath{-}160}\mathrm{Er}$; $E(^{14}\mathrm{N})=167$ MeV; measured $\ensuremath{\gamma}$-ray multiplicity, mass distribution of residual nuclei; deduced localized $l$ window of entrance channel; discussed massive transfer model.

Neutron emission inC12+Gd158andC13+Gd157reactions between 8 and 12 MeV/nucleon

Neutron spectra in coincidence with evaporation residues and with projectilelike fragments emitted in inelastic scattering reactions have been measured at several bombarding energies for /sup 12/C- and /sup 13/C-induced reactions leading to the same compound nucleus /sup 170/Yb. In the fusion reactions, a nonequilibrium component was observed in the neutron spectra at all beam energies. This component is forward peaked and is associated with a high temperature. The spectra can be parametrized by assuming the nonequilibrium part to result from a hot region (Tapprox.4 MeV) emitting neutrons isotropically and moving with a velocity of approximately 1 cm/ns. This apparent velocity decreases with decreasing beam velocity. Comparisons are made with predictions based on the generalized critical angular momentum model of incomplete fusion of Siwek-Wilczynska et al. No significant difference has been observed between nonequilibrium neutron emission from /sup 12/C- and /sup 13/C-induced reactions. Neutron emission associated with inelastic scattering reactions cannot be described by simple statistical evaporation from two fragments of equal temperature. Effects which may give rise to the observed energy and angular distributions of neutrons in coincidence with inelastic products are discussed.

Angular-momentum transfer and alignment following preequilibrium α-particle emission in the reaction 209Bi + 14N

The magnitude and alignment of angular momenta transferred to a fusionlike product following fast α-particle emission at 20° and 50° have been determined by in-plane and out-of-plane angular correlations measured in the reaction 209Bi( 14N, αf) at 115 MeV. The result indicates that the preequilibrium α-particle emission mainly originates from entrance angular momenta smaller than the critical angular momentum for complete fusion.

S-matrix description of anomalous large-angle heavy-ion scattering

We present a quantitative description of the well-known anomalous features observed in the large-angle scattering of nα type heavy ions, in particular of the pronounced structures in the back-angle excitation function for 16O + 28Si. Our treatment is based on the close connection between these anomalies and particular structural deviations of the partial-wave S-matrix from normal strong-absorption behaviour. The properties of these deviations are found to be rather well specified by the data: they are localized within a narrow “l- window” centered at a critical angular momentum significantly smaller than the grazing value, and have a parity-dependent as well as a parity-independent part. These properties provide important clues as to the physical processes causing the large-angle enhancement.

Nuclear Structure Effects in the Quasi-Continuum Deexcitation Process of 152Dy and 156Dy Nuclei Produced in Complete and Incomplete Fusion Reactions

Intensities and energy dependent multiplicity distributions of γ-rays have been measured for 152Dy and 156Dy nuclei populated in (12C, xn) and (12C, αxn) reactions at E = 70-101 MeV. The relative population of the yrast states in 156Dy is found to be almost independent of the input angular momentum, which is not the case for 152Dy. In the latter nucleus the yrast states up to spin values close to the maximum input angular momentum are strongly populated whereas in the former the transition intensities decrease very rapidly with increasing level spin. Quasi-continuum feeding cascades in 156Dy are found to have considerably higher multiplicity than those in 152Dy at comparable input angular momentum. These features can be understood in 156Dy by assuming the existence of a number of collective bands which funnel the γ-ray deexcitation below the entry region away from the high spin yrast states whereas in 152Dy short γ-ray cascades feed directly the yrast states. The entry regions in 156Dy have been determined as a function of bombarding energy for the (12C, 6n) reaction. A decrease of the entry angular momentum above 90 MeV beam energy is found and explained by the existence of strong competing (12C, αxn) incomplete fusion reaction channels. Similar γ-ray sidefeeding patterns and multiplicity distributions for yrast states are observed in 12C induced complete (CF) and incomplete fusion (ICF) reactions leading to 156Dy. However, the data for quasi-continuum feeding multiplicites indicate a more narrow initial angular momentum distribution for ICF than for CF reactions. The mean initial angular momentum for ICF is found to be about 10 h higher than the one for CF and it is close to the critical angular momentum for CF as deduced from a simple reaction model.

Fusion-like reactions ofO16withSm154:γ-ray multiplicity versus bombarding energy

The cross section and average ..gamma..-ray multiplicity were measured for reactions of /sup 16/O+/sup 154/Sm leading to specific xn and ..cap alpha..xn final channels at five /sup 16/O energies from 111 to 168 MeV. For the 6n, 7n, and 8n channels the cross sections show nonstatistical tails and saturates at high energies, indicating that emission of one or more fast neutrons is occurring. The data suggest that the partial waves involved in this nonstatistical behavior are predominantly peripheral. Consideration of all available data from this and other systems indicates that a strong correlation exists between the structure of the projectile and the first appearance of nonstatistical emission of neutrons and alpha particles. The generalized critical angular momentum model of incomplete fusion is extended, providing successful predictions for all data of the energy at which nonstatistical neutron emission sets in and of the energy variation of in the various xn exit channels.

Liquid drop model and heavy ion collisions

A macroscopic liquid drop model is considered in order to demonstrate the deep inelastic processes that take place in heavy ion collisions. The colliding nuclei, treated as two liquid drops, are assumed to form a single rotating and vibrating compound drop. This drop will either separate again into the parent nuclei, in addition to some smaller particles (satellites), or will form an equilibrium compound nucleus which decays either by particle evaporation or through fission. The maximum and minimum values of the critical angular momentum between which complete fusion occurs are calculated according to this model for several heavy ion reactions and good agreement with the experimental values is observed.NUCLEAR REACTIONS Heavy ion scattering; modified model for interaction of two liquid drops, its application to deep inelastic collisions between two heavy nuclei; calculations of critical angular momentum.

12C + 7Li Reaction measurements and the 12C( 7Li, t) 16O reaction

A measurement of the residues from the 12C + 7Li reaction has been obtained for 7Li energies from 10 to 38 MeV. From these measurements the fusion cross sections and critical angular momenta for the 12C + 7Li system have been deduced. Cross sections for the 7Li( 12C, t) 16O reaction have been obtained for 12C energies from 54 to 62 MeV at θ lab = 2.7°. The critical angular momenta obtained from the fusion cross sections have been used to perform Hauser-Feshbach calculations for the 12C( 7Li, t) 16O reaction. These calculations have been compared to measured angular distributions over a wide energy range. By comparing the fusion cross sections required by the Hauser-Feshbach calculations to fit the 12C( 7Li, t) 16O(8.87 MeV) reaction and the measured residue cross section it is estimated that at least 80 % of the measured residues are fusion products. The calculations also indicate that direct processes dominate the population of many 16O levels at forward angles and the 10.35 MeV state at backward angles. The necessity for using a critical angular momentum in Hauser-Feshbach calculations is discussed.

Synthesis of superheavy elements in heavy-ion fusion reactions

Cross sections for the production of elements 108-116 in heavy-ion fusion reactions have been estimated using the statistical model. The influence of the various parameters on the estimated cross sections has been studied: attention was paid to the interaction barriers for which more realistic values have been determined with the model of Krappe, Nix and Sierk (1979). A semi-empirical value of 45 h(cross) was taken for the critical angular momentum corresponding to the vanishing of the compound-nucleus fission barrier. Few of the estimated cross sections are above the actual sensitivity limit of the detection methods.

Microscopic calculations of fission barriers and critical angular momenta for excited heavy nuclear systems

Abstract An extended version of Strutinsky's macro-microscopic method is used to calculate effective potential energies for rotating, excited heavy compound nuclei undergoing fission. Nuclear deformation is parameterized in terms of Lawrence's family of shapes. A two-center single-particle potential corresponding to these shapes is employed, with BCS pairing added. Statistical excitation is introduced by temperature-dependent occupation of (quasi-) particle energy levels. We calculate shell corrections to the energy, the free energy and the entropy as functions of deformation and temperature. The associated average quantities are derived from a temperature-dependent liquid drop model. The resulting static deformation energy is augmented by the rotational energy to yield the isothermal effective potential energy as a function of deformation, temperature and angular momentum. Moments of inertia are obtained from the adiabatic cranking model with temperature-dependent pairing included. We have also calculated the effective potential for constant entropy rather than constant temperature. Although this isentropic process physically is more appropriate than the isothermal process, it has not been treated before. For the same amount of excitation energy in the spherical state of the compound nucleus, the isentropic barriers turn out higher than the isothermal ones. For both processes we have extracted the critical angular momentum (defined as the one for which the barrier approximately vanishes) as a function of excitation. Our model is applied to the super-heavy nuclei 270 110, 278 110, 298 114, 292 118 and 322 128, which have been tried to form in krypton and argon induced heavy ion reactions.

APPLICATION OF CATASTROPHE THEORY TO NUCLEAR STRUCTURE*

Three two-parameter models, one describing an A-body system (the atomic nucleus) and two describing many-body systems (the van der Waals gas and the ferroelectric (perovskite) system) are compared within the framework of catastrophe theory. It is shown that each has a critical point (second-order phase transition) when the two counteracting forces controlling it are in balance; further, each undergoes a first-order phase transition when one of the forces vanishes (the deforming force for the nucleus, the attractive force for the van der Waals gas, and the dielectric constant for the perovskite). Finally, when both parameters are kept constant, a kind of phase transition may occur at a critical angular momentum, critical pressure, and critical electric field. 3 figures, 1 table.

Spinning particles orbiting the Kerr black hole: cosmic censorship at work

Equatorial accretion of spinning particles onto a Kerr black hole is considered, and the impossibility of spinning up the hole above the critical value angular momentum = mass squared is proved.

Heavy-ion fusion and the production of elements 103, 105 and 107

The synthesis of elements 103, 105 and 107 through heavy-ion reactions is discussed in the context of the fragmentation theory by estimating the production cross sections with the help of the statistical model, including fission competition. It is shown that the most favourable target-projectile combinations predicted by theory coincide with the ones already used in experiments to produce transfermium elements, provided that the critical angular momentum value is determined by the condition that the fission barrier vanishes.

Pseudomagic nuclei

Below a critical angular momentum, yrast bands of non-magic nuclei are well described by the two-parameter variable moment of inertia model. Some striking exceptions to this rule are found in nuclei which have the same mass number as doubly magic nuclei but possess either one (or two) proton pairs beyond a magic number and one (or two) neutron hole pairs, or vice versa. Yrast bands in these 'pseudomagic' nuclei resemble those in magic nuclei.

Incomplete fusion in 12C+160Gd collisions

The mechanism of the production of fast α-particles in 12C induced reactions was studied over a wide range of bombarding energies (7.5–16.7 MeV/A) by measuring α-γ coincidences. Absolute cross sections for 160Gd(12C, αxn)168−xEr and 160Gd(12C, 2αxn)164−xDy reactions, as well as inclusive α-particle production cross sections, have been determined. Depending on the bombarding energy, a fraction of 0.2–0.4 of the singles α-particles can be explained as resulting from incomplete fusion reactions (12C, α) and (12C, 2α) which correspond to a capture of “8Be” and “4He”, respectively. The remaining fragments of the projectile have, on the average, the beam-velocity energies and their angular distributions are forward peaked. Distributions of side-feeding to the yrast bands in the target-residue nuclei indicate that low partial waves are strongly hindered in the incomplete fusion reactions. The energy dependence of the cross sections for (12C, α) and (12C, 2α) incomplete fusion as well as for (12C, 3α) projectile breakup is given. A generalized concept of critical angular momentum which explains a competition between complete fusion, incomplete fusion and breakup reactions is proposed.