Angular momentum polarization of the molecules in the Li + HF reaction

A theoretical analysis of the orientation and alignment of the rotational angular momenta of the reactants and products of the Li + HF(v _r = 0, j _r = 3) → LiF(v, j) + H reaction at a collision energy of E _coll = 0.317 eV is performed. The polarization of the angular momentum of the molecules involved in the reaction is based on the technique of spherical tensor operators (state multipoles). Quantum-mechanical calculations of the S-matrix of the reaction are carried out using the wave packet method. In particular, the influence of the orientation of the angular momentum of the HF reactant on the differential cross section is examined. It is shown that the contribution to the differential cross section comes only from be reactants with an angular momentum perpendicular to the reaction plane. In addition, the angular dependence of the orientation and alignment of the angular momenta of the reaction products are examined. It is shown that, for an isotropic distribution of reactant molecules, the orientation of the angular momenta of the products differs from zero only in the direction perpendicular to the reaction plane. Different experimental geometries, based on radiation enhanced multiphoton ionization, are proposed to detect the predicted effects.     

Prior-form DWBA analysis of (3He,pd) elastic breakup at 90 MeV

Proton-deuteron coincident cross sections in ¹²C,⁵¹V,⁹⁰Zr(³He,pd) elastic breakup at 90 MeV have been calculated within the framework of the prior-form distorted-wave Born approximation (DWBA). Sufficient convergence of the calculations was obtained by including the pd relative angular momenta up to l = 4. The calculations reproduced the general trend of the coincident energy spectra and the angular correlation data, though deficiencies of the calculations were seen at some angles. The peripheral feature of the (³He, pd) elastic breakup is discussed from the angular momentum dependence of the transition amplitude.     

Energy and angular distributions in 6He photodisintegration

Energy and angular distributions of the neutrons and the α particle from the reaction ⁶He(γ, 2n)⁴He is examined in the minimal approximation of the hyperspherical-function method in the algebraic version of the resonating-group method. The differential cross section for ⁶He photodisintegration is calculated as a function of the energies of the product particles, the angles between their momenta, and their emission angles with respect to the incident-photon momentum.     

Fission instability of nuclei at very high angular momenta

Deformation energy surfaces at high angular momenta ($\text{I ≧ 30?}$) are calculated for different nuclear shapes characterized by the deformation β and a neck parameter r. This parametrization has the advantage that it is a natural extension of the Bohr-Mottelson shape parameters β and γ. This choice allows one to study the neck degree of freedom near the fission instability at high angular momenta and also the sudden change of the nuclear shape from an oblate deformation (β > 0; γ = ?60°) to a prolate one (β > 0, γ = 0°) which gives rise to the so called giant backbending (g.b.b.). The deformation energy surface is calculated using the Strutinsky approach with the rotating liquid-drop model (RLDM) and the shell corrections based on a cranked Saxon-Woods potential. The heights of the first and, if present, the second barrier are studied at γ = 0° as a function of the total angular momentum for even mass rare earth and actinide nuclei. The critical angular momenta at which the fission barriers vanish are often higher than that predicted by the RLDM.     

A representation of angular momentum (SU(2)) algebra

This paper seeks to construct a representation of the algebra of angular momentum (SU(2) algebra) in terms of the operator relations corresponding to Gentile statistics in which one quantum state can be occupied by n particles. First, we present an operator realization of Gentile statistics. Then, we propose a representation of angular momenta. The result shows that there exist certain underlying connections between the operator realization of the Gentile statistics and the angular momentum (SU(2)) algebra.     

QCD jets ine + e −-annihilation and the transition into hadrons

A model has been developed describing QCD jets in the leading logarithmic approximation (LLA) and the subsequent transition into hadrons via a chain decay model. Besides of the production of mesons, the model is also able to describe baryon production. Agreement with recent data frome ⁺ e ^?-annihilation is found. This includes average multiplicities, average transverse momenta and transverse momentum distributions, longitudinal momentum distributions as well as particle production ratios π^α:K ^π : p(0070), charge compensation probabilities and energy flux correlations. The model is compared to similar models developed by other authors.     

Assessment of the equivalent photon approximation for the process ee → ee π+π−

The contribution of the virtual process γγ → π⁺π^? is evaluated, first treating the quantum electrodynamics exactly and then using the equivalent photon approximation. The dependence on electron scattering angles, electron energies, ππ invariant mass and γπ momentum transfer is investigated. The approximation is very good if both electron scattering angles are less than 0.1 rad, but is 20%–40% too big (depending on the precise version used) if either angle is integrated over. It is explained that the approximation is not Lorentz invariant; numerical results are given only for beams with anti-parallel momenta.     

Measurement of the total and differential cross sections for the reaction π − p → ηn with the Crystal Ball detector

The first results obtained in 1998 by the Crystal Ball collaboration from a measurement of the total and differential cross sections for the reaction π ^? p → ηn are presented. These new experimental results for the total cross sections are compared with the predictions of the K-matrix model for pion-nucleon scattering. The angular distribution at momenta near the reaction threshold (685 MeV/c) is determined by the S-wave contribution. The P-wave contribution begins to manifest itself from a momentum of 720 MeV/c.     

Angular momenta of fission fragments in the α-accompanied fission of 252Cf

For the first time, average angular momenta of the ternary fission fragments ^{100, 102}Zr, ¹⁰⁶Mo, ^{144, 146}Ba and ^{138, 140, 142}Xe from the α-accompanied fission of ²⁵²Cf were obtained from relative intensities of prompt γ-ray transitions with the use of the statistical model calculation. Average values of the angular momenta were compared with the corresponding values for the same fission fragments from the binary fission of ²⁵²Cf. Results indicate the presence of a decreasing trend in the average values of angular momenta induced in ternary fission fragments compared to the same binary fission fragments. On the average, the total angular momentum extracted for ternary fission fragments is ∼1.4 ℏ lower than in binary fission. Consequently, results indicate that the mechanism of the ternary α-particles emission may directly effect an induction of angular momenta of fission fragments, and possible scenarios of such mechanisms are discussed. Further, the dependence of the angular momenta of ¹⁰⁶Mo and ¹⁴⁰Xe on the number of emitted neutrons from correlated pairs of primary fragments was obtained also showing a decreasing dependence of average angular momenta with increasing number of emitted neutrons. Consequences are briefly discussed.     

On the experimental value of the intrinsic angular momentum of the A-phase of superfluid helium-3

A simple relation between the equilibrium spin and orbital angular momenta of the superfluid phases of helium-3 close to T_c has been obtained. The intrinsic angular momentum of the A-phase has been found from the existing experimental data using this relation.     

Differential cross-sections for pp → π−π+, K−K+ between 0.8 and 2.4 GeV/c

We present measurements from a spark chamber experiment of the differential cross-sections for $\text{p}$p → π^?π⁺, K^?K⁺ at 20 momenta in the range 0.8–2.4 GeV/c (c.m. energy 2.02 to 2.57 GeV). The c.m. angular range was $\text{?0.95 <}\text{cos}\text{θ}{}^1\text{< 0.95}$. There are about 2000π^?π⁺ events and about 300 K^?K⁺ events at each momentum.     

Isomeric yield ratios of fission products in the system of 24 MeV proton-induced fission of238U

Isomeric yield ratios of 30 fission products in 24 MeV proton-induced fission of²³⁸U were measured by the use of the ion-guide isotope separator on-line. The obtained isomeric yield ratios were converted to the angular momenta of primary fission fragments based on the statistical model. The deduced angular momenta were examined from various aspects. It is found that in general the angular momentum continuously increases with the fragment mass number including the region of symmetric mass division. However, there are some exceptions. For Sn isotopes the deduced angular momenta are quite small due to the spherical shape of the nuclear shell configuration. It is also concluded from the consideration of the charge distribution that the angular momentum of fission product scatters considerably within the narrow range of mass division. The dependence of the angular momentum on the available energy of fragments at scission point indicates that the individual fragment possesses a characteristic deformation at scission and/or the deduced angular momentum is seriously affected by the particle excitation after scission.     

Fragile black holes and an angular momentum cutoff in peripheral heavy ion collisions

In collisions of heavy ions at extremely high energies, it is possible for a significant quantity of angular momentum to be deposited into the Quark–Gluon Plasma which is thought to be produced. We develop a simple geometric model of such a system, and show that it is dual, in the AdS/CFT sense, to a rotating AdS black hole with a topologically planar event horizon. However, when this black hole is embedded in string theory, it proves to be unstable, for all non-zero angular momenta, to a certain non-perturbative effect: the familiar planar black hole, as used in most AdS/CFT analyses of QGP physics, is “fragile”. The upshot is that the AdS/CFT duality apparently predicts that the QGP should always become unstable when it is produced in peripheral collisions. However, we argue that holography indicates that relatively low angular momenta delay the development of the instability, so that in practice it may be observable only for peripheral collisions involving favorable impact parameters, generating extremely large angular momenta. In principle, the result may be holographic prediction of a cutoff for the observable angular momenta of the QGP, or perhaps of an analogous phenomenon in condensed matter physics.     

The (π, 2π) reaction and spin-isospin strength distribution in nuclei

We study pion production on nuclei within the distorted wave impulse approximation (DWIA) and using the local density approximation (LDA) for the treatment of possible nuclear spin-isospin mode enhancements. The scattering amplitude input is based on a one-nucleon mechanism since two-nucleon processes are here estimatedito be relatively unimportant. For discrete nuclear levels, we study differential and total (angle-integrated) cross sections for various pion-like levels (J^P = 0^?, 1⁺, 2^?,…; T = 1); these are also compared with non-pion-like excitations. The cross sections for discrete excitations are quite small. The inclusive cross sections, achieved by summing over all nuclear states, are considerably larger, of the order of 0.1–10 mb. We use the Fermi gas model to test the importance of the quasi-free peak for various incident pion momenta k, and to study the closure approximation for summing over nuclear levels when calculating inclusive cross sections. It is found that for k of the order of about twice the Fermi momentum most of the quasi-free peak region contributes to the nuclear excitations, and the use of closure is justified and practical. All cases are studied as a function of g', the Migdal spin-isospin parameter, and it is found that the dependence upon this parameter may range from changes of an order of magnitude to a factor of two over the range 0.4 ? g' ? 0.7.     

Microscopic study of the 12C + 16O system

An angular momentum projected microscopic calculation is performed for the ¹²C + ¹⁶O system with an effective nuclear force and the exact Coulomb interaction. The ¹²C wave function is projected on a 0⁺ state. Parametrizations of the Coulomb interaction between the nuclei are fitted. The L-projected energy curves present a quite complicated structure especially for the negative parity states. The role played by critical angular momenta is put into evidence. A generator coordinate calculation gives several bands of bound, quasibound and virtual states. Excellent agreement in energy and angular momentum is obtained with the 13.7 MeV (J = 9), 19.7 MeV (J = 14), 22.7 MeV (J = 15) and other resonances.     

Computing spin networks

We expand a set of notions recently introduced providing the general setting for a universal representation of the quantum structure on which quantum information stands. The dynamical evolution process associated with generic quantum information manipulation is based on the (re)coupling theory of SU (2) angular momenta. Such scheme automatically incorporates all the essential features that make quantum information encoding much more efficient than classical: it is fully discrete; it deals with inherently entangled states, naturally endowed with a tensor product structure; it allows for generic encoding patterns. The model proposed can be thought of as the non-Boolean generalization of the quantum circuit model, with unitary gates expressed in terms of 3nj coefficients connecting inequivalent binary coupling schemes of n + 1 angular momentum variables, as well as Wigner rotations in the eigenspace of the total angular momentum. A crucial role is played by elementary j-gates (6j symbols) which satisfy algebraic identities that make the structure of the model similar to “state sum models” employed in discretizing topological quantum field theories and quantum gravity. The spin network simulator can thus be viewed also as a Combinatorial QFT model for computation. The semiclassical limit (large j) is discussed.     

Influence of quadrupole pairing on backbending

The influence of the different quadrupole pairing forces ∝ Y_2m (m = 0, 1, 2) and the spin-dependent particle-hole force on backbending (BB) is studied. A cranked Hartree-Fock-Bogoliubov approach with particle number projection before the variation of the important degrees of freedom is used. To discuss the numerical results qualitatively perturbative formulas for the moment of inertia and the gap parameters are given. The results are the following: (i) The quadrupole pairing Y₂₁ is not affecting the backbending. (ii) The Y₂₀ pairing is reducing the moment of inertia at low angular momenta by about 20 %. This just cancels the increase of the moment of inertia by Y₂₁ pairing at low angular momenta, (iii) The Y₂₁ and Y₂₀ pairing together shift the backbending point to higher angular momenta and better agreement with the experimental data. (iv) A spin-dependent ph force does not affect the moment of inertia at low angular momentum. But above backbending it reduces the moment of inertia by about 13 % to the correct experimental value if a strength parameter adapted in ²⁰⁸Pb is used.     

Renormalisation of Noncommutative ϕ 4-Theory by Multi-Scale Analysis

In this paper we give a much more efficient proof that the real Euclidean ? ⁴-model on the four-dimensional Moyal plane is renormalisable to all orders. We prove rigorous bounds on the propagator which complete the previous renormalisation proof based on renormalisation group equations for non-local matrix models. On the other hand, our bounds permit a powerful multi-scale analysis of the resulting ribbon graphs. Here, the dual graphs play a particular rôle because the angular momentum conservation is conveniently represented in the dual picture. Choosing a spanning tree in the dual graph according to the scale attribution, we prove that the summation over the loop angular momenta can be performed at no cost so that the power-counting is reduced to the balance of the number of propagators versus the number of completely inner vertices in subgraphs of the dual graph.     

Effect of entrance channel parameters on fission fragment angular momentum in medium energy fission

Independent isomeric yield ratios of¹³²I were radiochemically determined in alpha particle induced fission of²³⁸U in the energy range 25–44 MeV. Fission fragment angular momenta were deduced from the measured isomeric yield ratios using spin dependent statistical model analysis. It was seen that angular momentum of¹³²I increases with increase of excitation energy and angular momentum of the fissioning nucleus. Comparison of the present data on¹³²I in²³⁸U(α,f) with the literature data for the same product in²³⁸U(p, f) and²³⁸U(γ, f) at various excitation energies show that fragment angular momentum strongly depends on the input angular momentum in the range of excitation energy considered. Experimental fragment angular momentum at all excitation energies were seen to be in agreement with the theoretical values calculated based on thermal equilibration of the various collective rotational degrees after considering the occurence of multichance fission. Thus, strong effect of input angular momentum as well as the statistical equilibration among the various collective rotational degrees of freedom in medium energy fission is corroborated.