Correlated spin networks in frustrated systems

We introduce a network model for frustrated spin systems based on highly correlated spin fluctuations, to quantify and visualize their ordering. This model shows that networks of strongly correlated but non-contiguous spins exist at low temperatures on a triangular Ising lattice with competing nearest-neighbor interactions. This finding is consistent with chaotic renormalization-group trajectories previously reported for frustrated hierarchical lattices.     

Investigation of high spin states in23Na and23Mg and the12C+12C resonance atE c.m.=19.3 MeV

The resonance in the¹²C+¹²C system atE _c.m.=19.3 MeV has been studied in the neutron and proton decay channels. From(p, γ), (n, p) and (n, γ) coincidence measurements high spin states could be localized inA=23 nuclei, in²³Mg up to possibly 21/2⁺. These states were resonantly populated. The present data favorJ ^π=17/2⁺ for the 9.61 MeV state in²³Mg and therefore also for the probable parent state at 9.81 MeV in²³Na. AJ ^π=12⁺ assignment to the resonance is supported and evidence was found that the resonant excitation of the lowest 15/2⁺ and 17/2⁺ states in mass 23 nuclei is caused by a change of the intrinsic structure of the Yrast levels aroundJ ^π=15/2⁺ towards larger deformation.     

Spin alignment in12C+12C inelastic scattering

The spin alignment P_zz of¹²C(2 ₁ ⁺ ) produced in¹²C+¹²C inelastic scattering at bombarding energies in the region of known resonances between E_cm=18.5 and 32.8 MeV has been determined with a γ-ray detector positioned in the direction of the scattering normal. The values obtained in the centers of three resonances as well as those obtained off-resonance are spread over a range between ?.05 and +.80 with no clear indication in favour of simple pictures of molecular resonances.     

Neutron branching in the reaction 12C + 12C

The cross section for the reaction ¹²C(¹²C, n)²³Mg has been measured in the energy range E_c.m. = 3.54?4.94 MeV by counting the delayed γ-rays from ²³Mg decays (half-life = 11.57 sec), and a theoretical model has been employed to extrapolate the results to threshold (E_c.m = 2.60 MeV). By combining these results with previous measurements of the reactions ¹²C(¹²C, p)²³Na and ¹²C(¹²C, α)²⁰Ne, the neutron branching ratio in the energy interval from threshold to 8 MeV is deduced, and a thermal average is computed that should be valid for use in astrophysical environments characterized by temperatures in the range (0.5–5) × 10⁹ °K. The neutron branching at temperatures appropriate to hydrostatic carbon burning in stars (T ≈ 109 °K) is found to be much smaller than previously estimated.     

Proton decay of spin isospin modes excited by the12C(6Li,6He)12N reaction

First investigations of the reaction¹²C(⁶Li,⁶He)-¹²N(p)¹¹C were used to study spin-isospin strength in the nucleus¹²N at E_Li=156 MeV. While the⁶He ejectiles were detected at _He=0° using a magnetic spectrograph, the decay protons were analysed in a wide range of backward angles (100°_p<170°) with=" an=" arrangement=" of=" semiconductor=" strip=" detectors.=" singles=" spectra=" were=" extracted=" as=" well=" as=" coincident=" excitation=" strength=" for=" the=" decay=" to=" low=" lying=" levels=">¹¹C. For the decay to the¹¹C ground state angular correlations were evaluated for six different energy regions in¹²N^*.The authors wish to thank the staff of the Karlsruhe Cyclotron Laboratory for their cooperation. This work has been funded by the German Federal Minister for Research and Technology (BMFT) under contract no. 06ER262I and by the Kernforschungs-zentrum Karlsruhe.     

Interaction of 80 MeV12C with88Sr; Neutron transfer,inelastic scattering and spin alignment of the 2+ State of12C

Level structure of¹⁰²Cd has been studied via both¹⁰²In decay and nuclear reactions. Using⁹²Mo+¹⁴N at 86 MeV, the nucleus¹⁰²In was identified and its decay (T _1/2=24 ±4s) studied with the aid of on-line mass separation techniques. Levels of¹⁰²Cd were also populated with⁹²Mo+¹²C at 50 MeV and¹⁰²Pd+³He at 35 MeV reactions and investigated by means of standard in-beam techniques. A level scheme including states up to 4.5 MeV excitation energy is proposed and then discussed in the frame of available calculations.     

Correlated spin dynamics in 2-D quantum Heisenberg antiferromagnets from NMR relaxation in copper formiate tetradeuterate

Proton nuclear magnetic resonance (NMR) T₁ in a single crystal of copper formiate tetradeuterate is used to study the correlated Cu²⁺ spin dynamics and to derive the temperature behavior of the in-plane magnetic correlation length. The results are compared with the predictions of recent theoretical models for the spin dynamics in planar quantum Heisenberg antiferromagnets in a wide temperature range (from the Néel temperature up to a reduced temperatureT/J ～ 1.4, withJ in-plane exchange integral). In particular, it is shown that, in contrast to the predictions of the nonlinear σ model, no crossover to a quantum critical regime occurs and that the experimental findings are well reproduced by deriving the NMR relaxation rate in the framework of the standard mode-mode coupling theory.     

A model independent12C−12C potential

By using the modified Newton-Sabatier inversion method, a model independent local potential is presented which describes elastic scattering of two¹²C nuclei at c.m. energy ofE=14.1 MeV. Only the physical partial waves of even angular momenta are involved in the inversion procedure. The potential obtained is in general smooth and real in the outer (Coulombic) and inner (fusion) regions, between which it becomes complex showing characteristic oscillations responsible for reactions and nonlocal effects.     

Fusion, resonances and scattering in12C+12C reaction

The variation of fusion cross-section (σJ_fus) with energy in the¹²C+¹²C collision is linked to the underlying resonance phenomenon through the behavior of reaction cross-section (σ) of which σ_fus is taken as a part. The calculation of σ_fus is done through an energy-dependent imaginary potential in the optical model potential (OMP). Through dispersion relation, such an imaginary potential gives rise to energy-dependent real potential which is incorporated in the OMP. In our calculation, a form of potential for the nuclear part which has a soft repulsive in-built core is introduced based on similar works done earlier. The calculated results of σ_fus are used to explain the oscillatory structure, astrophysical S-factor and the decreasing trend at higher energies of the experimental σ_fus data in the case of¹²C+¹²C system with remarkable success. The potential used for fusion calculation is tested for fitting elastic scattering data at some energies and is found good in forward angles. Further improvement of the fitting of these data is obtained by incorporating a coupling potential in the surface region. About twenty resonances are observed in our calculation in the specific partial waves and some of them are found close to the experimentally identified resonances in¹²C+¹²C reaction. Thus, we provide an integrated and comprehensive analysis of fusion, resonance and scattering data in the best studied case of¹²C+¹²C reaction within the framework of optical potential model.     

Gammadecay of quasimolecular resonances in the12C+12C system

We have studied the heavy-ion radiative capture reaction¹²C(¹²C,γ)²⁴Mg forE _cm =4.7–6.0 MeV. Transitions to the ground-, first and unresolved second and third excited states in the final nucleus²⁴Mg have been observed with cross sections as low as 1 nb/sr. Forγ ₁ two strong resonance-like structures at 4.9 and 5.0 MeV were found correlated in energy with established 2⁺ resonances. Statistical model calculations cannot account for the observed yield. The branching ratioΓ _γ /Γ associated with theγ ₁ decay channel of the 5 MeV resonance was estimated to be 1.1·10^?5 yielding aγ-ray strength of 0.8 eV. The experimental result is in agreement with calculations based on the generator coordinate method where broad barrier resonances are viewed as short lived states of quasimolecular nature.     

The 12C + 12C sub-coulomb fusion cross section

The ¹²C + ¹²C fusion cross section has been studied over the energy range 2.46 ≦ E_c.m. ≦ 5.88 MeV. The yields of the γ-rays emitted from the first excited states of ²³Na and ²⁰Ne, following ²⁴Mg compound nucleus decay via proton- and α-emissions, were measured using a Ge(Li) detector. The fusion cross section was obtained by normalizing these yields to previously reported ¹²C(¹²C, p)²³Na and ¹²C(¹²C, α)²⁰Ne cross sections. The data indicate that the cross section below 3.5 MeV is dominated by two or more resonances, and that the average trend in this energy region does not show the absorption-under-the barrier features of the optical model. For astrophysical extrapolations to lower energies, the new results are consistent with the extrapolation proposed by Fowler, Caughlan and Zimmerman.     

Isospin mixing in 12C

Gamma-ray decays of the 12.71 and 16.11 MeV states of ¹²C are investigated in a coincidence study of the ¹⁰B(τ, pγ) reaction, and using the 163 keV ¹¹B(p, γ) resonance. This information together with existing data on M1 transitions and stripping and pickup spectroscopic factors is used to determine the isospin mixing between the 12.71 and 15.11 MeV levels. A charge dependent mixing matrix element of 110 ± 30 keV is deduced.     

Isospin mixing in 12C

We observe a yield to the 1⁺T = 1 level in ¹²C at 15.11 MeV in the isospin forbidden ¹²C(d, d') and ¹⁰B(α, d) reactions at about 1 % of the yield to the 1⁺T = 0 level at 12.71 MeV. Observed yields to the T = 12⁺ level at 16.11 MeV in both reactions at about half the yield to the 15.11 MeV level preclude attributing this observed isospin violation entirely to final state mixing. From the ratios of the spectroscopic factors for the 12.71 and 15.11 MeV levels in ¹²C and the ground state of ¹²B from the ¹³C(d, t) and ¹³C(d, ³He) reactions, we find a charge dependent matrix element between the 1⁺ states in ¹²C of 179 ± 75 keV.     

On spectral temperatures of negative pions produced in d 12C, 4He12C, and 12C12C collisions at 4.2 A GeV/c

The experimental transverse momentum distributions of negative pions produced in d ¹²C, ⁴He¹²C, and ¹²C¹²C collisions at 4.2 A GeV/c were analyzed in the framework of Hagedorn Thermodynamic Model. The spectral temperatures of π ^? mesons as well as their relative contributions to the total multiplicity of π ^? mesons were extracted from fitting the p _t spectra by two-temperature Hagedorn function. The results were compared systematically with the earlier results obtained from analysis of non-invariant center-of-mass energy spectra of negative pions produced in the analyzed collisions.     

High spin level structure in127Ba produced by the118Sn(12C, 3n) reaction

High-spin states in¹²⁷Ba have been produced by the reaction¹²⁸Sn(¹²C,3n)¹²⁷Ba and studied by in-beamγ-ray spectroscopic techniques. The odd-parity states form a level system based upon a 9/2^? state and generated by an odd neutron in theh _11/2 shell coupled to a triaxial core. Theg _7/2 shell is responsible for theΔ I=1, even-parity band.     

Deformation effects in the12C-12C system

The quantized adiabatic time dependent Hartree-Fock (quantized ATDHF) theory is applied to the¹²C-¹²C-system. Especially the intrinsic oblate ground state deformation of this nucleus is considered. For four relevant mutual orientations of the two nuclei the optimal, i.e. maximally decoupled collective paths, associated to relative motion, are evaluated by solving a coupled set of nonlinear differential equations on three dimensional grids in coordinate and momentum space. In a second step, the constituents of the corresponding collective Hamiltonian are calculated. Besides the collective potentials this includes the evaluation of the appropriate mass parameters, of the quantum corrections with regard to rotation, translation and collective relative motion and of the centrifugal potentials, all of which are shown to be important. By means of generalized WKB methods, subbarrier fusion cross sections are evaluated for different assumptions on the reaction process and compared with experimental data. Finally, the collective Hamiltonian is calculated for a head-on-collision of two¹²C-chains.