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.     

Influence of strongly coupled inelastic excitations on the optical potential for12C+12C

The contributions of some of the strongly coupled collective excitations in¹²C+¹²C to the heavy ion optical potential have been explicitly obtained by calculating the exact Green's function for this problem. The resulting nonlocal heavy ion potential and the trivially equivalent local potential are calculated and theirJ- andE-dependence are discussed. It is shown that the strong direct excitations contribute significantly to the absorptive part of the heavy ion potential in the surface region.     

Time-dependent Hartree-Fock calculation of 12C + 12C with a realistic potential

We have used a realistic single-panicle K-matrix model to compute the head-on scattering of ¹²C + ¹²C at incident projectile lab energies of 3.2, 6.4, 12.8, 19.2, 25.6, 32, 51.2 and 64 $\text{MeV}\text{nucleon}$, above the Coulomb barrier, in the time-dependent Hartree-Fock approximation. Direct and exchange Coulomb forces as well as spin-orbit forces are included. A large deformed harmonic oscillator basis is used. Spatial density and current distributions at various times are shown. The outgoing energy is found to be E₀ = 0.8E_in?28 (MeV), in the c.m. system. Fusion and fully relaxed scattering are observed at low energy. Some compression is seen at higher energies but no shock waves can be detected. Consequences for heavy-ion reactions are discussed.     

Nuclear molecular resonances in α+12C and α+16O systems

The nuclear molecular resonances observed in α+¹²C and α+¹⁶O systems are described in a diatomic-like molecular picture using a Morse-type bonding potential. The depths of the bonding potentials are found to be 11.5 MeV and 11 MeV respectively, with long range of about 15 fm. Both the bound and resonance states of these potentials are calculated which compare quite well with the observed states. The diatomic-like rotational and vibrational picture of the quasi-molecular states proposed earlier for¹²C+¹²C system system is found to be quite valid for α+¹²C and α+¹⁶O systems. In these two systems, the rotational vibrational characteristics are equally well pronounced as in the¹²C+¹²C system.     

Spins of resonances in the 12C + 16O system

The spins of resonances appearing at 22 MeV c.m. entrance channel energy in the ¹²C + ¹⁶O system are determined. Several inelastic transitions are used and a value of J^π = 15^? is deduced. This value disagrees with a previous J^π = 14⁺ assignment based on elastic scattering, but agrees with the J^π = 15^? value predicted at this energy by a recent microscopic calculation of ¹²C + ¹⁶O scattering.     

Dynamic polarization potential of 12C+12C system at molecular-resonance energies

The nuclear reaction dynamics leading to the formation of recently discovered resonance in the mutual-0₂ ⁺ channel of the ¹²C+¹²C inelastic scattering around E _c.m.≃ 32 MeV is studied in terms of the dynamic polarization potential (DPP) induced by the channel coupling among various excited states in ¹²C. The microscopic 3α cluster-model wave functions are used to generate the ¹²C−¹²C diagonal and coupling potentials in the double-folding model. It is found that DPP for the 0₂ ⁺+ 0₂ ⁺ channel is an unusually strong attractive potential which even exceeds the zeroth-order folding-model potential of this channel around the nuclear surface region and that the strong coupling between the 0₂ ⁺ and 2₂ ⁺ states is predominantly responsible for the unusual DPP in this channel. The effective potential, the sum of the original folding-model potential and the attractive DPP, is found to generates resonance states in the same energy region as that of the resonance states generated by the original folding-model potential but the former states are found to be higher-nodal states having four additional radial nodes. Similar but more moderate property of DPP is also found in the entrance (elastic) channel. These results suggest that the reaction dynamics of generating the resonance in the ¹²C(0₂ ⁺) +¹²C(0₂ ⁺) channel may rather differ from that of the simple crossing of the zeroth-order molecular band generated by the potentials in the entrance and exit channels suggested by the standard band-crossing model. Received: 17 December 1998 / Revised version: 1 March 1999     

S+C band optical amplification in Er3+-Tm3+ co-doped fiber

A new type of optical amplifier based on co-doping erbium in thulium doped fiber is proposed to realize S+C band gain by dual-wavelength (800+1410 nm) pumping scheme which is obtainable from laser diode.A novel model is established for the co-doped fiber considering the Er3+ to Tm3+ energy transfer process.Using appropriate fiber parameters and energy transfer parameters, the coupled rate equations are analyzed and solved; the concentrations of Er3+ and Tm3+ and fiber length were optimized to get more uniform gain. The results predicted that the S+C band gain can be achieved at the same time by co-doping erbium in thulium doped fluoride fiber.     

Optical potential for 12C + 28Si scattering

¹²C + ²⁸Si elastic scattering angular distributions are smooth functions, relatively easily fit by optical potential predictions, at laboratory bombarding energies, E_1ab, within ≈ 10 MeV of the Coulomb barrier (i.e. up to E_1ab ≈ 27 MeV). Between E_1ab = 27 and 36 MeV the angular distributions show pronounced oscillatory structure which is not easily fit with an optical potential. No optical potential has been found to give a very good account of all the angular distributions simultaneously; the best simultaneous fit to all the data was achieved with a surface-transparent potential whose real and imaginary well depths are energy dependent.     

Decay of giant resonances in12C nucleus

Decay properties of (J ^– T= 1) resonances are calculated on the basis of the wave functions of the shell model with intermediate coupling. The results are compared with experimental data on the photodisintegration and radiative capture of pions.Submitted to the symposium Mesons and Light Nuclei, Liblice, Czechoslovakia, June 1981.     

Exploration of resonances by using complex momentum representation

Resonance research is a hot topic in nuclear physics,and many methods have been developed for resonances.In this paper,we explore resonances by solving the Schrodinger equation in complex momentum representation,in which the bound states and resonant states are separated completely from the continuum and exposed clearly in the complex momentum plane.We have checked the convergence of the calculations on the grid numbers of the Gauss-Hermite quadrature and the Gauss-Legendre quadrature,and the dependence on the contour of momentum integration.Satisfactory results are obtained.~(17)O is chosen as an example,and we have calculated the bound and resonant states to be in excellent agreement with those calculated in the coordinate representation.     

Inclusion of the Δ resonance in the optical potential between two nuclei and its application to medium energy12C-12C scattering

An energy dependent complex optical potential between two nuclei is calculated from the potential energy density for two colliding nuclear matters generated by solving the Bethe-Goldstone equation in whichNΔ and ΔΔ channels are explicitly coupled to theNN channel. By adding the contributions from the third and fourth order ring diagrams and the relativistic correction to the calculated potential energy density, the saturation property of a nuclear matter is reasonably well reproduced. This is used together with the kinetic energy density to calculate the optical potential for the¹²C+¹²C system in the energy density formalism with the local density approximation. The surface correction term and the symmetry energy term in the energy density functional are determined to reproduce the observed binding energy and the rms radius of¹²C. Using this potential, the differential cross sections for elastic¹²C-¹²C scattering atE _lab=1440 and 2400 MeV are calculated and compared with recent experimental data.     

Energy dependence of heavy ion collisions 4He + 12C and 12C + 12C elastic scattering

We have studied the transparency of heavy ion collisions at high energies by using Glauber's multiple scattering theory. The good agreement between our calculation and the existing data available strongly emphasizes the dominance of the nucleon-nucleon interaction in nucleus-nucleus collisions at high energies.     

High speed optical sampling covering C band and L band using CPPLN waveguide

Two means of high speed optical sampling covering C band and L band based on sum frequency generation (SFG) in chirped periodically poled LiNbO₃(CPPLN) waveguide are studied in this paper. For the first method, arbitrary waveband inside C and L band can be sampled by tuning pump wavelength and the bandwidth is controllable by choosing suitable waveguide length and chirped coefficient of CPPLN waveguide. For another, the broad bandwidth covering C band and L band can be obtained with a fixed pump. The numerical simulations based on coupled-wave equations are carried out. The NRZ sequences of 10 Gb/s and 640 Gb/s transmission rate are sampled in simulation. Distinct eye diagrams and quality factors (Q) are obtained by software-synchronized algorithm. The results show that the two means of the optical sampling both can cover C band and L band. SFG in CPPLN waveguide used for optical sampling system has a broad bandwidth and more flexible selectivity.     

Rotational analysis of a vibronic band of gaseous CeF

Rotational analysis of an absorption band at 5679.4 Å leads to the following estimates of constants for the lower state, which is probably the ground state: B₀ = 0.240182(90) cm^?, ω = 589(13) cm^?1, and $\text{r}{}_0\text{= 2.0484(4)}\text{A}\text{?}$, where the values in parentheses are of 2σ.     

Rotational control within optical tweezers by use of a rotating aperture

We demonstrate a simplified method of rotational control of objects trapped within optical tweezers that does not require high-order modes, interferometric precision, or computer-controlled optical modulators. Inserting a rectangular aperture into the optical beam results in a focused spot that also has rectangular symmetry. We show that an asymmetric object trapped in the beam has its angular orientation fixed such that rotation of the aperture results in a direct rotation of the particle.     

Resonant Structure Described by a Deep Folded Potential for the 12C+12C Scattering at Lower-Energy Region

Based on the analyses of the elastic angular distributions,an energy-dependent folding potential for the 12C+12C system is established.This potential has a deep real part,and can reasonably well describe the resonant structure in the 12C+12C elastic scattering in the low-energy region of 10 ～ 70 MeV.     

Low energy spectrum and giant multipole resonances of12C (I)

In a consistent shell model approach excitation energies and electromagnetic transitions are calculated for the low energy part of the¹²C spectrum up to the giant resonance region within a (1p1h+2p2h) configuration space. Comparison with available experimental data shows that almost the complete spectrum up to 40MeV can be described consistently. Thereby it is found that whereas the low lying collective states remain nearly unchanged by the inclusion of (2p2h) configurations, the spreading widths of all (2?ω) giant resonances are influenced drastically. For serious discrepancies in a few levels (4p4h) configurations or mesonic and baryonic degrees of freedom might be responsible.