Levels In 12C Research Articles

Triple α -particle resonances in the decay of hot nuclear systems * * Supported by the National Natural Science Foundation of China (1176014, 11605097, 11421505,11865010), the US Department of Energy (DE-FG02-93ER40773, NNSA DE-NA0003841 (CENTAUR)), and the Robert A. Welch Foundation (A-1266). This work was also supported by the Chinese Academy of Sciences (CAS) President’s International Fellowship Initiative (2015VWA070), Strategic Priority

The Efimov (Thomas) trimers in excited 12C nuclei, for which no observation exists yet, are discussed by means of analyzing the experimental data of 70(64)Zn(64Ni) + 70(64)Zn(64Ni) reactions at the beam energy of E/A = 35 MeV/nucleon. In heavy ion collisions, -particles interact with each other and can form complex systems such as 8Be and 12C. For the 3 -particle systems, multi-resonance processes give rise to excited levels of 12C. The interaction between any two of the 3 -particles provides events with one, two or three 8Be. Their interfering levels are clearly seen in the minimum relative energy distributions. Events with the three -particle relative energies consistent with the ground state of 8Be are observed with the decrease of the instrumental error for the reconstructed 7.458 MeV excitation level in 12C, which was suggested as the Efimov (Thomas) state.

A connection between γ-ray and parsec-scale radio flares in the blazar 3C 273

We present a comprehensive 5-43 GHz VLBA study of the blazar 3C 273 initiated after an onset of a strong $\gamma$-ray flare in this source. We have analyzed the kinematics of new-born components, light curves, and position of the apparent core to pinpoint the location of the $\gamma$-ray emission. Estimated location of the $\gamma$-ray emission zone is close to the jet apex, 2 pc to 7 pc upstream from the observed 7 mm core. This is supported by ejection of a new component. The apparent core position was found to be inversely proportional to frequency. The brightness temperature in the 7 mm core reached values up to at least $10^{13}$ K during the flare. This supports the dominance of particle energy density over that of magnetic field in the 7 mm core. Particle density increased during the radio flare at the apparent jet base, affecting synchrotron opacity. This manifested itself as an apparent core shuttle along the jet during the 7 mm flare. It is also shown that a region where optical depth decreases from $\tau\sim1$ to $\tau<<1$ spans over several parsecs along the jet. The jet bulk flow speed estimated at the level of 12c on the basis of time lags between 7 mm light curves of stationary jet features is 1.5 times higher than that derived from VLBI apparent kinematics analysis.

Particle gamma correlations in 12C measured with the CsI(Tl) based detector array CHIMERA

The gamma decay of the first excited 4.44MeV 2+level of 12C, populated by inelastic scattering of proton and 16O beams at various energies was studied in order to test γ-ray detection efficiency and the quality of angular distribution information given by the CsI(Tl) detectors of the 4π CHIMERA array. The γ-decay was measured in coincidence with ejectile scattered particles in an approximately 4π geometry allowing to extract the angular distribution in the reference frame of recoiling 12C target. The typical sin2(2θ) behavior of angular distribution was observed in the case of 16O beam. Besides that, for the proton beam, in order to explain the observed distribution, the addition of an incoherent flat contribution was required. This latter is the effect of proton spin flip events allowing the population of M=±1 magnetic substates, that is not possible in reactions induced by 16O beam. A comparison with previously collected data, obtained measuring only in and out of plane proton-γ-ray coincidences, confirms the good quality of the angular distribution information given by the apparatus. Possible applications with radioactive beams are outlined.

Testing effective nucleon-nucleon forces to describe diagonal spin-transfer coefficients for the scattering of polarized protons with the excitation of the 1+ levels in 12C

The diagonal coefficients of spin-transfer Dii in the small-angle inelastic scattering of polarized protons with the excitation of the two lowest 1+ levels in 12C are analyzed. The isoscalar (T = 0, E* = 12.71MeV) and isovector (T = 1, E* = 15.11 MeV) transitions are considered. The coefficients Dii are calculated within DWBA using different effective nucleon-nucleon (NN) interactions between an incident proton and the nucleons of the nucleus. We consider the Franey-Love interaction and the Geramb effective interactions based on the Paris NN potential, and also the effective NN potential based on the chiral perturbation theory, etc. The impact of the wave function antisymmetrization is studied from the coefficients Dii in a system that includes a projectile and nucleons of the nucleus, along with the impact of other effects.

Optimization of the imaginary time step evolution for the Dirac equation

Taking the single neutron levels of 12C in the Fermi sea as examples, the optimization of the imaginary time step (ITS) evolution with the box size and mesh size for the Dirac equation is investigated. For the weakly bound states, in order to reproduce the exact single-particle energies and wave functions, a relatively large box size is required. As long as the exact results can be reproduced, the ITS evolution with a smaller box size converges faster, while for both the weakly and deeply bound states, the ITS evolutions are less sensitive to the mesh size. Moreover, one can find a parabola relationship between the mesh size and the corresponding critical time step, i.e., the largest time step to guarantee the convergence, which suggests that the ITS evolution with a larger mesh size allows larger critical time step, and thus can converge faster to the exact result. These conclusions are very helpful for optimizing the evolution procedure in the future self-consistent calculations.

Convergence for Imaginary Time Step evolution in the Fermi and Dirac seas

The convergence for the Imaginary Time Step (ITS) evolution with time step is investigated by performing the ITS evolution for the Schrodinger-like equation and the charge-conjugate Schrodinger-like equation deduced from Dirac equation for the single proton levels of 12C in both the Fermi and Dirac seas. For the guaranteed convergence of the ITS evolution to the “exact” results, the time step should be smaller than a “critical” time step Δtc for a given single-particle level. The “critical” time step Δtc is more sensitive to the quantum numbers |κ| than to the energy of the single-particle level. For the single-particle levels with the same κ, their “critical” time steps are in the same order. For the single-particle levels with similar energy, a relatively small (large) “critical” time step for larger (smaller) |κ| is needed. These conclusions can be used in the future self-consistent calculation to optimize the evolution procedure.

Alpha-particle condensation in nuclei: Experimental problems

Recently, it was supposed the nα light nuclei may have structures resembling the diluted gas of α particles which could be considered as Bose-Einstein condensate (αBEC) in nuclear systems. At the present time, the only more or less definite candidate for an αBEC state predicted by theory is the second 0+ state of 12C (E = 7.65 MeV) located near the threshold 12C → 3α. We discuss several possible experimental approaches to study the properties of interest of the 7.65-MeV level of 12C. Among them are shift of the positions of the rainbow minima in the inelastic scattering to this level, extraction of the empirical inelastic form factor from the α and 3He scattering and its comparison with theoretical predictions, and getting information on the 8Be transfer reaction form factor. The conclusion was drawn that new measurements of 12C(α, α′) 12C(7.65) inelastic scattering at ∼120 MeV in the full angular range would be most adequate to solving the problem. The possibility of observation of αBEC effects in heavier nα nuclei is also discussed. In particular, 112Ba is of great interest owing to possible existence of an α-particle “halo” outside the Z = N = 50 core.

The three-body continuum Coulomb problem and the 3α structure of 12C

We introduce an approach, based on the coordinate space Faddeev equations, to solve the quantum mechanical three-body Coulomb problem in the continuum. We apply the approach to compute measured properties of the first two 0 + levels in 12C, including the width of the excited level, in a 3α-particle model. We use the two-body interaction which reproduces the low energy α-α scattering data and add a three-body force to account for the compound state admixture.

A deviation in internal pair conversion

The E1 e + e − decay of the 17.2 MeV level in 12C, and the M1 e + e − decay of the 17.6 MeV level in 8Be have been studied in a search for possible signals of short-lived neutral bosons with masses between 5 and 15 MeV/c 2. Whereas for the E1 decay at large correlation angles no deviation is found from internal pair conversion (IPC), surprisingly the M1 angular correlation deviates from IPC at the 4.5σ level.

Calculation of the Matrix Elements of 12C for the 15.1 MeV Level

We present here the result of the calculation on the ratio of |⟨1+||T1mag||0+⟩|2/|1/q⟨1+||T1mag||0+⟩|q=02 for the 15.1 MeV level in 12C. We use the wave function corresponding to the nucleons moving in a common harmonic potential plus a hard core.

Electronic stopping power for 7Li, 11B, 12C, 14N and 16O at energies 0.4 to 2.1 MeV/nucleon in Ta and Au, and for 12C at energies 0.4, 0.8 and 1.4 MeV/nucleon in 18 elemental solids

Stopping powers have been measured for 0.4 to 2.1 MeV/nucleon beams of 7Li, 11B, 12C, 14N and 16O in Au and of 7Li, 12C and 14N in Ta. The results are compared with the predictions of an empirical model. By application of the Doppler-shift attenuation method, the measured electronic stopping powers for 12C in Ta and Au are used to deduce the mean lifetime 58 ± 5 fs for the 4.439 MeV level in 12C. Deviations of the electronic stopping power from the predictions of the empirical model have been studied for 12C at energies 0.4, 0.8 and 1.4 MeV/nucleon in 18 Z = 14–82 elemental solids by application of the Doppler-shift attenuation method and the lifetime value of the 4.439 MeV level.

Excitation of the 15.11 MeV level in 12C by pion scattering

Experimental results on the (π,π') M1 transition to the 12C level at 15.11 MeV are interpreted by a DWIA calculation using nuclear transition densities obtained by fitting the (e,e') data. Ambiguities in (e,e') fits can be resolved through the (π,π') data.

Finite-nucleus treatment of the response to sigmaμτλprobes and pion-like excitations. II. The role of rho-meson exchange

For pt.I see ibid., vol.10, p.1347, 1984. The author presents an exact finite-nucleus study of the effect of the rho -meson-exchange piece of the particle-hole interaction on the response to spin-isospin-sensitive ( sigma mu tau lambda ) probes. He studies the nuclear response for various forms of the effective rho exchange interaction for a large range of momentum transfer (q approximately 0-600 MeV/c). The renormalisation of matrix elements of spin-isospin-sensitive probes ( sigma mu tau lambda ) is given for the JP=1+, T=1 level of 12C. The exact results are compared with calculations based on infinite nuclear matter with a constant density of rho =0.17 fm-3 and rho =0.07 fm-3. He also compares with local-density-approximation results using three different density distributions (square well, Fermi and modified harmonic oscillator). All these approximate calculations are found to be unsatisfactory in describing the finite-nucleus features and the effect of the rho meson itself.

Alpha-cluster states in16O based on a12C(O2+) core

A 12C- alpha model for rotational bands in 16O based on the 12C core in its ground and first excited states has been extended to include the 12C(O2+) level at 7.65 MeV. A double folding prescription has been used to determine the potential matrix with transition densities taken from a 3 alpha RGM calculation of 12C. The coupled-channels problem including the 01+, 21+ and 02+ levels of 12C has been solved and positive- and negative-parity bands based on the 12C(02+) state have been identified with known 16O excited states. The calculation also confirms earlier assignments of 16O levels based on 12C(01+ and 21+).

Finite-nucleus treatment of the response to σμτλprobes and pion-like excitations

Presents an exact finite-nucleus treatment of the response to spin-isospin-sensitive probes. Since linear momentum is not a good quantum number here, the author adopts a formalism suggested by Toki and Weise (1980) which incorporates an expansion in partial waves of good nuclear total angular momentum. The author starts from the pion self-energy Pi , which is non-local in momentum space. Iterations of this quantity lead to the response function R, obtained by solving a matrix integral equation exactly (using numerical methods). R is used to renormalise the matrix element of a spin-isospin ( sigma mu tau lambda ) probe and find large effects for intermediate and large momenta (q>mpi ). These effects are unimportant for very low momenta. He also finds very important effects of the non-locality in momentum space. The formalism is applied to the JP=1+, T=1 level in 12C. The results are compared with approximations in current use: the infinite nuclear matter approximation, the local density approximation and the approximations of Toki and Weise. All these approximations are found to be unsatisfactory, especially for q to 0 and near the critical momentum region (q approximately (2-3)mpi ).

Electron scattering studies of magnetic isovector transitions in 12C at high momentum transfer

The inelastic electron scattering cross sections for the M1 transition to the 15.11 MeV (1 +, T = 1) level and for the M2 transition to the 16.58 MeV (2 −, T = 1) level in 12C have been measured in the momentum transfer region q = 0.4–3.0 fm −1, with emphasis on precise data at high momentum transfers. Additionally, a broad state near 15.4 MeV excitation has been observed and its excitation energy and natural width have been established as 15.44 ± 0.04 MeV and 1.5 ± 0.2 MeV, respectively. The Fourier-Bessel technique for determining the Mλ transition current density has been applied to the M1 and M2 transitions. Particular attention has been paid to the Coulomb corrections required to deduce the PWBA form factors. The M1 radiative width is Γ γ0 = 38.5 ± 0.8 eV.

Excitation of two nucleons into the continuum as a doorway process for bound-pion absorption by nuclei

The problem of bound-pion absorption by nuclei has been studied in a semimicroscopic way. Calculations of the widths of the 1s, 2p and 3d levels in 12C, 14N, 16-18O, 19F, 20Ne, 23Na, 24-26Mg, 27Al, 28Si, 31P, 32S, 35Cl, 39K, 40Ar, 40-48Ca, 46-50Ti, 51V and 52Cr and the 4f level in 209Bi pi --atoms based on the nuclear self-consistent theory of Birbrair et al. (1978) and Alkhazov et al. (1978) are performed assuming that the 'two-nucleon' mechanism is the doorway process for nuclear pion absorption (Birbrair and Kalashnikov). Both P and S absorption mechanisms together with their interference are included here. This enables us to calculate the widths of the 1s levels where S absorption dominates. The results are in good agreement with experiment.

A determination of the spin of the hypernucleus 12ΛB : (II). A complete analysis

The probability distribution calculated for the decay sequence 12 ΛB(g.s.) → 12C ∗π − → αααπ − passing through the ( J P N) = (2 +, 1) intermediate state 12C ∗ (16.11 MeV) is cast in a symmetrical form and used to calculate the likelihood for J = 1 relative to J = 2 for 12 Λ B(g.s.) on the basis of the 85 examples available for this decay process. This procedure has optimum sensitivity, is free from the uncertainties of the comparisons previously made using only projected angular distributions, and strongly indicates that J P = 1 − holds for 12 ΛB(g.s.). An appendix points out that all the data for the decay sequence passing through the ( J P N, T) = (1 +, 0) level of 12C ∗ is well fitted for J = 1 if the J = 1 → J n = 1 transition amplitude a s1 takes a value in the range a s1/ s = 0.08 to 0.09.

Photoformation of ? mesons in carbon

A calculation is made of the total cross section of the12C(γ,π−)12N reaction as a function of the energy of theγ quanta, by means of the technique of nonrelativistic diagrams, which permitted the differential cross sections of this reaction and the electroexcitation of the 15.11-MeV level in12C to be directly related. For the amplitude of the photocreation ofπ-mesons in the nucleons we take the relativistic- and gradient-invariant expression, which follows from the model of the algebra of currents with physical pions. An analysis is made of the effect of the contributions of Δ(1232) resonance and vector mesons to the amplitude, and also the different choice of the reaction kinematics in the nucleon.

Lithium-induced reactions on carbon at 48 MeV

Angular distributions have been measured for transitions to states in 13N and 13C populated by the 12C( 7Li, 6He) 13N and the 12C( 7Li, 6Li) 13C reactions at E = 48 MeV. Elastic scattering of 7Li at 48 MeV on 12C and 12Li on 13C at 40 MeV were measured. Optical-model parameters extracted from fits to these data were used in the DWBA analysis of inelastic scattering to levels in 12C and 7Li and for particle transfers to levels in 13N and 13C. The calculations generally reproduced the data, except for the 3.09 MeV 1 2 + level in 13C, which was seriously out of phase. Spectroscopic factors were obtained from the transfer data and deformation lengths from the inelastic scattering to the 4.44 MeV 2 +, and the 9.64 MeV 3 − levels in 12C and to the 0.48 MeV 1 2 − level in 7Li.