We perform calculations for the binding energies and low-lying levels of ${}^{10,11,12,13,14,15,16,17,18,19,20,21,22}C$ nuclei starting from the chiral $N3LO$ nucleon-nucleon potential within the framework of the Hybrid Multideterminant scheme. The calculations are restricted to 4 major harmonic oscillator shells, via the Lee-Suzuki renormalization scheme. The results are compared with the experimental data.
Reaction cross sections of carbon isotopes for proton scattering are calculated in large energy region. Density distributions of carbon isotopes are obtained from relativistic mean field results. Calculations are based on two procedures: the Glauber theory and relativistic impulse approximation, and results are compared with each other as well as with experimental data. A strong relationship between reaction cross section and root-mean-square radius is clearly shown for 12C using a model distribution.
We describe odd isotopes as formed of a core plus one neutron. We have calculated the modification of single neutron energies brought by couplings of the neutron with collective $2^+$ phonons in the cores. The results reproduce very well the inversion of $2s$ and $1d_{5/2}$ shells in carbon isotopes up to $^{19}$C while in oxygen isotopes the correction is also large but do not show any inversion in agreement with experiments. The calculated energies are close to the experimental ones in both series of isotopes except in $^{21}$C for the $2s$ state for which our coupling is too weak.
Shell model calculations are done to study the structure of neutron-rich carbon isotopes. For both even-A and odd-A neutron-rich carbon isotopes, the energy levels are strongly affected by the configuration mixing of valence neutrons. The calculated energy levels in the nucleus $^{17}$C are significantly improved compared with experimental values when the model space of the three valence neutrons is enlarged from pure $ν(0d_{5/2})^{3}$ configuration to full $sd$ space. We also investigate the configuration mixing effect on the $B(E2)$ values in even-even nuclei $^{16-20}$C.
We have investigated the ground-state properties of carbon isotopes in the framework of the relativistic mean-field (RMF) theory. RMF calculations have been performed with the non-linear scalar self-coupling of the $σ$ meson using an axially symmetric deformed configuration. We have also introduced the vector self-coupling of the $ω$ meson for the deformed mean-field calculations. The results show that the RMF predictions on radii and deformations are in good agreement with the available experimental data. It is shown that several carbon isotopes possess a highly deformed shape akin to a super…
We have studied neutron-rich carbon isotopes in terms of the shell model employing a realistic effective hamiltonian derived from the chiral N3LOW nucleon-nucleon potential. The single-particle energies and effective two-body interaction have been both determined within the framework of the time-dependent degenerate linked-diagram perturbation theory. The calculated results are in very good agreement with the available experimental data, providing a sound description of this isotopic chain toward the neutron dripline. The correct location of the dripline is reproduced.
We systematically study total reaction cross sections of carbon isotopes with N=6-16 on a proton target for wide range of incident energies, putting an emphasis on the difference from the case of a carbon target. The analysis includes the reaction cross sections of ^{19,20,22}C at 40 AMeV, the data of which have recently been measured at RIKEN. The Glauber theory is used to calculate the reaction cross sections. To describe the intrinsic structure of the carbon isotopes, we use a Slater determinant generated from a phenomenological mean-field potential, and construct the density distributions.…
The $α$ particle and $^6$He emissions from possible molecular states in beryllium and carbon isotopes have been studied using a mean-field-type cluster potential. Calculations can reproduce well the $α$-decay widths of excited states in $^{8}$Be, $^{12}$C and $^{20}$Ne. For the nucleus $^{10}$Be, we discussed the $α$-decay widths with different shapes or decay modes, in order to understand the very different decay widths of two excited states. The widths of $^{6}$He decay from $^{12}$Be and $α$ decays from $^{13,14}$C are predicted, which could be useful for future experiments.
We systematically analyze total reaction cross sections of carbon isotopes with N=6--16 on a $^{12}$C target for wide range of incident energy. The intrinsic structure of the carbon isotope is described by a Slater determinant generated from a phenomenological mean-field potential, which reasonably well reproduces the ground state properties for most of the even $N$ isotopes. We need separate studies not only for odd nuclei but also for $^{16}$C and $^{22}$C. The density of the carbon isotope is constructed by eliminating the effect of the center of mass motion. For the calculations of the cro…
Within the relativistic Hartree-Fock-Bogoliubov (RHFB) theory, the structure properties of Carbon isotopes are systematically studied. In order to reproduce the experiment data, we take the finite-range Gogny D1S with a strength factor $f$ as the pairing force. The self-consistent RHFB calculations with density-dependent meson-nucleon couplings indicate the single-neutron halo structures in both $^{17}$C and $^{19}$C, whereas the two-neutron halo in $^{22}$C is not well supported. It is also found that close to the neutron drip line there exists distinct odd-even staggering on neutron radii, w…
Full shell-model diagonalization has been performed to study the structure of neutron-rich nuclei around $^{20}$C. We investigate in detail the roles played by the different monopole components of the effective interaction in the evolution of the N=14 shell in C, N and O isotopes. It is found that the relevant neutron-neutron monopole terms, $V^{nn}_{d_{5/2}d_{5/2}}$ and $V^{nn}_{s_{1/2}s_{1/2}}$, contribute significantly to the reduction of the N=14 shell gap in C and N isotopes in comparison with that in O isotopes. The origin of this unexpectedly large effect, which is comparable with (some…
We study boron, carbon, nitrogen and oxygen isotopes with a newly constructed shell-model Hamiltonian developed from monopole-based-universal interaction ($V_{MU}$). The present Hamiltonian can reproduce well the ground-state energies, energy levels, electric quadrupole properties and spin properties of these nuclei in full psd model space including $(0-3)\hbarω$ excitations. Especially, it correctly describes the drip lines of carbon and oxygen isotopes and the spins of the ground states of $^{10}$B and $^{18}$N while some former interactions such as WBP and WBT fail. We point out that the in…
The one-neutron nuclear breakup from the Carbon isotopes $^{19}$C and $^{17}$C, is calculated as an example of application of the theory of transfer to the continuum reactions in the formulation which includes spin coupling. The effect of the energy sharing between the parallel and transverse neutron momentum distributions is taken into account thus resulting in a theory which is more general than sudden eikonal approaches. Both effects are necessary to understand properly the breakup from not too weakly bound $l_i>1$ orbitals. Breakup which leaves the core into an excited state below particle…
We studied firstly the ground state properties of C-isotopes using a deformed Hartree-Fock (HF)+ BCS model with Skyrme interactions. Shallow deformation minima are found in several neutron$-$rich C-isotopes. It is shown also that the deformation minima appear in both the oblate and the prolate sides in $^{17}$C and $^{19}$C having almost the same binding energies. Secondly, we carried out shell model calculations to study electromagnetic moments and electric dipole transitions of the C-isotopes. We point out the clear configuration dependence of the quadrupole and magnetic moments in the odd C…
Proton-rich nuclei possess unique properties in the nuclear chart. Due to the presence of both continuum coupling and Coulomb interaction, phenomena such as halos, Thomas-Ehrman shift, and proton emissions can occur. Experimental data are difficult to be obtained therein, so that theoretical calculations are needed to understand nuclei at drip-lines and guide experimentalists for that matter. In particular, the $^{16}$Ne and $^{18}$Mg isotopes are supposed to be one-proton and/or two-proton emitting nuclei, but associated experimental data are either incomplete or even unavailable. Consequentl…
Production cross sections of nitrogen isotopes from high-energy carbon isotopes on hydrogen and carbon targets have been measured for the first time for a wide range of isotopes. The fragment separator FRS at GSI was used to deliver C isotope beams. The cross sections of the production of N isotopes were determined by charge measurements of forward going fragments. The cross sections show a rapid increase with the number of neutrons in the projectile. Since the production of nitrogen is mostly due to charge exchange reactions below the proton separation energies, the present data suggests a co…
We derive and compute effective valence-space shell-model interactions from ab-initio coupled-cluster theory and apply them to open-shell and neutron-rich oxygen and carbon isotopes. Our shell-model interactions are based on nucleon-nucleon and three-nucleon forces from chiral effective-field theory. We compute the energies of ground and low-lying states, and find good agreement with experiment. In particular our calculations are consistent with the N=14, 16 shell closures in oxygen-22 and oxygen-24, while for carbon-20 the corresponding N=14 closure is weaker. We find good agreement between o…
The interplay between the formation of neutron skin and alpha cluster at the dilute surface of neutron-rich nuclei is one of the interesting subjects in the study of neutron-rich nuclei and nuclear clustering. A theoretical model has predicted that the growth of neutron skin will prevent the alpha clustering at the nuclear surface. Quite recently, this theoretical perspective; the suppression of alpha clustering by the neutron-skin formation was first confirmed experimentally in Sn isotopes as the reduction of the (p, p alpha) reaction cross-section. Motivated by the novel discovery, in this w…
We present an exploratory study of structure of 13C, 15C, 17C and 19C, showing that the simple one-quasiparticle projected BCS (PBCS) model is capable to account for several important properties of these nuclei. Next we discuss the importance of the Pauli Principle in the particle-core models of normal-parity states in 13C and 11Be. This is done by considering the pairing interaction between nucleons moving in an over-all deformed potential. To assess the importance of pairing correlations in these light nuclei we use both the simple BCS and the PBCS approximations. We show that the Pauli Prin…
Ground state properties of carbon isotopes, including root-mean-square radii, neutron separation energies, single particle spectra, and shapes are systematically studied with the deformed relativistic Hartree-Bogoliubov theory in continuum. The calculations with the effective interaction PK1 reproduce the available data reasonably well. The shell evolution in this isotopic chain is investigated by examining the single particle spectra. The inversion of neutron orbitals $ν2s_{1/2}$ and $ν1d_{5/2}$ compared with the order of neutron orbitals in stable nuclei is revealed in $^{15-20,22}\mathrm{C}…
At energies below the Coulomb barrier, the fusion excitation function for the $^{12}$C+$^{12}$C system shows prominent fine structures, whereas that for the $^{12}$C+$^{13}$C system behaves more smoothly as a function of energy. We demonstrate that these different behaviors can be simultaneously reproduced using an optical potential in which the strength of the imaginary part is proportional to the level density of each compound nucleus. We also discuss the oscillatory behavior of fusion excitation function for these systems observed at energies above the Coulomb barrier from a view point of q…
We compute the populations of isotopes of Boron, Carbon and Nitrogen measured experimentally in intermediate energy heavy ion collisions. A two component soluble statistical model is used to find the initial populations of different nuclei at a finite temperature. These initial populations are both in particle stable and particle unstable states. The particle unstable states then decay. The final populations after these decays are computed and compared with experimental data.
The properties of $\isotope[12]{C}$, $\isotope[16]{O}$, and $\isotope[20]{Ne}$ nuclei in strong magnetic fields $B\simeq 10^{17}\,$G are studied in the context of strongly magnetized neutron stars and white dwarfs. The SKY3D code is extended to incorporate the interaction of nucleons with the magnetic field and is utilized to solve the time-independent Hartree-Fock equations with a Skyrme interaction on a Cartesian three-dimensional grid. The numerical solutions demonstrate a number of phenomena, which include a splitting of the energy levels of spin-up and -down nucleons, spontaneous rearrang…
The absolute differential cross sections for small-angle proton elastic scattering off the nuclei $^{12,14-17}$C have been measured in inverse kinematics at energies near 700 MeV/u at GSI Darmstadt. The hydrogen-filled ionization chamber IKAR served simultaneously as a gas target and a detector for the recoil protons. The projectile scattering angles were measured with multi-wire tracking detectors. The radial nuclear matter density distributions and the root-mean-square nuclear matter radii were deduced from the measured cross sections using the Glauber multiple-scattering theory. A possible …
Fusion data for $^{13}$C+$^{13}$C, $^{12}$C+$^{13}$C and $^{12}$C+$^{12}$C are analyzed by coupled-channels calculations that are based on the M3Y+repulsion, double-folding potential. The fusion is determined by ingoing-wave-boundary conditions (IWBC) that are imposed at the minimum of the pocket in the entrance channel potential. Quadrupole and octupole transitions to low-lying states in projectile and target are included in the calculations, as well as mutual excitations of these states. The effect of one-neutron transfer is also considered but the effect is small in the measured energy regi…
The nuclear shell structure, which originates in the nearly independent motion of nucleons in an average potential, provides an important guide for our understanding of nuclear structure and the underlying nuclear forces. Its most remarkable fingerprint is the existence of the so-called `magic numbers' of protons and neutrons associated with extra stability. Although the introduction of a phenomenological spin-orbit (SO) coupling force in 1949 helped explain the nuclear magic numbers, its origins are still open questions. Here, we present experimental evidence for the smallest SO-originated ma…
Encouraged with the evidence for Z = 6 magic number in neutron-rich carbon isotopes, we have performed relativistic mean-field plus BCS calculations to investigate ground state properties of entire chains of isotopes(isotones) with Z(N) = 6 including even and odd mass nuclei. Our calculations include deformation, binding energy, separation energy, single particle energy, rms radii along with charge and neutron density profile etc., and are found in an excellent match with latest experimental results demonstrating Z = 6 as a strong magic number. N = 6 is also found to own similar kind of strong…
We present the first calculations to follow the evolution of all stable isotopes (and their abundant radioactive progenitors) in a finely zoned stellar model computed from the onset of central hydrogen burning through explosion as a Type II supernova. The calculations were performed for a 15 solar mass Pop I star using the most recently available set of experimental and theoretical nuclear data, revised opacity tables, and taking into account mass loss due to stellar winds. We find the approximately solar production of proton-rich isotopes above a mass number of A=120 due to the gamma-process.…
