Proton radii of 12−19 C densities derived from first accurate charge changing cross section measurements at 900A MeV with a carbon target are reported. A thick neutron surface evolves from ∼ 0.5 fm in 15 C to ∼ 1 fm in 19 C. The halo radius in 19 C is found to be 6.4±0.7 fm as large as 11 Li. Ab initio calculations based on chiral nucleon-nucleon and three-nucleon forces reproduce well the radii.
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 in explaining the magic numbers, its origins are still open questions. Here, we present experimental evidence for the smallest SO-originated magic number (subshell closure) at the proton number six in 13–20C obtained from systematic analysis of point-proton distribution radii, electromagnetic transition rates and atomic masses of light nuclei. Performing ab initio calculations on 14,15C, we show that the observed proton distribution radii and subshell closure can be explained by the state-of-the-art nuclear theory with chiral nucleon–nucleon and three-nucleon forces, which are rooted in the quantum chromodynamics.
Proton inelastic scattering off a neutron halo nucleus, 11 Li, has been studied in inverse kinematics at the IRIS facility at TRIUMF. The aim was to establish a soft dipole resonance and to obtain its dipole strength. Using a high quality 66 MeV 11 Li beam, a strongly populated excited state in 11 Li was observed at E x =0.80 ± 0.02 MeV with a width of Γ = 1.15 ± 0.06 MeV. A DWBA (distorted-wave Born approximation) analysis of the measured differential cross section with isoscalar macroscopic form factors leads to conclude that this observed state is excited in an electric dipole (E1) transition. Under the assumption of isoscalar E1 transition, the strength is evaluated to be ex- * Corresponding author.
A dipole resonance of $^{11}$Li is found by a $^9$Li + $n$ + $n$ three-body model analysis with the complex-scaling method. The resonance can be interpreted as a bound state in the $^{10}$Li + $n$ system, i.e., a Feshbach resonance in the $^9$Li + $n$ + $n$ system. As a characteristic feature of the Feshbach resonance of $^{11}$Li, the $^{10}$Li + $n$ threshold is open above the $^{9}$Li + $n$ + $n$ one, which reflects a distinctive property of the Borromean system. A microscopic four-body reaction calculation for the $^{11}$Li($p$,$p'$) reaction at 6 MeV/nucleon is performed by taking into account the resonant and nonresonant continuum states of the three-body system. The calculation of angular distributions of the elastic and inelastic scattering as well as the energy spectrum reproduced a recent experimental result. Furthermore, the $E1$ strength distribution from a Coulomb dissociation experiment was also reproduced in this framework. This means that the existence of the Borromean Feshbach resonance may consistently answer a long-standing open question of an excited state of $^{11}$Li.
The first determination of radii of point proton distribution (proton radii) of (12-17)B from charge-changing cross sections (σ(CC)) measurements at the FRS, GSI, Darmstadt is reported. The proton radii are deduced from a finite-range Glauber model analysis of the σ(CC). The radii show an increase from ¹³B to ¹⁷B and are consistent with predictions from the antisymmetrized molecular dynamics model for the neutron-rich nuclei. The measurements show the existence of a thick neutron surface with neutron-proton radius difference of 0.51(0.11) fm in ¹⁷B.
Charge-changing cross sections at high energies are expected to provide useful information on nuclear charge radii. No reliable theory to calculate the cross section has yet been available. We develop a formula using Glauber and eikonal approximations and test its validity with recent new data on carbon isotopes measured at around 900A MeV. We first confirm that our theory reproduces the cross sections of 12,13,14 C + 12 C consistently with the known charge radii. Next we show that the cross sections of 12−19 C on a proton target are all well reproduced provided the role of neutrons is accounted for. We also discuss the energy dependence of the charge-changing cross sections. DOI: 10.1103/PhysRevC.94.011602 A study of unstable nuclei is one of the fields that have been promoted most intensively. Charge distribution or charge radius, among others, is one of the fundamental quantities to characterize the ground-state properties of nuclei. Electron scattering measurement is ideal for probing the distribution but so far not applicable to short-lived unstable nuclei. We note, however, that the electron-ion scattering experiment will be available in the near future, as planned in Refs. [1,2]. Isotope shift measurement allows us to precisely deduce the charge (proton) radius for some limited unstable nuclei. The measurement of the charge-changing cross section (CCCS) newly appears as a potential means to extract the proton radius since it has the great advantage that the cross section can be measured for almost all nuclei by the same setup as the total reaction or interaction cross section that plays a decisive role in determining the nuclear matter radius [3]. In fact the CCCS has recently been measured to get information on the proton radii of light unstable nuclei [4][5][6][7][8].A theoretical tool for extracting the matter radius from the high-energy total reaction cross sections is well established with the help of Glauber theory [9]. See Refs. [10,11] for a useful application to determining both proton and neutron radii. The reaction mechanism for the charge-changing reaction (CCR) is, however, not well understood and energydependent adjustments are introduced to analyze the CCCS data [4][5][6]12], which makes it difficult to obtain proton radii from the measurement. The purpose of this paper is to show * Present address: Department of Physics, Niigata University, Niigata 950-2181, Japan.that recent new CCCS data of carbon isotopes on both 12 C [13] and proton targets are all satisfactorily reproduced in the framework of the Glauber and eikonal models. The role of neutrons becomes evident for the proton target. This is an important step toward constructing a method of analyzing CCCSs with the use of no adjustable parameters.The total reaction cross section can be calculated bywhere b is a two-dimensional (2D) impact parameter vector perpendicular to the beam (z) direction, |0 = |0 P 0 T is a product of the projectile and target ground-state wave functions, and, e.g., χ p is a sum of the phase-shift functions χ...
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