Parameter-free calculation of charge-changing cross sections at high energy

Abstract

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...

Neutron skins as laboratory constraints on properties of neutron stars and on what we can learn from heavy ion fragmentation reactions

“…Similar studies to access information on the neutron skin in nuclei using the Glauber theory for high energy scattering have been published in, e.g., Refs. [29][30][31][32].…”

Properties of exotic nuclei and their linkage to the nucleonic interaction

“…The point (ii), which was given in Ref. 69, has been proven in more general cases 164 that the tensor force effects are canceled in the spin-saturated systems. As shown in Fig.…”

“…For the same reason, the spherical GEM bases are applicable to deformed nuclei without serious loss of precision, unless the deformation is too strong, as have been shown for axially deformed cases. 159,[164][165][166] Let us here assume the rotational symmetry with respect to the intrinsic z-axis, the parity conservation, the T -symmetry, and the symmetry with respect to the rotation around the y-axis by the angle π (i.e. the R-symmetry).…”

“…The tensor force does not influence the w.f. 's significantly, 164 and its effects are represented perturbatively by E (TN) defined in Eq. (35).…”

“…From the comparison between E(q 0 ) and E − E (TN) (q 0 ), the following conclusions are addressed as tensor-force effects, 164 in addition to those listed in Sec. 5.2.…”