One-neutron removal reactions on light neutron-rich nuclei

A study of high-energy $\left(43–68\text{MeV}∕\text{nucleon}\right)$ one-neutron removal reactions on a range of neutron-rich $psd$-shell nuclei $\left(Z=5–9,A=12–25\right)$ has been undertaken. The inclusive longitudinal and transverse momentum distributions for the core fragments together with the cross sections have been measured for breakup on a carbon target. Momentum distributions for reactions on tantalum were also measured for a subset of nuclei. An extended version of the Glauber model incorporating second-order noneikonal corrections to the Jeukenne, Lejeune, and Mahaux parametrization of the optical potential has been used to describe the nuclear breakup, while the Coulomb dissociation is treated within first-order perturbation theory. The projectile structure has been taken into account via shell-model calculations employing the $psd$ interaction of Warburton and Brown. Both the longitudinal and transverse momentum distributions together with the integrated cross sections were well reproduced by these calculations and spin-parity assignments are thus proposed for ${}^{15}\mathrm{B},{}^{17}\mathrm{C},{}^{19–21}\mathrm{N},{}^{21,23}\mathrm{O},{}^{23–25}\mathrm{F}$. In addition to the large spectroscopic amplitudes for the $\nu 2s_{1∕2}$ intruder configuration in the $N=9$ isotones, ${}^{14}\mathrm{B}$ and ${}^{15}\mathrm{C}$, significant $\nu 2s_{1∕2}^2$ admixtures appear to occur in the ground state of the neighboring $N=10$ nuclei ${}^{15}\mathrm{B}$ and ${}^{16}\mathrm{C}$. Similarly, crossing the $N=14$ subshell, the occupation of the $\nu 2s_{1∕2}$ orbital is observed for ${}^{23}\mathrm{O}$, ${}^{24,25}\mathrm{F}$. Recent claims of a modified shell structure for ${}^{23}\mathrm{O}$ are investigated and the original suggestion of a ground state $J^{\pi }=1∕2^{+}$ is confirmed. Analysis of the longitudinal and transverse momentum distributions reveals that both carry spectroscopic information, often of a complementary nature. The general utility of high-energy nucleon removal reactions as a spectroscopic tool is also examined.

Figure 1

Comparison of the core fragment longitudinal momentum $\left(p_z\right)$ distributions obtained using a carbon target and the Glauber model calculations (solid line).

Figure 2

Comparison of the widths (FWHM) of the longitudinal (filled circles) and transverse (open circles) core fragment momentum distributions for reactions on the carbon target.

Figure 3

Experimental one-neutron removal cross sections (filled circles) compared to the results of the Glauber calculations—open circle, total cross section; open triangle, absorption; and open diamond, diffraction (see text for details). The points are connected by lines to guide the eye.

Figure 4

Comparison of the core fragment transverse momentum $\left(p_x\right)$ distributions obtained using a carbon target and the Glauber model calculations (solid line).

Figure 5

Comparison of the core fragment longitudinal momentum $\left(p_z\right)$ distributions obtained using a tantalum target and the Glauber model calculations (solid line).

Figure 6

Coordinate system used in the Glauber model calculations.

Figure 7

rms matter radii extracted from $\text{Hartree-Fock}+\text{BCS}$ calculations of single-particle densities (black line), compared with experimental values from Liatard et al. [70] (filled circles), Ozawa et al. [74] (open circles), and Tanihata et al. [75] (open diamonds). The relativistic mean field calculations of Ren et al. [71, 72, 73] are indicated by the dashed lines.

Figure 8

$S$ matrix, absorption profiles, and transmission coefficients for $n\text{−}{}^{12}\mathrm{C}$ (left panels) and ${}^{14}\mathrm{C}-{}^{12}\mathrm{C}$ (right panels) interactions at $30\text{MeV}∕\text{nucleon}$ obtained from the JLM folding model calculations. Results using the lowest order of the eikonal approximation are shown as a dotted line, those using the first-order corrections by the dot-dashed line, and those using second-order corrections by the solid line. For ${}^{14}\mathrm{C}+{}^{12}\mathrm{C}$ the calculations converge with the use of first-order corrections.

Figure 9

The effect of noneikonal corrections on the distortion kernels (see the text for definitions) as a function of impact parameter $s$, for neutron absorption and diffraction, core $\left({}^{14}\mathrm{C}\right)$ absorption and for absorption of both the core and neutron by ${}^{12}\mathrm{C}$ at $30\text{MeV}∕\text{nucleon}$. Dotted lines: lowest order eikonal approximation. Dashed-dotted lines: first-order noneikonal corrections included. Solid line: second-order corrections included.

Figure 10

Elastic (dotted), reaction (dash-dotted), and total (solid line) cross sections for reactions of neutrons on Be, C, Si, and Ta targets as a function of incident energy. The calculations were performed using JLM microscopic potentials in the eikonal approximation. Noneikonal corrections up to second order were included and the effects on the total cross section are shown for Be, C, and Si targets by the solid lines (the calculations employing the second-order corrections provide the best agreement with the data). For the Ta target, the eikonal series does not converge in the range of energies shown. The experimental data for the total, elastic, and reaction cross sections (open and closed circles and open squares) were taken from Refs. 77, 78.

Figure 11

Selected examples (see text) of the core fragment longitudinal momentum distributions obtained using the carbon target showing the contributions from the different reaction mechanisms. The calculated distributions (thick solid lines) include the absorption (thin solid lines), diffraction (dashed), and Coulomb (dash-dotted) components.

Figure 12

Calculated absorption (solid lines) and diffraction (dashed lines) cross sections vs binding energy for $s$- and $d$-wave states of an $A=17$ system at $50\text{MeV}∕\text{nucleon}$ on a carbon target using the JLM interaction and various orders of eikonal theory.

Figure 13

Ratio of experimental to theoretical cross sections $\left(R_s\right)$ as a function of projectile mass number for the data obtained with the carbon target. The dotted line indicates the mean value and the shaded band the $1\sigma$ variance.

Figure 14

Test case calculations of the longitudinal $\left(k_z\right)$ and transverse $\left(k_x\right)$ core fragment momentum distributions for one-neutron removal by a carbon target at $50\text{MeV}∕\text{nucleon}$ assuming an $s$-, $p$-, or $d$-wave state in an $A=14$ system with $S_n=1\text{MeV}$. The total (solid line), absorption (dashed), diffraction (dash-dotted), and Coulomb (dotted) components are indicated.

Figure 15

Correlations between the longitudinal and transverse ${}^{14}\mathrm{C}$ core fragment momenta for one-neutron removal from ${}^{15}\mathrm{C}$ by the carbon target.

Figure 16

Core fragment transverse momentum distributions for one-neutron removal from ${}^{15}\mathrm{C}$ by the tantalum target (filled circles). Dashed line: calculated transverse momentum distribution for Coulomb induced breakup. Solid line: same calculation after convolution with the orbital deflection in the Coulomb field of the target (see text for details).

Figure 17

Examples of the core fragment longitudinal momentum distributions for reactions on the Ta target. The filled circles represent the data. To aid in the comparison the calculated distributions for the total (solid lines), nuclear (dotted), and Coulomb dissociation (dashed line) are normalized to the data.

Figure 18

Comparison of the measured core fragment longitudinal momentum distributions (from reactions on the carbon target) with those predicted for different projectile ground-state spin-parity assignments. The favored assignments are displayed as solid lines (see text).

Figure 19

Comparison of the measured ${}^{16}\mathrm{C}$ core fragment transverse momentum distribution for reactions of ${}^{17}\mathrm{C}$ on the carbon target with the distributions calculated for the three possible ground-state spin-parity assignments.