Coulomb dissociation of ${}^{15}\mathrm{C}$ and radiative neutron capture on ${}^{14}\mathrm{C}$

The semiclassical, dynamical description of diffraction dissociation of weakly bound nuclei is applied to analyze the decay-energy spectra of ${}^{15}\mathrm{C}$ that have been measured at 68 MeV/nucleon on a Pb target. The optical potentials that are used to describe the nuclear interaction of ${}^{15}\mathrm{C}$ with the target nucleus are realistic because the fits to the two measured spectra, one with a small and one with a very large acceptance angle, are consistent and of similar quality. The cross section for the radiative neutron capture on ${}^{14}\mathrm{C}$ to the ${1/2}^{+}$ ground state of ${}^{15}\mathrm{C}$ is deduced from the analysis. When combined with an estimated contribution from the capture to the ${5/2}^{+}$ excited state of ${}^{15}\mathrm{C}$, an excellent agreement with a recent direct capture measurement is achieved.

Figure 1

The calculated dipole and quadrupole responses of ${}^{15}\mathrm{C}$ shown as functions of the relative energy $E_{\mathrm{rel}}$ of the neutron and the ${}^{14}\mathrm{C}$ fragment in the final state.

Figure 2

Coulomb dissociation cross sections for ${}^{15}\mathrm{C}$ on a Pb target as functions of the beam energy. The results of first-order dipole excitations are shown for straight-line, corrected straight-line ($b_{\mathrm{eff}}=b+\pi a/2$), and exact Coulomb trajectories. Dipole excitations up to $E_{\mathrm{rel}}=4$ MeV are included, and the distance of closest approach is larger than $R_1+R_2=1.2(A^{1/3}+A_2^{1/3})$.

Figure 3

The diffraction dissociation probability $P_{\mathrm{diff}}(b)$ for ${}^{15}\mathrm{C}$ on a Pb target at 68 MeV/nucleon (solid red curve) shown as a function of the impact parameter $b$ and compared to the first-order $E1$ Coulomb dissociation probability (black dashed curve). The steeply falling (green) dashed curve shows the total absorption probability.

Figure 4

Decay energy spectra at the impact parameter $b=12,20$, and 30 fm. The solid curves are dynamic calculations, whereas the dashed curves are first-order perturbation calculations.

Figure 5

Occupation probabilities of the continuum as a function of the orbital angular momentum $L$ of the $n+{}^{14}\mathrm{C}$ system, at the fixed impact parameter $b=12$ fm. The probabilities are shown for different values of the maximum orbital angular momentum, $L_{\max }$. The occupation probability of the excited $5/2^{+}$ bound state (BS) is indicated for $L=2$ inside the lower left box.

Figure 6

Decay energy spectra obtained in dynamic calculations with $L_{\max }=2$ and 4, respectively. The nominal acceptance angle is $6^{°}$ but the calculated spectra have already converged at a smaller angle (see text).

Figure 7

Decay energy spectra obtained in first-order perturbation theory (a) and in the dynamic calculations with $L_{\max }=4$ (b) compared to the data of Ref. [4]. The dashed curves show the calculated spectra. The solid curves include the experimental energy resolution and have been scaled to give an optimum fit to the data.

Figure 8

Calculated cross sections for the radiative neutron capture on ${}^{14}\mathrm{C}$ to the $1/2^{+}$ ground state (G.S.) and to the $5/2^{+}$ bound state (B.S.) of ${}^{15}\mathrm{C}$ and the sum (Total) shown as functions of the ${}^{14}\mathrm{C}+n$ relative energy, $E_{\mathrm{rel}}$. The measured cross sections are from Ref. [3].