Spectroscopy of ${}^9\mathrm{C}$ via resonance scattering of protons on ${}^8\mathrm{B}$

The structure of the neutron-deficient ${}^9\mathrm{C}$ isotope was studied via elastic scattering of radioactive ${}^8\mathrm{B}$ on protons. An excitation function for resonance elastic scattering was measured in the energy range from 0.5 to 3.2 MeV in the center-of-momentum system. A new excited state in ${}^9\mathrm{C}$ was observed at an excitation energy of 3.6 MeV. An $R$-matrix analysis indicates spin-parity $5/2^{-}$ for the new state. The results of this experiment are compared with continuum shell-model calculations.

Figure 1

The total energy of a beam ion vs. its time of flight measured with the Au target by a Si $\Delta E\text{−}E$ telescope placed at $7.7^{°}$. The start signal was taken from the $E$ detector of the telescope and the stop signal came from the beam buncher.

Figure 2

The raw spectrum of protons measured by one of the telescopes and gated on ${}^8\mathrm{B}$ TOF. The sharp peak at 9 MeV is due to direct protons scattered by the plastic target. The dashed line is a spectrum of protons produced by gating on the TOF between ${}^8\mathrm{B}$ and ${}^7\mathrm{Be}$.

Figure 3

The laboratory spectrum of protons from both telescopes measured with the plastic target. The background associated with the direct protons from the beam has been subtracted. The normalized proton background from the interaction of ${}^8\mathrm{B}$ with carbon in the plastic target is shown as the shaded histogram. The solid line represents the polynomial fit to the carbon background which was used for subtraction of this background from the total spectrum.

Figure 4

Excitation function for resonance scattering of ${}^8\mathrm{B}$ on protons at ${164}^{°}\pm 7^{°}$. The ${}^9\mathrm{C}$ excitation energy is shown on the x axis (this is the c.m. energy plus the proton binding energy of 1.3 MeV).

Figure 5

The proton spectrum in the laboratory system with the carbon background subtracted. The Monte Carlo simulation of the inelastic process ${}^1\mathrm{H}({}^8\mathrm{B},p^{\text{'}}){}^8{\mathrm{B}}^{*}(1^{+}$; 0.77 MeV) is shown as a shaded histogram. The two peaks at 5 and 9 MeV in the shaded histogram are associated with the proton decay of the ${}^8\mathrm{B}$ excited state and the inelastically scattered proton, respectively.

Figure 6

The excitation function of resonance elastic scattering of ${}^8\mathrm{B}$ on protons after subtraction of “direct,” “carbon,” and “inelastic” backgrounds. The solid curve is an $R$-matrix fit with the known $1/2^{-}$ resonance plus a $5/2^{-}$ state at an excitation energy of 3.6 MeV having a width of 1.5 MeV. The dotted curve shows the contribution of the $1/2^{-}$ state alone. $R$-matrix calculations for the $1/2^{-}$ state together with $3/2^{-}$ or $5/2^{+}$ states are shown as dash-dotted and dashed curves, respectively.

Figure 7

Solid curve is an $R$-matrix fit of the ${}^8\mathrm{B}$$+p$ excitation function which includes $1/2^{-},5/2^{-}$ and $3/2^{-}$ resonances. Dotted curve is the calculated excitation function of the resonance inelastic scattering (it is mostly due to the $3/2^{-}$ resonance).

Figure 8

The total cross section of the inelastic scattering process ${}^8\mathrm{B}(p,p^{\text{'}}){}^8\mathrm{B}(1^{+})$. The dotted curve was calculated using the $R$-matrix approach with resonance parameters given in Table . The solid curve is the CSM calculation, which automatically take into account the influence of higher- lying resonances.