Coulomb dissociation of ${}^{27}\mathrm{P}$ at 500 MeV/u

The proton-capture reaction ${}^{26}\mathrm{Si}\left(\mathrm{p},\gamma \right){}^{27}\mathrm{P}$ was studied via Coulomb dissociation (CD) of ${}^{27}\mathrm{P}$ at an incident energy of about 500 MeV/u. The three lowest-lying resonances in ${}^{27}\mathrm{P}$ have been populated and their resonance strengths have been measured. In addition, a nonresonant direct-capture component was clearly identified and its astrophysical $S$ factor measured. The experimental results are compared to Monte Carlo simulations of the CD process using a semiclassical model. Our thermonuclear reaction rates show good agreement with the rates from a recent compilation. With respect to the nuclear structure of ${}^{27}\mathrm{P}$ we have found evidence for a negative-parity intruder state at 2.88-MeV excitation energy.

Figure 1

Levels in ${}^{27}\mathrm{P}$ from the present and other experiments [4, 8, 11, 12] in comparison with those of the mirror nucleus ${}^{27}\mathrm{Mg}$ [10]. The proton-separation energy $S_p$ was taken from Ref. [9].

Figure 2

Multipole contributions to the astrophysical $S$ factor of the radiative-capture reaction ${}^{26}\mathrm{Si}\left(\mathrm{p},\gamma \right){}^{27}\mathrm{P}$.

Figure 3

Multipole contributions to the differential cross section of the breakup reaction ${}^{208}\mathrm{Pb}({}^{27}\mathrm{P},{}^{26}\mathrm{Si}$ p $\gamma ){}^{208}\mathrm{Pb}$ at $491.3A$ MeV incident beam energy.

Figure 4

Schematic view of the experimental setup used to detect CD of ${}^{27}\mathrm{P}$ in complete kinematics. The physical quantities measured with the various detectors are indicated. Some technical details for the detectors are given in the text. The figure is adapted from Ref. [24].

Figure 5

Particle-identification plot of the secondary beam from the FRS as derived from magnetic-rigidity, time-of-flight, and energy-loss measurements. The two-dimensional gate used to select ${}^{27}\mathrm{P}$ is indicated by the dashed contour line. The color scale is logarithmic.

Figure 6

Energy loss measured in the two-layer double-sided Si microstrip detector (DSSSD) behind the Pb target plotted versus the energy loss in the plastic-scintillator wall $\left(\mathrm{PW}\_\mathrm{f}\right)$. The color scale is logarithmic.

Figure 7

Mass distribution of Si fragments detected behind the Pb breakup target. Events have been selected with gates on ${}^{27}\mathrm{P}$ in front of and on $Z=14$ (Si) behind the target, in coincidence with a proton in the proton arm.

Figure 8

Position correlations of tracked breakup protons on both DCH detectors; top panel, correlation of $x$ positions; bottom panel, correlation of $y$ positions. The empty spaces in the data originate from broken wires in the DCH, which was taken care of in the simulation.

Figure 9

Geometric acceptance of the experimental setup obtained by Monte Carlo simulations.

Figure 10

Reconstructed $\gamma$-ray spectrum from the Crystal Ball for the reaction ${}^{27}\mathrm{P}\to {}^{26}\mathrm{Si}+$ proton in a ${}^{\mathrm{nat}}\mathrm{Pb}$ target (black circles). The red histogram represents a simulation of the XB response, made with the r3broot package. The dashed histogram marks the atomic background (see text for details).

Figure 11

Invariant-mass spectra for ${}^{27}\mathrm{P}$ impinging on (a) a ${}^{\mathrm{nat}}\mathrm{Pb}$ target, (b) a ${}^{12}\mathrm{C}$ target, and (c) an empty target frame.

Figure 12

Invariant-mass spectrum for the CD of ${}^{27}\mathrm{P}$ feeding directly the ground state of ${}^{26}\mathrm{Si}$. Nuclear and empty-target contributions have been subtracted (see text).

Figure 13

Comparison between the experimental invariant-mass spectrum (solid circles with error bars) and a simulated one using the theoretical predictions (histogram). The solid curves represent Gaussian peaks fitted to the histogram. The red dashed curves and their sum curve (long dashed) result from fits to the experimental data. Note that in the simulation the strength of the fourth resonance at $E_r=2.01$ MeV was scaled down to match the experimental cross section.

Figure 14

Calculated thermonuclear reaction rates (a) The single-resonance and direct-capture contributions from this work; (b) the $\pm 1\sigma$-uncertainty bands of the total reaction rates from this work (shaded band) in comparison with those from Togano et al. ([8], short dashed), and Iliadis et al. ([5], long dashed); (c) ratios of the Togano et al. [8] and the Iliadis et al. [5] reaction rates divided by those of the present work.