Assessing the near threshold cross section of the ${}^{17}\mathrm{O}(n,\alpha ){}^{14}\mathrm{C}$ reaction by means of the Trojan horse method

The study of the ${}^{17}\mathrm{O}(n,\alpha ){}^{14}\mathrm{C}$ reaction has been performed by means of the Trojan horse method (THM) applied to the quasifree ${}^2\mathrm{H}\left({}^{17}\mathrm{O},\alpha {}^{14}\mathrm{C}\right){}^1\mathrm{H}$ reaction induced at a beam energy of 43.5 MeV. The THM allowed us to study the 8121-keV ${}^{18}\mathrm{O}^{*}$ resonant level, for which the previous THM investigation pointed out the ability of the method to overcome the centrifugal barrier suppression effects in the entrance channel. Here, in view of the developments of the method for resonant reactions, the detailed analysis of the performed experiment will be discussed, focusing on the extraction of the 8121-keV resonance strength for which no information is present in scientific literature. Moreover, the experimental results clearly show the excitation of the subthreshold level centered at $-6$ keV in the center-of-mass system, which is fundamental to determine the ${}^{17}\mathrm{O}(n,\alpha ){}^{14}\mathrm{C}$ reaction rate of astrophysical interest. Finally, a new recommended reaction rate is presented for future astrophysical application.

Figure 1

The ${}^{17}\mathrm{O}(n,\alpha ){}^{14}\mathrm{C}$ excitation function by using the experimental data available in the literature. The lines connecting the experimental data have only the aim of guiding the eye.

Figure 2

Pole diagram describing the quasifree (QF) $a+A\to c+d+s$ reaction discussed in the text. Nucleus $A$ breaks up into fragments $x$ and $s$. The former is the $participant$ of the binary reaction $a(x,c)d$, while the $spectators$ does not take part to the reaction.

Figure 3

Sketch of the experimental setup. The ${}^{17}\mathrm{O}$ beam was impinging on a ${\mathrm{CD}}_2$ target. The emitted particles were detected by four PSDs (A2, A3, B2, and B3) and by two $\mathrm{\Delta }E-E$ telescopes (DE1-A1 and DE2-B1).

Figure 4

$\mathrm{\Delta }E-E$ matrix for C identification in the DE1-A1 telescope. The DE2-B1 telescope provides similar results.

Figure 5

Identification of particle $s$ according to the procedure described in Ref. [33], applied to the A1–B2 coincidences. In axes, $Y=E_{\mathrm{beam}}-E_c-E_C$ and $X=p_s^2/2u$, where $E_c$ and $E_C$ are the energies of $\alpha$ and ${}^{14}\mathrm{C}$ nuclei, while $p_s$ is the momentum of the undetected particle $s$ from momentum conservation. Energy conservation implies $Y=\frac{1}{A_s}X-Q_{2\to 3}$; thus, the mass of $s$ can be determined.

Figure 6

Experimental $Q$-value spectrum. A single peak shows up, whose centroid agrees well with the theoretical $Q$ value of $-0.407$ MeV for the ${}^2\mathrm{H}\left({}^{17}\mathrm{O},\alpha {}^{14}\mathrm{C}\right){}^1\mathrm{H}$ reaction.

Figure 7

The $E_{A1}-E_{B2}$ kinematical loci for three different angular conditions marked in the pictures. The experimental data (red points) are compared here with simulated ones for the ${}^2\mathrm{H}\left({}^{17}\mathrm{O},\alpha {}^{14}\mathrm{C}\right){}^1\mathrm{H}$ reaction channel (black points).

Figure 8

Two-dimensional plot for the ${}^{14}\mathrm{C}-p$ and $\alpha -p$ relative energies as a function of the ${}^{14}\mathrm{C}-\alpha$ one. Very clear vertical loci are detectable, due to the population of the 7.114 MeV ($J^{\pi }=4^{+}$), 7.620 MeV ($J^{\pi }=1^{-}$), 7.864 MeV ($J^{\pi }=5^{-}$), 8.039 MeV ($J^{\pi }=1^{-}$), 8.121 MeV ($J^{\pi }=5^{-}$), 8.224 MeV ($J^{\pi }=2^{+}$), and 8.289 MeV ($J^{\pi }=3^{-}$) ${}^{18}\mathrm{O}$ excited levels.

Figure 9

Normalized reaction yield for different $p_s$ ranges. The reaction yield monotonically decreases, moving to high $p_s$ values, as expected for a QF reaction using deuteron as TH nucleus. This represent a first test of the occurrence of the QF mechanism in the ${}^{17}\mathrm{O}(n,\alpha ){}^{14}\mathrm{C}$ reaction.

Figure 10

Experimental momentum distribution (black points), compared with the theoretical Hulthén function in momentum space (red line).

Figure 11

Trend of the FWHM of the $p-n$ momentum distribution measured in THM experiments as function of the corresponding transferred momentum defined as in Pizzone et al. [40]; i.e., larger transferred momentum values agree with the asymptotic value of the FWHM. The red triangles show the FWHM measured in the present work.

Figure 12

Experimental THM data, referring to the center-of-mass angular range covered in the present experiment, i.e., ${40}^{\circ }<{\theta }_{\text{c.m.}}<{90}^{\circ }$ (NSL data) and ${50}^{\circ }<{\theta }_{\text{c.m.}}<{60}^{\circ }$ (LNS data).

Figure 13

QF cross section of the ${}^2\mathrm{H}\left({}^{17}\mathrm{O},\alpha {}^{14}\mathrm{C}\right){}^1\mathrm{H}$ reaction in arbitrary units. The black points are the experimental data with the vertical error bars taking into account the statistical and angular distribution integration uncertainties. The line represents the best fit to the data calculated in the modified $R$-matrix approach, normalized to the peaks at about 178 and 244 keV.

Figure 14

The THM reaction rate (red band), compared with the others by Koehler and Graff [7] (blue line) and by Wagemans et al. [6] (black line).

Figure 15

Contribution of each resonant state to the total reaction rate. At low temperature, the rate is strongly affected by the subthreshold level (dot-dashed line) rather than the $1/v$ shape (black line). The major part of the contribution at high energy comes from the 244-keV level (dotted line) while the 178-keV level (dashed line) has a maximum contribution of $20\%$. As expected, the 75-keV level (blue line) gives a contribution less than $1\%$ due to its angular momentum.

Figure 16

Total reaction rate of the ${}^{17}\mathrm{O}\left(n,\alpha \right){}^{14}\mathrm{C}$ reaction calculated merging the best results of Wagemans et al. [6] in the energy region above 100 keV in the center-of-mass system and the result coming from THM measurement at low energy.