Effects of distortion of the intercluster motion in ${}^2\mathrm{H}$, ${}^3\mathrm{He}$, ${}^3\mathrm{H}$, ${}^6\mathrm{Li}$, and ${}^9\mathrm{Be}$ on Trojan horse applications

Deuteron induced quasifree scattering and reactions have been extensively investigated in the past few decades as well as ${}^6\mathrm{Li}$, ${}^3\mathrm{H}$, ${}^3\mathrm{He}$, and ${}^9\mathrm{Be}$ induced reactions. This was done not only for the investigation of nuclear structure and reaction mechanisms but also for important astrophysical applications (Trojan horse method). In particular the widths of the spectator momentum distributions in several nuclei, which have been used as Trojan horses, have been obtained as a function of the transferred momentum. Applications of Trojan horse method will also be discussed because the momentum distribution of the spectator particle inside the nucleus is a important input for this method. This gives hints on distortion effects at low energies important for nuclear astrophysics.

Figure 1

(a): Pole diagram describing the quasifree mechanism; (b) the triangular diagram taking into account the final-state interaction as discussed in the text (a $c-C$ exchange in this diagram is equivalent).

Figure 2

Quasifree energy $E_{\alpha \hspace{0.5em}{}^8\mathrm{Be}}$ as a function of the spectator momentum $p_s$ for the ${}^2\mathrm{H}({}^{11}\mathrm{B},\alpha {}^8\mathrm{Be})n$ reaction. A narrow cut was used for extraction of the momentum distribution as explained in the text.

Figure 3

Experimental momentum distribution for the proton inside deuteron derived according to the method explained in the text for the ${}^2\mathrm{H}(p,\mathit{pp})n$ (a) and ${}^2\mathrm{H}({}^{11}\mathrm{B}\alpha {}^8\mathrm{Be})n$ (b) reactions. The squared Hulthen function in momentum space is superimposed to data.

Figure 4

Width (FWHM) for the momentum distribution of the proton inside deuteron as a function of the transferred momentum $q_t$. Open symbols represent previous results by Refs. [16, 17, 41, 42], full dots are new data from different experiments reported in Table . The line represents an empirical fit described in the text.

Figure 5

Width (FWHM) for the momentum distribution of the $\alpha$ particle inside ${}^6\mathrm{Li}$ as a function of the transferred momentum $q_t$. Data are taken from the case discussed in Ref. [14]. The line represents an empirical fit described in the text.

Figure 6

Experimental momentum distribution for $d$ inside ${}^6\mathrm{Li}$ for the ${}^6\mathrm{Li}({}^6\mathrm{Li},\alpha \alpha ){}^4\mathrm{He}$ reaction at 3.6 (a) and 5.9 MeV (b). Dashed line is the theoretical one discussed in the text.

Figure 7

Experimental momentum distribution for $p$ in ${}^3\mathrm{He}$ for the ${}^2\mathrm{H}({}^3\mathrm{He},p{}^3\mathrm{He})n$ reaction at 17 MeV (a) and the ${}^3\mathrm{He}(p,\mathit{pd})\mathrm{H}$ at 100 MeV (b). Line is the theoretical prediction discussed in the text.

Figure 8

Width (FWHM) for the momentum distribution of the $p$ inside ${}^3\mathrm{He}$ as a function of the transferred momentum $q_t$. The solid line represents an empirical fit described in the text.

Figure 9

Experimental momentum distribution for ${}^4\mathrm{He}$ in ${}^9\mathrm{Be}$ for the ${}^9\mathrm{Be}(p,p\alpha ){}^5\mathrm{He}$ reaction at 47 MeV (a) and the ${}^9\mathrm{Be}({}^7\mathrm{Li},{}^7\mathrm{Li}\alpha ){}^5\mathrm{He}$ at 52 MeV (b). The solid line is the theoretical prediction as discussed in the text.

Figure 10

Width (FWHM) of the momentum distribution of the $\alpha$ inside ${}^9\mathrm{Be}$ as a function of the transferred momentum $q_t$. The line represents an empirical fit described in the text.

Figure 11

Experimental momentum distribution for ${}^2\mathrm{H}$ in ${}^3\mathrm{H}$ for the ${}^3\mathrm{H}({}^3\mathrm{He},d{}^3\mathrm{He})n$ reaction at 65 MeV (a) and ${}^3\mathrm{H}({}^3\mathrm{He},\mathit{pt}){}^2\mathrm{H}$ reaction at 78 MeV as reported in Ref. [46] (b). The square of the wave function in the momentum space (Hulthen function) [47] is shown as a solid line.

Figure 12

Width (FWHM) of the momentum distribution of the $d$ inside ${}^3\mathrm{H}$ as a function of the transferred momentum $q_t$. The line represents an empirical fit described in the text.

Figure 13

Correlation between $q_0$ and ${\kappa }_{\mathit{sx}}$ as discussed in the text. A linear regression is superimposed to the experimental points.