Thermonuclear ${}^{42}\mathrm{Ti}$($p,\gamma$)${}^{43}\mathrm{V}$ rate in type-I x-ray bursts

The thermonuclear rate of the ${}^{42}\mathrm{Ti}$(${p,\gamma )}^{43}$V reaction has been reevaluated based on a recent precise proton separation energy measurement of $S_p{(}^{43}\mathrm{V})=83\pm 43$ keV. The astrophysical impact of our new rates has been investigated through one-zone postprocessing type-I x-ray burst calculations. It shows that the new experimental value of $S_p$ significantly affects the yields of species for $A\approx 40$–45. As well, the precision of the recent experimental $S_p$ value constrains these yields to better than a factor of 3.

Figure 1

Total reaction rate calculated for the ${}^{42}\mathrm{Ti}$(${p,\gamma )}^{43}$V reaction (in units of cm${}^3$ mole${}^{-1}$ s${}^{-1}$). The upper and lower limits of the present rate (with $S_p=83\pm 43$ keV [27]) are shown by the (red) thicker lines, and those of the Herndl et al. rate (with $S_p=90\pm 200$ keV [16]) are shown by the black thin lines. See text for details.

Figure 2

Ratios between the present rate (see Table 2) and other available ones (Herndl 1995 [16], Wormer 1994 [13], rath_v2 [17], and ths8_v4 [17]).

Figure 3

Abundances following one-zone XRB calculations using the K04 thermodynamic history [39]. Abundance variations determined using the present ${}^{42}\mathrm{Ti}$(${p,\gamma )}^{43}$V forward rate with reverse rates calculated using $\Delta S_p=43$ keV (IMP [27], solid black line), and $\Delta S_p=233$ keV (AME03 [23], dotted grey line) are indicated. As well, abundances determined using the rath_v2 forward rate [17] along with reverse rates calculated with $S_p=-411$ keV (FRDM [38], open squares) and $S_p=83$ keV (IMP [27], open circles) are shown. Abundances determined with the ths8_v4 rate [17] ($S_p=-19$ keV [37], open triangles) are also shown. The calculated exact numbers are listed in Table 3.

Figure 4

Direct-capture $S_{\mathrm{dc}}$ factors calculated with the three parameter sets listed in Table 4. A previous constant value of $S_{\mathrm{dc}}\left(E_0\right)=4.91$$\times$10${}^{-2}$ MeV b (Herndl 1995 [16]) is shown for comparison.

Figure 5

Dependence of $S_{\mathrm{dc}}$ factors on parameters (a) spin-orbit potential $V_{\mathrm{so}}$, (b) Coulomb radius parameter $r_c$, (c) diffuseness $a$, and (d) optical-model (real) potential radius parameter $r_0$. Here, radius $r$ is defined as $r=R/A^{\frac{1}{3}}$, with $r_0=r_{\mathrm{so}}$, and $a_0=a_{\mathrm{so}}$ in all calculations.