Compatibility of the asymptotic normalization coefficient for the ${}^{14}\mathrm{C}\to {}^{13}\mathrm{B}+p$ overlap extracted from the ${}^{14}\mathrm{C}({}^{11}\mathrm{B},{}^{12}\mathrm{C}){}^{13}\mathrm{B}$ reaction with ${}^{14}\mathrm{C}(d,{}^3\mathrm{He}){}^{13}\mathrm{B}$ data

When the asymptotic normalization coefficient (ANC) for the ${}^{\mathrm{A}+1}(Z+1)\to {}^{\mathrm{A}}Z+p$ overlap is extracted from data for proton pickup from the ${}^{\mathrm{A}+1}(Z+1)$ nucleus, the value obtained may strongly depend on the degree of completeness of the modeling of the reaction mechanism, particularly when heavy-ion probes are employed. Taking the specific case of the ANC for the ${}^{14}\mathrm{C}\to {}^{13}\mathrm{B}+p$ overlap, an analysis of data for the heavy-ion ${}^{14}\mathrm{C}({}^{11}\mathrm{B},{}^{12}\mathrm{C}){}^{13}\mathrm{B}$ reaction showed that the distorted wave Born approximation (DWBA) yields a significantly larger ANC than the coupled reaction channel (CRC) technique, incorporating multistep reaction paths. In this paper we present an analysis of data from the literature for the light-ion ${}^{14}\mathrm{C}(d,{}^3\mathrm{He}){}^{13}\mathrm{B}$ pickup reaction and show that the ANC extracted from the heavy-ion data using the CRC technique is entirely compatible with the light-ion data when used in either DWBA or more complete coupled discretized continuum channel plus CRC calculations. The present results also show that the ANC extracted from the light-ion reaction is essentially unaffected by multistep reaction paths, in contrast with the heavy-ion case.

Figure 1

The $E_d=52$ MeV ${}^{14}\mathrm{C}(d,{}^3\mathrm{He}){}^{13}\mathrm{B}$ data of Ref. [7] (filled circles) compared with DWBA calculations using the ${\langle }^{14}\mathrm{C}\mid {}^{13}\mathrm{B}+p\rangle$ overlaps obtained from the full CRC analysis of Ref. [6] for values of the $p+{}^{13}\mathrm{B}$ binding potential radius parameter $r_0=1.25$ fm (dashed curve), 1.55 fm (solid curve), and 1.75 fm (dotted curve).

Figure 2

The $E_d=52$ MeV ${}^{14}\mathrm{C}(d,{}^3\mathrm{He}){}^{13}\mathrm{B}$ data of Ref. [7] (filled circles) compared with a DWBA calculation using the ${\langle }^{14}\mathrm{C}\mid {}^{13}\mathrm{B}+p\rangle$ overlap obtained from the full CRC analysis of Ref. [6] with a $p+{}^{13}\mathrm{B}$ binding potential radius parameter $r_0=1.55$ fm (solid curve). The shaded area represents the uncertainty band on the ANC, as in Ref. [6].

Figure 3

The $E_d=52$ MeV ${}^{14}\mathrm{C}(d,{}^3\mathrm{He}){}^{13}\mathrm{B}$ data of Ref. [7] (filled circles) compared with CRC calculations using the ${\langle }^{14}\mathrm{C}\mid {}^{13}\mathrm{B}+p\rangle$ overlaps obtained from the full CRC analysis of Ref. [6] for values of the $p+{}^{13}\mathrm{B}$ binding potential radius parameter $r_0=1.25$ fm (dashed curve), 1.55 fm (solid curve), and 1.75 fm (dotted curve).

Figure 4

The $E_d=52$ MeV ${}^{14}\mathrm{C}(d,{}^3\mathrm{He}){}^{13}\mathrm{B}$ data of Ref. [7] (filled circles) compared with a CRC calculation using the ${\langle }^{14}\mathrm{C}\mid {}^{13}\mathrm{B}+p\rangle$ overlap obtained from the full CRC analysis of Ref. [6] with a $p+{}^{13}\mathrm{B}$ binding potential radius parameter $r_0=1.55$ fm (solid curve). The shaded area represents the uncertainty band on the ANC, as in Ref. [6].

Figure 5

The $E_d=52$ MeV ${}^{14}\mathrm{C}(d,{}^3\mathrm{He}){}^{13}\mathrm{B}$ data of Ref. [7] (filled circles) compared with DWBA calculations using the ${\langle }^{14}\mathrm{C}\mid {}^{13}\mathrm{B}+p\rangle$ overlap obtained from the full CRC analysis of Ref. [6] with a $p+{}^{13}\mathrm{B}$ binding potential radius parameter $r_0=1.55$ fm and deuteron and ${}^3\mathrm{He}$ optical potentials from Ref. [7] (solid curve), the deuteron potential of Ref. [9] plus the ${}^3\mathrm{He}$ potential used in Ref. [7] (dotted curve), and the deuteron potential used in Ref. [7] plus the ht1p ${}^3\mathrm{He}$ potential [10] (dashed curve).