Are spectroscopic factors from transfer reactions consistent with asymptotic normalization coefficients?

It is extremely important to devise a reliable method to extract spectroscopic factors from transfer cross sections. We analyze the standard DWBA procedure and combine it with the asymptotic normalization coefficient, extracted from an independent data set. We find that the single particle parameters used in the past generate inconsistent asymptotic normalization coefficients. In order to obtain a consistent spectroscopic factor, nonstandard parameters for the single particle overlap functions can be used but, as a consequence, often reduced spectroscopic strengths emerge. Different choices of optical potentials and higher order effects in the reaction model are also studied. Our test cases consist of ${}^{14}\mathrm{C}$($d,p$)${}^{15}\mathrm{C}$(g.s.) at $E_d^{\mathrm{lab}}=14$ MeV, ${}^{16}\mathrm{O}$($d,p$)${}^{17}\mathrm{O}$(g.s.) at $E_d^{\mathrm{lab}}=15$ MeV and ${}^{40}\mathrm{Ca}$($d,p$)${}^{41}\mathrm{Ca}$(g.s.) at $E_d^{\mathrm{lab}}=11$ MeV. We underline the importance of performing experiments specifically designed to extract asymptotic normalization coefficients for these systems.

Figure 1

${}^{14}\mathrm{C}$$(d,p)$${}^{15}\mathrm{C}$ at $E_d=14$ MeV with a global deuteron potential (DWBAg). Data from [32].

Figure 2

${}^{16}\mathrm{O}$$(d,p)$${}^{17}\mathrm{O}$ at $E_d=15$ MeV with a global deuteron potential (DWBAg). Data from [33].

Figure 3

${}^{40}\mathrm{Ca}$$(d,p)$${}^{41}\mathrm{Ca}$ at $E_d=11$ MeV with a global deuteron potential (DWBAg). Data from [34].

Figure 4

(a) Elastic scattering fit ${}^{14}\mathrm{C}$$+d$; (b) ${}^{14}\mathrm{C}$$(d,p)$${}^{15}\mathrm{C}$ at $E_d=14$ MeV with a fitted deuteron potentials (DWBAf). Both elastic and transfer data from [32].

Figure 5

(a) Elastic scattering fit ${}^{14}\mathrm{C}$$+d$; (b) ${}^{16}\mathrm{O}$$(d,p)$${}^{17}\mathrm{O}$ at $E_d=15$ MeV with a fitted deuteron potentials (DWBAf). Elastic data from [37] and transfer data from [33].

Figure 6

(a) Elastic scattering fit ${}^{14}\mathrm{C}$$+d$; (b) ${}^{40}\mathrm{Ca}$$(d,p)$${}^{41}\mathrm{Ca}$ at $E_d=11$ MeV with a fitted deuteron potentials (DWBAf). Elastic data from [38] and transfer data from [34].

Figure 7

${}^{14}\mathrm{C}$$(d,p)$${}^{15}\mathrm{C}$ at $E_d=14$ MeV with ADWA. Data from [32].

Figure 8

${}^{16}\mathrm{O}$$(d,p)$${}^{17}\mathrm{O}$ at $E_d=15$ MeV with ADWA. Data from [33].

Figure 9

${}^{40}\mathrm{Ca}$$(d,p)$${}^{41}\mathrm{Ca}$ at $E_d=11$ MeV with ADWA. Data from [34].

Figure 10

Optical potentials: fits to elastic scattering only—real (Vfit1) and imaginary (Wfit1)—and simultaneous fits to the elastic and transfer channel—real (Vfit2) and imaginary (Wfit2). (a) ${}^{14}\mathrm{C}$$+d$ at $E_d=14$ MeV, (b) ${}^{16}\mathrm{O}$$+d$ at $E_d=15$ MeV, (c) ${}^{41}\mathrm{Ca}$$+d$ at $E_d=11$ MeV.

Figure 11

Peripherality test for the reactions (using a cut in the radial distance between projectile and target): (a) ${}^{14}\mathrm{C}$$+d$ at $E_d=14$ MeV, (b) ${}^{16}\mathrm{O}$$+d$ at $E_d=15$ MeV, (c) ${}^{41}\mathrm{Ca}$$+d$ at $E_d=11$ MeV. The solid line corresponds to fit 1 potential and the dashed line to fit 2.

Figure 12

Peripherality test for the reactions (using cutoff in the radial distance $R_{\mathrm{nA}}$): (a) ${}^{14}\mathrm{C}$$+d$ at $E_d=14$ MeV, (b) ${}^{16}\mathrm{O}$$+d$ at $E_d=15$ MeV, (c) ${}^{41}\mathrm{Ca}$$+d$ at $E_d=11$ MeV. The solid line corresponds to fit 1 potential and the dashed line to fit 2.