Single-particle strength from nucleon transfer in oxygen isotopes: Sensitivity to model parameters

In the analysis of transfer reaction data to extract nuclear structure information the choice of input parameters to the reaction model such as distorting potentials and overlap functions has a significant impact. In this paper we consider a set of data for the ($d,t$) and ($d,{}^3\mathrm{He}$) reactions on ${}^{14,16,18}\mathrm{O}$ as a well-delimited subject for a study of the sensitivity of such analyses to different choices of distorting potentials and overlap functions with particular reference to a previous investigation of the variation of valence nucleon correlations as a function of the difference in nucleon separation energy $\mathrm{\Delta }S=|S_p-S_n|$ [Phys. Rev. Lett. 110, 122503 (2013)].

Figure 1

Experimental setup with the MUST2 array and VAMOS spectrometer.

Figure 2

Identification of reaction channels with the MUST2 array and VAMOS spectrometer: (a) $\mathrm{\Delta }E\text{−}E$ identification with MUST2 (DSSSD-CsI) for light particles punching through the DSSSD detector; (b) 2D plot of the energy of tritons detected in MUST2 as a function of their detection angle in the laboratory frame gated on the detection of ${}^{13}\mathrm{O}$ in the focal plane of VAMOS. The kinematics of the ${}^{14}\mathrm{O}(d,t)$ transfer reaction to the ground state of ${}^{13}\mathrm{O}$ is superimposed as the red line.

Figure 3

Coupling scheme used in the CRC calculations of the single-nucleon pick-up for ${}^{14}\mathrm{O}$.

Figure 4

Elastic scattering angular distributions for: (a) ${}^{14}\mathrm{O}+d$ at $E_d=36$ MeV [31], (b) ${}^{16}\mathrm{O}+d$ at $E_d=52$ MeV [46], (c) ${}^{16}\mathrm{O}+d$ at $E_d=28$ MeV [36]. The curves denote the results of CRC calculations based on four different input potentials: Koning and Delaroche [42] (solid red line), CH89 [44] (dashed green line), Becchetti and Greenlees [43] (dotted blue line), and Watson et al. [45] (dot-dashed magenta line). In all cases the exit channel potentials were calculated using the GDP08 [49] parameters.

Figure 5

Results of CRC calculations based on the parameters of Ref. [42] in the entrance channel and each of the potentials of Refs. [47, 49, 50] in the exit channels compared with the data for: (a) the ${}^{14}\mathrm{O}(d,t){}^{13}\mathrm{O}$ reaction at 18 MeV/nucleon [31] (b) the ${}^{14}\mathrm{O}(d,{}^3\mathrm{He}){}^{13}\mathrm{N}$ reaction at 18 MeV/nucleon [31] (c) the ${}^{16}\mathrm{O}(d,{}^3\mathrm{He}){}^{15}\mathrm{N}$ reaction at 26 MeV/nucleon [35] (d) the ${}^{16}\mathrm{O}(d,t){}^{15}\mathrm{O}$ reaction at 14 MeV/nucleon [36], and (e) the ${}^{18}\mathrm{O}(d,{}^3\mathrm{He}){}^{17}\mathrm{N}$ reaction at 26 MeV/nucleon [37].

Figure 6

Dependence of ${\mathrm{C}}^2{\mathrm{S}}_{\exp }$ on $r_0$ for the different transfer reactions involved in this study. All the transferred particles have angular momentum $\ell =1\hslash$ relative to their respective core nuclei. The values are the results of CRC calculations based on the same optical potential parameter sets for the entrance [42] and exit [49] channels. The diamonds denote the values of $r_0$ used in the present analysis, which reproduce the rms radii of the HFB calculations. A vertical dashed line is shown to indicate the values of ${\mathrm{C}}^2{\mathrm{S}}_{\exp }$ obtained with the conventional choice of $r_0=1.25$ fm.

Figure 7

Angular distributions for: (a) the ${}^{14}\mathrm{O}$($d,t$) and (b) and (c) the ${}^{14}\mathrm{O}$($d,{}^3\mathrm{He}$) transfer reactions at 18 MeV/u [31]. Calculations were performed with different prescriptions for the $〈{}^{14}\mathrm{O}\mid {}^{13}\mathrm{O}+n〉$ and $〈{}^{14}\mathrm{O}\mid {}^{13}\mathrm{N}+p〉$ OFs: WS (solid red curve), SCGF (dashed green curve), and extrapolated SCGF (dotted blue curve). The curves are the results of CRC calculations based on the same optical potential parameter sets for the entrance [42] and exit [49] channels.

Figure 8

Overlap functions on linear and log scale (top and middle rows) for the $〈{}^{14}\mathrm{O}\mid {}^{13}\mathrm{O}+n〉$ (left column), $〈{}^{14}\mathrm{O}\mid {}^{13}\mathrm{N}+p\left(1{\mathrm{p}}_{1/2}\right)〉$ (middle column), and $〈{}^{14}\mathrm{O}\mid {}^{13}\mathrm{N}+p\left(1{\mathrm{p}}_{3/2}\right)〉$ (right column). For each case two prescriptions for the OF (described in the text) are shown: Woods-Saxon (black line), SCGF (dashed red line). Bottom row: Notch tests performed for each channel as a function of the radius (see text for details).

Figure 9

Comparison of DWBA (dashed blue) and CRC (solid red) calculations for the single-nucleon stripping reactions. Reaction energies are the same as in Fig. 5. See text for the choice of potentials.

Figure 10

Reduction factor $R_s$ values obtained from CRC calculations with WS OFs and exit-channel optical model potentials: (a) B-G from Ref. [47], (b) GDP08 from Ref. [49], and (c) $\mathrm{HT}1p$ from Ref. [50]. The symbols correspond to the use of different input-channel optical model potentials and the lines denote linear fits to the corresponding $R_s$ sets.

Figure 11

Percentage deviations of ${\mathrm{C}}^2{\mathrm{S}}_{\exp }$ from the mean values of Ref. [31] as a function of different analysis input choices. See text for details.