Implications for $(d,p)$ reaction theory from nonlocal dispersive optical model analysis of ${}^{40}\mathrm{Ca}(d,p){}^{41}\mathrm{Ca}$

The nonlocal dispersive optical model (NLDOM) nucleon potentials are used for the first time in the adiabatic analysis of a $(d,p)$ reaction to generate distorted waves both in the entrance and exit channels. These potentials were designed and fitted by Mahzoon et al. [Phys. Rev. Lett. 112, 162503 (2014)] to constrain relevant single-particle physics in a consistent way by imposing the fundamental properties, such as nonlocality, energy-dependence and dispersive relations, that follow from the complex nature of nuclei. However, the NLDOM prediction for the ${}^{40}\mathrm{Ca}(d,p){}^{41}\mathrm{Ca}$ cross sections at low energy, typical for some modern radioactive beam ISOL (isotope separation online) facilities, is about 70% higher than the experimental data despite being reduced by the NLDOM spectroscopic factor of 0.73. This overestimation comes most likely either from insufficient absorption or due to constructive interference between ingoing and outgoing waves. This indicates strongly that additional physics arising from many-body effects is missing in the widely used current versions of $(d,p)$ reaction theories.

Figure 1

Differential cross sections normalized by the Rutherford cross section for proton scattering on ${}^{40}\mathrm{Ca}$ at (a) 9.86 MeV, (b) 17.57 MeV, (c) 40 MeV, and (d) 65 MeV, calculated using the fully nonlocal DOM potential (solid), using the local potential $U_{\mathrm{loc}}$ from Eq. (4) with the Coulomb and spin-orbit potentials included (dot-dashed), and using this equivalent local potential but with the correction $\mathrm{\Delta }{U}_p$ included as well (dashed). These are compared with the experimental data (dots).

Figure 2

(a) Real and (b) imaginary parts of ${\beta }_{\text{eff}}$ for $E=9.86$ MeV (solid), 17.57 MeV (long dashed), 40 MeV (long dot-dashed), 65 MeV (short dashed), 100 MeV (short dot-dashed), and 200 MeV (dot-dot-dashed).

Figure 3

Absolute value of the Perey factor evaluated at $E_{cm}=17.37$ MeV for NLDOM (solid), LDOM (dashed), and CH89 (dot-dashed).

Figure 4

Real and imaginary parts of the local-equivalent NLDOM potential calculated using the exponential form (solid and dotted lines, respectively) and using the series form (thick short-dashed and long-dashed lines, respectively) with $n_{\max }=6$.

Figure 5

Perey factors $f_0$ (solid), $f_1$ (dot-dashed), and $f$ (dashed) calculated with NLDOM for $E_d=11.8$ MeV.

Figure 6

(a) The real parts and (b) the imaginary parts of $\mathrm{\Delta }{U}_0$ (solid) and the first (dashed), second (dotted), and third (dot-dashed) terms in Eq. (31).

Figure 7

(a) The real parts and (b) the imaginary parts of $\mathrm{\Delta }{U}_1$ (solid) and the first (short-dashed), second (long-dashed), third (dot-dashed), and fourth (dotted) terms in Eq. (47).

Figure 8

Real part (solid) and imaginary part (dashed) of effective deuteron nonlocality as a function of $r$ for $E_d=11.8$ MeV.

Figure 9

Overlap functions calculated using NLDOM (solid), LDOM (dashed), a Woods-Saxon potential with standard geometry (dot-dashed), and a Woods-Saxon potential but corrected with a Perey factor with $\beta =0.85$ fm (dot-dot-dashed).

Figure 10

The differential ${}^{40}\mathrm{Ca}(d,p){}^{41}\mathrm{Ca}(7/2^{-})$ cross sections with $E_d=11.8$ MeV generated using NLDOM without the corrections from Eqs. (5), (10) and Eqs. (46), (50) (solid), with the corrections for the proton channel (long-dashed), with the corrections for both the proton and deuteron channels (short-dashed), and with the spin-orbit potential in addition to the other corrections (dot-dashed). The experimental data are also shown (dots).

Figure 11

The differential ${}^{40}\mathrm{Ca}(d,p){}^{41}\mathrm{Ca}(7/2^{-})$ cross sections with $E_d=11.8$ MeV generated using the NLDOM (solid), GRZ (dashed), GR (dot-dashed), and TPM (dotted) nonlocal parametrizations.

Figure 12

Panels (a) and (b) show the real and imaginary parts of the entrance channel potentials for the NLDOM (solid), GRZ (dashed), GR (dot-dashed), and TPM (dotted) nonlocal parametrizations used in Fig. 11, while panels (c) and (d) show these quantities for the exit channel. Panels (c) and (d) also show the potentials calculated using LDOM (dot-dot-dashed) and CH89 (dash-dash-dotted).

Figure 13

The differential ${}^{40}\mathrm{Ca}(d,p){}^{41}\mathrm{Ca}(7/2^{-})$ cross sections with $E_d=11.8$ MeV generated using NLDOM for the entrance channel and the overlap function and using NLDOM (solid), GRZ (dot-dashed), GR (long-dashed), TPM (dotted), LDOM (dash-dash-dotted), and CH89 (short-dashed) for the exit channel.

Figure 14

The differential ${}^{40}\mathrm{Ca}(d,p){}^{41}\mathrm{Ca}(7/2^{-})$ cross sections with $E_d=11.8$ MeV calculated with NLDOM (solid) and LDOM (dot-dot-dashed) using the TJ prescription, which evaluates the optical potentials at the shifted energy $E=E_d/2+57$ MeV. Also shown are the results from using the JS prescription, which evaluates the optical potentials at the usual energy $E=E_d/2$, with both NLDOM (dashed) and LDOM (dot-dashed).

Figure 15

(a) Real and (b) imaginary parts of the deuteron potential for the ${}^{40}\mathrm{Ca}(d,p){}^{41}\mathrm{Ca}(7/2^{-})$ reaction at $E_d=11.8$ MeV calculated with NLDOM (solid) and LDOM (dot-dot-dashed) using the TJ prescription, which evaluates the optical potentials at the shifted energy $E=E_d/2+57$ MeV. Also shown are the results from using the JS prescription, which evaluates the optical potentials at the usual energy $E=E_d/2$, with both NLDOM (dashed) and LDOM (dot-dashed).