Microscopic global optical potential for nucleon-nucleus systems in the energy range 50–400 MeV

We provide a microscopic global optical potential (MGOP) for nucleon-nucleus ($NA$) systems in a wide range of nuclear mass numbers ($A=10–276$) and incident energies ($E=50–400\mathrm{MeV}$). The potential is microscopically constructed based on a single-folding (SF) model with the complex $G$-matrix interaction. The nuclear densities used in the SF model are generated, in a nonempirical way, from two kinds of microscopic mean-field models: the relativistic-mean-field (RMF) and Skyrme-Hartree-Fock + BCS (HF+BCS) models. We calculate the $NA$ potentials for more than 1000 even-even nuclei with atomic number $Z=6–92$, involving proton- and neutron-rich unstable nuclei. We confirm that both the MGOP models well reproduce the available experimental data of the total reaction cross sections, the total neutron cross sections, the elastic-scattering cross sections, the analyzing power, and the spin-rotation function $Q$. We also calculate the proton scattering cross sections of ${}^{22}\mathrm{O}$, ${}^{24}\mathrm{O}$, and ${}^{56}\mathrm{Ni}$ targets to compare the experimental data and then the cross sections for unknown ${}^{48}\mathrm{S}$, ${}^{100}\mathrm{Zr}$, and ${}^{110}\mathrm{Zr}$ are presented for future measurements. For the sake of convenience, the real and imaginary parts of the central and spin-orbit components of the $NA$ potentials are respectively represented in a linear combination of 12-range Gaussians. They are provided on the website [http://www2.yukawa.kyoto-u.ac.jp/∼takenori.furumoto/] with a program source file for reconstructing the MGOP.

Figure 1

Display examples of tables shown in the website [43].

Figure 2

Comparison of charge radii $r_C$ calculated from the RMF and HF + BCS densities of (a) Ne, (b) Ca, (c) Zr, (d) Sn, (e) Yb, and (f) Pb isotopes. The experimental data are taken from Ref. [70].

Figure 3

Point-neutron, proton, and matter density distributions of (a) ${}^{32}\mathrm{S}$, (b) ${}^{36}\mathrm{S}$, (c) ${}^{40}\mathrm{S}$, (d) ${}^{44}\mathrm{S}$, and (e) ${}^{48}\mathrm{S}$ obtained with the RMF and HF + BCS models.

Figure 4

Point-neutron, proton, and matter density distributions of (a) ${}^{80}\mathrm{Zr}$, (b) ${}^{90}\mathrm{Zr}$, (c) ${}^{100}\mathrm{Zr}$, and (d) ${}^{110}\mathrm{Zr}$.

Figure 5

Real parts of (a1) central and (a2) spin-orbit components and imaginary parts of (b1) central and (b2) spin-orbit components of the SF potentials. The original and 12-range Gaussian form factors are compared for $n+{}^{10}\mathrm{C}$ at $E_n=50\mathrm{MeV}$ and $p+{}^{242}\mathrm{U}$ at $E_p=400\mathrm{MeV}$ with the RMF densities (MGOP1); and $p+{}^{12}\mathrm{C}$ at $E_p=400\mathrm{MeV}$ and the $n+{}^{276}\mathrm{U}$ at $E_n=50\mathrm{MeV}$ with the HF + BCS densities (MGOP2).

Figure 6

Total reaction cross sections of $p+{}^{12}\mathrm{C}$, ${}^{40}\mathrm{Ca}$, ${}^{56}\mathrm{Fe}$, ${}^{90}\mathrm{Zr}$, and ${}^{208}\mathrm{Pb}$ systems as a function of incident proton energy $E_p$. The RMF (MGOP1) and HF + BCS (MGOP2) densities are employed to construct the SF potential, respectively. The experimental data for ${}^{\mathrm{Nat}.}\mathrm{C}$ (natural carbon), ${}^{12}\mathrm{C}$, ${}^{\mathrm{Nat}.}\mathrm{Ca}$ (natural calcium), ${}^{40}\mathrm{Ca}$, ${}^{\mathrm{Nat}.}\mathrm{Fe}$ (natural iron), ${}^{56}\mathrm{Fe}$, ${}^{\mathrm{Nat}.}\mathrm{Zr}$ (natural zirconium), ${}^{90}\mathrm{Zr}$, ${}^{\mathrm{Nat}.}\mathrm{Pb}$ (natural lead), and ${}^{208}\mathrm{Pb}$ targets are taken from Refs. [74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85].

Figure 7

Total reaction cross sections at $E_p=60$, 65.5, and 99 MeV as a function of the proton number of a target nucleus $Z_T$ calculated with the MGOP1 and MGOP2 models. See text for more details. The experimental data are taken from Refs. [74, 81, 82, 84].

Figure 8

Total reaction cross sections of $p+\mathrm{Ni}$ and $p+\mathrm{Sn}$ systems at $E_p=60$ and 65.5 MeV, respectively, calculated with the MGOP1 and MGOP2 models. The experimental data for ${}^{58-64}\mathrm{Ni}$ and ${}^{112-124}\mathrm{Sn}$ targets are taken from Refs. [74, 80, 82, 84].

Figure 9

Total reaction cross sections of $n+{}^{12}\mathrm{C}$, ${}^{56}\mathrm{Fe}$, ${}^{114}\mathrm{Cd}$, and ${}^{208}\mathrm{Pb}$ systems as a function of incident neutron energy $E_n$ calculated with the MGOP1 and MGOP2 models. Experimental data for ${}^{\mathrm{Nat}.}\mathrm{C}$, ${}^{\mathrm{Nat}.}\mathrm{Fe}$, ${}^{\mathrm{Nat}.}\mathrm{Cd}$ (natural cadmium), and ${}^{\mathrm{Nat}.}\mathrm{Pb}$ targets are taken from Refs. [74, 86, 87, 88, 89, 90].

Figure 10

Total reaction cross sections of $nA$ systems at $E_n=50$ and 379 MeV as a function of the proton number of a target nucleus $Z_T$ calculated with the MGOP1 and MGOP2 models. See text for more details. The experimental data are taken from Refs. [74, 87, 88, 89, 90].

Figure 11

Total neutron cross sections of $nA$ systems at $E_n=50$ and 400 MeV as a function of the incident neutron energy $E_n$, calculated with the MGOP1 and MGOP2 models. The experimental data are taken from Refs. [74, 91, 92, 93].

Figure 12

Elastic-scattering cross sections of (a) $n+{}^{12}\mathrm{C}$, (b) ${}^{40}\mathrm{Ca}$, and (c) ${}^{208}\mathrm{Pb}$ systems at $E_n=65–225\mathrm{MeV}$ with the MGOP1 (RMF) and MGOP2 (HF + BCS) models. The experimental data are taken from Refs. [74, 94, 95, 96, 97, 98, 99, 100].

Figure 13

Elastic-scattering cross sections of (a) $n+{}^{28}\mathrm{Si}$, (b) ${}^{56}\mathrm{Fe}$, and (c) ${}^{90}\mathrm{Zr}$ systems at $E_n=55$, 65, and 75 MeV. The experimental data for natural Si, Fe, and Zr targets are taken from Refs. [74, 95].

Figure 14

Elastic-scattering cross sections of $n+{}^{16}\mathrm{O}$, ${}^{40}\mathrm{Ca}$, ${}^{56}\mathrm{Fe}$, ${}^{140}\mathrm{Cd}$, and ${}^{120}\mathrm{Sn}$ systems at $E_n=65–351.5\mathrm{MeV}$. The experimental data for ${}^{16}\mathrm{O}$, ${}^{56}\mathrm{Fe}$, natural O, Ca, Cd, and Sn targets are taken from Refs. [74, 94, 98, 99, 100, 102, 103, 104].

Figure 15

Elastic-scattering cross sections of $n+{}^{238}\mathrm{U}$ system at $E_n=52.5–120\mathrm{MeV}$. The experimental data for a natural U target are taken from Refs. [74, 94, 105].

Figure 16

(a) Elastic-scattering cross sections in the Rutherford ratio and (b) analyzing power of $pA$ systems with $Z_T=6–92$ at $E_p=65\mathrm{MeV}$. The experimental data are taken from Refs. [74, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120].

Figure 17

(a) Elastic-scattering cross sections in the Rutherford ratio at $E_p=51.93$–340 MeV and (b) analyzing power at $E_p=54.4$–250 MeV of $p+{}^{12}\mathrm{C}$ system. The experimental data are taken from Refs. [74, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149].

Figure 18

(a) Elastic-scattering cross sections in the Rutherford ratio at $E_p=61–317.4\mathrm{MeV}$ and (b) analyzing power at $E_p=135–317.4\mathrm{MeV}$ of $p+{}^{16}\mathrm{O}$ system. The experimental data are taken from Refs. [74, 124, 125, 128, 134, 150, 151, 152, 153, 154, 155, 156].

Figure 19

(a) Elastic-scattering cross sections of $p+{}^{24}\mathrm{Mg}$, ${}^{28}\mathrm{Si}$, ${}^{30}\mathrm{Si}$, ${}^{32}\mathrm{S}$, and ${}^{34}\mathrm{S}$ systems at $E_p=51.9–400\mathrm{MeV}$ in the Rutherford ratio and (b) analyzing power of $p+{}^{24}\mathrm{Mg}$, ${}^{28}\mathrm{Si}$, ${}^{30}\mathrm{Si}$, ${}^{32}\mathrm{S}$, and ${}^{34}\mathrm{S}$ systems at $E_p=55–317.7\mathrm{MeV}$. The experimental data are taken from Refs. [74, 112, 137, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166].

Figure 20

(a) Elastic-scattering cross sections of $p+{}^{40}\mathrm{Ca}$ and ${}^{48}\mathrm{Ca}$ systems at $E_p=51.93–400\mathrm{MeV}$ in the Rutherford ratio; (b) analyzing power of $p+{}^{40}\mathrm{Ca}$ and ${}^{48}\mathrm{Ca}$ systems at $E_p=75–400\mathrm{MeV}$; and (c) spin-rotation function $Q$ of $p+{}^{40}\mathrm{Ca}$ system at $E_p=65–300\mathrm{MeV}$. The experimental data are taken from Refs. [4, 32, 33, 74, 124, 125, 127, 132, 133, 135, 137, 155, 159, 166, 167, 168, 169, 170, 171, 172, 173].

Figure 21

(a) Elastic-scattering cross sections of $p+{}^{46}\mathrm{Ti}$, ${}^{48}\mathrm{Ti}$, ${}^{50}\mathrm{Ti}$, ${}^{50}\mathrm{Cr}$, ${}^{54}\mathrm{Fe}$, ${}^{56}\mathrm{Fe}$, ${}^{58}\mathrm{Ni}$, ${}^{60}\mathrm{Ni}$, ${}^{62}\mathrm{Ni}$, ${}^{66}\mathrm{Zn}$, ${}^{68}\mathrm{Zn}$, ${}^{74}\mathrm{Se}$, ${}^{76}\mathrm{Se}$, ${}^{78}\mathrm{Se}$, ${}^{80}\mathrm{Se}$, and ${}^{82}\mathrm{Se}$ systems at $E_p=51.9–333\mathrm{MeV}$ in the Rutherford ratio; (b) analyzing power of $p+{}^{54}\mathrm{Fe}$, ${}^{56}\mathrm{Fe}$, ${}^{58}\mathrm{Ni}$, and ${}^{60}\mathrm{Ni}$ systems at $E_p=60.2–295\mathrm{MeV}$; and (c) spin-rotation function $Q$ of $p+{}^{58}\mathrm{Ni}$ at $E_p=200$ and 300 MeV. The experimental data are taken from Refs. [74, 129, 133, 134, 135, 137, 168, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188].

Figure 22

(a) Elastic-scattering cross sections in the Rutherford ratio at $E_p=57.5–200\mathrm{MeV}$; (b) analyzing power at $E_p=57.5–200.4\mathrm{MeV}$ of $p+{}^{88}\mathrm{Sr}$, ${}^{90}\mathrm{Zr}$, and ${}^{92}\mathrm{Zr}$ systems; and (c) Spin-rotation function $Q$ at $E_p=65\mathrm{MeV}$ of $p+{}^{90}\mathrm{Zr}$ system. The experimental data are taken from Refs. [4, 32, 74, 133, 135, 159, 178, 189, 190, 191, 192].

Figure 23

Elastic-scattering cross sections of $p+{}^{106}\mathrm{Pd}$, ${}^{108}\mathrm{Pd}$, ${}^{110}\mathrm{Pd}$, ${}^{112}\mathrm{Cd}$, and ${}^{116}\mathrm{Sn}$ systems in the Rutherford ratio at $E_p=51–61.4\mathrm{MeV}$. The experimental data are taken from Refs. [74, 133, 193, 194].

Figure 24

(a) Elastic-scattering cross sections in the Rutherford ratio at $E_p=61.5–300\mathrm{MeV}$; (b) analyzing power at $E_p=103.5–300\mathrm{MeV}$ of $p+{}^{116}\mathrm{Sn}$, ${}^{118}\mathrm{Sn}$, ${}^{120}\mathrm{Sn}$, ${}^{122}\mathrm{Sn}$, and ${}^{124}\mathrm{Sn}$ systems; and (c) Spin-rotation function $Q$ at $E_p=200$ and 300 MeV of $p+{}^{120}\mathrm{Sn}$ system. The experimental data are taken from Refs. [74, 134, 135, 159, 168, 178, 186, 191, 195].

Figure 25

(a) Elastic-scattering cross sections of $p+{}^{148}\mathrm{Sm}$, ${}^{154}\mathrm{Sm}$, ${}^{192}\mathrm{Os}$, ${}^{194}\mathrm{Pt}$, ${}^{198}\mathrm{Pt}$, ${}^{204}\mathrm{Pb}$, ${}^{206}\mathrm{Pb}$, and ${}^{208}\mathrm{Pb}$ systems in the Rutherford ratio at $E_p=61.4–400\mathrm{MeV}$; (b) analyzing power of $p+{}^{192}\mathrm{Os}$, ${}^{194}\mathrm{Pt}$, ${}^{198}\mathrm{Pt}$, ${}^{204}\mathrm{Pb}$, ${}^{206}\mathrm{Pb}$, and ${}^{208}\mathrm{Pb}$ systems at $E_p=79.8–400\mathrm{MeV}$; and (c) spin-rotation function $Q$ of $p+{}^{208}\mathrm{Pb}$ system at $E_p=65–300\mathrm{MeV}$. The experimental data are taken from Refs. [4, 32, 33, 74, 133, 135, 159, 168, 172, 178, 183, 188, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205].

Figure 26

Elastic-scattering cross sections in the Rutherford ratio of $p+{}^{22}\mathrm{O}$, ${}^{24}\mathrm{O}$, and ${}^{56}\mathrm{Ni}$ systems at $E_p=46.6–285\mathrm{MeV}$. The experimental data are taken from Refs. [206, 207, 208].

Figure 27

(a) Elastic-scattering cross sections in the Rutherford ratio and (b) analyzing power of of $p+{}^{48}\mathrm{S}$ system at $E_p=100–400\mathrm{MeV}$. The MGOP1 (RMF) and MGOP2 (HF + BCS) models are employed.

Figure 28

(a) Elastic-scattering cross section in the Rutherford ratio and (b) analyzing power of $p+{}^{100}\mathrm{Zr}$ and ${}^{110}\mathrm{Zr}$ systems at $E_p=100–400\mathrm{MeV}$. The MGOP1 (RMF) and MGOP2 (HF + BCS) models are employed.