Author Affiliations
1Institute of Cyclotron, Texas A&M Univ4Institute of Cyclotron, Texas A&M Univ, College Stn, TX 77843, USA1Institute of Particle and Nuclear Physics, Henan Normal University1Institute of Particle and Nuclear Physics, Henan Normal University, Xinxiang 453007, China1School of Physics and Materials Science, Anhui University3School of Physics and Materials Science, Anhui University, Hefei 230601, China1School of Physics, Henan Normal University2School of Physics, Henan Normal University, Xinxiang 453007, China2School of Physics, Henan Normal University2School of Physics, Henan Normal University, Xinxiang 453007, Chinashow less
Fig. 1. (color online) A schematic diagram of a neural network with a single hidden layer, three hidden neurons (H = 3) and two input variables (I = 2).
Fig. 2. (color online) BNN predictions for selected residue fragments with Z=60 to 65 in the 800 MeV/u 197Au + p spallation reaction. Three different numbers of hidden nodes are tested, H = 34 (circles), 35 (triangles), 36 (triangles). The measured results are shown as black squares.
Fig. 3. (color online) Similar as Fig. 2, but for Z=66 to 73.
Fig. 4. (color online) Similar as Fig. 2, but for Z=75 to 80.
Fig. 5. (color online) BNN predictions for the 500 MeV/u 56Fe + p reaction with H = 34, 35 and 36. The results for the selected residues Z=10 to 15 are compared to the measured residue fragments [41]. The symbols are the same as in Fig. 2.
Fig. 6. (color online) Similar as Fig. 5, but for Z = 16 to 21.
Fig. 7. (color online) Similar as Fig. 5, but for Z = 22 to 27.
Fig. 8. (color online) BNN predictions (with TS1 and H = 35) (circles) for selected fragments with Z = 3 to 22 in the 1000 MeV/u 136Xe + p spallation reaction, compared to the experimental data (squares, from [44]) and the SPACS results (triangles, from [25]. The experimental and BNN error bars are smaller than the symbols.
Fig. 9. (color online) Similar as Fig. 8, but for Z = 36 to 54.
Fig. 10. (color online) Predictions of isotopic distributions by BNN (squares) and SPACS (circles) for the 1000 MeV/u 238U + p spallation reaction for Z = 54 to 70 [48]. Experimental distributions are not available for
. The BNN error bars are smaller than the symbol size.
Fig. 11. (color online) Similar as Fig. 8, but for 1000 MeV/u 238U + p and for Z = 74 to 92.
Fig. 12. (color online) Similar as Fig. 8, but for the 763 MeV/u 40Ca + p spallation reaction [9]. Experimental data are not available for fragments with
.
Fig. 13. (color online) Similar as Fig. 8, but for the 361 MeV/u 36Ar + p reaction with Z = 3 to 17 [8].
Fig. 14. (color online) Correlation between the isotopic cross-sections and the average binding energy B'. The squares, triangles, and circles denote the measured data, BNN predictions, and SPACS predictions, respectively. The lines denote the linear fit of the correlation between
and B'.
+ p | E/(MeV/u)
| Numbers | Charge Range | Reference |
---|
36Ar + p | 361 | 42 | 9-17 | [8]
| 546 | 42 | 9-17 | 765 | 38 | 9-17 | 40Ar + p | 352 | 45 | 9-17 | [8]
| 40Ca + p | 356 | 48 | 10-20 | [9]
| 565 | 54 | 10-20 | 763 | 54 | 10-20 | 56Fe + p | 300 | 128 | 10-27 | [41]
| 500 | 136 | 10-27 | 750 | 148 | 8-27 | 1000 | 152 | 8-26 | 1500 | 157 | 8-27 | 136Xe + p | 200 | 96 | 48-55 | [42]
| 500 | 271 | 41-56 | [43]
| 1000 | 604 | 3-56 | [44]
| 197Au + p | 800 | 352 | 60-80 | [45]
| 208Pb + p | 500 | 249 | 69-83 | [46]
| | 1000 | 459 | 61-82 | [47]
| 238U + p | 1000 | 364 | 74-92 | [48]
|
|
Table 1. The number of measured fragments in 19 measured
+ p spallation reactions.
+ p | E/(MeV/u)
| Numbers | Charge Range |
---|
103Rh + p | 800 | 40 | 36-41 | 150Nd + p | 700 | 333 | 40-60 | 169Tm + p | 600 | 239 | 53-69 | 181Ta + p | 800 | 375 | 55-74 | 208Pb+p | 600 | 179 | 76-82 |
|
Table 2. The number of fragments in spallation reactions predicted using the SPACS parametrization.