Low energy deuteron-induced reactions on Fe isotopes

The activation cross sections for production of ${}^{51}\mathrm{Cr}$, ${}^{52,54,56}\mathrm{Mn}$, ${}^{59}\mathrm{Fe}$, and ${}^{55,56,57,58}\mathrm{Co}$ radioisotopes in deuteron-induced reactions on natural Fe were measured at deuteron energies up to 20 MeV. Then, within an extended analysis of deuteron interactions with ${}^{\mathrm{nat}}$Fe, all processes from elastic scattering until the evaporation from fully equilibrated compound system have been taken into account. Following the available elastic-scattering data analysis that supports the deuteron optical potential for reaction cross sections calculations, increased attention is paid especially to the breakup (BU) mechanism and direct reactions (DR). The deuteron activation cross-section analysis is completed by consideration of the preequilibrium and compound-nucleus contributions, corrected for decrease of the total reaction cross section due to the leakage of the initial deuteron flux towards BU and DR processes. The overall agreement of the measured data and model calculations validates the description of nuclear mechanisms taken into account, particularly the strong effects of direct interactions that have still not been appropriately considered within previous deuteron activation evaluations.

Figure 1

Comparison of measured [40] and calculated elastic-scattering angular distributions of deuterons on ${}^{54}\mathrm{Fe}$ (left side) and ${}^{56}\mathrm{Fe}$ (right side), from 5 to $\sim$60 MeV, using the global OMPs of Refs. [41, 42, 43, 44, 45].

Figure 2

(Left) As for Fig. 1 but for the target nucleus ${}^{58}\mathrm{Fe}$ [40]. (Right) Comparison of measured [40] and calculated total reaction cross sections of deuterons incident on ${}^{54,56,58}$Fe from 5 to $\sim$60 MeV, using the global OMPs of Refs. [41, 42, 43, 44, 45].

Figure 3

The energy dependence of the deuteron total reaction cross sections [43] (dotted curves) and the total proton-emission breakup cross sections given by parametrizations of Refs. [1] (solid curves), [46] (dashed curves), and [47] (dash-dotted curves), for deuteron interactions with ${}^{54,56,57}\mathrm{Fe}$ (upper row). The energy dependence of the total BU (dotted curves), BU nucleon emission (solid curves), BF (dashed curves), and EB (dash-dotted curves) cross sections [1] for the deuteron interactions with the same Fe isotopes (lower row).

Figure 4

Comparison of experimental [48, 49, 50, 51] total proton-emission breakup fraction and the corresponding parametrizations of Refs. [1] (solid curves), [46] (dashed curves), and [47] (dash-dotted curves), for deuteron interactions with ${}^{27}\mathrm{Al}$, ${}^{58,62}\mathrm{Ni}$, ${}^{90}\mathrm{Zr}$,${}^{93}\mathrm{Nb}$, ${}^{119}\mathrm{Sn}$, ${}^{181}\mathrm{Ta}$, ${}^{208}\mathrm{Pb}$, and ${}^{232}\mathrm{Th}$.

Figure 5

Comparison of measured [66] and calculated (solid curves) proton angular distributions from the ${}^{54}\mathrm{Fe}$$(d,p){}^{55}\mathrm{Fe}$ stripping reaction at $E=14$ MeV.

Figure 6

(a) Calculated cross sections of the ${}^{54}\mathrm{Fe}$$(d,p){}^{55}\mathrm{Fe}$ stripping reaction, and (b) comparison of the measured [69], presently calculated (solid curves), and TENDL-2013 [19] (dotted curves) cross sections of the ${}^{54}\mathrm{Fe}$$(d,x){}^{53}\mathrm{Fe}$ reaction. The $(d,t)$, $(d,dn)$, and $(d,p2n)$ reaction thresholds are also shown (arrows).

Figure 7

Total-reaction (thin solid curves), BU (dashed curves), stripping $(d,n)$ (dash-dotted curves) and $(d,p)$ (dash-dot-dotted curves), and pick-up $(d,t)$ (dotted curves) and $(d,\alpha )$ (short dash-dotted curves) reaction cross sections for deuterons on ${}^{54,56,57,58}\mathrm{Fe}$, and the corresponding reduction factors of the deuteron flux going towards statistical processes (thick solid curves).

Figure 8

Comparison of previous [25, 26] and present (solid circles) measurements, TENDL-2013 [19] predictions (dotted curves), and present calculation (solid curves) of cross sections for (a) ${}^{\mathrm{nat}}$Fe$(d,x){}^{59}\mathrm{Fe}$ and (b) ${}^{58}\mathrm{Fe}$$(d,p){}^{59}\mathrm{Fe}$ reactions, along with inelastic breakup enhancement (dashed curves), stripping $(d,p)$ reaction (dash-dotted curve), and PE + CN components (dash-dot-dotted curves) corrected for initial deuteron flux leakage through DI (see text).

Figure 9

Comparison of previous [25, 26, 27, 28] and present (solid circles) measurements, TENDL-2013 [19] predictions (dotted curves), and present calculations (solid curves) of cross sections for (a) the ${}^{\mathrm{nat}}$Fe${(d,xn)}^{58}$Co, (b) ${}^{57}\mathrm{Fe}$$(d,n){}^{58}\mathrm{Co}$, and (c) ${}^{58}\mathrm{Fe}$${(d,2n)}^{58}$Co reactions, along with inelastic breakup enhancement (dashed curves), stripping $(d,n)$ reaction (dash-dotted curve), and PE + CN components (dash-dot-dotted curves) corrected for initial deuteron flux leakage through DI (see text).

Figure 10

(a),(b) Calculated cross sections of Fe isotopes for stripping reactions $(d,n)$ and $(d,p)$, respectively, (c) experimental isomeric cross-section ratios of the ${}^{\mathrm{nat}}$Fe${(d,xn)}^{58}$Co${}^{m,g}$ reaction [29] as well as the linear interpolation (dashed curve) and constant extrapolation for $E>20$ MeV (dotted line), and (d) the derived stripping component of the ${}^{\mathrm{nat}}$Fe${(d,xn)}^{58}$Co${}^m$ reaction cross sections (dashed curve).

Figure 11

Same as Fig. 9 but for (a) ${}^{\mathrm{nat}}$Fe${(d,xn)}^{58}$Co${}^m$ [28], (b) ${}^{57}\mathrm{Fe}$$(d,n){}^{58}\mathrm{Co}$${}^m$, and (c) ${}^{58}\mathrm{Fe}$${(d,2n)}^{58}$Co${}^m$ reactions.

Figure 12

Same as Fig. 9 but for (a) ${}^{\mathrm{nat}}$Fe${(d,xn)}^{57}$Co [25, 26, 27, 30, 31, 32], (b) ${}^{56}\mathrm{Fe}$$(d,n){}^{57}\mathrm{Co}$ [33], (c) ${}^{57}\mathrm{Fe}$${(d,2n)}^{57}$Co, and (d) ${}^{58}\mathrm{Fe}$${(d,3n)}^{57}$Co reactions.

Figure 13

Comparison of previous [25, 26, 27, 28, 32, 33, 34, 35] and present (solid circles) measurements, TENDL-2013 [19] predictions (dotted curves), and present calculations (solid curves) of cross sections for (a) ${}^{\mathrm{nat}}$Fe${(d,xn)}^{56}$Co, (b) ${}^{56}\mathrm{Fe}$${(d,2n)}^{56}$Co, (c) ${}^{57}\mathrm{Fe}$${(d,3n)}^{56}$Co, and (d) ${}^{58}\mathrm{Fe}$${(d,4n)}^{56}$Co reactions, along with inelastic breakup enhancement (dashed curves), and PE + CN components (dash-dot-dotted curves) corrected for initial deuteron flux leakage through DI (see text).

Figure 14

Same as Fig. 9 but for (a) the ${}^{\mathrm{nat}}$Fe${(d,xn)}^{55}$Co reaction [25, 26, 27, 31, 36], with the arrows corresponding to the $(d,xn)$ reaction thresholds, where $x=3$, 4, and 5, and for (b) ${}^{54}\mathrm{Fe}$$(d,n){}^{55}\mathrm{Co}$ [33, 37, 38], (c) ${}^{56}\mathrm{Fe}$${(d,3n)}^{55}$Co, (d) ${}^{57}\mathrm{Fe}$${(d,4n)}^{55}$Co, and (e) ${}^{58}\mathrm{Fe}$${(d,5n)}^{55}$Co reactions.

Figure 15

Comparison of previous [26] and present (solid circles) measurements, TENDL-2013 [19] predictions (dotted curves), and present calculations (solid curves) of cross sections for (a) ${}^{\mathrm{nat}}$Fe$(d,x){}^{56}\mathrm{Mn}$, (b) ${}^{56}\mathrm{Fe}$${(d,2p)}^{56}$Mn, (c) ${}^{57}\mathrm{Fe}$$(d,x){}^{56}\mathrm{Mn}$, and (d) ${}^{58}\mathrm{Fe}$$(d,x){}^{56}\mathrm{Mn}$ reactions, along with inelastic breakup enhancement (dashed curves), pick-up $(d,\alpha )$ reaction (dash-dotted curve), and PE + CN components (dash-dot-dotted curves), corrected for initial deuteron flux leakage through DI (see text).

Figure 16

Same as Fig. 15 but for (a) ${}^{\mathrm{nat}}$Fe$(d,x){}^{54}\mathrm{Mn}$ [25, 26, 27, 31, 32], (b) ${}^{54}\mathrm{Fe}$${(d,2p)}^{54}$Mn, (c) ${}^{56}\mathrm{Fe}$$(d,x){}^{54}\mathrm{Mn}$ [28], (d) ${}^{57}\mathrm{Fe}$$(d,x){}^{54}\mathrm{Mn}$, and (e) ${}^{58}\mathrm{Fe}$$(d,x){}^{54}\mathrm{Mn}$ reactions.

Figure 17

Same as Fig. 15 but for (a) ${}^{54}\mathrm{Fe}$${(d,\alpha )}^{52}$Mn${}^m$ [37], (b) ${}^{\mathrm{nat}}$Fe$(d,x){}^{52}\mathrm{Mn}$ [27, 31], (c) ${}^{54}\mathrm{Fe}$${(d,\alpha )}^{52}$Mn [33], (d) ${}^{56}\mathrm{Fe}$$(d,x){}^{52}\mathrm{Mn}$, (e) ${}^{57}\mathrm{Fe}$$(d,x){}^{52}\mathrm{Mn}$, and (f) ${}^{58}\mathrm{Fe}$$(d,x){}^{52}\mathrm{Mn}$ reactions.

Figure 18

(a) Schematic decay of ${}^{51}\mathrm{Mn}$ and ${}^{51}\mathrm{Cr}$ nuclei [65, 73, 74, 75]; comparison of previous [26, 31] and present (solid circles) measurements, present calculations (solid curves), and TENDL-2013 [19] predictions (dotted curves) of cross sections, for (b) ${}^{\mathrm{nat}}$Fe$(d,x){}^{51}\mathrm{Cr}$, (c) ${}^{54}\mathrm{Fe}$$(d,x){}^{51}\mathrm{Cr}$, (d) ${}^{56}\mathrm{Fe}$$(d,x){}^{51}\mathrm{Cr}$, (e) ${}^{57}\mathrm{Fe}$$(d,x){}^{51}\mathrm{Cr}$, and (e) ${}^{58}\mathrm{Fe}$$(d,x){}^{51}\mathrm{Cr}$ reactions, along with BF enhancement reactions ${}^{54}\mathrm{Fe}$${(n,\alpha )}^{51}$Cr (dashed curve) and ${}^{54}\mathrm{Fe}$${(p,\alpha )}^{51}$Mn (dash-dotted curve) and PE and CN components for ${}^{51}\mathrm{Cr}$ (thick dash-dot-dotted curves) and ${}^{51}\mathrm{Mn}$ (thin dash-dot-dotted curves) residual nuclei (see text).

Figure 19

Comparison of previous [25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38] and present measurements (solid circles), present calculations (solid curves), and TENDL-2013 [19] predictions (dotted curves) of cross sections for deuteron interactions with ${}^{\mathrm{nat}}$Fe (see text).