Consistent account of deuteron-induced reactions on ${}^{\mathrm{nat}}\mathrm{Cr}$ up to 60 MeV

Background: Specific noncompound processes such as breakup (BU) and distinct direct reactions (DR) make deuteron-induced reactions different from reactions with other incident particles. Significant discrepancies with measured cross sections were caused by taking into account only the pre-equilibrium emission (PE) and compound-nucleus (CN) mechanisms while microscopic calculation of inclusive BU and DR cross sections is still investigated numerically. Thus, reaction cross sections recommended most recently for high-priority elements are still based on data fit.

Purpose: Accurate new measurements of low-energy deuteron-induced reaction cross sections for natural Cr target can enhance the related database and the opportunity for a unitary and consistent account of the involved reaction mechanisms.

Methods: The activation cross sections of ${}^{51,52,54}\mathrm{Mn}$, ${}^{51}\mathrm{Cr}$, and ${}^{48}\mathrm{V}$ nuclei for deuterons incident on natural Cr at energies up to 20 MeV were measured by the stacked-foil technique and high resolution $\gamma$ spectrometry using the U-120M cyclotron of the Center of Accelerators and Nuclear Analytical Methods (CANAM) of the Nuclear Physics Institute of the Czech Academy of Sciences (NPI CAS). They, as well as formerly available data for deuteron interactions with Cr isotopes up to 60 MeV, are the object of an extended analysis of all processes from elastic scattering until the evaporation from a fully equilibrated compound system, but with particular attention given to the BU and DR mechanisms.

Results: The new measured activation excitation functions proved essential for the enrichment of the deuteron database, while the theoretical analysis of all available data strengthens for the first time their consistent account, provided that a suitable BU and DR assessment is completed by the assumption of PE and CN contributions corrected for decrease of the total-reaction cross section due to the leakage of the initial deuteron flux towards BU and DR processes.

Conclusions: The suitable description of nuclear mechanisms involved within deuteron-induced reactions on chromium, taking into account especially the BU and DR direct processes, is validated by an overall agreement of the calculated and measured cross sections, including particularly the new experimental data at low energies.

Figure 1

The schematic picture of the foil stacks used in the experiment. The Cr foil was obtained on a plastic support.

Figure 2

Comparison of (top) measured [26, 27, 28, 29, 30, 31, 32, 33, 34] and calculated elastic-scattering angular distributions of deuterons on ${}^{50,52,53,54}\mathrm{Cr}$ at energies from $\sim 5$ to $\sim 34$ MeV, using the global OMP of Daehnick et al. [35], and (bottom) measured [34, 36] and similarly calculated total-reaction cross sections for deuterons on ${}^{52,53,54}\mathrm{Cr}$ from 3 to 60 MeV.

Figure 3

Comparison of the total-reaction cross sections (solid curves) as well as cross sections of total BU (dashed curves), total BU nucleon emission (dash-dotted curves), inelastic-breakup nucleon emission (dash-dot-dotted curves), and EB (dotted curves) provided by (a) microscopic predictions of Mustafa et al. [7] and (b) currently used parametrization [1, 13].

Figure 4

(Top) Total-reaction (thick solid curves), DR (thin solid curves), stripping $(d,n)$ (dash-dot-dotted curves) and $(d,p)$ (dash-dotted curves), and pickup $(d,t)$ (short-dotted curves) and $(d,\alpha )$ (dotted curves) reaction cross sections of deuterons on ${}^{50,52-54}\mathrm{Cr}$. (Bottom) The fractions of ${\sigma }_R$ corresponding to the contributions of BU (dashed curves), DR (solid curves), DI (dash-dotted curves), and PE+CN (dash-dot-dotted curves) mechanisms involved in $d+{}^{54}\mathrm{Cr}$ interactions (see text).

Figure 5

Comparison of measured (solid circles) [50] and calculated (solid curves) proton angular distributions of ${}^{50}\mathrm{Cr}(d,p){}^{51}\mathrm{Cr}$ stripping transitions to states with excitation energies in MeV, at an incident energy of 12 MeV.

Figure 6

As in Fig. 5 but for (a) ${}^{52}\mathrm{Cr}(d,p){}^{53}\mathrm{Cr}$ stripping [51] and (b) ${}^{52}\mathrm{Cr}(d,\alpha ){}^{50}\mathrm{V}$ pickup [52] transitions, at incident energies of 7.5 and 17 MeV, respectively.

Figure 7

As in Fig. 5 but for ${}^{53}\mathrm{Cr}(d,t){}^{52}\mathrm{Cr}$ pickup [29] transitions at an incident energy of 11.8 MeV.

Figure 8

As in Fig. 5 but for (a) ${}^{54}\mathrm{Cr}(d,p){}^{55}\mathrm{Cr}$ stripping [53] and (b) ${}^{54}\mathrm{Cr}(d,t){}^{53}\mathrm{Cr}$ pickup [54, 55] transitions, at incident energies of 10 MeV and, respectively, 11.8 and 12 MeV.

Figure 9

Comparison of previous [65] and present (solid circles) measurements, TENDL-2017 [21] evaluation (dotted curves), and present calculation (solid curves) of ${}^{\mathrm{nat}}\mathrm{Cr}(d,xn){}^{54}\mathrm{Mn}$, ${}^{53}\mathrm{Cr}(d,n){}^{54}\mathrm{Mn}$, and ${}^{54}\mathrm{Cr}(d,2n){}^{54}\mathrm{Mn}$ reaction cross sections, along with BF enhancement (dashed curves), stripping $(d,n)$ reaction (dash-dotted curve), and PE+CN components (dash-dot-dotted curves) corrected for DI deuteron flux leakage. Contributions of ${}^{53}\mathrm{Cr}$ (short-dashed curve) and ${}^{54}\mathrm{Cr}$ (short-dotted curve) isotopes to ${}^{\mathrm{nat}}\mathrm{Cr}$ activation are also shown.

Figure 10

As in Fig. 9 but for the population of (a)–(d) ${}^{52}\mathrm{Mn}^m$, (f)–(i) ${}^{52}\mathrm{Mn}^g$, and (j)–(m) ${}^{52}\mathrm{Mn}^{g+m}$ by the corresponding $(d,xn)$ reactions on ${}^{\mathrm{nat},52,53,54}\mathrm{Cr}$ [65, 66, 67, 68, 69, 70], as well as (e) the isomeric cross section ratio ${\sigma }^m/{\sigma }^g$ of these reactions on ${}^{\mathrm{nat}}\mathrm{Cr}$.

Figure 11

As in Fig. 9 but for the population of (a)-(e) ${}^{51}\mathrm{Mn}$ and (f)-(j) ${}^{51}\mathrm{Cr}$ by the corresponding $(d,xn)$ and $(d,pxn)$ reactions, respectively, on ${}^{\mathrm{nat},52,53,54}\mathrm{Cr}$ [65, 70, 71, 72, 73], including (a) the contributions of ${}^{50}\mathrm{Cr}$ (short-dashed curve) and ${}^{52}\mathrm{Cr}$ (short-dotted curve) isotopes to ${}^{\mathrm{nat}}\mathrm{Cr}$ activation for the former residual nucleus ${}^{51}\mathrm{Mn}$, and [(f) and (g)] ${}^{51}\mathrm{Cr}$ cumulative population (additional crosses) due to the decay of ${}^{51}\mathrm{Mn}$ residual nucleus, in comparison with the measured data for deuterons on ${}^{\mathrm{nat},50}\mathrm{Cr}$ [65, 71, 72, 73] (see text).

Figure 12

As Fig. 11 but for the population of (a-e) ${}^{48}\mathrm{V}$ by the corresponding $(d,x)$ reactions on ${}^{\mathrm{nat},52,53,54}\mathrm{Cr}$ [65, 71, 72, 74], including (a) the contributions of ${}^{50}\mathrm{Cr}$ (short-dashed curve) and ${}^{52}\mathrm{Cr}$ (short-dotted curve) isotopes to ${}^{\mathrm{nat}}\mathrm{Cr}$ activation.

Figure 13

As Fig. 11 but for the population of (a-e) ${}^{47}\mathrm{Sc}$ and (f-j) ${}^{46}\mathrm{Sc}$ by the corresponding $(d,x)$ reactions on ${}^{\mathrm{nat},52,53,54}\mathrm{Cr}$ [65], including (a,f) the contributions of ${}^{52}\mathrm{Cr}$ (short-dashed curves), ${}^{53}\mathrm{Cr}$ (short-dotted curves), and ${}^{54}\mathrm{Cr}$ (short dash-dotted curves) isotopes to ${}^{\mathrm{nat}}\mathrm{Cr}$ activation.

Figure 14

Comparison of previous [65, 66, 67, 68, 69, 70, 71, 72, 73, 74] (open circles) and present measurements (solid circles), TENDL-2017 [21] predictions (dotted curves), and present calculations (solid curves) of cross sections for deuteron interactions with ${}^{\mathrm{nat}}\mathrm{Cr}$ (see text).