Low-energy deuteron-induced reactions on ${}^{93}$Nb

The activation cross sections of $(d,p)$, $(d,2n)$, $(d,2np+nd+t)$, $(d,2n\alpha )$, and $(d,p\alpha )$ reactions on ${}^{93}$Nb were measured in the energy range from 1 to 20 MeV using the stacked-foil technique. Then, within a simultaneous analysis of elastic scattering and reaction data, the available elastic-scattering data analysis was carried out in order to obtain the optical potential for reaction cross-section calculations. Particular attention was paid to the description of the breakup mechanism and direct reaction stripping and pick-up, followed by pre-equilibrium and compound-nucleus calculations. The measured cross sections as well as all available deuteron activation data of ${}^{93}$Nb were compared with results of local model calculations carried out using the codes fresco and stapre-h and both default and particular predictions of the code talys-1.4 and tendl-2012-evaluated data.

Figure 1

Comparison of (a) measured [21] deuteron elastic-scattering angular distributions for the ${}^{93}$Nb target nucleus and calculated values using the OMP parameters given in Table (solid curves), previous optical potentials [26] (dashed curves), [27] (dash-dotted curves), and [28] (dotted curves), and (b) the corresponding total reaction cross sections.

Figure 2

The energy dependence of (a) the deuteron total reaction cross section (dashed curves) and total breakup cross sections given by parametrizations of Avrigeanu et al. [4] (solid curve) and Kalbach [33] (dotted curve) for deuteron interactions with the ${}^{93}$Nb target nucleus, (b) the BF (dashed curve) and EB (dash-dotted curve) breakup components [4], and (c) the comparison of the empirical [4] (dash-dotted curve) and CDCC [17] (solid curve) EB cross sections and values of Kleinfeller et al. [31] systematics (solid circles).

Figure 3

[(a) and (b)] The centroid of assumed Gaussian line shape [33, 38] for deuteron breakup-peak energies of emitted neutrons (solid line) and protons (dashed line), and the corresponding $E\pm \Gamma /2$ values (dotted lines) for the BU (a) neutrons and (b) protons, calculated for deuterons interacting with ${}^{93}$Nb. [(c) and (d)] The convolution of the cross-section ratios (c) ${\sigma }_{(n,2n)}$/${\sigma }_T$ and (d) ${\sigma }_{(p,n)}$/${\sigma }_R^p$ for the target nucleus ${}^{93}$Nb, leading to residual-nucleus isomeric states (dotted curves), with the Gaussian line shape of the deuteron-breakup peak energies of the corresponding emitted (c) neutrons and (d) protons, for deuterons with energies of 20, 30, and 40 MeV (thin dash-dot-dotted, dash-dotted, and dashed curves, respectively, with the incident energy noted above their maxima) and the convolution results at each deuteron energy (thick curves).

Figure 4

Comparison of the measured [50, 51] and calculated cross sections for the reactions ${}^{93}$Nb${(p,\gamma )}^{94}$Mo (solid curve) and ${}^{93}$Nb${(p,n)}^{93}$Mo (dashed curve), respectively, by means of the nucleon OMPs and $\gamma$-ray transmission coefficients used in this work. The proton total reaction cross sections is also shown (dotted curve).

Figure 5

The excitation-energy dependence of the level density spin cutoff for the nucleus ${}^{93}$Mo, corresponding to the rigid-body (dashed curve), half-rigid-body (dash-dotted), and variable [61] (solid curve) moment of inertia, the discrete value for the range of levels given in Table for ${}^{93}$Mo as well the energy-dependent form at higher energies of Koning et al. [63] (dash-dot-dotted curve), the energy-dependent parametrization of Ref. [64] (dotted curve), and the maximum likelihood estimator [65] (solid circles).

Figure 6

Comparison of measured [73] and non-normalized calculated EGLO strength functions for $E1$ radiations (solid curves) for the ${}^{93,94,95}$Mo isotopes. The RSF obtained by normalization of the corresponding $s$-wave average radiative widths $\langle$${\Gamma }_{\gamma }$$\rangle$ (in meV) to the lower (dashed curves) or upper (dash-dotted curves) limits of the measured data [42], for ${}^{93,95}$Mo, or estimated from systematics [73], for ${}^{94}$Mo, are also shown.

Figure 7

Comparison of previous [11, 12] and measured deuteron activation cross sections of ${}^{93}$Nb in this work (solid circles) and the present analysis results (solid curves), taking into account various mechanism contributions, namely the deuteron inelastic-breakup enhancement (dash-dotted and short dash-dotted curves), the DR (dot curves), and the PE+CN (dashed curves) with particular emphasis of the $(d,xnd)$ (dash-dot-dotted curves) and $(d,xnt)$ (short dashed) reactions, where $x$ $=$ 1–3.

Figure 8

Comparison of measured data already shown in Fig. 7, the present analysis results (solid curves), evaluated data within the TENDL-2012 library [16] (dashed curves), and calculated results obtained with TALYS-1.4 code using either the whole default input (dotted curves) or the particular options mentioned in the text (dash-dotted curves).