Level density and mechanism of deuteron-induced reactions on ${}^{54,56,58}\text{Fe}$

Deuteron elastic cross sections, as well as neutron, proton, and $\alpha$-particle emission spectra, from $d+{}^{54,56,58}\text{Fe}$ reactions have been measured with deuteron beam energies of 5, 7, and 9 MeV. Optical model parameters have been tested against our experimental data. The fraction of total reaction cross section responsible for the formation of compound nuclei has been deduced from the angular distributions. The degree of discrepancy between calculated and experimental compound cross sections was found to increase with increasing neutron number. The nuclear level densities of the residual nuclei ${}^{55}\text{Co},{}^{57}\text{Co},{}^{55}\text{Fe},{}^{57}\text{Fe},{}^{52}\text{Mn}$, and ${}^{54}\text{Mn}$ have been deduced from the compound double differential cross sections. The Gilbert-Cameron model with Iljinov parameter systematics [A. S. Iljinov and M. V. Mebel, Nucl. Phys. A 543, 517 (1992)] was found to have a good agreement with our results.

Figure 1

Schematic of the charged particle spectrometer.

Figure 2

Ratio of deuteron elastic scattering to Rutherford cross sections in the center-of-mass system for ${}^{54}\text{Fe}(d,d){}^{54}\text{Fe}$ with $E_d=5$ MeV (a), $E_d=7$ MeV (b), and $E_d=9$ MeV (c); ${}^{56}\text{Fe}(d,d){}^{56}\text{Fe}$ with $E_d=5$ MeV (d), $E_d=7$ MeV (e), and $E_d=9$ MeV (f); ${}^{58}\text{Fe}(d,d){}^{58}\text{Fe}$ with $E_d=5$ MeV (g), $E_d=7$ MeV (h), and $E_d=9$ MeV (i). Lines are theoretical calculations from optical parameters of Bojowald et al. [12] (dashed-dotted), Lohr et al. [11] (solid line), and Haixia et al. [13] (dashed) while points are experimental data from this work (solid square) and from Al-Quraishi et al. [14] (open circle).

Figure 3

Angular distributions in the CM system from ${}^{54}\text{Fe}(d,p)$ (a), ${}^{54}\text{Fe}(d,\alpha )$ (b), ${}^{56}\text{Fe}(d,p)$ (c), ${}^{56}\text{Fe}(d,\alpha )$ (d), ${}^{58}\text{Fe}(d,p)$ (e), and ${}^{58}\text{Fe}(d,\alpha )$ (f) emission spectra integrated over selected energy intervals for a deuteron energy of 9 MeV.

Figure 4

Neutron (circle), proton (square), and $\alpha$-particle (diamond) cross sections measured at backward angles from the $d+{}^{54}\text{Fe}$ reaction with $E_d=7$ (a) and 9 MeV (b), $d+{}^{56}\text{Fe}$ reaction with $E_d=7$ (c) and 9 MeV (d), and $d+{}^{58}\text{Fe}$ reaction with $E_d=7$ (e) and 9 MeV (f).

Figure 5

Comparison of experimental and theoretical calculations of differential cross sections for ${}^{54}\text{Fe}(d,n)$ (a), ${}^{54}\text{Fe}(d,p)$ (b), ${}^{54}\text{Fe}(d,\alpha )$ (c), ${}^{56}\text{Fe}(d,n)$ (d), ${}^{56}\text{Fe}(d,p)$ (e), ${}^{56}\text{Fe}(d,\alpha )$ (f), ${}^{58}\text{Fe}(d,n)$ (g), ${}^{58}\text{Fe}(d,p)$ (h), and ${}^{58}\text{Fe}(d,\alpha )$ (i) reactions measured at backward angles. Lines are theoretical calculations. The dashed-dotted line (red) is the calculation using the GCM without the correction from compound fraction.

Figure 6

Level densities of ${}^{55}\text{Co}$ (a), ${}^{55}\text{Fe}$ (b), ${}^{52}\text{Mn}$ (c), ${}^{57}\text{Co}$ (d), ${}^{57}\text{Fe}$ (e), and ${}^{54}\text{Mn}$ (f) nuclei. Solid points are present experimental values; open points are data from Mishra 1994 [19], Voinov 2007 [6], Schiller 2003 [28], and Zhuralev 2011 [27]; histograms are densities of low-lying discrete levels; and lines are calculations from the Gilbert-Cameron model (solid), Fermi gas model (dashed-dotted), and microscopic model (dashed).