Deuteron-induced reactions on ${}^{89}\mathrm{Y}$ and nuclear level density of ${}^{90}\mathrm{Zr}$

Experimental elastic scattering and double differential cross sections of ${}^{89}\mathrm{Y}\left(d,n\right)$ and ${}^{89}\mathrm{Y}\left(d,p\right)$ reactions have been measured with 5, 6, and 7.44 MeV deuteron beams. It was found that about 76% of the total reaction cross sections are determined by the compound mechanism and the rest is due to direct and preequilibrium interactions. Cross sections measured at backward angles were compared with calculations based on the compound nuclear Hauser-Feshbach model. It was found that it is possible to reproduce the backward angle neutron cross sections by the compound model, but it fails to describe proton cross sections. A pronounced peak is observed in neutron differential cross section which might result from strongly populated states $0^{+},4^{-}$, and $5^{-}$ of ${}^{90}\mathrm{Zr}$ via direct stripping reactions. The level density of ${}^{90}\mathrm{Zr}$ has been obtained from neutron cross sections measured at backward angles. It is best described with the constant-temperature level density model versus the traditional Fermi-gas one.

Figure 1

The angular distribution of elastically scattered deuterons on ${}^{89}\mathrm{Y}$. Points are experiment, lines are calculations with different optical model parameters according to Ref. [11] (Daehnick et al.), Ref. [12] (Perey et al.), Ref. [13] (Haixia et al.).

Figure 2

Angular distribution for different energy intervals of emitting neutrons from the ${}^{89}\mathrm{Y}\left(d,n\right){}^{90}\mathrm{Zr}$ reaction with 7.44 MeV deuteron beam. Solid lines represent the result of fitting Eq. (1) to experimental data points.

Figure 3

Experimental neutron evaporation spectrum (points) from the ${}^{89}\mathrm{Y}\left(d,n\right){}^{90}\mathrm{Zr}$ reaction measured at backward angles with 7.44 and 6 MeV deuteron beams. Lines are empire calculations with different level density input models.

Figure 4

Proton single-particle states of ${}^{89}\mathrm{Y}$ (consists of 39 protons and 50 neutrons). In the ${}^{89}\mathrm{Y}\left(d,n\right){}^{90}\mathrm{Zr}$ reaction, ${}^{89}\mathrm{Y}$ absorbs a proton, producing the residual nucleus ${}^{90}\mathrm{Zr}$. The proton can occupy the $2p_{1/2}$ state corresponding to the $0^{+}$ state of ${}^{90}\mathrm{Zr}$ or may occupy the $1g_{9/2}$ state leading to $4^{-}$ or $5^{-}$ excited states. The numerical values in parentheses represent the occupation limit for each state.

Figure 5

The angle-integrated neutron energy spectrum from the ${}^{89}\mathrm{Y}\left(d,n\right){}^{90}\mathrm{Zr}$ reaction with 7.44 MeV deuteron beam (see text). The double differential cross section measured at ${150}^{\circ }$ and multiplied by $4\pi$ is also displayed for comparison.

Figure 6

Comparison of the experimental level density of ${}^{90}\mathrm{Zr}$ (full circle) with the density of known discrete levels from Ref. [24]. The fits of the Fermi-gas and the constant-temperature models and the theoretical predictions for both models from Ref. [23] are shown. The level density obtained with the microscopic HFB model [21] is also displayed.

Figure 7

Differential cross section of ${}^{89}\mathrm{Y}\left(d,xp\right)$. Points are experimental cross sections averaged over backward angle measurements, lines are calculations with different input level density models.

Figure 8

Angular distribution of protons from ${}^{89}\mathrm{Y}\left(d,xp\right)$. Points are experimental cross sections integrated over indicated energy intervals.