${}^{137,138,139}\mathbf{La}(n,\gamma )$ cross sections constrained with statistical decay properties of ${}^{138,139,140}\mathbf{La}$ nuclei

The nuclear level densities and $\gamma$-ray strength functions of ${}^{138,139,140}\mathrm{La}$ were measured using the ${}^{139}\mathrm{La}$(${}^3\mathrm{He},\alpha$), ${}^{139}\mathrm{La}$(${}^3\mathrm{He},\stackrel{\prime }{{}^3\mathrm{He}}$), and ${}^{139}\mathrm{La}$($d,p$) reactions. The particle-$\gamma$ coincidences were recorded with the silicon particle telescope (SiRi) and NaI(Tl) (CACTUS) arrays. In the context of these experimental results, the low-energy enhancement in the $A\sim 140$ region is discussed. The ${}^{137,138,139}\mathrm{La}$($n,\gamma$) cross sections were calculated at $s$- and $p$-process temperatures using the experimentally measured nuclear level densities and $\gamma$-ray strength functions. Good agreement is found between ${}^{139}\mathrm{La}$($n,\gamma$) calculated cross sections and previous measurements.

Figure 1

The $E_x$ vs $E_{\gamma }$ matrix for ${}^{140}\mathrm{La}$. The ${45}^{\circ }$ diagonal line is intended to guide the eye and shows the location of one-step decays to the $3^{-}$ ground state of ${}^{140}\mathrm{La}$. The neutron separation energy, $S_n$, is indicated by the horizontal red line. This comprises the raw $\gamma$ spectra before unfolding.

Figure 2

The goodness-of-fit between first-generation matrices for ${}^{140}\mathrm{La}$. The calculated $P_{th}(E_x,E_{\gamma })$ (red curve) and experimental $P(E_x,E_{\gamma })$ (black data points) at different excitation energies, $E_x$.

Figure 3

The experimental NLD (black data) of ${}^{138}\mathrm{La}$ (a), ${}^{139}\mathrm{La}$ (b), and ${}^{140}\mathrm{La}$ (c), and the microscopic calculated (red line) $\rho \left(E_x\right)$. The solid black lines are the level densities of know discrete states, while the sets of vertical arrows at low and high energies show regions where the experimental $\rho \left(E_x\right)$ was normalized to the level density of known discrete states and $\rho \left(S_n\right)$.

Figure 4

The NLD (black data) normalized using the Fermi gas model based on Eq. (8), for the three La nuclei. The red line shows the CT model used for extrapolation of level density. The solid black lines are the level densities of know discrete states, while the sets of vertical arrows at low and high energies show regions where the experimental $\rho \left(E_x\right)$ were normalized to the level density of known discrete states and $\rho \left(S_n\right)$.

Figure 5

NLD (black data) normalized to $\rho \left(S_n\right)$ obtained with the Fermi gas model as implemented in talys [39]. The solid black lines are the level densities of know discrete states, while the sets of vertical arrows at low and high energies show regions where the experimental $\rho \left(E_x\right)$ was normalized to the level density of known discrete states and $\rho \left(S_n\right)$.

Figure 6

The $\gamma \mathrm{SF}$ of ${}^{139}\mathrm{La}$, normalized using spin distributions obtained within HFB + Comb. (red data) and Fermi gas (BSFG1 + CT (black data) and BSFG2 + CT (green data)) models, and compared with photoneutron data [43, 44].

Figure 7

The $\gamma \mathrm{SF}$ of ${}^{138,140}\mathrm{La}$ [(a) and (b)], normalized using spin distributions from Fermi gas [Eqs. (8) (black data) and (11) (green data)] and HFB + Comb. (red data) models.

Figure 8

The $\gamma$-ray strength function of ${}^{138}\mathrm{La}$ extracted for two different excitation energy regions, and normalized with the HFB + Comb. spin distribution.

Figure 9

Calculated ${}^{137}\mathrm{La}(n,\gamma ),{}^{138}\mathrm{La}(n,\gamma )$, and ${}^{139}\mathrm{La}(n,\gamma )$ cross sections calculated with the talys reaction code using the measured NLDs and $\gamma \mathrm{SFs}$ as inputs. The ${}^{139}\mathrm{La}(n,\gamma )$ cross sections (c) are compared to available data from neutron-time of flight measurements (black data points) [58, 59, 60, 61, 62, 63]. The red lines indicate the upper and lower limits of the calculated cross sections.