Photoneutron cross-section measurements in the ${}^{209}\mathrm{Bi}$($\gamma ,xn$) reaction with a new method of direct neutron-multiplicity sorting

Photoneutron cross sections were measured in the ${}^{209}\mathrm{Bi}$($\gamma , xn$) reaction with $x=1–4$ at energies from the neutron threshold to 40 MeV using quasimonochromatic laser Compton-scattering $\gamma$-ray beams. A novel technique of direct neutron-multiplicity sorting with a flat-efficiency detector was used. Results are compared with the positron in-flight annihilation data of Livermore and Saclay as well as with bremsstrahlung data. The present neutron yields are consistent with the latest photoactivation measurement with bremsstrahlung. The giant dipole resonance component of the total photoneutron cross section is reasonably reproduced by model calculations of the Hartree-Fock Bogoliubov plus quasiparticle random phase approximation based on the Gogny D1M interaction for both E1 and M1 components. In contrast, the quasideuteron component of the total photoneutron cross section requires a factor of $\sim 3$ enhancement of the Levinger parameter. Furthermore, a survival of large $(\gamma ,n)$ cross sections above 20 MeV may indicate the surface effect on the two-component particle-hole state density. The threshold behavior of photoneutron emission is discussed in terms of the average neutron kinetic energy.

Figure 1

An excerpt of the chart of nuclei depicting our ${}^{209}\mathrm{Bi}(\gamma ,xn)$ measurements with $x=1–4$. The residual nuclei of the induced reactions are marked by blue background. Both the $(\gamma ,xn)$ and $(\gamma ,xnp)$ reactions were induced, populating the ${}^{205-208}\mathrm{Bi}$ and the ${}^{204-207}\mathrm{Pb}$ isotopes.

Figure 2

The $\gamma$-ray beam line at the NewSUBARU synchrotron radiation facility.

Figure 3

(a) shows typical spectra of the $\gamma$-ray beams recorded with the ${\mathrm{LaBr}}_3$:Ce detector (solid black lines) and the simulations of the response function (dotted blue lines), while the corresponding incident $\gamma$-ray beam spectra are displayed in (b). The threshold values for the emission of one ($S_n=7.46$ MeV), two ($S_{2n}=14.3$ MeV), three ($S_{3n}=22.4$ MeV), four ($S_{4n}=29.5$ MeV), and five ($S_{5n}=37.8$ MeV) neutrons are displayed by blue arrows in (b).

Figure 4

Time and energy spectra of incident 23.9 MeV LCS $\gamma$-ray beam recorded with the NaI(Tl) detector. (a) Time variation of the $\gamma$-ray count rate. (b) Time structure of the $\gamma$-ray beam relative to the preceding main $\gamma$-ray bunch. (c) Multiphoton energy spectra generated by main-bunch (solid black) and leakage (solid blue) contributions and single photon spectrum (dashed).

Figure 5

(a) The detection efficiencies of the inner (R1), middle (R2), and outer (R3) counter rings and the total efficiency, as follows: MCNP simulations for neutron evaporation spectra (lines), experimental values obtained using a calibrated ${}^{252}\mathrm{Cf}$ source (full symbols), MCNP simulations for ${}^{252}\mathrm{Cf}$ neutron spectrum (empty symbols). (b) The ring ratio for the neutron detection system. See text for details.

Figure 6

Neutron moderation time spectra of (a) single, (b) double, (c) triple, and (d) quadruple neutron events generated in ${}^{209}\mathrm{Bi}(\gamma ,xn)$ reactions induced by 42.2 MeV maximum energy LCS $\gamma$-rays. The experimental time spectra (solid black) are displayed along with the corresponding best fit (solid blue). The fit functions for reaction neutrons (dashed) produced by the main $\gamma$-ray bunches and the background (dotted) contributions are displayed separately.

Figure 7

Comparison between experimental (solid blue) and simulated (solid black) time spectra of neutrons emitted in ${}^{209}\mathrm{Bi}(\gamma ,xn)$ reactions for incident photon energy of 29 MeV and recorded by the neutron detection system. The spectra are obtained by applying coincidence conditions of (a) one, (b) two, and (c) three recorded neutrons during the same event.

Figure 8

The multiple-firing effect uncorrected (open triangles) and corrected (open circles) monochromatic and the nonmonochromatic ${}^{209}\mathrm{Bi}(\gamma ,xn)$ cross sections, where (a) $x=1$, (b) $x=2$, (c) $x=3$, and (d) $x=4$. The energy dependence functions used for applying the unfolding methods are also displayed (solid curves).

Figure 9

Comparison between present data and existing positron in flight annihilation [29, 30] and bremsstrahlung [31] data on the neutron yield cross section, $\sigma (\gamma ,Sn)$.

Figure 10

The fitted and extrapolated $(\gamma ,2-4n)$ cross sections and the bremsstrahlung spectrum used for the comparison with the experimental reaction yields measured by Ref. [32].

Figure 11

Comparison of our total experimental cross section $\sigma (\gamma ,\mathrm{tot})={\sum }_{\mathrm{x}=1}^4\sigma (\gamma ,\mathrm{xn})$ with previous measurements [30] and with the talys predictions for two values of the Levinger parameter $L=6.5$ (solid line) and $L=20$ (dashed line).

Figure 12

Comparison of the experimental partial cross section $\sigma (\gamma ,xn)$ ($x=1–4$) with the talys calculation obtained with the default preequilibrium parametrization (solid lines), the modified parameter $L=20$ but no surface effects (dashed lines) and $L=20$ with surface effects ($E_{\mathrm{surf}}=1$ MeV) (dotted lines).

Figure 13

Comparison of the experimental average energy of the emitted neutrons $\langle E_n\rangle$ as a function of the photon energy with the talys estimates obtained with different nuclear level density descriptions [56, 57, 58, 59] of the low-lying states in ${}^{208}\mathrm{Bi}$. The dotted black curve referred to as “Maximum” corresponds to the emission of neutrons directly and uniquely to the ground state of ${}^{208}\mathrm{Bi}$.