Dipole response of ${}^{87}\mathrm{Rb}$ and its impact on the ${}^{86}\mathrm{Rb}(n,\gamma ){}^{87}\mathrm{Rb}$ cross section

Background: Detailed information on the low-lying dipole response in atomic nuclei along isotonic or isotopic chains is well suited to systematically investigate the structure and evolution of the pygmy dipole resonance (PDR). Moreover, the dipole strength below and around the neutron separation energy $S_n$ has impact on statistical model calculations for nucleosynthesis processes.

Purpose: The photon strength function (PSF) of ${}^{87}\mathrm{Rb}$, which is directly connected to the photoabsorption cross section, is a crucial input for statistical model calculations constraining the Maxwellian-averaged cross section (MACS) of the neutron capture of the unstable $s$-process branching-point nucleus ${}^{86}\mathrm{Rb}$. Within this work, the photoabsorption cross section is investigated.

Methods: The photoabsorption cross section of the $N=50$ nucleus ${}^{87}\mathrm{Rb}$ was determined from photon-scattering experiments via the nuclear resonance fluorescence (NRF) technique. Bremsstrahlung beams at the $\gamma \mathrm{ELBE}$ facility in conjunction with monoenergetic photon beams at the $\mathrm{HI}\gamma \mathrm{S}$ facility were used to determine the integrated cross sections $I_s$ of isolated states as well as the averaged cross section as function of the excitation energy. Decays to the ground state were disentangled from decays to first low-lying excited states. Statistical and experimental approaches for the $\gamma$-decay properties at various excitation energies were applied. The linearly polarized photon beams at $\mathrm{HI}\gamma \mathrm{S}$ provide information on the ratio of electric and magnetic type of radiation.

Results: Within this work, more than 200 ground-state decays and associated levels in ${}^{87}\mathrm{Rb}$ were identified. Moreover, transitions below the sensitivity limit of the state-by-state analysis were taken into account via a statistical approach from the bremsstrahlung data as well as model-independently from the $\mathrm{HI}\gamma \mathrm{S}$ data. The photoabsorption cross sections at various excitation energies were determined. The dipole response between 6 and 10 MeV of ${}^{87}\mathrm{Rb}$ is in agreement with assuming contributions of electric multipolarity, only.

Conclusions: The photoabsorption cross section of ${}^{87}\mathrm{Rb}$ does not contradict with the trend of decreasing $E1$ strength with increasing proton number along the $N=50$ isotonic chain but might also be associated with a constant trend. The experimental $\gamma$ decay at various excitation energies of the $\mathrm{HI}\gamma \mathrm{S}$ data supports the statistical approach but does not provide a stringent proof due to the limited sensitivity in the decay channels. The additional $E1$ strength observed in the present experiments significantly enhances the MACSs compared only to recent microscopic $\mathrm{HFB}+\mathrm{QRPA}$ (Hartree-Fock-Bogoliubov plus quasiparticle random-phase approximation) calculations using the D1M interaction. Moreover, theoretical estimations provided by the KADoNiS project could be significantly improved.

Figure 1

HPGe spectra for the bremsstrahlung measurement at $E_{e^{-}}=13.2$ MeV are illustrated in black ($\theta ={90}^{\circ }$) and red ($\theta ={127}^{\circ }$). Above the neutron separation threshold $S_n=9.92$ MeV spectra of detectors at both angles are added to increase the sensitivity (shown in green). The sum of all HPGe spectra ($\theta ={127}^{\circ }$) at $E_{e^{-}}=8.2$ MeV is shown in blue.

Figure 2

The absolute photon fluxes are illustrated for the measurements at $E_{e^{-}}=13.2$ MeV and $E_{e^{-}}=8.2$ MeV with dashed and solid lines, respectively. The calibration points of ${}^{11}\mathrm{B}$ are illustrated with dots.

Figure 3

The ratio of energy-integrated cross sections $I_s$ is illustrated for bremsstrahlung measurements at different endpoint energies. Data from the $E_e^{-}=4$ MeV measurement are taken from Ref. [73]. For details see text.

Figure 4

Ratios of intensities $I_{\gamma }\left({90}^{\circ }\right)/I_{\gamma }\left({127}^{\circ }\right)$ for the $E_{e^{-}}=13.2$ MeV bremsstrahlung measurement. The intensity ratios of transitions in ${}^{87}\mathrm{Rb}$ and the calibration standard ${}^{11}\mathrm{B}$ are illustrated with black dots and red triangles, respectively. Both nuclei have the same ground-state spin and parity quantum number ($J^{\pi }=3/2^{-}$). For details see text.

Figure 5

HPGe sum spectra are shown for beam-energy settings at $E_{\gamma }=8.1$ MeV (a) and $E_{\gamma }=6.25$ MeV (b) in black. The spectra corrected for detector response are shown in red. The dashed blue lines illustrate the beam profiles that are scaled to excited states of the target nucleus ${}^{87}\mathrm{Rb}$ (blue dots). The elastic part of the photoabsorption cross section is determined by the integrated intensity of the deconvoluted spectra shown in shaded red. For details see text.

Figure 6

Photoabsorption cross sections determined from the $\gamma \mathrm{ELBE}$ data before (black dots) and after correction for inelastic transitions and branching ratios (blue triangles). The ($\gamma ,n$) data are illustrated with red squares [78].

Figure 7

The photoabsorption cross sections ${\sigma }_{\gamma }$ of ${}^{87}\mathrm{Rb}$ determined from the $\gamma \mathrm{ELBE}$ data (blue triangles) and the $\mathrm{HI}\gamma \mathrm{S}$ data (red dots) as well as the ($\gamma ,n$) data (black squares) [78] with the associated standard Lorentzian (SLO) are illustrated in (a). The elastic part of the photoabsorption cross section ${\sigma }_{\gamma \gamma }$ is shown in (b). The average branching ratios to the ground state $\langle b_0\rangle$ from the statistical approach (blue line) and the model-independent $\mathrm{HI}\gamma \mathrm{S}$ data (red dots) are depicted in (c). For details see text.

Figure 8

Average experimental azimuthal asymmetries $A$ per beam-energy setting measured at $\mathrm{HI}\gamma \mathrm{S}$ are illustrated for ${}^{87}\mathrm{Rb}$, ${}^{11}\mathrm{B}$, and ${}^{32}\mathrm{S}$ with black dots, a blue triangle, and a red square, respectively. For details see text.

Figure 9

The $E1$-PSFs are illustrated for the results of the present work (red dots: $\mathrm{HI}\gamma \mathrm{S}$; blue triangles: $\gamma \mathrm{ELBE}$). QRPA calculations as well as global parametrization for the $M1$-PSF with (without) low-energy upbend are illustrated with orange solid (dotted) lines from Refs. [84, 85]. The $(\gamma ,n)$ data are shown with black squares as well as their SLO parametrization (black dashed line) from Ref. [78]. For details see text.

Figure 10

The NLDs given by the Gilbert-Cameron model [87] (green, close-dotted line) and the BSFG model (orange, short-dashed line) as well as from microscopic Hartree-Fock-Bogolyubov calculations based on the Skyrme (red, wide-dotted line) and Gogny (blue, long-dashed line) forces are shown [88, 89]. Known levels are illustrated in 100 keV bins with black lines [62]. For details see text.

Figure 11

The MACSs are illustrated for different PSF inputs, see Fig. 9. The PSF is held constant (ldmodel 5). The black diamond depicts the recommended value of the KADoNiS project [61]. For details see text.

Figure 12

The MACSs are illustrated for different NLD models; cf. Fig. 10. The PSF is hold constant ($E1$ QRPA $+M1$ resonance $+0^{+}$ lim $+E1\mathrm{HI}\gamma \mathrm{S}$); cf. Fig. 9. The black diamond depicts the recommended value of the KADoNiS project [61]. For details see text.

Figure 13

The fraction of the TRK sum rule between 6 and 10 MeV is illustrated for the $N=50$ isotones. Values extracted directly from $\gamma \mathrm{ELBE}$ data are illustrated with blue triangles [35, 36, 37, 38, 39]. For ${}^{87}\mathrm{Rb}$ the value determined at $\mathrm{HI}\gamma \mathrm{S}$ is illustrated with a red dot. For details see text.