Systematic study of the low-lying electric dipole strength in Sn isotopes and its astrophysical implications

The $\gamma$-ray strength functions (GSFs) and nuclear level densities (NLDs) below the neutron threshold have been extracted for ${}^{111–113,116–122,124}\mathrm{Sn}$ from particle-$\gamma$ coincidence data with the Oslo method. The evolution of bulk properties of the low-lying electric dipole response has been investigated on the basis of the Oslo GSF data and results of a recent systematic study of electric- and magnetic dipole strengths in even-even Sn isotopes with relativistic Coulomb excitation. The obtained GSFs reveal a resonance-like peak on top of the tail of the isovector giant dipole resonance centered at $\approx 8$ MeV and exhausting $\approx 2\%$ of the classical Thomas-Reiche-Kuhn (TRK) sum. For mass numbers $\ge 118$ the data suggest also a second peak centered at $\approx 6.5$ MeV. It corresponds to 0.1%–0.5% of the TRK sum rule and shows an approximate linear increase with the mass number. In contrast with predictions of the relativistic quasiparticle random-phase and time-blocking approximation calculations, no monotonic increase in the total low-lying $E1$ strength was observed in the experimental data from ${}^{111}\mathrm{Sn}$ to ${}^{124}\mathrm{Sn}$, demonstrating rather similar strength distributions in these nuclei. The Oslo GSFs and NLDs were further used as inputs to constrain the cross sections and Maxwellian-averaged cross sections of $(n,\gamma )$ reactions in the Sn isotopic chain using talys. The obtained results agree well with other available experimental data and the recommended values from the JINA REACLIB, BRUSLIB, and KADoNiS libraries. Despite relatively small exhausted fractions of the TRK sum rule, the low-lying electric dipole strength makes a noticeable impact on the radiative neutron-capture cross sections in stable Sn isotopes. Moreover, the experimental Oslo inputs for the ${}^{121,123}\mathrm{Sn}(n,\gamma ){}^{122,124}\mathrm{Sn}$ reactions were found to affect the production of Sb in the astrophysical $i$ process, providing new constraints on the uncertainties of the resulting chemical abundances from multizone low-metallicity asymptotic giant branch stellar models.

Figure 1

The first-generation matrix for ${}^{117}\mathrm{Sn}$ extracted in the ($p,p^{\prime }\gamma$) experiment. The yellow dashed line corresponds to the neutron separation energy, while the blue solid lines confine the area used for the Oslo method. The bin size is $64\mathrm{keV}\times 64$ keV.

Figure 2

Experimental NLDs for ${}^{111–113,116–122,124}\mathrm{Sn}$ obtained with the Oslo method shown together with the $\rho \left(S_n\right)$ values and the constant-temperature fits. The orange band indicates the NLD of for ${}^{124}\mathrm{Sn}$ from the fluctuation analysis of the Coulomb excitation data [33].

Figure 3

Experimental NLDs for ${}^{111–113,116–122,124}\mathrm{Sn}$ obtained with the Oslo method. The uncertainty bands are omitted for enhancing the clarity of the figure.

Figure 4

Experimental GSFs of (a) ${}^{111}\mathrm{Sn}$, (b) ${}^{112}\mathrm{Sn}$, (c) ${}^{113}\mathrm{Sn}$, (d) ${}^{116}\mathrm{Sn}$, (e) ${}^{117}\mathrm{Sn}$, (f) ${}^{118}\mathrm{Sn}$, (g) ${}^{119}\mathrm{Sn}$, (h) ${}^{120}\mathrm{Sn}$, (i) ${}^{121}\mathrm{Sn}$, (j) ${}^{122}\mathrm{Sn}$, and (k) ${}^{124}\mathrm{Sn}$ shown together with the $(p,p^{\prime })$ data from Ref. [33] (Bass2020) and the ($\gamma ,n$) experimental data by Varlamov et al. [95] (Var2009), Fultz et al. [93] (Ful1969), Leprêtre et al. [94] (Lep1974), Utsunomiya et al. [96, 97] (Uts2009 and Uts2011), and Govaert et al. [28] (Gov1998). The total fits of the experimental data are shown as solid magenta lines and the fits of the IVGDR as solid blue lines. The low-lying $E1$ components (LEDR), obtained from fits with Eq. (17), are shown as shaded light-blue areas. The $M1$ data from the Coulomb excitation experiment [33] are shown for ${}^{112,116,118,120,124}\mathrm{Sn}$ with corresponding Lorentzian fits (dashed red lines).

Figure 5

(a) TRK values and (b) energy centroids for the total extracted LEDR in Sn isotopes, its lower-lying, and higher-lying components. Hollow squares correspond to a single Gaussian peak fit, filled squares correspond (a) to the sum and (b) strength-averaged centroids of two Gaussian peaks.

Figure 6

Calculated dipole strengths for ${}^{112,116,118}\mathrm{Sn}$. (a), (c), (e) The low-lying $E1$ transitions computed with the 20-keV (thin solid line) and 200-keV (thick dashed line) artificial widths are shown up to 10 MeV. (b), (d), (f) The strengths computed with the 200-keV artificial width are also shown up to 22 MeV. The blue and orange bands indicate the corresponding Oslo and $(p,p^{\prime })$ data (Bass2020). Calculations within the RQRPA and the RQTBA are shown with magenta and violet lines, respectively.

Figure 7

Same as in Fig. 6 but for ${}^{120,122,124}\mathrm{Sn}$. For ${}^{122}\mathrm{Sn}$, both ${}^{120}\mathrm{Sn}$ and ${}^{124}\mathrm{Sn}(p,p^{\prime })$ data are shown.

Figure 8

The evolution of the energy-weighted electric dipole strength extracted from the RQRPA and RQTBA calculations and the combined experimental Oslo and $(p,p^{\prime })$, integrated from 4 MeV up to (a) 8 MeV, (b) 10 MeV, and (c) $S_n$.

Figure 9

Cross sections (CS) for the (a) ${}^{112}\mathrm{Sn}(n,\gamma ){}^{113}\mathrm{Sn}$, (b) ${}^{115}\mathrm{Sn}(n,\gamma ){}^{116}\mathrm{Sn}$, (c) ${}^{116}\mathrm{Sn}(n,\gamma ){}^{117}\mathrm{Sn}$, (d) ${}^{117}\mathrm{Sn}(n,\gamma ){}^{118}\mathrm{Sn}$, (e) ${}^{118}\mathrm{Sn}(n,\gamma ){}^{119}\mathrm{Sn}$, (f) ${}^{119}\mathrm{Sn}(n,\gamma ){}^{120}\mathrm{Sn}$, (g) ${}^{120}\mathrm{Sn}(n,\gamma ){}^{121}\mathrm{Sn}$, (h) ${}^{121}\mathrm{Sn}(n,\gamma ){}^{122}\mathrm{Sn}$, and (i) ${}^{123}\mathrm{Sn}(n,\gamma ){}^{124}\mathrm{Sn}$ reactions. The predictions with the Oslo method inputs (blue bands) are compared with experimental data by Macklin et al. [48], Timokhov et al. [128], Wisshak et al. [49], Koehler et al. [50], Nishiyama et al. [129], and the talys uncertainty range obtained with different available GSFs, NLDs, and optical model potentials (beige band).

Figure 10

Maxwellian-averaged cross sections (MACS) for the (a) ${}^{112}\mathrm{Sn}(n,\gamma ){}^{113}\mathrm{Sn}$, (b) ${}^{115}\mathrm{Sn}(n,\gamma ){}^{116}\mathrm{Sn}$, (c) ${}^{116}\mathrm{Sn}(n,\gamma ){}^{117}\mathrm{Sn}$, (d) ${}^{117}\mathrm{Sn}(n,\gamma ){}^{118}\mathrm{Sn}$, (e) ${}^{118}\mathrm{Sn}(n,\gamma ){}^{119}\mathrm{Sn}$, (f) ${}^{119}\mathrm{Sn}(n,\gamma ){}^{120}\mathrm{Sn}$, (g) ${}^{120}\mathrm{Sn}(n,\gamma ){}^{121}\mathrm{Sn}$, (h) ${}^{121}\mathrm{Sn}(n,\gamma ){}^{122}\mathrm{Sn}$, (i) and ${}^{123}\mathrm{Sn}(n,\gamma ){}^{124}\mathrm{Sn}$ reactions. The predictions with the Oslo method inputs (blue bands) are compared with recommended values from JINA REACLIB [131], BRUSLIB [132], KADoNiS [133], and the talys uncertainty range obtained with different available GSFs, NLDs, and optical model potentials (beige band).

Figure 11

MACS for the ${}^{119}\mathrm{Sn}(n,\gamma ){}^{120}\mathrm{Sn}$ reaction with and without the low-lying electric dipole strength included. The Oslo results with the LEDR (blue band) and without (red band) are compared with the talys uncertainty range (beige band) and recommended values from KADoNiS [133].

Figure 12

Uncertainty bands for the neutron capture rates in the (a) ${}^{121}\mathrm{Sn}(n,\gamma ){}^{122}\mathrm{Sn}$ and (b) ${}^{123}\mathrm{Sn}(n,\gamma ){}^{124}\mathrm{Sn}$ reactions. The blue band corresponds to the span of experimentally constrained reaction rates due to uncertainties of the input Oslo NLD and GSF. The hatched band denotes the span of talys rates for all available GSF, NLD, and optical model potential combinations (model uncertainty). The purple band is due to the variation of the HFB $+$ combinatorial NLD and D1M $+$ QRPA GSF model parameters according to the procedure of Ref. [152] (parameter uncertainty).

Figure 13

Final surface elemental abundances (after decays) of multizone AGB stellar models experiencing $i$-process nucleosynthesis, computed with different combinations of ${}^{121,123}\mathrm{Sn}(n,\gamma )$ rates. Shown are the [X/Fe] ratios defined as $[\mathrm{X}/\mathrm{Fe}]={log}_{10}{(N_{\mathrm{X}}/N_{\mathrm{Fe}})}_{★}-{log}_{10}{(N_{\mathrm{X}}/N_{\mathrm{Fe}})}_{\odot }$ with $N_{\mathrm{X}}$ the number density of an element X. The first and second ${log}_{10}$ terms refer to the abundances of the model and the Sun, respectively. (a) Eight theoretical rates combinations are considered. These are theoretical estimates of parameter and model uncertainties affecting talys predictions of ${}^{121}\mathrm{Sn}(n,\gamma )$ and ${}^{123}\mathrm{Sn}(n,\gamma )$ reaction rates. (b) Same but with the new experimentally constrained rates from this work.

Figure 14

Same as Fig. 13 but for the isotopic mass fraction $X$ as a function of the mass number $A$, around the Sn region.