Evolution of the pygmy dipole resonance in Sn isotopes

Nuclear level density and $\gamma$-ray strength functions of ${}^{121,122}\mathrm{Sn}$ below the neutron separation energy are extracted with the Oslo method using the (${}^3\mathrm{He}$,${}^3\mathrm{He}$${}^{\text{'}}\gamma$) and (${}^3\mathrm{He}$,$\alpha \gamma$) reactions. The level densities of ${}^{121,122}\mathrm{Sn}$ display steplike structures, interpreted as signatures of neutron pair breaking. An enhancement in both strength functions, compared to standard models for radiative strength, is observed in our measurements for $E_{\gamma }\gtrsim 5.2$ MeV. This enhancement is compatible with pygmy resonances centered at $\approx 8.4(1)$ and $\approx 8.6(2)$ MeV, respectively, and with integrated strengths corresponding to $\approx 1.8_{-5}^{+1}\%$ of the classical Thomas-Reiche-Kuhn sum rule. Similar resonances were also seen in ${}^{116-119}\mathrm{Sn}$. Experimental neutron-capture cross reactions are well reproduced by our pygmy resonance predictions, while standard strength models are less successful. The evolution as a function of neutron number of the pygmy resonance in ${}^{116-122}\mathrm{Sn}$ is described as a clear increase of centroid energy from 8.0(1) to 8.6(2) MeV, but with no observable difference in integrated strengths.

Figure 1

The first-generation matrix $P$ of ${}^{122}\mathrm{Sn}$. The solid lines indicate the region for the data used in the Oslo method ($E_{\gamma }>1.6$ MeV, $3.8<E<9.4$ MeV). The dashed line ($E=6.6$ MeV) is the middle between the upper and lower ranges in excitation energy.

Figure 2

Comparison between experimental (squares) and ${\chi }^2$ fitted (solid lines) $P$ matrix for ${}^{122}\mathrm{Sn}$. The energy bins have been compressed to 240 keV/ch in $E$ and $E_{\gamma }$. While the panels show the results for the indicated example excitation energies, the fit has been performed globally for the entire region of the $P$ matrix that has been selected for the analysis (see Fig. 1).

Figure 3

Comparison of unnormalized $\gamma$-ray strength functions (arbitrary units) for ${}^{122}\mathrm{Sn}$. The shown strength functions are derived from the independent data sets of the upper and lower parts of the selected region of the $P$ matrix, as well as from the total selected region for comparison.

Figure 4

Estimation (cross) of the experimental value of $\rho (S_n)$ for ${}^{122}\mathrm{Sn}$ from systematics. Experimental values (squares) and global BSFG predictions (triangles) for $\rho (S_n)$ are shown for various Sn isotopes as a function of $S_n$ (see text).

Figure 5

Normalized level densities of ${}^{121,122}\mathrm{Sn}$ (filled squares) as a function of excitation energy with energy bins of 120 keV/ch. The solid lines represent the discrete level densities obtained from spectroscopy. The dashed line in both panels is the BSFG prediction, which is used for interpolation, scaled with $\eta$ to coincide with $\rho (S_n)$ (open square). The value of $\rho (S_n)$ has been calculated from neutron resonance data. The arrows indicate the two regions used for normalization.

Figure 6

Estimation of the average radiative width at $S_n$, $\langle {\Gamma }_{\gamma }(S_n)\rangle$, for ${}^{122}\mathrm{Sn}$. The respective values of other Sn isotopes are plotted (squares) as a function of $S_n$ (see text).

Figure 7

Normalized $\gamma$-ray strength functions of ${}^{121,122}\mathrm{Sn}$ as functions of $\gamma$-ray energy. The energy bins are 120 keV/ch.

Figure 8

Comparison of the prediction of the total strength functions with the OCL experimental measurements for ${}^{116-119,121,122}$Sn. The strength function of ${}^{118}\mathrm{Sn}$ is shown both as multiplied with 1.8 (filled squares) and as the original normalization (open squares). The arrows indicate $S_n$. The total strength predictions (solid lines) are modeled as Gaussian pygmy resonance additions to the GLO ($E$1 + $M$1) baselines. The SLO ($E$1 + $M$1) baselines are also shown. Upper left panel: ${}^{117}\mathrm{Sn}(\gamma ,n)$ from Utsunomiya et al. [19], ${}^{119,124}\mathrm{Sn}(\gamma ,x)$ from Fultz et al. [18], and ${}^{120}\mathrm{Sn}(\gamma ,x)$ from Varlamov et al. [21]. Upper right panel: ${}^{116}\mathrm{Sn}(\gamma ,n)$ [19], ${}^{120,124}\mathrm{Sn}(\gamma ,x)$ [18], and ${}^{122}\mathrm{Sn}(\gamma ,n)$ from Varlamov et al. [20]. Middle left panel: ${}^{117}\mathrm{Sn}(\gamma ,n)$ [19], ${}^{119}\mathrm{Sn}(\gamma ,x)$ [18], and ${}^{119}\mathrm{Sn}(\gamma ,n)$ [20]. Middle right panel: ${}^{116}\mathrm{Sn}(\gamma ,n)$ [19], ${}^{118}\mathrm{Sn}(\gamma ,x)$ [18], ${}^{118}\mathrm{Sn}(\gamma ,x)$ from Varlamov et al. [21], and ${}^{118}\mathrm{Sn}(\gamma ,x)$ from Leprêtre et al. [22]. Lower left panel: ${}^{117}\mathrm{Sn}(\gamma ,n)$ [19], ${}^{117}\mathrm{Sn}(\gamma ,x)$ [18], ${}^{117}\mathrm{Sn}(\gamma ,x)$ [21], and ${}^{117}\mathrm{Sn}(\gamma ,x)$ [22]. Lower right panel: ${}^{116}\mathrm{Sn}(\gamma ,n)$ [19], ${}^{116}\mathrm{Sn}(\gamma ,x)$ [18], ${}^{116}\mathrm{Sn}(\gamma ,x)$ [21], and ${}^{116}\mathrm{Sn}(\gamma ,x)$ [22].

Figure 9

Normalized $\gamma$-ray strength functions as functions of $\gamma$-ray energy for the Sn isotopes measured at the OCL. The even-odd isotopes ${}^{117,119,121}\mathrm{Sn}$ are shown in the upper panel, while the even-even isotopes ${}^{116,118,122}\mathrm{Sn}$ are shown in the lower panel. The measured strength of ${}^{118}\mathrm{Sn}$ has been multiplied by 1.8 (see Ref. [3]). The energy bins are 120 keV/ch for ${}^{116,117,121,122}\mathrm{Sn}$, 240 keV/ch for ${}^{119}\mathrm{Sn}$, and 360 keV/ch for ${}^{118}\mathrm{Sn}$.

Figure 10

Level-density measurements on ${}^{117}\mathrm{Sn}$ compared with microscopic calculations from Ref. [28].

Figure 11

Data on neutron-capture cross sections for the target nuclei ${}^{116-118,120}$Sn compared with calculations for neutron energies $\gtrsim 20$ keV. GLO1 (dotted line) is the GLO model assuming constant temperatures (given in Tables and ) and GLO2 (solid line) is the GLO1 model plus the prediction of the pygmy resonance. Measurements are from Koehler et al. [30], Macklin et al. [31], Nishiyama et al. [32], Wisshak et al. [33], and Timokhov et al. [34].

Figure 12

Estimated centroid energies $E_{\mathrm{pyg}}$ (squares) as a function of neutron number $N$, deduced from our measurements on ${}^{116-119,121,122}$Sn. The solid line is a linear ${\chi }^2$ fit to the measurements.

Figure 13

TRK values for Sn estimated from our measurements (squares) compared to the theoretical prediction from Van Isacker et al. [42] (multiplied by a factor 14) (solid line) as a function of neutron number $N$.