$E1$ and $M1$ strength functions from average resonance capture data

The average resonance capture (ARC) data measured at different filter beam facilities are re-analyzed. They include all measurements made between 1970 and 1990, but only partially exploited. Updated spectroscopic information on the states of interest as well as on $s$-wave resonance spacing are used to extract the $E1$ and $M1$ photon strength function. This re-evaluation aims at providing experimental information on the $E1$ and $M1$ strength function around the neutron binding energy and in doing so provides also constraints for existing models used in statistical reaction codes. The revised data are compared to the photon strength function extracted from other experimental methods, such as photoneutron data and Oslo-method data. We also compare the ARC data with recent quasiparticle random phase approximation calculations based on the D1M Gogny force. The ratio of the $E1$ to $M1$ strength functions is also analyzed and proposed as a new stringent test for the future elaboration of theoretical models for the dipole strength function.

Figure 1

(a) $E1$ and $M1$ strength in ${}^{198}\mathrm{Au}$ from the 2 keV ARC data measured at BNL filter beam facility in $I_{\gamma }/E_{\gamma }^3$ arbitrary units. (b) Same after conversion into the dipole strength $f\left(L\right)$ in ${10}^{-8}{\mathrm{MeV}}^{-3}$ scale, using the systematic table [64] and averaging over four $E1$ transitions.

Figure 2

(a) The PT dispersion estimated from the $\sqrt{2/\nu }$ approximation for ${}^{198}\mathrm{Au}$ for $E1$ and $M1$ transitions. The ARC data taken from Ref. [64] measured at the BNL 2 keV filter beam facility. The general trend is depicted by the hashed area.

Figure 3

Ratio of the $E1$ to $M1$ strengths extracted from ARC data as a function of the ratio $S_1/S_0$. The black squares correspond to the 2-keV data and the red circles to the boron data. The general trends in both cases are shown by the regression solid lines.

Figure 4

Comparison between $E1$ and $M1$ strength functions derived from ARC data and D1M + QRPA calculations [76, 77]. Also shown are the total strength functions extracted from other measurements, in particular $(\gamma ,n)$ cross section or transfer reaction through the Oslo method, for ${}^{96}\mathrm{Mo}$ [78, 79], ${}^{106}\mathrm{Pd}$ [80, 81, 82], ${}^{124}\mathrm{Te}$ [83], ${}^{146}\mathrm{Nd}$ [84], ${}^{162}\mathrm{Dy}$ [85, 86], ${}^{163-164}\mathrm{Dy}$ [87].

Figure 5

Same as Fig. 4. Experimental strengths are taken from [88] for ${}^{172}\mathrm{Yb}$, [89] for ${}^{188}\mathrm{Os}$, [90] for ${}^{189}\mathrm{Os}$, and from [91] for ${}^{233}\mathrm{Th}$ and ${}^{239}\mathrm{U}$.

Figure 6

Ratio of the $E1$ to $M1$ strengths extracted from ARC data as a function of the atomic mass $A$. The read squares correspond to the ratio at the measured average energy and the blue circles to data renormalized at 6.5 MeV. The solid line is the newly proposed systematics of $f_{E1}/f_{M1}=0.25A^{0.6}$ at 6.5 MeV. The dashed line is the widely used RIPL-3 systematics $f_{E1}/f_{M1}=0.059A^{0.87}$ [23, 92].

Figure 7

Comparison of the ratio of the $E1$ to $M1$ strengths extracted from ARC data with the one obtained within the D1M + QRPA framework as a function of the atomic mass $A$.