Low-lying dipole response of ${}^{64}\mathrm{Ni}$

Two complementary real-photon scattering experiments were conducted on the proton-magic ${}^{64}\mathrm{Ni}$ nucleus to study the dipole response up to its neutron-separation energy of $S_n=9.7\mathrm{MeV}$. By combining both measurements, 87 $E1$ and 23 $M1$ transitions were identified above 4.3 MeV. The results of the observed $M1$ transitions were compared to shell-model calculations using two different model spaces. It was found that the inclusion of excitations across the $Z=28$ shell gap in the calculations has a large impact. Furthermore, average cross sections for decays to the ground state (elastic transitions) as well as to lower-lying excited states (inelastic decays) were determined. The corresponding $E1$ channel was compared to calculations within the relativistic equation of motion (REOM) framework. Whereas the calculations of highest possible complexity reproduce the fragmentation and overall behavior of the $E1$ average elastic cross section well, the predicted absolute cross sections are approximately twice as high as the experimental upper limits even though the latter also include an estimate of the inelastic-decay channel.

Figure 1

Deexcitation spectra recorded by the detectors at backward angles of the 7.3 MeV (green) and the 9.4 MeV (black) bremsstrahlung measurements. The most prominent transitions of the calibration target ${}^{11}\mathrm{B}$ are indicated.

Figure 2

The deexcitation spectra recorded by the $M1$ detector $({90}^{\circ },0^{\circ })$ and the $E1$ detector $({90}^{\circ },{90}^{\circ }$) at $\mathrm{HI}\gamma \mathrm{S}$ at a beam energy of 8.05 MeV are shown as orange and blue histograms, respectively. The photon-flux distribution in arbitrary units, which impinged on the target, is depicted in gray. The summed deexcitation spectrum recorded by the $\theta ={127}^{\circ }$ detectors of the bremsstrahlung experiment is illustrated in black.

Figure 3

The products of photon flux and detection efficiency of the backward detectors for the HE and the LE bremsstrahlung measurements are depicted in black and green, respectively. The shapes were scaled to the corresponding ${}^{11}\mathrm{B}$ values (full circles). See text for details.

Figure 4

The recorded photon spectrum of the $0^{\circ }$ detector for a beam energy of $8.55\mathrm{MeV}$ is illustrated in gray and the deconvoluted spectrum as the black histogram. In addition, the same quantity was calculated by utilizing the electron-beam parameters (red points). Experimentally expected photon-current densities using transitions of ${}^{64}\mathrm{Ni}$ investigated with the backward, $E1$, and $M1$ detectors are displayed as light blue, dark blue, and orange circles, respectively.

Figure 5

The absolute photon-current densities are shown for all beam energies between 5.86 and 9.05 MeV. The absolute photon-current densities were obtained by scaling, on the one hand, each distribution to the corresponding ${}^{64}\mathrm{Ni}$ data (dashed curve) and, on the other hand, all shapes to the ${}^{64}\mathrm{Ni}$ data of all beam-energy settings at once. The different colors serve for the distinction between the different beam-energy settings. See text for further details.

Figure 6

In panel (a), the moving average over a range of 200 keV of the elastic cross sections of the $E1$ and $M1$ channels deduced in 50 keV steps is shown in blue and orange, respectively. The statistical uncertainties (shaded areas) are small. The systematic uncertainties (resulting from the photon fluxes of the $\gamma \mathrm{ELBE}$ and $\mathrm{HI}\gamma \mathrm{S}$ measurements, see text) are depicted as crosshatched areas. Panel (b) illustrates the fraction of the $E1$ contribution with respect to the total cross section. This ratio was calculated not only for beam energies between 6.38 and 9.05 MeV (black), but also for the beam-energy settings of 9.3 and 9.6 MeV for which absolute measurements were not possible (purple).

Figure 7

The comparison of the average elastic cross section ${\sigma }_{\gamma \gamma ,E1}$ with respect to the $E1$ channel is shown, extracted in 50 keV steps in terms of the moving average over an energy range of 200 keV (blue histogram) and from the investigation of the total excitation-energy region at once (black points). Additionally, the average inelastic cross sections ${\sigma }_{\gamma {\gamma }^{\prime }}$, which include $E1$ and $M1$ transitions, are illustrated in dark green. The corresponding upper limit for the photoabsorption cross section ${\sigma }_{\gamma ,E1}$ was calculated (brown). Only statistical uncertainties are included. For details, see text.

Figure 8

(a) The $E1$ photoabsorption cross section ${\sigma }_{\gamma ,E1}$ of ${}^{64}\mathrm{Ni}$ in the three many-body approximations of growing complexity: relativistic QRPA (RQRPA) (gray), relativistic $2q\otimes 1\mathrm{phonon}$ EOM (${\mathrm{REOM}}^2$) (dashed black), and relativistic $2q\otimes 2\mathrm{phonon}$ EOM (${\mathrm{REOM}}^3$) (solid black). The results up to 17 MeV were obtained with the $\mathrm{\Delta }=200\mathrm{keV}$ smearing parameter (the imaginary part of the energy argument and corresponding to half the width of the individual peaks) in comparison with the experimental NRF elastic cross section ${\sigma }_{\gamma \gamma ,E1}$ (blue). These data are depicted as moving averages over a range of 200 keV. The statistical (systematic) uncertainties are shown as blue shaded (light-blue crosshatched) areas. Furthermore, the upper limits for the $E1$ photoabsorption cross sections ${\sigma }_{\gamma ,E1}$, which also include the average inelastic cross sections, and the statistical uncertainties determined in the NRF experiment are depicted as dark-red points. The corresponding systematic uncertainties are illustrated as light-red error bars. Additionally, the total photoabsorption cross section ${\sigma }_{\gamma }$ extracted from a $(\gamma ,n)$ measurement by Utsonomiya et al. (orange triangles) [60] are given. (b) The same data as in (a) but just up to 9500 keV to emphasize the energy region associated with the PDR. (c) For a better comparison of the fine structure observed in the NRF experiment with the ${\mathrm{REOM}}^3$ calculation, the experimental results extracted in 50 keV steps are illustrated together with the ${\mathrm{REOM}}^3$ results obtained with a smearing parameter of $\mathrm{\Delta }=50\mathrm{keV}$.

Figure 9

The running sums of the $E1$ photoabsorption cross sections $\mathrm{\Sigma }{\sigma }_{\gamma ,E1}$ of ${}^{64}\mathrm{Ni}$ deduced from RQRPA (gray), ${\mathrm{REOM}}^2$ (dashed black), and ${\mathrm{REOM}}^3$ calculations are depicted. In the case of the ${\mathrm{REOM}}^3$, the result using a smearing parameter of $\mathrm{\Delta }=200\mathrm{keV}$ is shown as a black solid curve, and the $\mathrm{\Delta }=50\mathrm{keV}$ calculation as a purple solid one. The running sums of the experimentally deduced upper limit for the total photoabsorption cross section of the $E1$ contribution and the corresponding statistical uncertainties are depicted in dark red. The systematic uncertainties are shown in lighter red. The running sum of the experimental NRF elastic cross section ${\sigma }_{\gamma \gamma ,E1}$ is illustrated in blue (systematic uncertainties as light-blue crosshatched areas) with the corresponding $y$ axis on the right side.

Figure 10

Upper panel: The products of experimental $B(M1,1^{+}\to 0_1^{+})$ and the ground-state decay branching ratio ${\mathrm{\Gamma }}_0/\mathrm{\Gamma }$ are illustrated for all firmly identified $M1$ transitions as orange bars and for all transitions with unknown radiation character as gray bars. The maximum energy, for which absolute values could experimentally be determined, is indicated by a dashed vertical line. Lower panel: $B(M1,1^{+}\to 0_1^{+})$ values for the lowest 100 $1^{+}$ states deduced by the shell-model calculations using, on the one hand, the CA48MH1 Hamiltonian and, on the other, the GX1A Hamiltonian are shown as red and black bars, respectively. Here, the neutron-separation threshold of ${}^{64}\mathrm{Ni}$ is indicated by a dashed vertical line.

Figure 11

Running sums $\sum B(M1,1^{+}\to 0_1^{+})$ of the calculated values using the CA48MH1 and GX1A Hamiltonians are shown as red and black squares, respectively. The experimentally extracted products of $B(M1,1^{+}\to 0_1^{+})$ and ground-state decay branching ratio ${\mathrm{\Gamma }}_0/\mathrm{\Gamma }$ (right $y$ axis) of ${}^{64}\mathrm{Ni}$ are given by orange circles with the corresponding statistical uncertainties. The systematic uncertainties are depicted in gray.