Nuclear Structure Studies with Gamma-Ray Beams

In stable and weakly bound neutron-rich nuclei, a resonance-like concentration of dipole states has been observed for excitation energies below the neutron-separation energy. This clustering of strong dipole states has been named the Pygmy Dipole Resonance (PDR) in contrast to the Giant Dipole Resonance (GDR) that dominates the E1 response. Understanding the PDR is presently of great interest in nuclear structure and nuclear astrophysics. High-sensitivity studies of E1 and M1 transitions in closed-shell nuclei using monoenergetic and 100% linearly-polarized photon beams are presented.

There are different theoretical mechanisms explaining the amplitude and the distribution of the nuclear dipole strength of PDR observed in the experiments [11,18,33].This new structure phenomenon is described as a neutron skin oscillation against a protonneutron saturated core.In the simple three-fluid nuclear model, three fluids were introduced to take into account the difference in the interaction of excess neutrons and the remainder of the neutrons and protons [25].This simple hydrodynamic model was able to qualitatively explain the existence of two independent modes, one located at around 13 MeV (GDR) and the other at about 4-5 MeV (PDR).A clear correlation of the total PDR strength and the thickness of the neutron skin is obtained in calculations for N = 82 isotonic chains [2,[4][5][6]32] and Z=50 nuclei [18].In addition, the recently observed fundamental differences [8] between the (γ,γ') and (α,α') data, provide a new challenge for model calculations.This comparison leads to the believe, that the PDR is split into two parts with different underlying structures.
The existence of PDR is now well established as E1 excitations in spherical and transitional nuclei [19].A concentration of the electric dipole excitations exhausting up to 1% of the isovector E1 energy weighted sum rule [32].A nonstatistical distribution of the E1 strengths close to the threshold has a strong impact on the astrophysical r-process nucleosynthesis [26].In addition, the PDR is sensitive to nuclear properties at the nuclear surface and at low density.Thus, its property may provide a useful constraint on the energy density functional, to identify the equation of state (EOS) of the nuclear and neutron matters [11].
In this paper, we focus on another scope of these nuclear structure studies with monoenergetic and polarized photon beams from the High-Intensity Gamma-Ray Source (HIGS) facility: investigating the E1 dipole strength distribution of the PDR overlapping with the spin-flip M1 strength and E2 quadruple responses.The data are compared with predictions from statistical and quasi-phonon model [18].

Experimental technique
The Nuclear Resonance Fluorescence method (NRF) is used at HIGS to study low-multipolarity ground-state transitions i.e., E1, M1 and to a lesser extent E2.The NRF technique represents an outstanding tool for measuring dipole transitions with a high detection sensitivity.The main advantage of this method is that both the excitation and the de-excitation processes proceed via the electromagnetic interaction, which is the most understood fundamental interaction in physics.The angular distribution of the scattered γ rays from excited nuclei to the ground state or the secondary transitions from the first 2 + states to the ground state were measured.
The monoenergetic and 100% linearly polarized photon beams were produced by intra-cavity Compton backscattering of intense free-electron-laser light from electron beams in the Duke storage ring.The energy of the backward scattered photons can be tuned within a wide range, presently from 1 to 100 MeV.The collimated photon flux on target exceeds 1000 eV -1 s -1 within an energy spread from 1 to 4%.The backscattered photons were collimated by a lead collimator of 30.5 cm in length with a cylindrical hole of 1.9 cm in diameter.After proper attenuation, the energy distribution of the photon beam was measured with a 123% HPGe detector placed in the beam.The photon flux was measured by Compton scattering of the beam from a 1.0-mm-thick copper plate, positioned 3 meters behind the scattering target.Photons scattered from the copper plate through 7.0°±1.6°were detected with the same 123% HPGe detector.At energies above 8.1 MeV, the photon flux was also monitored by the 197 Au(γ,n) reaction.

Electric dipole strength in N=82 nuclei
The 138 Ba, 140 Ce, 142 Nd, and 144 Sm scattering targets were placed in an evacuated plastic tube at the center of an array of six large-volume HPGe detectors.These detectors were arranged around the target at three positions: (θ, φ) = (90°, 90° and 270°), (90°, 0° and 180°), and (135°, 0°), where θ is the polar angle with respect to the horizontally-polarized incoming photon beam, and φ is the azimuthal angle measured from the polarization vector.This detector configuration allows for the unambiguous determination of E1, M1, and E2 transitions.The experimental results of the E1 strength distribution in N = 82 isotones is shown in Fig. 1.These results represent the fine structure of the E1 PDR distribution.If one integrates the E1 strengths between 4.0 MeV and the neutron separation energy for each of the N = 82 isotones, excluding the 2-phonon state, then the summed B(E1)↑ = 960 ± 153, 600 ± 119, 576 ± 98, 536 ± 96 (10 -3 e 2 fm 2 ) for 138 Ba, 140 Ce, 142 Nd, and 144 Sm, respectively.One can see a decrease in strength with increasing proton number.The distribution of the magnetic dipole transition strength in 90 Zr has been measured at excitation energies between 7 and 11 MeV.Total M1 strength of 4.17(50) μ N 2 with a centroid of 9 MeV was found in a photon-scattering experiment with monoenergetic and 100% linearly polarized beams.More than 40 J=1 + states have been identified from observed ground-state transitions [17].The deduced M1 values in 90 Zr are shown in Fig. 2. The experiment shows a rather fragmented excitation spectrum with many 1 + states, each of them with a strength below 1 μ N 2 .The fragmentation pattern of the M1 strength below and above the neutron-separation energy (S n = 12.0 MeV) was obtained with an extended version of the QPM [18].M1 transitions are calculated with a quenched effective spin-magnetic factor g eff s = 0.8 g bare s .The analysis of the QRPA M1 strength of 1 + -state excitations with energies up to 20 MeV indicates that it is mostly due to single p-h spin-flip states.One surprising result from these calculations is that the M1 strength at excitation energies between 7 and 11 MeV contains a considerable orbital part of about 22%.Nevertheless, the total orbital QRPA strength for the whole energy range up to 20 MeV is very small, less than 2% of the total QRPA M1 strength.An interference between spin and orbital strengths leads to the suppression of the total M1 response.An additional observation was exploited in 90 Zr measurements to investigate the nature of the PDR and collect complementary information on the decay pattern of the PDR states.This includes studying the branching ratios of the PDR states to the low-lying excited states.The partial decay width Γ i of transitions to low-lying excited states or to the ground state are directly linked to the electromagnetic transition matrix elements between the corresponding states.Therefore, each decay channel is sensitive to a different component in the wave function.The observation of these transitions and the determination of branching ratios revealed important experimental information, which is needed to provide stringent and sensitive tests to modern model calculations.Extracting the underlying spectrum from a measured spectrum with a known detector response function is shown on Fig. 3.The measured spectrum with incident photons of 9.8 MeV and energy spread of 260 keV is shown on the top panel (black histogram).Atomic background stemming from non-resonant scattering is shown by the red curve.The resulting unfolded spectrum, after subtraction of the atomic background, with the intensity distribution of the primary γ-ray transitions is shown in the panel below.The primary transitions decaying to the first four excited states in 90 Zr are shown in the level scheme below the unfolded spectrum.As can be seen, the unfolding method [29] revealed important decay information about the intensity and the distribution of the primary γ-ray transitions stemming from the PDR.

Magnetic dipole strength in 206 Pb
The strength and the location of the M1 resonance in medium-and heavy-mass nuclei has been a long-standing problem in nuclear structure physics because of the large discrepancies between experimental and theoretical results [31].Prediction of the magnitude and the distribution of the M1 strength is a major problem for theory since there is no model-independent sum rule.In general, the total M1 strength depends on the properties of the ground-state wave function.The experimental deficiency of the observed M1 strength in comparison to the predicted one was called quenching.Most of the experimental and theoretical works of the M1 spin-flip resonance were devoted to the doubly magic 208 Pb nucleus [3,21]. 206Pb has two neutrons less than 208 Pb, but the excitation spectra of these two nuclei differ significantly.Passing from the magic 208 Pb nucleus to its neighbor results in much higher density of complex configurations in 206 Pb at the same excitation energies.Hence, there is an expectation of strong fragmentation of the M1 strength in 206 Pb in comparison to 208 Pb.The neutron separation energy of 208 Pb is 7.4 MeV and very close to where the isovector M1 resonance should be located [20] while the neutron separation energy of 206 Pb is 8.1 MeV.Hence, a larger part of the total M1 strength in 206 Pb can be observed with real photons.We measured the spin-flip M1 strengths in 206 Pb have been measured in a photon-scattering experiment.The HIGS beams in combination with high-resolution HPGe detectors, positioned at specific angles relative to the initially 100% linearly polarized photon beams, open up the possibility to precisely deducing the strengths and locations of individual M1 transitions, comprising the giant M1 resonance, and to distinguish them unambiguously from the E1 and E2 deexcitations.Two γray spectra from vertical (top panel) and horizontal (bottom panel) 60% HPGe detectors at a beam energy of 7.3 MeV is shown are Fig. 4.
First preliminary results of the electric-(top panel) and magnetic-dipole (bottom panel) strength in 206 Pb are shown in Fig. 5.As can be seen the magnetic M1 strength is concentrated in two energy regions around 6.0 and 7.3 MeV.It should be noted that this strength was obtained from the elastic dipole (E1 or M1) transitions in 206 Pb.A considerable amount of inelastic strength stemming from high excitation energies, near the neutron-separation energy, is observed from the first excited states.

Indirect neutron capture cross-section measurement on unstable 8Kr nucleus
The amount of 86 Kr produced by the s-process is determined by the branching point at the unstable 85 Kr, which has a half-life of 10.76 years.When the s-process reaches this isotope, two events can occur.If the neutron density remains fairly low, it will decay to 85 Rb as shown in Fig. 6.However, if the neutron density is high (≥5×10 8 n/cm 3 ), more than 50% of the time 85 Kr will capture a neutron and make 86 Kr.The measured isotopic composition of Kr clearly reveals the signature of the s (slow neutron-capture) process.It is thought that Kr is ionised and implanted in stardust SiC grains via stellar winds in two different energy components: one during the AGB phase in small grains showing low 86 Kr/ 82 Kr, and another during the post-AGB phase in large grains showing high 86 Kr/ 82 Kr ratios [27].
There are a few reasons why the capture reaction on 85 Kr is important.Firstly, the branching at 85 Kr is significant for s-process modeling.Secondly, this branching is independent of the temperature and depends only on the neutron density.Thirdly, it helps to constrain the neutron density parameter in models of AGB stars.And finally, the 85 Kr neutron capture has not been measured.
The present measurements were carried out at HIGS facility.The target consisted of 1012 mg of Kr gas enriched to 99.4% in 86 Kr, contained in a stainless steel cell.An empty cell of identical material and dimension was used to subtract the background contribution.The neutrons emitted from the 86 Kr(γ,n) reaction were detected using a 4π assembly of 3 He proportional counters.The cross-section values from the present measurements are plotted in Fig. 7.As shown, the γ-strength function is now fully constrained at all photon energies relevant to the s process by our experimental data, below and above the neutron-separation energy [24].The experimental γray strength function, obtained by both the (γ,n) [23] and the (γ,γ') measurements [22], was directly included in the TALYS code [28], in a tabulated and interpolated form, for calculating the neutron capture cross section of 85 Kr.The transitional region around the neutron threshold has been described by the QRPA model, to reproduce the experimental data fairly well.The result of this calculation is presented in Fig. 8.The estimated uncertainties (shaded area) are dominated by the experimental errors of the γ-ray strength function (see Fig. 7) and the assumption for the nuclear level density.At a stellar temperature of kT = 30 keV, our new Maxwellian-averaged cross section amounts to a value of 83±23 mb.This value is about 50% higher than the result of Ref. [30] quoted above.Furthermore, the uncertainty is improved by a factor of about 3 to ≈50%.

Conclusions
Systematic spin and parity measurements on spherical and near spherical nuclei at the HIGS facility have verified that the observed dipole strength from 4 MeV to the neutron-separation energy is predominantly of electric nature.Our findings are in agreement with the QPM predictions for the character and strength of this dipole excitation mode.The deduced photoabsorption cross section exhibits a resonance-like shape distribution with pronounced peak structure.In addition, the fine structure of the M1 "spin-flip" mode was observed in 90 Zr and 206 Pb nuclei.

DOI: 10
.1051/ C Owned by the authors, published by EDP Sciences, 2015

Figure 2 .
Figure 2. Results for (a) the measured M1 strength of discrete levels in 90 Zr and (b) predictions from the quasiparticle-phonon model [17].

Figure 3 .
Figure 3.The unfolding algorithm applied to HPGe spectrum measured with 90 Zr target at 9.8 MeV photon energy.The lower part shows the primary transitions to the first excites states.

Figure 4 .
Figure 4. Photon-scattering spectra observed at θ = ± 90 • in the plane parallel (bottom panel) and perpendicular to the polarization plane (top panel) of the HIGS photon beam at Eγ = 7.3 MeV.The energy spread (FWHM) is about 220 keV.

Figure 6 .
Figure 6.Isotopic map near the s-process branching at 85 Kr.Isotopes shown as shaded (white) squares are stable (radioactive).The blue (red) arrows depict the s-process path at low (high) neutron densities.The ground state of 85 Kr can either β decay (T 1/2 = 10.75 y) to 85 Rb or capture a neutron to form 86 Kr.The isomeric state of 85 Kr can either β decay (T 1/2 = 4.48 h) or decay to the ground state via γ-ray emission.

Figure 7 .
Figure7.The blue point-up triangles represent the total cross section of the 86 Kr(γ,n) 85 Kr tot reaction while the green pointdown triangles denote the 86 Kr(γ,n) 85 Kr m cross section, both from the present measurements.The purple circles show the data from the 86 Kr(γ,γ')86 Kr reaction[22].The calculated cross section for the 86 Kr(γ,n) 85 Kr tot reaction, using the TALYS code, is represented by the red line.

Figure 8 .
Figure 8. Cross section of 85 Kr(n,γ) 86 Kr calculated with TALYS using experimental dipole (in black) and three-phonon quasiparticle-phonon model (QPM) strength functions (in red).The predicted uncertainties (shaded area) are derived from the experimental errors of the dipole strength function and from variations in the nuclear level density parameters.