First evidence of low energy enhancement in Ge isotopes

The γ-strength functions and level densities of 73,74Ge have been extracted from particle-γ coincidence data using the Oslo method. In addition the γ-strength function of 74Ge above the neutron separation threshold, Sn = 10.196 MeV has been extracted from photoneutron measurements. When combined, these two experiments give a γ-strength function covering the energy range of ∼1-13 MeV for 74Ge. This thorough investigation of 74Ge is a part of an international campaign to study the previously reported low energy enhancement in this mass region in the γ-strength function from ∼3 MeV towards lower γ energies. The obtained data show that both 73,74Ge display an increase in strength at low γ energies.


Introduction
The γ-ray strength function [1] has been proven to be a useful concept to characterize the average nuclear response to electromagnetic radiation when the nucleus is excited to high energies, and the density of quantum levels is high.There exists a wealth of information about the γ-strength function (γSF) for nuclei above the neutron binding energy, predominantly from photoneutron experiments [2].For γ energies below S n the information is more scarce, as the strength is quite challenging to extract in this area.Methods such as the Oslo method [3], the two-step cascade method [4] and a statistical treatment of nuclearresonance fluorescence spectra [5] are used to investigate the strength below the neutron separation energy.However, the results from the different techniques sometimes show large discrepancies in the resulting γSF.For energies below ∼3 MeV, the γSF of a nucleus is dominated by the receding tail of the giant electric dipole resonance.It therefore came as a surprise when a strong low-energy enhancement in the γSF, hereafter referred to as the upa e-mail: therese.renstrom@fys.uio.nobend, was discovered below 3 MeV for 56,57 Fe [6].The γSF measurement was performed at Oslo Cyclotron Laboratory (OCL), using charged particle reactions (and confirmed using the two-step cascade method), and the following years this phenomenon was observed in a wide range of nuclei [7][8][9][10][11][12][13]. A set of examples of upbends are shown in Fig. 1.Recently, the upbend was reported with a different experimental technique in 95 Mo [14].The physical mechanisms behind the upbend was a puzzle for many years, but recently three papers with theoretical explanations have been published [15][16][17].In addition, the upbend has been experimentally shown to be dominantly of dipole nature [18].An international collaboration was formed with the common goal of investigating one specific nucleus in the mass range where the upbend structure was likely to appear, using different experimental techniques.The nucleus 74 Ge was chosen, and four different experiments were performed: ( 3 He, 3 He ), (α, α ), (p,p ) and (γ, γ ) .In the following we will present our results from 3 He induced reactions on 74 Ge performed at OCL, and furthermore, we will show new results from a photoneutron experiment on 74 Ge performed at the NewSUBARU laboratory in Japan.

Experimental methods
We used two different approaches to investigate the γSF of 74 Ge, a charged particle reaction and a photoneutron experiment.We will in the following sections present the two different techniques briefly.

Oslo data
The experiment was performed at the OCL, where a ∼ 0.5 enA 3 He beam at 38 MeV bombarded a self-supporting, 0.5 mg/cm 2 thick 74 Ge target.The two reaction channels of interest were 74 Ge( 3 He, 3 He γ) and 74 Ge( 3 He, αγ).The charged outgoing particles were identified and their energies measured with the SiRi system [19], consisting of 64 Δ E -E silicon telescopes, with thicknesses of 130-μm and 1550-μm, respectively.SiRi was placed in forward direction, covering angles from θ=40 to 54 • .The γ rays were detected with the CACTUS array [20] consisting of 28 5 × 5 NaI(Tl) detectors surrounding the target and the particle detectors.The total efficiency of CACTUS is 15.2% at E γ =1.3 keV.Using reaction kinematics, the initial excitation energy of the residual nucleus can be deduced from the energy of the outgoing particles detected in SiRi.The particle-γ coincidence technique is used to assign each γ ray to a cascade depopulating a certain initial excitation energy in the residual nucleus.Fig. 2(a) shows the particle-γ matrix (E γ , E) of the 74 Ge( 3 He, 3 He γ) reaction, where the γ spectra have been unfolded with the NaI response functions [21].The neutron binding energy of 74 Ge is reflected clearly in a drop in γ intensity at E≈ S n =10.196MeV.A quite weak diagonal, where E=E γ reveals that the direct feeding to the 0 + ground state is not particularly favored.We see a second more pronounced diagonal that represents decay to the first excited 2 + state of 596 keV.We know that these γ rays stem from primary transitions in the γ cascades, but the rest of the matrix consists of a mix of higher generation γ rays.We would like to study the energy distribution of all primary γ-rays originating from various excitation energies, and extract the nuclear level density (NLD) and γSF simultaneously from this information.From the unfolded γ spectra, the distribution of primary γ rays P(E, E γ ), as shown in Fig. 2(b), has been extracted from the full cascades by the iterative subtraction method of Ref. [22].
In the quasi-continuum we assume that P is proportional to the NLD at the final excitation energy ρ(E − E γ ) and that the decay is governed by the γ-transmission coefficient T (E γ ), which according to the Brink hypothesis [23,24] is independent of excitation energy.Thus the decay probability is given by The γSF is related to the transmission coefficient by f (E γ ) = T (E γ )/2πE 3 γ , if we assume that statistical decay is dominated by dipole transitions.From Eq.(1) we see that the NLD and γSF can be determined from a simultaneous fit to the primary γ matrix, P.

NewSUBARU data
The photoneutron cross section measurements were performed at the synchrotron radiation facility NewSUB-ARU [25].Quasi monochromatic γ-ray beams [26] are produced in head-on collisions between laser photons and relativistic electrons, a so-called laser-Compton scattering (LCS).The energy of the laser photons increases from a few eV to several MeV in the collisions.In this experiment a 1.9916 g/cm 2 thick sample of 74 Ge, was placed inside an aluminum container and irrradiated with eight different γ-ray beams with energies from 10.4 to 12.7 MeV.The 74 Ge sample was mounted in the center of a 4π neutron detection array comprised of 20 3 He proportional counters embedded in a polyethylene moderator.The ring ratio technique [27] was used to measure the average energies of the detected neutrons, and from this the efficiency of the neutron detector is established.A 6 ×5 NaI(Tl) detector was used to measure the flux of the LCS beam.The detector was placed at the end of the γ ray beam line.The total number of γ rays on target for a certain beam was found using the well established pile up method described in Ref. [28].The almost monochromatic γ beam was monitored by a 3.5 ×4.0 LaBr 3 (Ce) detector.The spectra were reproduced using GEANT4 simulations, and unfolded to give the real energy profile of the incoming beam.The resolution of the γ-ray beams used in the experiment was excellent, typically 1-2% at FWHM.
The (γ, n) cross section is given by, where n γ (E γ ) gives the energy distribution of the γ-ray beam normalized to unity and σ(E γ ) is the photoneutron cross section to be determined.Furthermore, N n represents the number of neutrons detected, N t gives the number of target nuclei per unit area, N γ is the number of γ rays incident on target, n represents the neutron detection efficiency, and finally ξ = (1 − e μt )/(μt) is the correction factor for a thick target measurement.The factor g represents the fraction of γ flux above the neutron threshold S n .Eq.( 2) is solved for the cross section using the Taylor expansion method described in [29].In this way we find cross sections for eight different energies.The uncertainties in the measurements are ∼4.4% [29].The measured photoneutron cross section are shown in Fig. 3 together with existing data [31].We notice that our new data are on average 30% lower than the existing data.This is consisent with the (n, γ) cross sections measured for several Nd and Sm isotopes [29,30] during the same experimental campaign at NewSUBARU.  7Ge and previously measured ones [31].The results are preliminary.
The photoneutron cross sections are related to the γSF by which can be directly compared with the Oslo data from the principle of detailed balance, giving f up ≈ f down [1,32].

Discussion of results
After careful analysis of the photoneutron data and normalization of the Oslo data, we will briefly present at the NLDs, investigate if the two data set give us a consistent γSF for 74 Ge in this broad energy range and observe the shapes of the γSFs.
The normalized NLDs of 73,74 Ge are shown in Fig. 4. We notice that 74 Ge has a constant temperature shape, 73 Ge has slightly more structures.We also observe that two isotopes have quite parallel NLD curves, as previously observed in the NLDs of many pairs of neighboring isotopes investigated with the Oslo method, see Ref. [33].
We now turn to the normalized γSFs, shown in Fig. 5.The two Ge isotopes are in very good agreement, as we previously have observed for several isotopic chains, see Fig. 1.There is also a nice correspondence in slope between the Oslo data and the new photoneutron data.Around 7 MeV we see a distinct resonance-like structure in the strength of 74 Ge.This structure has also been observed in the 74 Ge(α,α') data analyzed as a part of the Ge collaboration, and should be investigated further.We also observe that both 73 Ge and 74 Ge show a clear enhancement in the γSF for gamma energies below ∼3 MeV.This means that the probability of γ decay increases with decreasing γ ray energy for both isotopes.The absolute value of the γSF increases by a factor of 3 between ∼ 3 MeV and 1 MeV.
We know that the radiative neutron capture cross sections are sensitively depending on the γSF around the neutron separation energy.The neutron threshold energy decreases for neutron rich nuclei, and if we assume that the upbend will persist when we move towards more neutron rich nuclei, approaching the neutron drip line this upbend  73,74 Ge, including the (γ, n) reaction for 74 Ge from the present experiment and from existing data [31].The red solid line is the sum of the M1 spin flip resonance and the E1 strength calculated using QRPA calculations.The red dotted line includes in addition a parameterization of the upbend.The results are preliminary.is likely to affect the (n, γ) reaction rates as previously shown in [34].

DOI: 10 Figure 1 .
Figure1.Some examples of low energy enhancements in the γ-ray strength function found in medium mass nuclei, using the Oslo method.

Figure 2 .
Figure 2. (a) Particle-γ coincidence matrix from the 74 Ge( 3 He, 3 He γ) 74 Ge reaction.The NaI spectra are unfolded with the NaI response functions.(b) The first generation matrix.

Figure 3 .
Figure 3.Comparison between present photoneutron emission cross sections for74 Ge and previously measured ones[31].The results are preliminary.

Figure 4 .
Figure 4.The NLDs of73,74 Ge.The red and black diamond shaped points represent the estimated NLD at the neutron binding energy of the two isotopes.The results are preliminary.

Figure 5 .
Figure 5.The γSFs of73,74 Ge, including the (γ, n) reaction for74 Ge from the present experiment and from existing data[31].The red solid line is the sum of the M1 spin flip resonance and the E1 strength calculated using QRPA calculations.The red dotted line includes in addition a parameterization of the upbend.The results are preliminary.