Nuclear structure data obtained by the (n th ,2γ) reaction

. The determination of nuclear structure parameters such as gamma transitions, level scheme, nuclear level density and radiative strength functions is one of the most important tasks in low-energy nuclear physics. The two-step gamma cascades method based on detection of gamma coincidences following neutron capture, ie. the (n,2γ) reaction has been proven to give spectroscopic data and data concerning level density and radiative strength function. This method allows for the study of the dynamics of interaction and inter-transition between Fermi-and Bose-states of the nucleus near the neutron binding energy. There is an essential difference between these intranuclear processes from those in classical and high-temperature superfluidity, which is determined by a shape of the investigated nucleus, the nucleon parity in it, existence of nucleons of different types (protons and neutrons) etc. Two-step gamma cascades technique has so far been successfully applied for 45 nuclei in the mass region 28<A<200. Brief description of the method will be included here with examples from the recent research


Introduction
Development of models of nuclear structure requires accurate and precise experimental data in order to confirm the theoretical prediction. On the other hand, practical applications of many materials used in nuclear physics greatly benefit from this kind of data. Two-step gamma cascade model combined with the practical model of the cascade gamma decay has two main areas of application [1][2][3][4]. First part is related to the level scheme, as this method can provide insight into new energy levels and transitions and can also confirm and improve the existing data. The second part is related to the determination of level density (LD), radiative strength function (RSF) and other related parameters. This method has been successfully applied in recent research to obtain spectroscopic data, as well as on 45 nuclei in the mass region from 28 to 200 to obtain level density and radiative strength function. The method is based on the detection of two consecutively emitted gamma-rays after the neutron capture on the target nucleus, ie. the (nth,2γ) reaction

Experimental setup
Typical experimental setup for the two step gamma cascades experiment, in this case from the recent research of 94 Nb is presented in Figure 1 [5,6]. It consists of a thermal/cold neutron beam directed at the target of interest, as well as two HPGe detectors with appropriate neutron and gamma shielding. Data acquisition system should be able to record the time and the energy of the detected gamma-ray, which is a standard requirement for coincidence measurements. One other requirement for the successful application of the method is close geometry in order to maximise the number of coincidences. The analysis of the experimental data is done in the offline mode. The measurements for the most recent nuclei investigated were performed at the research reactors in Budapest, Hungary and Garching, Germany.

Spectroscopic data
First step of the analysis consists of finding the coincident events in the detectors and constructing the spectrum of sums of amplitudes for coincident pulses (SACP). Example of this spectrum for 94 Nb is shown in Figure 2. The peaks that are found in the SACP spectrum represent the total energy of two consecutively emitted gamma rays from the neutron capture state to the ground state or low-lying excited states.  [5,6].
After the peaks are identified in the SACP and assigned to the correct final energy levels, for each peak in the SACP, the two-step-cascade (TSC) spectra is constructed. TSC spectra for a peak in SACP contains all the gamma rays from cascades that go from the initial capture state to the final level identified in the SACP. The elimination of Compton background and random coincidences is done by gating on the region near the peaks of interest. Example of the TSC spectrum for 94 Nb is shown in Figure 3. Since the capture state of 94 Nb is 7227 keV, the TSC shown on Figure three represents all the gamma rays from the cascade that go to the 58.7 keV excited state of 94 Nb. Details of the method and the maximum likelihood function used to determine the order of the cascade gamma rays can be found in [5,6].  [5,6].
After the identification of all resolved cascades from TSC distributions, the next step is comparison of experimentally obtained data with the ENSDF database. Comparison with databases lead to a number of new information.
The first result is identification of new energy levels involved in a cascade. There are the energy levels involved in a cascade. Initial and final levels are well known, but not all intermediate levels detected in the experiment can be found in the database. By this comparison, for 94 Nb, 29 recommendations for new energy levels were found, and 24 for 56 Mn [5,6].
Second result is the identification of new transitions (primary and secondary). For 94 Nb, 210 new recommendations for new transitions were found, and 55 in the case of 56 Mn [5,6].
Some of the detected gamma rays in the database are not placed in the level scheme [10,11]. This method enables placing a number of existing gamma rays from the database in the level scheme.
As the spins of the initial and final states are usually well known, it is also possible to put constraints on the values of the spins for the intermediate levels detected in the experiment.

Determination of LD and RSF functions
One of the information from the spectroscopic part concerns the intensity of the cascades observed in the experiment. These intensities are used to construct the spectrum of intensities of cascades, Iγγ, as function of the energy of the first gamma ray from the cascade [7,8]. Example of this spectrum for 56 Mn is shown on Figure  4. This spectrum is obtained by binning the whole energy region in equal energy bins and summing the intensities of cascades that have primary transition energy in the region of the bin in question. This spectrum is important in further analysis, as the shape of this experimentally obtained spectrum directly depends on the shapes of LD and RSF functions.

Practical model of the cascade gammadecay
The dependence of Iγγ on the values of LD and RSF is given as [7,8]: where is excitation energy, = 6 2 ⁄ is the density of the single-particle states near the Fermisurface, is the energy of the l-th Cooper pair breaking threshold. The cut-off factor of the spin for the excited state of compound-nucleus above the maximal excitation energy of the "discrete" level area is taken for the Fermi-gas model. is a phenomenological coefficient describes increase of density of collective levels -a phenomenological relation between entropies of phases of the nuclear matter with taking into account a cyclical breaking of Cooper pairs: where are parameters of densities of the vibrational levels above the breaking point of each l-th Cooper pair, and determine a change in the nuclear entropy and a change of the quasi-particles excitation energies, correspondingly. The coefficients for different pairs are fitted independently. Coefficient is used as a description of the rotation level density. The RSF function is a combination of KMF function for E1 and M1 transition strength function with the added part to describe the peaks that appear in the function [9]: ( 1, ) = 2 ( 2 + 4 2 2 ) ( 1, ) = 2 ( 2 + 4 2 2 ) Here EGE (or EGM) and ΓGE (or ГGM) are location of the centre and width of the maximum of the giant dipole resonance, TE (or TM) is a varied nuclear thermodynamic temperature, for E1-(or M1-) transitions. And for each i-th peak (i ≤ 2) of the strength functions of E1-(or M1-) transition: EEi (or EMi) is a centre position, ΓEi (or ГMi)width, W Ei (or W Mi ) -amplitude, and α Ei (or α Mi ) ~ T 2 is an asymmetry parameter. A necessity of taking into account a local peak asymmetry in the radiative strength function results from theoretical analysis of features of the fragmentation of single-particle states in the nuclear potential. In the fitting process the functions vary in a wide range of parameters. The shell inhomogeneities of a single-partial spectrum are also taken into account in analysis. Fig. 6. Example of the obtained RSF [8].
The results of the LD and RSF obtained in this way are shown on Figures 5 and 6. Figure 5 represents the obtained level density (dots) and also BS Fermi-gas level density (line) for part of the nuclei analysed so far. Figure 6 represents the obtained radiative strength function for E1 (closed circles) and M1(open circles), compared with the KMF model (triangles).

Conclusion
The method of two-step gamma cascades has been applied so far to obtain structural data for 45 nuclei. The technique has proven to be very powerful for collecting new spectroscopic data such as information about gamma transitions and energy levels. In addition, this method provides new information about LD and RSF, which can be the basis for studying other characteristics of the atomic nucleus, such as superfluidity parameters. In the future, new measurements on previously unexamined nuclei are planned, as well as an improvement of the existing gamma decay model.