ЯДЕРНАЯ ФИЗИКА, 2015, том 78, № 1-2, с. 57-68
(7, 2n)-REACTION CROSS-SECTION CALCULATIONS OF SEVERAL EVEN-EVEN LANTHANIDE NUCLEI USING DIFFERENT LEVEL DENSITY MODELS
©2015 A. Kaplan1)*, I. H. Sarpun2), A.Aydin3), E.Tel4), V. Capali1), H. Ozdo^an1)'5)
Received May 7, 2014
There are several level density models that can be used to predict photo-neutron cross sections. Some of them are Constant Temperature + Fermi Gas Model (CTFGM), Back-Shifted Fermi Gas Model (BSFM), Generalized Superfluid Model (GSM), Hartree—Fock—Bogoliubov microscopic Model (HFBM). In this study, the theoretical photo-neutron cross sections produced by (7, 2n) reactions for several even—even lanthanide nuclei such as 140'142Ce, i42,i44,i46,i48,is0Nd, i44,i48,i50,i52,i54Sm, and 160Gd have been calculated on the different level density models as mentioned above by using TALYS 1.6 and EMPIRE 3.1 computer codes for incident photon energies up to 30 MeV. The obtained results have been compared with each other and available experimental data existing in the EXFOR database. Generally, at least one level density model cross-section calculations are in agreement with the experimental results for all reactions except i44Sm(Y, 2n)i42Sm along the incident photon energy, TALYS 1.6 BSFM option for the level density model cross-section calculations can be chosen if the experimental data are not available or are improbable to be produced due to the experimental difficulty.
Several radionuclides of the lanthanide group are important in the areas of nuclear medicine, radiation therapy, imaging and industrial applications as metals and compounds [1,2].
For understanding of the structure and dynamics of the atomic nucleus, photonuclear reaction data are very important. Besides, photo-neutron cross sections are also important for some applications as fission and fusion reactor technology, activation analysis including protection, analysis of radiation transport and shielding, absorbed dose calculations in the human body throughout photon radiotherapy and material analysis studies for photon-induced nuclear reactions and transmutation of nuclear waste [3,4]. In addition, the cross-section data obtained by various
''Suleyman Demirel Univesity, Faculty of Arts and Sciences, Department of Physics, Isparta, Turkey.
2)Afyon Kocatepe University, Faculty of Arts and Sciences, Department of Physics, Afyonkarahisar, Turkey.
3)Kjnkkale University, Faculty of Arts and Sciences, Department of Physics, Kirikkale, Turkey.
4)Osmaniye Korkut Ata University, Faculty of Arts and Sciences, Department of Physics, Osmaniye, Turkey.
5)Akdeniz University, Faculty of Medicine, Department of Biophysics, Antalya, Turkey.
techniques are significant to improve additional theoretical nuclear models to illustrate nuclear reaction techniques and the properties of the excited states in various energy regions [5, 6].
The theoretical models of nuclear reaction are generally required to get the prediction of the reaction cross sections, especially if no experimental data obtained or in cases where it is difficult to carry out the experimental measurements [7—11]. Also, level density studies have important applications in nuclear medicine, fission/fusion reactor design, estimations of reaction cross sections, low-energy neutron capture, all kinds of nuclear reaction rates and astrophysics (thermonuclear rates for nuclear synthesis). In our previous works [12, 13], we investigated (7, n) and (7, 2n) cross-section calculations of several structural fusion materials. In this study, the theoretical (7, 2n) reaction cross sections of several even—even lanthanide nuclei such as
140,142 Ce 142,144,146,148,150 Nd 144,148,150,152,154 gm
and 160Gd in photon-induced reactions have been examined. The calculations on photo-neutron cross sections of 140Ce(7, 2n)138Ce, 142Ce(7, 2n)140Ce, 142Nd(7, 2n)140Nd, 144Nd(7, 2n)142Nd, 146Nd(7, 2n)144Nd, 148Nd(7, 2n)146Nd, 150Nd(7, 2n)148Nd, 144 Sm(7, 2n)142 Sm, 148 Sm(7, 2n)146 Sm, 150 Sm(7, 2n)148 Sm,152 Sm(7, 2n)150 Sm,154 Sm(7, 2n)152 Sm,
and 160Gd(7, 2n)158Gd reactions have been carried out for incident photon energies up to 30 MeV. The theoretical cross sections as a function of photon energy have been calculated using different level density models of TALYS 1.6 and EMPIRE 3.1  computer codes. The calculated results have been compared with each other and available experimental data existing in the EXFOR  library.
2. CALCULATION METHODS
The photo-neutron cross sections of several even— even lanthanide nuclei as a function of photon energy have been calculated using TALYS 1.6 and EMPIRE 3.1 computer codes for the different level density models such as CTFGM, BSFM, GSM, and HFBM.
TALYS  is a computer code for the prediction and analysis of nuclear reactions that contain photons, neutrons, protons, tritons, deuterons, hellions, and alpha particles, in the 1 keV—1 GeV energy region. For this, TALYS integrates the optical model, direct, pre-equilibrium, fission, and statistical nuclear reaction models in one calculation scheme and thereby gives an estimation for all the open reaction channels. In TALYS, several options are included for the choice of different parameters such as nuclear level densities, 7-strength functions, and nuclear model parameters . The 7-ray strength function is obtained from the compilation by Kopecky and Uhl  and the nuclear level density is also dependent upon an approach using the Fermi Gas Model .
EMPIRE is a modular system of nuclear reaction calculation codes, comprising various nuclear reaction models, and designed for calculations over a broad energy range and projectiles. The system can be used for theoretical investigations of nuclear reactions as well as for nuclear data evaluation work. The projectiles can be selected as photons, tritons, deuterons, nucleons, helions, alpha particles, and light or heavy ions. The energy range starts just above the resonance region in the case of a neutron projectile, and extends up to few hundred MeV for heavy-ion-induced reactions. The code accounts for the major nuclear reaction models, such as optical model, Coupled Channels and DWBA (ECIS06), CoupledChannels' Soft-Rotator (OPTMAN), Multi-step Direct (ORION + TRISTAN), NVWY Multi-step Compound, exciton model (PCROSS and DEGAS), hybrid Monte Carlo simulation (DDHMS), and the full featured Hauser—Feshbach model including the optical model for fission. Heavy-ion fusion cross section can be calculated within the simplified coupledchannels approach (CCFUS) .
The short descriptions of level density models are given below. The details of model parameters and
options of TALYS 1.6 and EMPIRE 3.1 can be found in [14, 15, 20].
The Constant Temperature Model (CTM) as introduced by Gilbert and Cameron [14, 21] indicates an independence of temperature with respect to excitation energy. The CTM requires solving the problem of matching the constant temperature part at low excitation energies and Fermi gas expression at high excitation energies. At low excitation energies, the constant temperature treatments could be applied in the range of 0 MeV to a matching energy, whereas the Fermi gas expression could be applied above the matching energy. Fermi Gas Model (FGM) is based on the assumption that the single-particle states which construct the excited levels of the nucleus are equally spaced, and that collective levels are absent . In the BFM , the matching problem has been overcome by treatment of pairing energy as an adjustable parameter and the Fermi gas indication could be used for all energy range down to 0 MeV. At low excitation energies, standard model of the Fermi gas explanation cause numerical divergence. TALYS 1.6-GSM takes superconductive pairing correlations into account according to the Barden—Cooper— Schrieffer Theory [14, 23,24] which is described by a phase transition from a superfluid behavior at low energy, where pairing correlations strongly influence the level density, to a high-energy region which is characterized by the Fermi Gas Model. In this model there is no unsolved problem for the parameterization. EMPIRE 3.1-GSM is characterized by a phase transition from superfluid behavior at low energy where pairing correlations strongly influence the level density, to a high-energy region which is described by the FGM. Thus, the GSM resembles the Gilbert—Cameron (GC) to the extent that the model distinguishes between low-energy and high-energy region, although for the GSM this distinction follows naturally from the theory and does not depend on specific discrete levels that determine a matching energy. HFBM is the microscopic combinatorial approach developed during the Reference Input Parameter Library (RIPL3) project . The method consists in using single-particle level schemes obtained from constrained axially symmetric HFBM .
3. RESULTS AND DISCUSSION
In the present study, (7, 2n) reaction cross sections of 140Ce(7, 2n)138Ce, 142Ce(7, 2n)140Ce, 142Nd(7, 2n)140Nd, 144Nd(7, 2n)142Nd, 146Nd(7, 2n)144Nd, 148Nd(7, 2n)146Nd, 150Nd(7, 2n)148Nd, 144 Sm(7, 2n)142 Sm, 148 Sm(7, 2n)146 Sm, 150 Sm(7, 2n)148 Sm,152 Sm(7, 2n)150 Sm,154 Sm(7, 2n)152 Sm,
140Ce(Y, 2rc)138Ce • A. Lepretre et al., 1976
- TALYS 1.6 (Constant Temperature + Fermi Gas Model)
---TALYS 1.6 (Back-Shifted Fermi Gas Model)
----TALYS 1.6 (Generalized Superfluid Model)
.....EMPIRE 3.1 (Generalized Superfluid Model)
----- EMPIRE 3.1 (Hartree-Fock-Bogoliubov Microscopic Model)
Photon energy, MeV
Fig. 1. The comparison of calculated photo-neutron cross sections of140 Ce(7, 2n)138Ce reaction with the experimental values taken from EXFOR (EXFOR, 2013).
Cross section, mb 300 г
142Ce(Y, 2^)140Ce » A. Lepretre et al., 1976
— TALYS 1.6 (Constant Temperature + Fermi Gas Model)
— TALYS 1
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