ЯДЕРНАЯ ФИЗИКА, 2014, том 77, № 3, с. 334-339
ЯДРА
COMPARISON OF LEVEL DENSITY MODELS IN (7,n) REACTIONS
OF SOME LANTHANIDE NUCLEI
©2014 R. Unal*, I. H. Sarpun, H. A. Yalim
Afyon Kocatepe University, Physics Department, Afyonkarahisar, Turkey Received February 27, 2013; in final form, August 5, 2013
Level densities are required at excitation energies where discrete level information is not available or incomplete to get a reliable theoretical analysis of cross sections, spectra, and angular distributions. The total reaction cross sections of some lanthanides (141Pr,142Nd, 144Sm,153Eu,160Gd,159Tb,165Ho,175Lu) were calculated using TALYS 1.2 code for gamma-induced reactions through the five level density models in the incident gamma energy range from 5 to 30 MeV. All calculations from the present study were compared with each other and with the experimental data obtained from EXFOR library. The total photo-neutron reaction cross-section values obtained from the model calculations and experimental measurements taken from EXFOR confirm the presence of systematical disagreements reported in the literature, except165Ho case where one can see a satisfactory agreement.
DOI: 10.7868/S0044002714020172
1. INTRODUCTION
The knowledge of level densities for estimating nuclear reactions in statistical models is important at excitation energies where discrete level information is not available or incomplete. The most important step to get a reliable theoretical analysis of cross sections, spectra, angular distributions, and other nuclear reaction observables is to get a correct level density together with the optical model potential [1]. For this reason, level densities have been intensively studied using the models [2, 3].
This paper addresses a consistent parameterization for five level density models used in TALYS, namely the
Constant Temperature Model, Back-shifted Fermi-gas Model, Generalized Superfluid Model, Microscopic Level Density, Goriely's Table, Microscopic Level Density, Hilaire's Table. The brief descriptions of models are given below where detailed information is available in the literature.
The Constant Temperature Model (CTM) [4, 5] treats the problem in low and high excitation energy regions separated by matching energy. Since this matching depends on experimental information (discrete levels, mean resonance spacings, shell corrections, separation energies, etc.) it may occur that the
E-mail: runal@aku.edu.tr
solution of the matching problem yields unrealistic even sometimes unphysical values for the matching parameters.
In the Back-shifted Fermi-gas Model (BFM) [5, 6], the pairing energy is taken as an adjustable parameter that avoids the matching problem. Otherwise, the standard version of the Fermi-gas expression at low excitation energies leads to numerical divergence.
The Generalized Superfluid Model (GSM) takes superconductive pairing correlations into account according to the Bardeen—Cooper—Schrieffer theory [5, 7, 8]. However, there are no basic unsolvable problems in the parameterization of this model.
The phenomenological models (CTM, BFM, GSM) are described briefly above. However, for non-fissile nuclides an effective level density model is employed that accounts for all collective enhancements in the level density parameter a [5].
Besides these three phenomenological models, there are other microscopic approaches based on Hartree—Fock calculations. These microscopic models treat the shell effects, pairing correlations, deformation effects, and collective excitations [2]. One of these is microscopic level density of Goriely's Table (mGT) [9] and the other microscopic level density model is Hilaire's Table (mHT), proposed by Hilaire and Goriely [10]. Moreover, the microscopic approaches' prediction power of neutron resonance spacings is comparable to that of the phenomenolog-ical BFM formulae [5].
o, mb 350
300250200 150 100 50 0
Utsunomiya et al., 2006 [12] Varlamov et al., 1993 [13] Belyaev and Semenov, 1991 [14] Berman et al., 1987 [15]
* Beil et al., 1971 [16]
★ Sund et al., 1970 [17]
T Bramblett et al., 1966 [18]
- TALYS/CTM
----TALYS/BFM
......... TALYS/GSM
---TALYS/mGT
----TALYS/mHT
28
E, MeV
8 12 16 20
Fig. 1. Total cross section of (j,n) reactions for141 Pr nucleus according to different level density models [12—18].
o, mb 400 r
350 -
300
250
200
150
100
50
0
8
▲ Belyaev et al., 1991 [14] □ Carlos et al., 1971 [19]
24
E, MeV
Fig. 2. Same as in Fig. 1, but for 142Nd[14, 19].
In this paper, theoretical total cross sections of some lanthanides (141Pr, 142Nd, 144Sm, 153Eu, 160Gd, 159Tb, 165Ho, 175Lu) were calculated using TALYS 1.2 code [5] for gamma-induced reactions through the five level density models. All the calculations were compared with each other and with the experimental data obtained from EXFOR [11] library.
2. CALCULATION METHODS
In this study lanthanides are chosen due to their various nuclear applications. In nuclear reactors, they are used as control rods to regulate nuclear reactors, as shielding materials, and as structural components because of their neutron absorption properties.
In the calculations the TALYS 1.2 code was used.
o, mb
Fig. 3. Same as in Fig. 1, but for144Sm [20].
o, mb
Fig. 4. Same as in Fig. 1, but for153Eu [21].
Nuclear structure and model parameters are implemented through an internal reference library. Projectile nuclei, target element, target mass, and incident projectile energy parameters must be defined in the input file to calculate the cross sections. However, the input file should include appropriate input and output
keywords to vary nuclear models and parameters in order to tune calculations to experimental data as well as to control which cross sections are generated in the output file [1, 5]. The obtained results are presented in the following section.
o, mb
E, MeV
Fig. 5. Same as in Fig. 1, but for160Gd [21, 22].
o, mb
E, MeV
Fig. 6. Same as in Fig. 1, but for159Tb [23-25].
3. RESULTS AND DISCUSSION
The total (y, n)-reaction cross sections of 141 Pr, 142Nd, 144 Sm, 153Eu, 160Gd, 159Tb, 165Ho, and 175Lu targets were calculated for five level density models using TALYS 1.2 code in 5- to 30-MeV incident gamma energy range. The calculated results
and available experimental data are presented in Figs. 1-8.
According to the neutron contents, the target elements used in this study can be categorized into two groups as magic and deformed. The targets 141 Pr, 142Nd, and 144 Sm have 82 neutrons and are called
о, mb
E, MeV
Fig. 7. Same as in Fig. 1, but for165Ho [21, 23, 24].
E, MeV
Fig. 8. Same as in Fig. 1, but for175Lu [26].
magic, and the targets 153Eu, 160Gd, 159Tb, 165Ho, and 175Lu are called deformed. As expected for a spherical nucleus, the results for magic nuclei show clearly the Giant Dipole Resonance (GDR) does not split into two or more components (Figs. 1—3) whereas it splits into two components for deformed nuclei (Figs. 4, 6—8), except for 160Gd (Fig. 5).
The calculated values roughly agree with the experimental results (Figs. 1—8). The exception comes from Belyaev and Semenov [14] measurements in Figs. 1 and 2 in which a discrepancy arises at the (Y, 2n)-peak region. The further analysis of data, obtained from Beil et al. [16] , Sund et al. [17], Bramblett et al. [18], Carlos et al. [19], and Bergeere et al. [23] available separately in EXFOR library, in-
ЯДЕРНАЯ ФИЗИКА том 77 № 3 2014
dicated that proper subtraction of (7,2n) contribution from Belyaev and Semenov [14] measurements leads to perfect agreement between the calculated values and experimental measurements. On the other hand, the calculated values are in good agreement with the experimental data of Carlos et al. [20] for 144 Sm nucleus (Fig. 3).
Moreover, the small disagreements between theoretical and experimental data for 142Nd (Fig. 2), 153Eu (Fig. 4), and 160Gd (Fig. 5) obtained using quasi-monoenergetic annihilation gamma quanta have small contribution. The production of positron annihilation gamma quanta is a result of bremsstrahlung production, production of pairs and positron annihiliation [27]. The observed double-humps could be attributed to comparable deformation between (7, n) and (7,2n) reaction cross sections, except for 160Gd (Fig. 5) as mentioned by Berman and Fultz [28] the higher-energy hump of the giant resonance manifests itself entirely in the (7,2n) cross section. Characteristic double-humped splitting could be observed in this deformed nucleus in total cross section.
4. CONCLUSION
The five level density models applied using TALYS 1.2 code gave similar results for all target nuclei in 5-to 30-MeV incident gamma energy range.
All the calculated values obtained using the mentioned models are also in good agreement with the experimental results, except for the measurements of Belyaev and Semenov [14] which indicates the importance of (7, n) and (7,2n) proper separation in experiment.
The double-humps could be expected for the deformed nuclei. However, this could not be seen for 160Gd in our calculations where the higher-energy hump of the giant resonance manifests itself entirely in the (y, 2n) cross section as mentioned by Berman and Fultz [28].
The present study indicates that some of the disagreement between experimental and theoretical data may be minimized using newly experimental resources as mentioned by Ishkhanov and Var-lamov [27].
The study was supported by Afyon Kocatepe University Science Research Projects Coordination Unit with the grant number 10.REK.01.
REFERENCES
1. A. J. Koning, S. Hilaire, and M. C. Duijvestijn, in Proceedings of the International Conference
on Nuclear Data for Science and Technology — ND2007, Nice, France, Apr. 22-27, 2007, Ed. by O. Bersillon et al. (EDP Sciences, 2008), p. 211.
2. P. Demetriou and S. Goriely, Nucl. Phys. A 695, 95 (2001).
3. S. Hilaire and S. Goriely, Nucl. Phys. A 779, 63 (2006).
4. A. Gilbert and A. G. W. Cameron
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