- Email: [email protected]
Cross section evaluation in the photodisintegration of152Sm isotope
Available online at www.sciencedirect.com
Physics Procedia 31 (2012) 178 – 184
GAMMA-1 Emission of Prompt Gamma-Rays in Fission and Related Topics
Cross section evaluation in the photodisintegration of 152 Sm isotope C. Opreaa, A. Opreaa,b, A. Mihula,b∗ a
Joint Institute for Nuclear Research (JINR), Joliot- Curie 6, Dubna 141980, Russia b University of Bucharest, Bucharest-Magurele, RO-077125, Romania
Abstract We have evaluated the cross section of the 152Sm(γ, n)151Sm reaction in the frame of the Hauser – Feshbach formalism using the Talys computer codes as well as by using the computer codes written by the authors. The obtained results were compared with experimental data existing in the literature. The named computer codes allowed estimating the necessary penetrability coefficients with no approximations for charged and neutral particles emission in the exit channels.
© 2012 Published by Elsevier B.V. Selection and/or peer-review under responsibility of Institute for Reference © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the organizer Materials and Measurements. Keywords: 152Sm ; photodesintegration cross section ; Hauser – Feshbach formalism ; direct and compound mechanism ; penetrability coefficients
* Corresponding author. Tel.: +7-49-621-62155; Fax.: +7-49-621-65429 E-mail addres: [email protected]
1875-3892 © 2012 Published by Elsevier B.V. Selection and/or peer-review under responsibility of Institute for Reference Materials and Measurements. doi:10.1016/j.phpro.2012.04.024
C. Oprea et al. / Physics Procedia 31 (2012) 178 – 184
Nomenclature α A C β B σ
αβ
λ
T c W M V(r) VCoul ze Ze VCfg E WW+ Dl αβ
Incident particle Target nucleus Compound nucleus Εmergent (outgoing) particle Residual nucleus (usually excited) Cross section, mb Incident particle reduced length, fm Transmission coefficient Reaction channel Widths fluctuation correction factor (WFC) Reduced mass of emitted particle, kg The real part of nuclear potential, MeV Coulomb potential, MeV Charge of emitted particle, C Charge of residual nucleus, C Centrifugal potential, MeV Energy of the emitted particle, MeV Ingoing wave function Outgoing wave function Logarithmic derivative of the wave function
1. Introduction 152
Sm is a transitional nucleus of significance in the fields of fundamental and applied researches [1-3]. The Samarium nucleus has seven natural isotopes as well as nine radioactive isotopes produced in fission process of Uranium and Plutonium. The unstable nucleus 151Sm, resulting from the photo-neutron disintegration of 152Sm is one of the radioactive fission products of nuclear waste; the capture cross section for thermal neutrons is required for transmutation studies and for nuclear astrophysics [4,5]. The 152Sm nucleus is a part of the group of nuclei with neutrons number from N=88-92 which drastically change the properties of nuclear surfaces [6]. In this range the nuclear surface passes from non-deformed spherical nuclei to deformed ones that corresponding to a phase transition through a critical point from a spherical vibrator to an axial rotor [7]. The photonuclear (γ,n), (γ,p) and (γ,α) reactions together with the capture of neutrons, protons and alpha particles play an important role in many different subfields of nuclear astrophysics [8-10]. In this 151 paper the 152 reaction was analyzed for gamma incident energy ranging from the threshold 90 Sm(γ , n) 90 Sm (~8.25 MeV) up to 30 MeV. As suggested in many papers we chose the Hauser – Feshbach formalism (HF) as the proper approach for the evaluation of the above photo-disintegration cross section [11,12]. For accomplishing of the experimental purposes, the Talys software, with his implemented nuclear database (nuclear structure, nuclear reaction, models, etc), can be an efficient, rapid and powerful tool for nuclear reaction simulation, for understanding of the dominant processes or the concurrence between them [13].
179
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C. Oprea et al. / Physics Procedia 31 (2012) 178 – 184
2. Hauser-Feshbach formalism (theoretical background) The HF formalism [11] was developed in ’50 years of the past century for binary nuclear reactions with formation of a compound nucleus. The compound nucleus is formed by interaction of the target nucleus with incident particle and is characterized by the same properties like, mass, rest energy, spin parity and others like any other stable nuclei. After a time much longer than the characteristic time for nuclear reaction (1020-22s), the compound nucleus is decaying on possible energetic channels “forgetting” the initial state (Bohr hypothesis). The short-range finite nuclear forces act between incident particles and target and also between emergent particle and residual nucleus (for example Wood Saxon potential). As indicated in [12] after applying the general laws of conservation for a binary reaction (α+Α=>C=>β+B) the cross section in the Hauser – Feshbach formalism has the following form:
σ αβ = πλ α2
Tα Tβ
∑ Tc
(1)
Wαβ
c
We mention that the sum in the nominator is effectuated on all open possible channels in the given reaction. The WFC take into account the correlation existing between ingoing and outgoing channels [13,14] but can be neglected for incident particle energy above some MeV. This factor is of order of unity and decrease with the increasing of the particle incident energy. There are a few methods for the calculation of this factor and three of them are implemented in Talys computer codes. First time the HF expression (1) was proposed without WFC factor (WFC=1). 2.1. Penetrability coefficients Penetrability coefficients (PCs) are important for the HF expression of the cross section. They are defined as the probability of an incident particle to pass through a barrier of potential. In quantum mechanics they are equal to the ratio between the squared modules of the wave functions of the particle emerging the barrier and the incident particle [13]. In case that the energy of the particle is lower then the barrier height than from classical mechanics point of view this particle will not pass the barrier. In quantum mechanics the probability of the particles to pass the barrier is non zero. If the particle energy is much smaller then the height of the barrier we can use the so-called “semi-classical” approximation and then the PCs can be written as [15]:
⎧ ⎫ 1/2 T(l, E) = exp⎨− 8m h 2 ∫ V(r) + VCoul + Vcfg − E dr ⎬ D ⎩ ⎭
[
(2)
]
More appropriate approach is to obtain the PCs from quantum mechanical consideration using the reflection factor Ul, [12]:
T(l, E) = 1 − Ul (E)
{
[(
2
)(
(3)
)] }{
[(
)(
)] }
Ul = Dl − R 1 Wl− dWl− dr Wl− Dl − R 1 Wl+ dWl+ dr Wl+
−1
r =R
(4)
The expression of W is a linear combination of Neumann and Bessel function for neutral particles but
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C. Oprea et al. / Physics Procedia 31 (2012) 178 – 184
for charged particles it is a linear combination of regular and irregular Coulomb functions. If for neutral particles the PCs can be calculated relatively easy, for charged particles it is necessary to use the Coulomb functions. The Coulomb functions are solutions of Schrödinger equation with Coulomb potential and they have quite complicated integral form [16]. The authors have evaluated numerically the PCs for charged particles (protons and alpha particles) using the quantum mechanical approach and the integral form of Coulomb functions by writing their own computer codes in Mathematica 4.1 [17] (Fig. 1). These codes were part of a program destined to evaluate the cross section in (n, α) reactions with fast neutrons using the HF formalism. The PCs, defined in [12], increase with the increasing of the energy but never will be greater than unity.
Penetrability coefficient
Penetrability coefficient
1.0 1.0 0.8 0.6 0.4 0.2
0.8
0.6
0.4
0.2
0.0 2
4
6
8
10
12
14
Proton energy [MeV]
a
16
0.0
0.4
0.8
1.2
1.6
Neutron energy [MeV]
b
Figure 1: Energy dependence of penetrability coefficients for protons (a) and neutrons (b).
3. Results and discussion In Fig. 1 are shown the PCs for neutrons and protons obtained by author’s computer codes. As it was expected the PCs for neutrons quickly rich the values close to 1. For protons (as charged particles) due to the Coulomb potential the emission trough the potential barrier is suppressed but with the increasing of the energy the PCs slowly tend to a value close to 1. The transitional nucleus 152Sm has the spin and parity 0+. The incident energy of gamma quanta yields from the threshold up to the 30 MeV. The cross section of the photoneutron reaction is evaluated using the HF formalism first of all for compound processes. We have included also in the evaluation the direct and preequilibrium processes, others possible open channels - like (n, p), (n, t), (n, α), multiple emission reaction, in order to analyze their influence to the final results of the (γ, n) reaction. The nuclear potential, energies, parities and density levels of residual nucleus were taken from the Talys nuclear database [15]. We’ll use the terms defined in Talys like binary inclusive cross section and exclusive cross section. Binary total reaction cross-section for neutrons means the cross section of neutrons obtained from all
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C. Oprea et al. / Physics Procedia 31 (2012) 178 – 184
channels. Exclusive neutron cross section (γ, n) means the cross section only in the open channel without the contribution of neutrons from other channels where like (γ, 2n), (γ, np) and others (Fig. 2a). From the threshold energy (8.26 MeV) up to 30 MeV the compound processes are relevant. In the beginning the compound processes on discrete levels are dominant, but after 10 - 12 MeV the compound processes on continuum become dominant. Even in the region of 25 - 30 MeV the direct processes are about a quarter of compound processes (Fig. 2a). The theoretical evaluation for the exclusive cross sections of the (γ, 1n), (γ, 2n), (γ, 3n), (γ, 4n) processes are presented in Fig. 3a. The superposition of these processes is the curve 5 from Fig. 3a and in fact the desired (γ, n) cross section. The presence of two peaks in Fig. 2a and Fig. 3a demonstrates the deformation of the 152Sm nucleus. The first peak is mainly due to the (γ, 1n) exclusive processes (see Fig. 3a) and practically coincides with experimental data from [6], [7] (Figs. 2b-3b). The second peak from Fig. 2a is mainly due to the (γ, 2n) processes (see 2 in Fig. 3a). The contribution of the (γ, 3n) and (γ, 4n) reactions are small and their contribution will became more important for energies higher than 30 MeV (see curves 3, 4 in Fig. 3a).
300
1 - Direct processes 2 - Compound processes 3 - Direct + Compound processes
250 200
1
150
3 2
100 50
Cross section [mb]
Cross section [mb]
300
Hara Experimental Data Carlos Experimental Data Talys evaluation
250 200 150 100 50
0
0 10
15
20
25
30
Neutron energy [MeV]
a
10
15
20
25
30
Neutron energy [MeV]
b
Figure 2: (a) Cross section of the 152Sm(γ, n) reaction due to the contribution of the compound and direct processes on discrete and continuum states of the residual nucleus 151Sm ; (b) Comparison between Carlos data [6], Hara data [5] and theoretical evaluation.
The processes with outgoing charged particles like protons, deuterons, tritons and alpha particles are not shown here graphically because these processes are not significant but in our HF calculations we have took them into account. Due to the Coulomb potential the PCs for charged particles are strongly reduced and therefore the cross sections for charged particles are much smaller than the (γ, n) cross sections.
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C. Oprea et al. / Physics Procedia 31 (2012) 178 – 184
300
5
250
1
200
2
150 100
1 - γ,1N 2 - γ,2N 3 - γ,3N 4 - γ,4N 5 - γ,N_tot
4
σ [mb]
σ [mb]
300
250
__ Talys Evaluation .... Carlos Exp. Data
200 150 100
3
50
50
0
0 10
15
20
25
Neutron energy [MeV]
a
30
10
15
20
25
30
Neutron energy [MeV]
b
Figure 3. (a) The cross section (exclusive) of (γ, xn) processes (x=1-4); the curve 5 is the contribution of all processes; (b) Comparison of theoretical (γ, 1n) (curve 1, Fig. 2a) and experimental data [6].
In Fig. 3a the curve 5 is the sum of the all xn processes and practically coincides with 3 from Fig. 2a. The contribution of neutrons from channels where charged particles are present is neglected. The measurement of photonuclear cross section is a difficult task. One region of interest is near the threshold because the data obtained here are of significance in nuclear astrophysics. The experimental data of Hara and Carlos (Fig. 2b) are in a very good agreement with theoretical evaluation of (γ, n) binary cross section with default parameters from Talys (see 3 in Fig. 2a, continuous line from Fig. 2b, and 5 from Fig. 3a). 4. Conclusions The cross sections of 152Sm(γ,n) reaction were evaluated with nuclear reaction computer code Talys and we used the default parameters (such as nuclear potential, parameters of the levels, density levels and others) of the program. The channels of charged particles (p, d, t and α) are present but their contribution is much lower, in comparison with that of the neutrons, due to the Coulomb potential, and they were neglected. From theoretical results we obtained that mainly (γ, 1n) compound processes are dominant followed by the (γ, 2n) processes and therefore the HF approach is appropriate to evaluate the photodisintegration cross section. The theoretical calculations are in a very good agreement with experimental data as follows from. Figs. 2-3. This work is a proposal for the scientific program on nuclear data evaluation for astrophysics employed at IREN facility - the new neutron source from Frank Laboratory for Neutron Physics of JINR. Acknowledgements The authors would like to thank to Prof. V. I. Furman and Dr. V. L. Kuznetzov for helpful discussions 151 used in the cross section 152 graphics interpretation. 90 Sm(γ , n) 90 Sm
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C. Oprea et al. / Physics Procedia 31 (2012) 178 – 184
References [1] Minkov N, Yotov P, Drenska S, Scheid W, et al., Nuclear collective motion with a coherent coupling interaction between quadrupole and octupole modes, Phys. Rev. C 73, 044315 1-14 (2006). [2] Wolfe PJ and Scharenberg RP., Nuclear g-Factors of the First Excited 2+ States in Samarium-152 and -154 and Gadolinium156, -158, and -160. Phys. Rev. 160 (1967) 866. [3] Semenko SF, Vasilijev OV and Semenov VA., On the effects of “phase transitions” at the giant dipole resonance excitations. Phys. Lett. 31B (1970) 429. [4] Carlos P, Beil H, Bergere R, Lepretre A, et al., The giant dipole resonance in the transition region of the Samarium isotopes. Nucl. Phys. A 225 (1974) 171. [5] Kaoru Y H, Hideo H, Fumito K, Shinji G, et al., Measurements of the 152Sm(γ,n) Cross Section with Laser-Compton Scattering γ Rays and the Photon Difference Method, J. Nucl. Sci. Tech. 44 (2007) 938. [6] Vasiljev OV, Zalenski GN, Semenko FE, Semenov VA., The giant dipole resonance in the transition region from spherical to deformed nuclear shapes. Phys. Lett. 30B (1969) 97. [7] Casten RF, Zamfir NV, Empirical realization of a Critical Point Description in Atomic Nuclei, Phys. Rev. Lett. 87 (2001) 052503 1-4. [8] Mohr P, Babilon M, Galaviz D, Sonnabend K, et al., Nucleosynthesis by photon-induced reactions, Nucl. Phys. A 271 (2003) 90c. [9] Shizuma T, Utsunomiya H, Mohr P, Hayakawa T, et al., Photodisintegration cross section measurements on 186W, 187Re, and 188 Os: Implications for the Re-Os cosmochronology, Phys. Rev. C 72, 025808 1-9 (2005). [10] Utsunomiya H, Akimune H, Gogo S, Ohta M, et al., Cross section measurements of the 181Ta(γ, n)180Ta reaction near neutron threshold and the p-process nucleosynthesis, Phys Rev C 67,015807 1-9 (2003). [11] Hauser W and Feshbach H. The Inelastic Scattering of Neutrons. Phys. Rev. 1952;87 2:366-373. [12] Foderaro A., The Neutron Interaction Theory, Cambridge, Massachusetts, and London, England: The MIT Press (1971). [13] Koning AJ, Hilaire S, Duijvestijn M. Talys-1.2, A nuclear reaction program, User manual. Peten: NRG (2009). [14] Moldauer PA., Unitary Models of Nuclear Resonance Reactions, Phys. Rev. 157 (1967) 907. [15] Vladuca G., Nuclear Physics (Course for Students), Bucharest University Press (1986). [16] Abramowitz M, Stegun I., Handbook of Mathematical Functions. Cambridge: Pergamon Press (1970). [17] Oprea A I, Oprea C, Pirvutoiu C, Vladoiu D., Rom. Rep. Phys. 63 (2011) 107.
Physics Procedia 31 (2012) 178 – 184
GAMMA-1 Emission of Prompt Gamma-Rays in Fission and Related Topics
Cross section evaluation in the photodisintegration of 152 Sm isotope C. Opreaa, A. Opreaa,b, A. Mihula,b∗ a
Joint Institute for Nuclear Research (JINR), Joliot- Curie 6, Dubna 141980, Russia b University of Bucharest, Bucharest-Magurele, RO-077125, Romania
Abstract We have evaluated the cross section of the 152Sm(γ, n)151Sm reaction in the frame of the Hauser – Feshbach formalism using the Talys computer codes as well as by using the computer codes written by the authors. The obtained results were compared with experimental data existing in the literature. The named computer codes allowed estimating the necessary penetrability coefficients with no approximations for charged and neutral particles emission in the exit channels.
© 2012 Published by Elsevier B.V. Selection and/or peer-review under responsibility of Institute for Reference © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the organizer Materials and Measurements. Keywords: 152Sm ; photodesintegration cross section ; Hauser – Feshbach formalism ; direct and compound mechanism ; penetrability coefficients
* Corresponding author. Tel.: +7-49-621-62155; Fax.: +7-49-621-65429 E-mail addres: [email protected]
1875-3892 © 2012 Published by Elsevier B.V. Selection and/or peer-review under responsibility of Institute for Reference Materials and Measurements. doi:10.1016/j.phpro.2012.04.024
C. Oprea et al. / Physics Procedia 31 (2012) 178 – 184
Nomenclature α A C β B σ
αβ
λ
T c W M V(r) VCoul ze Ze VCfg E WW+ Dl αβ
Incident particle Target nucleus Compound nucleus Εmergent (outgoing) particle Residual nucleus (usually excited) Cross section, mb Incident particle reduced length, fm Transmission coefficient Reaction channel Widths fluctuation correction factor (WFC) Reduced mass of emitted particle, kg The real part of nuclear potential, MeV Coulomb potential, MeV Charge of emitted particle, C Charge of residual nucleus, C Centrifugal potential, MeV Energy of the emitted particle, MeV Ingoing wave function Outgoing wave function Logarithmic derivative of the wave function
1. Introduction 152
Sm is a transitional nucleus of significance in the fields of fundamental and applied researches [1-3]. The Samarium nucleus has seven natural isotopes as well as nine radioactive isotopes produced in fission process of Uranium and Plutonium. The unstable nucleus 151Sm, resulting from the photo-neutron disintegration of 152Sm is one of the radioactive fission products of nuclear waste; the capture cross section for thermal neutrons is required for transmutation studies and for nuclear astrophysics [4,5]. The 152Sm nucleus is a part of the group of nuclei with neutrons number from N=88-92 which drastically change the properties of nuclear surfaces [6]. In this range the nuclear surface passes from non-deformed spherical nuclei to deformed ones that corresponding to a phase transition through a critical point from a spherical vibrator to an axial rotor [7]. The photonuclear (γ,n), (γ,p) and (γ,α) reactions together with the capture of neutrons, protons and alpha particles play an important role in many different subfields of nuclear astrophysics [8-10]. In this 151 paper the 152 reaction was analyzed for gamma incident energy ranging from the threshold 90 Sm(γ , n) 90 Sm (~8.25 MeV) up to 30 MeV. As suggested in many papers we chose the Hauser – Feshbach formalism (HF) as the proper approach for the evaluation of the above photo-disintegration cross section [11,12]. For accomplishing of the experimental purposes, the Talys software, with his implemented nuclear database (nuclear structure, nuclear reaction, models, etc), can be an efficient, rapid and powerful tool for nuclear reaction simulation, for understanding of the dominant processes or the concurrence between them [13].
179
180
C. Oprea et al. / Physics Procedia 31 (2012) 178 – 184
2. Hauser-Feshbach formalism (theoretical background) The HF formalism [11] was developed in ’50 years of the past century for binary nuclear reactions with formation of a compound nucleus. The compound nucleus is formed by interaction of the target nucleus with incident particle and is characterized by the same properties like, mass, rest energy, spin parity and others like any other stable nuclei. After a time much longer than the characteristic time for nuclear reaction (1020-22s), the compound nucleus is decaying on possible energetic channels “forgetting” the initial state (Bohr hypothesis). The short-range finite nuclear forces act between incident particles and target and also between emergent particle and residual nucleus (for example Wood Saxon potential). As indicated in [12] after applying the general laws of conservation for a binary reaction (α+Α=>C=>β+B) the cross section in the Hauser – Feshbach formalism has the following form:
σ αβ = πλ α2
Tα Tβ
∑ Tc
(1)
Wαβ
c
We mention that the sum in the nominator is effectuated on all open possible channels in the given reaction. The WFC take into account the correlation existing between ingoing and outgoing channels [13,14] but can be neglected for incident particle energy above some MeV. This factor is of order of unity and decrease with the increasing of the particle incident energy. There are a few methods for the calculation of this factor and three of them are implemented in Talys computer codes. First time the HF expression (1) was proposed without WFC factor (WFC=1). 2.1. Penetrability coefficients Penetrability coefficients (PCs) are important for the HF expression of the cross section. They are defined as the probability of an incident particle to pass through a barrier of potential. In quantum mechanics they are equal to the ratio between the squared modules of the wave functions of the particle emerging the barrier and the incident particle [13]. In case that the energy of the particle is lower then the barrier height than from classical mechanics point of view this particle will not pass the barrier. In quantum mechanics the probability of the particles to pass the barrier is non zero. If the particle energy is much smaller then the height of the barrier we can use the so-called “semi-classical” approximation and then the PCs can be written as [15]:
⎧ ⎫ 1/2 T(l, E) = exp⎨− 8m h 2 ∫ V(r) + VCoul + Vcfg − E dr ⎬ D ⎩ ⎭
[
(2)
]
More appropriate approach is to obtain the PCs from quantum mechanical consideration using the reflection factor Ul, [12]:
T(l, E) = 1 − Ul (E)
{
[(
2
)(
(3)
)] }{
[(
)(
)] }
Ul = Dl − R 1 Wl− dWl− dr Wl− Dl − R 1 Wl+ dWl+ dr Wl+
−1
r =R
(4)
The expression of W is a linear combination of Neumann and Bessel function for neutral particles but
181
C. Oprea et al. / Physics Procedia 31 (2012) 178 – 184
for charged particles it is a linear combination of regular and irregular Coulomb functions. If for neutral particles the PCs can be calculated relatively easy, for charged particles it is necessary to use the Coulomb functions. The Coulomb functions are solutions of Schrödinger equation with Coulomb potential and they have quite complicated integral form [16]. The authors have evaluated numerically the PCs for charged particles (protons and alpha particles) using the quantum mechanical approach and the integral form of Coulomb functions by writing their own computer codes in Mathematica 4.1 [17] (Fig. 1). These codes were part of a program destined to evaluate the cross section in (n, α) reactions with fast neutrons using the HF formalism. The PCs, defined in [12], increase with the increasing of the energy but never will be greater than unity.
Penetrability coefficient
Penetrability coefficient
1.0 1.0 0.8 0.6 0.4 0.2
0.8
0.6
0.4
0.2
0.0 2
4
6
8
10
12
14
Proton energy [MeV]
a
16
0.0
0.4
0.8
1.2
1.6
Neutron energy [MeV]
b
Figure 1: Energy dependence of penetrability coefficients for protons (a) and neutrons (b).
3. Results and discussion In Fig. 1 are shown the PCs for neutrons and protons obtained by author’s computer codes. As it was expected the PCs for neutrons quickly rich the values close to 1. For protons (as charged particles) due to the Coulomb potential the emission trough the potential barrier is suppressed but with the increasing of the energy the PCs slowly tend to a value close to 1. The transitional nucleus 152Sm has the spin and parity 0+. The incident energy of gamma quanta yields from the threshold up to the 30 MeV. The cross section of the photoneutron reaction is evaluated using the HF formalism first of all for compound processes. We have included also in the evaluation the direct and preequilibrium processes, others possible open channels - like (n, p), (n, t), (n, α), multiple emission reaction, in order to analyze their influence to the final results of the (γ, n) reaction. The nuclear potential, energies, parities and density levels of residual nucleus were taken from the Talys nuclear database [15]. We’ll use the terms defined in Talys like binary inclusive cross section and exclusive cross section. Binary total reaction cross-section for neutrons means the cross section of neutrons obtained from all
182
C. Oprea et al. / Physics Procedia 31 (2012) 178 – 184
channels. Exclusive neutron cross section (γ, n) means the cross section only in the open channel without the contribution of neutrons from other channels where like (γ, 2n), (γ, np) and others (Fig. 2a). From the threshold energy (8.26 MeV) up to 30 MeV the compound processes are relevant. In the beginning the compound processes on discrete levels are dominant, but after 10 - 12 MeV the compound processes on continuum become dominant. Even in the region of 25 - 30 MeV the direct processes are about a quarter of compound processes (Fig. 2a). The theoretical evaluation for the exclusive cross sections of the (γ, 1n), (γ, 2n), (γ, 3n), (γ, 4n) processes are presented in Fig. 3a. The superposition of these processes is the curve 5 from Fig. 3a and in fact the desired (γ, n) cross section. The presence of two peaks in Fig. 2a and Fig. 3a demonstrates the deformation of the 152Sm nucleus. The first peak is mainly due to the (γ, 1n) exclusive processes (see Fig. 3a) and practically coincides with experimental data from [6], [7] (Figs. 2b-3b). The second peak from Fig. 2a is mainly due to the (γ, 2n) processes (see 2 in Fig. 3a). The contribution of the (γ, 3n) and (γ, 4n) reactions are small and their contribution will became more important for energies higher than 30 MeV (see curves 3, 4 in Fig. 3a).
300
1 - Direct processes 2 - Compound processes 3 - Direct + Compound processes
250 200
1
150
3 2
100 50
Cross section [mb]
Cross section [mb]
300
Hara Experimental Data Carlos Experimental Data Talys evaluation
250 200 150 100 50
0
0 10
15
20
25
30
Neutron energy [MeV]
a
10
15
20
25
30
Neutron energy [MeV]
b
Figure 2: (a) Cross section of the 152Sm(γ, n) reaction due to the contribution of the compound and direct processes on discrete and continuum states of the residual nucleus 151Sm ; (b) Comparison between Carlos data [6], Hara data [5] and theoretical evaluation.
The processes with outgoing charged particles like protons, deuterons, tritons and alpha particles are not shown here graphically because these processes are not significant but in our HF calculations we have took them into account. Due to the Coulomb potential the PCs for charged particles are strongly reduced and therefore the cross sections for charged particles are much smaller than the (γ, n) cross sections.
183
C. Oprea et al. / Physics Procedia 31 (2012) 178 – 184
300
5
250
1
200
2
150 100
1 - γ,1N 2 - γ,2N 3 - γ,3N 4 - γ,4N 5 - γ,N_tot
4
σ [mb]
σ [mb]
300
250
__ Talys Evaluation .... Carlos Exp. Data
200 150 100
3
50
50
0
0 10
15
20
25
Neutron energy [MeV]
a
30
10
15
20
25
30
Neutron energy [MeV]
b
Figure 3. (a) The cross section (exclusive) of (γ, xn) processes (x=1-4); the curve 5 is the contribution of all processes; (b) Comparison of theoretical (γ, 1n) (curve 1, Fig. 2a) and experimental data [6].
In Fig. 3a the curve 5 is the sum of the all xn processes and practically coincides with 3 from Fig. 2a. The contribution of neutrons from channels where charged particles are present is neglected. The measurement of photonuclear cross section is a difficult task. One region of interest is near the threshold because the data obtained here are of significance in nuclear astrophysics. The experimental data of Hara and Carlos (Fig. 2b) are in a very good agreement with theoretical evaluation of (γ, n) binary cross section with default parameters from Talys (see 3 in Fig. 2a, continuous line from Fig. 2b, and 5 from Fig. 3a). 4. Conclusions The cross sections of 152Sm(γ,n) reaction were evaluated with nuclear reaction computer code Talys and we used the default parameters (such as nuclear potential, parameters of the levels, density levels and others) of the program. The channels of charged particles (p, d, t and α) are present but their contribution is much lower, in comparison with that of the neutrons, due to the Coulomb potential, and they were neglected. From theoretical results we obtained that mainly (γ, 1n) compound processes are dominant followed by the (γ, 2n) processes and therefore the HF approach is appropriate to evaluate the photodisintegration cross section. The theoretical calculations are in a very good agreement with experimental data as follows from. Figs. 2-3. This work is a proposal for the scientific program on nuclear data evaluation for astrophysics employed at IREN facility - the new neutron source from Frank Laboratory for Neutron Physics of JINR. Acknowledgements The authors would like to thank to Prof. V. I. Furman and Dr. V. L. Kuznetzov for helpful discussions 151 used in the cross section 152 graphics interpretation. 90 Sm(γ , n) 90 Sm
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