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Cross-Sections of 14 Mev Neutron Induced Reactions on Some Isotopes of Chromium, Zirconium and Tin

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Cross-Sections of 14 Mev Neutron Induced Reactions on Some Isotopes of Chromium, Zirconium and Tin Indian Journal of Pure & Applied Physics Vol. 44, March 2006, pp. 216-219 Cross-sections of 14 MeV neutron induced reactions on some isotopes of chromium, zirconium and tin Sneh Lata Goyal* & R K Mohindra *Department of Applied Physics, Guru Jambheshwar University, Hisar 125 001 Department of Physics, Kurukshetra University, Kurukshetra 132 119 Received 30 May 2005; revised 23 November 2005; accepted 6 January 2006 Neutron induced reaction cross-sections of the isotopes 52Cr, 53Cr, 90Zr, 91Zr, 92Zr, 94Zr, 116Sn, 118Sn and 120Sn for (n,p), (n,n’), (n,α) and (n, 2n) reactions have been evaluated at 14 MeV. The computations are based on the evaporation model considering the pre-equilibrium emission mechanism under some approximations. The computer codes ALICE-91, NX-1 and SC2N3N have been used. These cross-sections were also computed using the level density formula of Lang and Le Couteur with and without applying pairing energy correction. The compound nucleus theory based on Fermi gas and evaporation model with optical model potential parameters has been used. The neutron, proton and alpha penetrabilities and inverse reaction cross-sections have been computed using the computer code SCAT-2. The computed cross-sections have been compared with the available experimental values and the results are in fairly good agreement. Keywords: Neutron induced reactions, Nuclear physics, Neutron energy, Neutron multiplication, Nuclear heating, Nuclear transmutation, Radiation damage IPC Code: G01T3/00 1 Introduction the computation of (n,p), (n,n’), (n,α) and (n, 2n) Activation cross-sections for production of long- reaction cross-sections induced by 14 MeV neutrons. lived isotopes at around 14 MeV neutron energy are The computations of (n,p), (n, α) and (n, 2n) reaction of interest for testing nuclear reaction models. cross-sections have been carried out using the Furthermore, in the case of structural materials of a computer codes ALICE-91 given by Blann4-6, NX-1 fusion reactor, the data are important for the given by Zhao Zhixiang and Zhou Delin7,8 and estimation of neutron multiplication, nuclear heating, SC2N3N developed by Zhang Zin et al.9,10. These nuclear transmutation and radiation damage effects. codes are based on the pre-equilibrium emission Zircalloy-2 (composition1 – Zr = 98.2%, Sn = 1.5%, mechanism. Also, the statistical model of nuclear Cr = 0.1%, Fe = 0.15%, Ni = 0.05%) is used as reactions has been extended for the computation of 1,2 cladding material in Pressurized Water Reactors such cross-sections. The compound nucleus theory (PWR), Pressurized Heavy Water Reactors (PHWR) based on Fermi gas and evaporation model with and Boiling Water Reactors (BWR). In PWR, the core optical model potential parameters has been used. The of the plate type seed elements is zirconium– uranium Lang and Le Couteur level density formula11,12 has alloy clad with zirconium alloy (zircalloy–2). been used for these computations. Zirconium was selected because of its small absorption cross-section. In BWR, the core contains 2 Calculations 15.4% of zircalloy -2 by volume percentage. The computer code ALICE-91 (Refs 4-6) has been 3 Various nuclear reaction models are currently used for the computation of (n,p), (n,α) and (n, 2n) being applied to evaluate the neutron induced reaction reaction cross-sections induced by 14 MeV neutrons cross-sections. The success of optical model in of the isotopes 52Cr, 53Cr, 90Zr, 91Zr, 92Zr, 94Zr, 116Sn, explaining large number of features in elastic and 118Sn and 120Sn. This code is based on the hybrid and inelastic scattering of nucleons with nuclei has created geometry dependent hybrid (GDH) model for the pre- a need for the computation of neutron cross-sections; equilibrium process and the Weisskopf–Ewing obtained from a detailed optical model potential with evaporation model for the equilibrium process. These real and imaginary parts. The present work deals with cross-sections were also computed after applying GOYAL & MOHINDRA: CROSS-SECTIONS OF 14 MeV NEUTRON INDUCED REACTIONS ON SOME ISOTOPES 217 pairing energy correction and shell correction with Table 1 ⎯ Optical model parameters for neutrons by Wilmore 13 backshifted pairing6 simultaneously. The Fermi gas and Hodgson Parameter Neutrons level density used is of the form: Real Potential Vr(MeV) 48 (Woods-Saxon) Imaginary W (MeV) 9.0 -5/4 s ρ (U) ∝ (U-δ) exp2 a(U − δ) …(1) Spin Orbit Vso (MeV) 7.0 -4 -6 2 Radius Rv(fm) =(1.322-7.6x10 A+ 4x10 A The level density parameter a = A/9 and the pairing – 8x10-9A3)xA1/3 -4 -6 2 correction is defined by δ = 11/A1/2, where A is mass Rw(fm) =(1.266-3.7x10 A+ 2x10 A – 4x10-9A3)xA1/3 number of the residual nucleus. Rso(fm) =Rw 1/3 The optical model potential is defined as follows: Rcoulomb =1.25 A Diffusivity 2 a′ (f ) 0.66 ⎛ h ⎞ v v m U(r) = V − V f (r) − i − iota[−4W g(r) + W f (r)] + ⎜ ⎟ (1.sr)v50h(r) c r s v ⎜ ⎟ a′w(fm) 0.48 ⎝ mπc ⎠ a′so(fm) 0.48 …(2) The binding energies and Q-values used in the present where work were all based on experimental masses. The ALICE code includes experimental masses in block 2 ⎧ zz' e / r, data, so that a simple input parameter results in all Q- ⎪ 2 2 ifr ≥ R c Vc = ⎨zz' e ⎛ r ⎞, … (3) values and binding energies being internally ⎜3 − ⎟ ifr〈R ⎪ 2R ⎜ R 2 ⎟ c generated from experimental mass tables. ⎩ c ⎝ c ⎠ In another computation, the cross-sections for (n,p) and (n, α) reactions at 14 MeV neutron energy have where z and z’ are the charges of the incident particle been computed using the computer code NX-1 given and the target nucleus. The imaginary absorptive by Zhao Zhixiang and Zhou Delin7,8 and (n, 2n) potential is pure surface so Ws ≠ 0 and Wv = 0, which reaction cross-sections have been computed using the have a derivative Woods-Saxon shape and computer code SC2N3N given by Zhang Zin et al.9,10. These codes contain analytical formulae with f(r) = [1 + exp(r − R)/a′ ]−1 …(4) v parameters based on experimental data and derived by using a constant temperature evaporation model for ′ ′ −2 …(5) g(r) = exp[(r − R)/a w ][1 + exp(r − R)/a w ] statistical phenomena and the exciton model for the and pre-compound part. 1d The detailed formulae for the computation of these h(r) = f(r) …(6) rdr cross-sections have been described by Bansal and Mohindra14. Here the pre-equilibrium emission is are the Woods-Saxon, derivative Woods-Saxon considered to occur only at the state of exciton (surface peaked) and spin-orbit form factors with number n = 3. The energy level density of the appropriate radius and diffusivity parameters. R = compound nucleus is taken in the form of constant 1/3 r0A is the nuclear radius and a′ is the surface temperature. diffuseness parameter. ρ (A, E) ∝ exp [E/T(A)] … (8) 2 ⎛ h ⎞ 2 ⎜ ⎟ = 2.0()fermi where E is excitation energy of the compound nucleus ⎜ m c ⎟ ⎝ π ⎠ and the nuclear temperature T(A) is taken as T(A) = and 13A-1/2. For these computations, the Q-values and r separation energies have been taken from the 1.sr = j()()()i + 1 −11 + 1 − s s +1 /2 … (7) tabulation of Audi et al.15. The computations of (n,p), (n,n’), (n, α) and (n, 2n) where s is spin angular momentum, l is orbital angular reaction cross-sections at 14 MeV have also been momentum and j is total angular momentum. carried out using the compound nucleus theory based For neutrons, the optical model parameter set due on the Fermi gas and evaporation model. The level to Wilmore and Hodgson13 listed in Table 1 is used. density formula of Lang and Le Couteur11,12 with and 218 INDIAN J PURE & APPL PHYS, VOL 44, MARCH 2006 without applying pairing energy correction16 has been Table 2 ⎯ Optical model parameters for neutrons by Becchetti 20 used. The neutron and proton penetrabilities listed by and Greenless 17 Mani et al . and alpha induced inverse reaction cross- Parameter Neutrons 18 sections given by Huizenga and Igo have been used. Real Potential Vr (MeV) 56.3 – 0.32E – 24 (N-Z)/A The neutron, proton and alpha penetrabilities and Imaginary Ws (MeV) 13-0.25E -12 (N-Z)/A or zero, whichever inverse reaction cross-sections have been computed is greater using the computer code SCAT-2 developed by Wv (MeV) 0.22E – 1.56 or zero, whichever is greater Bersillon19. The optical model potential parameter set Spin Orbit Vso (MeV) 6.2 20 1/3 for neutrons given by Becchetti and Greenless listed Radius Rv(fm) 1.17 A 1/3 in Table 2 is used. These computed values of inverse Rw(fm) 1.26 A 1/3 reaction cross-sections have also been used for the Rso(fm) 1.01 A Diffusivity computation of (n,p), (n,n’) and (n, α) reaction cross- a′v (fm) 0.75 sections at 14 MeV neutron energy using Lang and Le a′w (fm) 0.58 Couteur level density formula with and without the a′so (fm) 0.75 Table 3⎯ Computed reaction cross-sections at 14 MeV Isotope Reaction Computed Cross-sections (mbs) using Experimental Pre-equilibrium Emission Lang & Le Couteur Level Density Formula With Cross-sections Computed Inverse Cross-sections of (mbs) NX- 1/ ALICE-91 SCAT-2 Earlier Codes SC2N3N Without With Pairing With Shell Without With Pairing Without With Pairing Code Correction Energy Correction Correction Energy Correction Energy (n, n’) - - - - 1412.7 1307.5 1266.7 1127.9 1304 52Cr (n, 2n) 252.1 423.0 63.9 0.0 - - 126.1 - 278±20 (n, p) 77.3 40.2 32.0 66.8 25.3 129.9 33.8 171.9 78±10 (n, α) 32.2 4.7 3.5 14.1 10.4 12.8 14.6 17.6 35±3 (n, n’) - - - - 1405.5 1427.4 1251.2 1282.0 1366 53Cr (n, 2n) 895.2 1020.0 1020.0 600.0 - - - - 700 (n, p) 46.2 28.7 28.9 49.9 18.4 16.6 27.2 24.0 45±6 (n, α) 26.0 16.5 17.0 9.4 26.2 5.9 31.1 9.0 45±4 (n, n’) - - - - 1823.4 1806.9 1640.2
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