Activ tivation ation bremss msstra trahl hlung ung yie ield lds s of th f the 112 Sn( Sn( ,n) ,n) 111 111 Sn Sn an and d 112 112 Sn( Sn( ,p) ,p) 11 1m,g In In 112 111m,g reaction ctions s and th d the fo foll llowing ing 111 111 Sn Sn de deca cay y -ray ay branch anching ing co coefficients fficients A. Chekhovska 1,2 I. Semisalov 2 V. Kasilov 2 Ye. Skakun 2 1. V. N. Karazin Kharkiv National University, Kharkiv, Ukraine [http://www.univer.kharkov.ua] 2. National Science Center “ Kharkiv Institute of Physics and Technology”, Kharkiv, Ukraine [https://www.kipt.kharkov.ua] Joint ICTP-IAEA Workshop on Nuclear Structure and Decay Data: Theory, Experiment and Evaluation
The valley of stability 2
Abundance of chemical elements in nature depending on mass number 112 Sn A A ≤ 11 11 – prim imordi rdial al nucleo cleosyn synthes thesis is A = 12-56 56 – fusio sion n reactio ctions ns A > 56 – r- and d s- process rocess neutro utron n radia diati tion on captu ture re 3
Gamma-activation method 4
The statistical theory of nuclear reactions 𝑲 𝝆 𝑼 𝑪 𝑲 𝝆 I - the spin of the target nucleus; 𝟐 𝑼 𝑩 𝟑 𝝉 𝑩𝑪 = 𝝆𝝁 𝑩 𝟑𝒋 + 𝟐 𝟑𝑲 + 𝟐 i - the spin of the incident particle; 𝟑𝑱 + 𝟐 𝑲 𝝆 J - the spin of the compound 𝑩 ′ 𝑼 𝑩 ′ 𝑲 𝝆 nucleus; Hause ser-Feshbach Feshbach model el T - coefficients of particle permeability; - density of the kernel levels. 𝝏 𝜻 𝒏𝒃𝒚 𝑲 𝝆 = 𝒋 𝜻 𝒋 , 𝑲′ 𝝆′ 𝝇 𝜻 𝒋 , 𝑲′ 𝝆′ 𝒆𝜻 𝒋 𝒋 𝑲 𝝆 𝑼 𝑩 𝑼 𝑩 + න 𝑼 𝑩 𝜻 𝝏 𝑲 ′ ,𝝆′ 𝒋=𝟏 𝟑 𝟑𝑲 + 𝟐 𝐟𝐲𝐪 − 𝑲 + 𝟐 /𝟑𝝉 𝟑 𝟑 𝝆 𝐟𝐲𝐪(𝟑 𝒃𝑭) 𝝇 𝑮 𝑭, 𝑲 = 𝝇 𝑮 𝑭 𝒉 𝑭, 𝑲 ≈ 𝒃 𝟐/𝟓 𝑭 𝟔/𝟓 𝟐𝟑 𝟑 𝟑𝝆𝝉 𝟒 Fermi Fe mi-gas gas mo model el E, J - the excitation and spin energies of the excited state 𝝉 𝟏 𝜻 𝜹 Г 𝟑 of the nucleus, respectively; 𝒈 𝑭𝟐 𝜻 𝜹 = 𝟗. 𝟕𝟗 ∙ 𝟐𝟏 −𝟗 (𝒏𝒄 −𝟐 𝑵𝒇𝑾 −𝟑 ) a - the density parameter of the 𝟑 − 𝑭 𝟑 𝟑 + 𝜻 𝜹 𝟑 Г 𝟑 𝜻 𝜹 levels; Brink-Axe Axel l approxim oximat ation ion - the spin dependence parameter. 5
The scheme of the experiment on a beam of bremsstrahlung -quanta 6
Decay cay cur urve ve of th the 111 111 Sn n isotop tope 111 𝑇𝑜 = 35.3 𝑛𝑗𝑜 𝑈 ൗ 1 2 E [keV eV] I [%] Decay ay mod ode 762 1.48 e + 1153 2.7 e + Accum cumulat ulation on and decay cay curves ves of the 111 111 In In isotop tope 111 𝐽𝑜 = 2.8 𝑒 𝑈 ൗ 1 2 E [keV eV] I [%] Decay ay mod ode 171 90 e + 245 94 e + 7
Calculation of the integral yields 𝑭𝑫,𝜸 − 𝜹,𝒐 𝟐𝟐𝟐 𝑻𝒐 𝑱𝑼 𝟐𝟐𝟐𝒉 𝑱𝒐 𝑭𝑫 𝟐𝟐𝟐 𝑫𝒆 𝟐𝟐𝟑 𝑻𝒐 𝟐𝟐𝟐𝒏 𝑱𝒐 ՜ ( 𝜹, 𝒒 ) N – number of events ( 𝜹, 𝒒 ) – efficiency B – branching The simple le activation ivation equation uation : n – number of nuclei ф – incident particles flux 𝑂 = 𝜁 ∙ 𝐶 ∙ 𝑜 ∙ ф ∙ 𝑍 ∙ (1 − 𝑓 − ∙𝑢 1 ) ∙ 𝑓 − ∙𝑢 2 ∙ (1 − 𝑓 − ∙𝑢 3 ) Y – yield – decay constant The activation ivation equati ation on for r genetica etically lly coupled pled pair : t t N 1 e p 1 1 e d 1 t t p d t t Y e p 2 (1 e p 3 ) e (1 e ) d 2 d 3 p 2 2 B n d p p d t 1 e d 1 t t Y e (1 e ) d 2 d 3 d d Y p – yield of the parent nuclei; Y d – yield of the daughter nuclei p , d – decay constants of the parent and daughter nuclei responsible; t 1 – irradiation time; t 2 – cool time; t 3 – measure time. 8
Results 9
Calculation of Branching Coefficients (for the decay of a nucleus 111 Sn) 𝑂 𝛿 ∙ 𝐶 𝑦 = X=1.64 𝜁 ∙ 𝑜 ∙ ф ∙ 𝑍 ∙ (1 − 𝑓 − ∙𝑢 1 ) ∙ 𝑓 − ∙𝑢 2 ∙ (1 − 𝑓 − ∙𝑢 3 ) Branching coefficient [%] E [keV] NUDAT LBLN Our data 0.42 0.08 0.42 0.02 0.26 0.05 372.3 0.38 0.08 0.38 0.02 0.23 0.04 457.1 0.30 0.08 0.30 0.02 0.19 0.03 564.3 1.47 0.01 1.48 0.05 0.90 0.08 761.9 0.50 0.08 0.50 0.02 0.31 0.03 954.1 0.63 0.02 0.64 0.05 0.39 0.04 1101.1 1.65 0.11 1152.9 2.7 2.7 1.31 0.01 1.31 0.05 0.80 0.07 1610.0 1.98 0.03 1.99 0.08 1.21 0.08 1914.7 10
Results 11
Results 12
Conclusions 112 Sn Sn ( , n ) 111 Sn n The Fermi gas model for the density of nuclear levels. The Brink-Axel model for radiation strength function. 112 Sn Sn ( , p ) 111 m In In The Fermi gas model for the density of nuclear levels. The Hartree-Fock model for radiation strength function. 112 Sn Sn ( , p ) 111 g In In The Fermi gas model for the density of nuclear levels. The Hartree-Fock model for radiation strength function. The new values of the branching coefficients of the -transitions following the decay of the 111 Sn nucleus are determined, which differ from the base values by a weighted average coefficient of 1.64 64. 13
Th Than ank k you you for for you your r at atten tention! tion!
Efficiency calculation (HPGe – detector) Sources – 60 Co, 133 Ba, 137 Cs, 152 Eu 15
The decay spectrum of the 111 Sn nucleus 16
Monitor reaction (standard reaction) (to determine the flux of incident photons) Measured in our experiment, Absolute integral yield the ratio of the yields of of the studied reaction reactions on the 112 Sn and 197 Au targets е𝑦𝑞 ( 112 𝑇𝑜) 𝑏𝑐𝑡 ( 112 𝑇𝑜) = 𝑍 197 𝐵𝑣 𝑍 ∙ 𝑍 𝑏𝑐𝑡 197 𝐵𝑣 𝑍 е𝑦𝑞 Absolute integral yield of the monitor reaction 𝐹 𝛿 𝑛𝑏𝑦 197 𝐵𝑣 = න 𝑍 𝜏 𝐹 𝛿 ∙ Ф 𝐹 𝛿 , 𝐹 𝛿 𝑛𝑏𝑦 𝑒𝐹 𝛿 𝑏𝑐𝑡 𝑇 𝑜 Energy spectrum of The cross section of the bremsstrahlung with finite reaction as a function of the energy of the -quantum energy E max 17
Nucleosynthesis • A<56 => nucleus fusion λ (T) - the ( γ ,n)-reaction rate for a • A>56 => neutron capture processes – (n, γ )-reaction : nucleus disposed in a thermal • s-process (slow) photon bath of a stellar medium • having temperature T; r-process (rapid) c – the speed of light ; • p-nuclei (35) forming in p-process ((p, γ )-reaction) σ (γ, n) (E) – the reaction cross section or in ( γ ,n), ( γ ,p) and ( γ , α ) reactions. depending on photon energy E; n(E,T) – the number of photons per unit energy and volume of a star interior. The reaction cross-section obtained under laboratory conditions Planck distribution 18
The computational code TALYS uses OPTICAL DENSITY MODEL OF POTENTIAL LEVEL RADIATION MODEL STRENGTH FUNCTION MODEL 1. Spherical OMP: 1. Constant temperature + 1. Kopecky-Uhl Neutrons and protons; Fermi gas model; generalized Lorentzian; 2. Spherical dispersive 2. Back-shifted Fermi gas 2. Brink-Axel OMP: Neutrons; model; Lorentzian; 3. Spherical OMP: 3. Generalised superfluid 3. Hartree-Fock BCS Complex particles; model; tables; 4. Semi-microscopic 4. Microscopic level 4. Hartree-Fock- optical model (JLM). densities (Skyrme force) Bogolyubov tables; from Goriely’s tables; 5. Goriely’s hybrid 5. Microscopic level model. densities (Skyrme force) from Hilaire’s combinatorial tables. 19
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