112 Sn( Sn( ,n) ,n) 111 111 Sn Sn an and d 112 112 Sn( Sn( ,p) - - PowerPoint PPT Presentation

Activ tivation ation bremss msstra trahl hlung ung yie ield lds s of th f the

112 112Sn(

Sn(,n) ,n)111

111Sn

Sn an and d 112

112Sn(

Sn(,p) ,p)11

111m,g 1m,gIn

In reaction ctions s and th d the fo foll llowing ing 111

111Sn

Sn de deca cay y -ray ay branch anching ing co coefficients fficients

Joint ICTP-IAEA Workshop on Nuclear Structure and Decay Data: Theory, Experiment and Evaluation

• A. Chekhovska 1,2
• I. Semisalov2
• V. Kasilov2
• Ye. Skakun2
• 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]

The valley of stability

2

Abundance of chemical elements in nature depending on mass number

3

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

• n captu

ture re

112Sn

Gamma-activation method

4

 The statistical theory of nuclear reactions

5

𝝉𝑩𝑪 = 𝝆𝝁𝑩

𝟑

𝟐 𝟑𝑱 + 𝟐 𝟑𝒋 + 𝟐 ෍

𝑲𝝆

𝟑𝑲 + 𝟐 𝑼𝑩

𝑲𝝆𝑼𝑪 𝑲𝝆

෍

𝑩′ 𝑼𝑩′ 𝑲𝝆

𝑼𝑩

𝑲𝝆 = ෍ 𝒋=𝟏 𝝏

𝑼𝑩

𝒋

𝑲𝝆 + න

𝜻𝝏 𝜻𝒏𝒃𝒚

෍

𝑲′,𝝆′

𝑼𝑩

𝒋 𝜻𝒋, 𝑲′𝝆′ 𝝇 𝜻𝒋, 𝑲′𝝆′ 𝒆𝜻𝒋

𝝇𝑮 𝑭, 𝑲 = 𝝇𝑮 𝑭 𝒉 𝑭, 𝑲 ≈ 𝝆 𝟐𝟑 𝐟𝐲𝐪(𝟑 𝒃𝑭) 𝒃𝟐/𝟓𝑭𝟔/𝟓 𝟑𝑲 + 𝟐 𝐟𝐲𝐪 − 𝑲 + 𝟐 𝟑

𝟑

/𝟑𝝉𝟑 𝟑 𝟑𝝆𝝉𝟒

𝒈𝑭𝟐 𝜻𝜹 = 𝟗. 𝟕𝟗 ∙ 𝟐𝟏−𝟗(𝒏𝒄−𝟐𝑵𝒇𝑾−𝟑) 𝝉𝟏𝜻𝜹Г𝟑 𝜻𝜹

𝟑 − 𝑭𝟑 𝟑 + 𝜻𝜹 𝟑Г𝟑

I - the spin of the target nucleus; i - the spin of the incident particle; J - the spin of the compound nucleus; T - coefficients of particle permeability; - density of the kernel levels. E, J - the excitation and spin energies of the excited state

• f the nucleus, respectively;

a - the density parameter of the levels;  - the spin dependence parameter.

Hause ser-Feshbach Feshbach model el Fe Fermi mi-gas gas mo model el Brink-Axe Axel l approxim

• ximat

ation ion

 The scheme of the experiment on a beam

• f bremsstrahlung -quanta

6

Accum cumulat ulation

• n and decay

cay curves ves of the 111

111In

In isotop tope

7

Decay cay cur urve ve of th the 111

111Sn

n isotop tope

𝑈 ൗ

1 2 111𝑇𝑜 = 35.3 𝑛𝑗𝑜

E [keV eV] I [%] Decay ay mod

• de

762 1.48 e+ 1153 2.7 e+ E [keV eV] I [%] Decay ay mod

• de

171 90 e+ 245 94 e+ 𝑈 ൗ

1 2 111𝐽𝑜 = 2.8 𝑒

 Calculation of the integral yields

The simple le activation ivation equation uation:

8

𝑂 = 𝜁 ∙ 𝐶 ∙ 𝑜 ∙ ф ∙ 𝑍  ∙ (1 − 𝑓−∙𝑢1) ∙ 𝑓−∙𝑢2 ∙ (1 − 𝑓−∙𝑢3)

1 1 2 3 2 3

2 2

1 1 (1 ) (1 )

p d p p d d

t t t t p d t t p d p p d

N e e Y e e e e B n

      

       

           

                        

1 2 3

1 (1 )

d d d

t t t d d

e Y e e

  



     

     

The activation ivation equati ation

• n for

r genetica etically lly coupled pled pair:

N – number of events  – efficiency B – branching n – number of nuclei ф – incident particles flux Y – yield  – decay constant Yp – yield of the parent nuclei; Yd – yield of the daughter nuclei p, d – decay constants of the parent and daughter nuclei responsible; t1 – irradiation time; t2 – cool time; t3 – measure time.

𝟐𝟐𝟑𝑻𝒐 𝜹,𝒐 𝟐𝟐𝟐𝑻𝒐 𝑭𝑫,𝜸− 𝟐𝟐𝟐𝒏𝑱𝒐 ՜ 𝑱𝑼 𝟐𝟐𝟐𝒉𝑱𝒐 𝑭𝑫 𝟐𝟐𝟐𝑫𝒆

(𝜹, 𝒒) (𝜹, 𝒒)

Results

9

 Calculation of Branching Coefficients

(for the decay of a nucleus 111Sn)

E [keV] Branching coefficient [%]

NUDAT LBLN Our data 372.3 0.42  0.08 0.42  0.02 0.26  0.05 457.1 0.38  0.08 0.38  0.02 0.23  0.04 564.3 0.30  0.08 0.30  0.02 0.19  0.03 761.9 1.47  0.01 1.48  0.05 0.90  0.08 954.1 0.50  0.08 0.50  0.02 0.31  0.03 1101.1 0.63  0.02 0.64  0.05 0.39  0.04 1152.9 2.7 2.7 1.65  0.11 1610.0 1.31  0.01 1.31  0.05 0.80  0.07 1914.7 1.98  0.03 1.99  0.08 1.21  0.08

10

𝐶𝑦 = 𝑂𝛿 ∙  𝜁 ∙ 𝑜 ∙ ф ∙ 𝑍 ∙ (1 − 𝑓−∙𝑢1) ∙ 𝑓−∙𝑢2 ∙ (1 − 𝑓−∙𝑢3)

X=1.64

 Results

11

Results

12

 Conclusions



112Sn

Sn (,n)111Sn n

The Fermi gas model for the density of nuclear levels. The Brink-Axel model for radiation strength function.



112Sn

Sn (,p)111mIn In

The Fermi gas model for the density of nuclear levels. The Hartree-Fock model for radiation strength function.



112Sn

Sn (,p)111gIn In

The Fermi gas model for the density of nuclear levels. The Hartree-Fock model for radiation strength function.

 The new values

• f

the branching coefficients

• f

the -transitions following the decay of the

111Sn 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 – 60Co, 133Ba, 137Cs, 152Eu

15

 The decay spectrum of the 111Sn nucleus

16

Monitor reaction (standard reaction)

(to determine the flux of incident photons)

17

𝑍

𝑏𝑐𝑡(112𝑇𝑜) = 𝑍 е𝑦𝑞(112𝑇𝑜)

𝑍

е𝑦𝑞 197𝐵𝑣

∙ 𝑍

𝑏𝑐𝑡 197𝐵𝑣

Absolute integral yield

• f the studied reaction

Measured in our experiment, the ratio of the yields of reactions on the 112Sn and

197Au targets

Absolute integral yield

• f the monitor reaction

𝑍

𝑏𝑐𝑡 197𝐵𝑣 = න 𝑇𝑜 𝐹𝛿 𝑛𝑏𝑦

𝜏 𝐹𝛿 ∙ Ф 𝐹𝛿, 𝐹𝛿 𝑛𝑏𝑦 𝑒𝐹𝛿

The cross section of the reaction as a function of the energy of the -quantum Energy spectrum of bremsstrahlung with finite energy E max

Nucleosynthesis

• A<56 => nucleus fusion
• A>56 => neutron capture processes – (n,γ)-reaction :
• s-process (slow)
• r-process (rapid)
• p-nuclei (35) forming in p-process ((p,γ)-reaction)
• r in (γ,n), (γ,p) and (γ,α) reactions.

18

λ (T) - the (γ,n)-reaction rate for a nucleus disposed in a thermal photon bath of a stellar medium having temperature T; c – the speed of light ; σ(γ,n)(E) – the reaction cross section 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

• btained under laboratory

conditions

Planck distribution

 The computational code TALYS uses

19

OPTICAL POTENTIAL MODEL

DENSITY LEVEL MODEL MODEL OF RADIATION STRENGTH FUNCTION

• 1. Spherical OMP:

Neutrons and protons;

• 2. Spherical dispersive

OMP: Neutrons;

• 3. Spherical OMP:

Complex particles;

• 4. Semi-microscopic
• ptical model (JLM).
• 1. Constant temperature +

Fermi gas model;

• 2. Back-shifted Fermi gas

model;

• 3. Generalised superfluid

model;

• 4. Microscopic level

densities (Skyrme force) from Goriely’s tables;

• 5. Microscopic level

densities (Skyrme force) from Hilaire’s combinatorial tables.

• 1. Kopecky-Uhl

generalized Lorentzian;

• 2. Brink-Axel

Lorentzian;

• 3. Hartree-Fock BCS

tables;

• 4. Hartree-Fock-

Bogolyubov tables;

• 5. Goriely’s hybrid

model.

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