NUCLEOSYTHESIS OF HEAVY ELEMENTS IN THERMONUCLEAR EXPLOSIONS “Mike”, “Par” and “Barbel” Yu. S. Lutostansky, V. I. Lyashuk. National Research Center "Kurchatov Institute" Institute for Nuclear Research, Russian Academy of Science --------------------------------------------------------------------------------- НУКЛЕОСИТЕЗ ТЯЖЕЛЫХ ЭЛЕМЕНТОВ В ТЕРМОЯДЕРНЫХ ВЗРЫВАХ “Майк”, “Пар” и “Барбел” Ю. С. Лютостанский, В. И. Ляшук. Национальный Исследовательский Центр "Курчатовский институт" Институт Ядерных Исследований, Российской Академии Наук, Москва ------------------------------------------------------ 3rd International Conference on Particle Physics and Astrophysics (ICPPA– 2017) 04.10.2017 1

DYNAMIC PROCESSES OF IMPULCE NUCLEOSYNTESIS. Superheavy nuclei β-decay fission s-process track r-process track β-decay The tracks of elements synthesis in s (slow)- and r (rapid)- processes. 2

DYNAMICAL NUCLEOSYNTHESIS Duration time calculations. Time of new nuclei synthesis The dependence of r-process duration time on mass A-value under different external conditions: curve 1) – constant nn = 1026 cm-3, T = 1.5 109K; 2) – the same nn, T = 1.109K; 3) – dynamical calc. with ρ0 = 2.105 g/cm5, T = 1.109K [(t) = 0 . ехp (-t/H), Т(t) = Т0 . ехр(-t/3H)]. Yu. S. Lyutostanskii and I. V. Panov. Astron Phys. Lett. v. 14, pp. 168-174 (1988). 3

dn(A, Z, t)/dt = – (A, Z).n(A, Z, t) – n(A, Z, t).n(A, Z, t) + r –process equations for the concentration calculations. Dynamic model: n/ n(A, Z)→  n/ n (A, Z, t); n(A, Z) → n(A, Z, t) Concentrations n(A,Z, t) are changing in time (may be more than 6000 equations):   dn(A, Z, t)/dt = – (A, Z).n(A, Z, t) – n(A, Z, t).n(A, Z, t) + + n(A+1, Z, t).n(A+1, Z, t) + n(A–1, Z, t).n(A–1, Z, t) – n(A, Z).n(A, Z, t) + + (A, Z–1).n(A, Z–1, t) × P(A, Z–1) + (A+1, Z–1).n(A+1, Z–1,t) × P1n(A+1, Z–1)+ + (A+2,Z–1).n(A+2, Z–1, t) × P2n(A+2,Z–1) + (A+3,Z–1)n(A+3, Z–1, t) × P3n(A+3,Z–1) + Ff (A, Z) + (A, Z, t) n(t) and n(t) – rates of (n,γ) and (γ,n) –reactions; all fluxes and spectra are time depended =ln2/T1/2 — -decay rate, P - probability of (A, Z) nuclide creation after –-decay of (A,Z-1) nuclide. Branching coefficients of isobaric chains - P1n, P2n, Р3n corresponds to probabilities of one-, two- and three- delayed neutrons emission in –- decay of the neutron-rich nuclei. Ff (A, Z) describes fission processes: (n, f) + spontaneous and beta-delayed fission. (A, Z) - neutrino capturing processes. 4

Prompt process in the explosive nucleosynthesis Multiple neutron capturing process on Uranium material (U – target) , t < 10-6 s. 5

+ n,2n(A+1, Z, t).n(A+1, Z, t) – n,2n(A, Z, t).n(A, Z, t) ”Prompt rapid” = pr –process equations for the concentration calculations Concentrations n(A,Z, t) are changing in “prompt” time (t = 0 – 10-6 s): dn(A, Z, t)/dt = – n(A, Z, t).n(A, Z, t) + n(A–1, Z, t).n(A–1, Z, t) + n,2n(A+1, Z, t).n(A+1, Z, t) – n,2n(A, Z, t).n(A, Z, t) – n,fn(A, Z, t).n(A, Z, t) + [ , n, α, sf ] Were n,(t), n,2n(t), n,fn(t) – rates of (n,γ), (n, 2n), (n, fn) –reactions; all fluxes and spectra are “prompt” time-t depended. [ , n, α, sf ] – is slow time – τ depended (τ = 0 – 100 min).  = ln2/T1/2 — -decay rate, n — rate of -delayed neutrons emission in –- decay of the neutron-rich nuclei, f — rate of -delayed fission in –- decay of the neutron-rich nuclei, α — α-decay rate, sf — rate of spontaneous fission. Adiabatic binary model (ABM) + Monte – Carlo method was used in t-interval calc. 6

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Significant Nuclear Tests in the U.S.A. Heavy Element Program Power there is no obvious relationship between the power of the explosion and the neutron flux There is no obvious relationship between the power of the explosion and the neutron flux 8

Standard rms deviation δi (%) Yields (concentrations in relative units) for “Mike”, “Par” and “Barbel” experiments Yields of transuranium nuclei measured in the thermonuclear explosions “Mike”, “Par” and “Barbel” (LANL data). Line – approximation Y(A)/Y(Ai) = exp(–bi.A + ci) i = 1 (“Mike”) A1 = 239, b1 = 1.570, c1 = 375.491; i = 2 (“Barbel”) A2 = 244, b2 = 1.395, c2= 340.584; i = 3 (“Par”) A3 = 245, b3 = 1.388, c3 = 341.015. Standard rms deviation δi (%) δ1 = 56% (“Mike”), δ2 = 60.2% (“Barbel”), δ3 = 86.8% (“Par”). Ю.С. Лютостанский, В.И. Ляшук, И.В. Панов. Известия АН СССР Сер. Физ. 1990, т. 54, стр. 2137; Препринт ИТЭФ 25-90, М. 1990. 9

“Mike” experiment - 1952 (Calc. Yields rel. to exp. data) 10 1) ● – This calculations ABM – model, δ = 91 %. 2,3) O – D. W. Dorn, Phys. Rev. B 126, 693 (1962), δ > 400%. 4) □ – V. I. Zagrebaev, A. V. Karpov, I. N. Mishustin, W. Greiner. Phys. Rev. C 84, 044617 (2011), δ = 180 %.

Calculations for “Par” experiment (1964) (Calc. Yields rel. to exp Calculations for “Par” experiment (1964) (Calc. Yields rel. to exp. data) 11 1) ● – This calculations ABM – model, δ = 33 %. 2,3) O – D. W. Dorn and R. W. Hoff , Phys. Rev. Lett., 14, 440 (1965), 2) δ = 76%, 3) δ = 417% 4) - - - - fitting: Y(A)/Y(Ai) = exp(–bi.A + ci) i = 3, A3 = 245, b3 = 1.388, c3 = 341.015, δ = 86.8%. 11

Calculations for “Barbel” experiment (1964) (Calc. Yields rel. to exp Calculations for “Barbel” experiment (1964) (Calc. Yields rel. to exp. data) 1) ● – This calculations ABM – model, δ = 29.3 %. 2) O – G. I. Bell, Phys. Rev. B 139, 1207 (1965), δ = 33.5 %, 3) - - - - fitting: Y(A)/Y(Ai) = exp(–bi.A + ci) i = 2, A3 = 244, b3 = 1.395, c2 = 340.6, δ = 60.2%. 12 12

Table 1. Calculated and experimental relative yields of transuranium nuclides. Calculations with adiabatic binary model (ABM) and standard deviations δ from experimental data (in %) of ABM calculations and exponential approximation. “Mike” “Par” “Barbel” A Y(A)exper [3] Y(A)calc ABM [4] [6] 239 1.00 240 3.6310-01 6.4810-01 241 3.9010-02 1.3410-01 242 1.9110-02 4.1110-02 243 2.1010-03 5.2510-03 244 1.1810-03 1.0310-03 245 1.2410-04 1.0610-04 1.6110-01 2.2110-01 246 4.7810-05 1.7010-05 8.5010-01 4.9310-01 1.1310-01 7.3810-02 247 3.9010-06 2.9110-06 1.1010-01 1.3910-01 1.3510-02 1.6310-02 248 1.2010-06 5.6110-07 5.1010-02 5.1510-02 5.2210-03 4.3610-03 249 1.1010-07 1.8310-07 9.0010-03 9.5710-04 1.2010-03 250 – 3.3310-08 4.1010-03 3.7910-03 2.5710-04 2.6510-04 251 1.0410-08 1.3010-03 9.6910-04 8.5910-05 252 1.0310-09 1.5810-09 2.2010-04 2.1310-04 2.3010-05 1.5810-05 253 4.010-10 4.0510-10 1.1010-04 5.3110-05 9.5710-06 4.8210-06 254 4.210-11 5.4410-11 1.2010-05 9.5810-06 7.8310-07 7.8710-07 255 5.710-11 1.2010-11 4.3010-06 2.3210-06 3.9610-07 2.1410-07 256 2.6010-07 3.5410-07 3.0810-08 257 5.6010-08 8.0710-08 5.6510-09 7.2410-09 δ % 56 (1a) 91 87 (1c) 39 60 (1b) 29 13