LXXI International conference "NUCLEUS – 2021. Nuclear physics and elementary particle physics. Nuclear physics technologies"

Non-statistical nature of fragments' spin distributions in binary nuclear fission

22 Sept 2021, 16:20

25m

Oral report Section 2. Experimental and theoretical studies of nuclear reactions. Section 2. Experimental and theoretical studies of nuclear reactions

Speaker

Dmitrii Lyubashevsky (Voronezh State University)

Description

Since for spontaneous and low-energy induced fission, compound fissile nuclei and primary fission fragments in the vicinity of the scission point are in cold nonequilibrium states [1], when constructing the spin distributions of these fragments, it is necessary to take into account [2,3] only zero transverse bending- and wriggling-vibrations of the indicated fissile nuclei. Expressing the normalized distribution function of $W\left({\mathbf{J}}_{\mathbf{1}}\mathbf{,}{\mathbf{J}}_{\mathbf{2}}\right)$ fission fragments over spins ${\mathbf{J}}_{\mathbf{1}}$ and ${\mathbf{J}}_{\mathbf{2}}$ in terms of the product of the squared moduli of the wave functions of zero bending- and wriggling-vibrations, one can obtain [4]:
$W\left({\mathbf{J}}_{\mathbf{1}}\mathbf{,}{\mathbf{J}}_{\mathbf{2}}\right)=\frac{4J_1{J}_2}{\pi C_b{C}_w}\exp [-\frac{1}{2}(\frac{1}{C_b}+\frac{1}{C_w})(J_1^2+J_2^2)+(\frac{1}{C_b}-\frac{1}{C_w})J_1^{}{J}_2^{}\cos \varphi ],(1)$
where $\varphi (0\le \varphi \le 2\pi )$ is the angle between the two-dimensional spin vectors of fragments ${\mathbf{J}}_{\mathbf{1}}$ and ${\mathbf{J}}_{\mathbf{2}}$ lying in plane $XY$. By integrating in (1) over variables $J_2$ and $\varphi$, one can obtain [4] the normalized distribution of spin $J_1$ of the first fission fragment and estimate the average value ${\overline{J}}_1$ of spin $J_1$:
$W(J_1)=\frac{4J_1}{C_b+C_w}\exp [-\frac{2J_1^2}{C_b+C_w}],\overline{J}{}_1=\underset{0}{\overset{\mathrm{\infty }}{\int }}{J}_{1}W(J_1)d{J}_1=\frac{1}{2}\sqrt{\frac{\pi }{2}}{(C_b+C_w)}^{1/2}.(2)$

For a fissile nucleus ${}^{236}$U at values [4] of parameters $M_w=1.6\cdot {10}^6\text{MeV}\cdot {\text{Fm}}^2\cdot {\text{s}}^2$; $M_b=2.0\cdot {10}^6\text{MeV}\cdot {\text{Fm}}^2\cdot {\text{s}}^2$; $K_w=295\text{MeV}\cdot {\text{rad}}^{–2}$; $K_b=52\text{MeV}\cdot {\text{rad}}^{–2}$; $\hslash {\omega }_w=2.3\text{MeV}$; $\hslash {\omega }_b=0.9\text{MeV}$; $C_w=132{\hslash }^2$ and $C_b=57{\hslash }^2$, it follows that the energies of vibrational quanta $\hslash {\omega }_w$ and coefficients $C_w$ for wriggling-vibrations turn out to be noticeably larger than those for bending-vibrations. This means that the main contribution to ${\overline{J}}_1$ (2) comes from wriggling vibrations. Then the calculated value ${\overline{J}}_1=8.6$ correlates well with the experimental [5] average values of the spins of fission fragments ${\overline{J}}_1=7–9$.

This means that the spin distribution of fission fragments is determined with a good degree of accuracy by taking into account zero wriggling and bending vibrations of a composite fissile system. This confirms the assumption [6] about the inequality of the statistical Gibbs distribution with temperature $T$ for the spin distribution of fragments, which is used in [1].

1. Bohr A. and Mottelson B. Nuclear Structure (W.A. Benjamin, NY, Amsterdam, 1969).

2. V.E. Bunakov, S.G. Kadmensky, D.E. Lyubashevsky // Phys. At. Nucl. V. 79. P. 304 (2016).

3. S.G. Kadmensky, V.E. Bunakov, D.E. Lyubashevsky // Phys. At. Nucl. V. 80. P. 447 (2017).

4. J.R. Nix and W.J. Swiateсki, Nucl. Phys. A V. 71. P. 1 (1965).

5. J.B. Wilhelmy, et al., Phys. Rev. C V. 5. P. 2041 (1972).

6. A. Gavron, Phys. Rev. C V. 13. P. 2562 (1976).

Presentation materials

Yadro_2021.pps