24P152-P
Kinetic Analysis of Nonthermal Nuclear Processes in the Early Universe Plasma
初期宇宙プラズマにおける非熱的核反応過程の運動論的解析
Yasuyuki Nakao, Kazuki Tsukida, Victor T. Voronchev*, and Kohei Sugita
中尾 安幸、附田 一起、V.T. ボロンチェフ*、杉田 昂平
Department of Applied Quantum Physics and Nuclear Engineering, Kyushu University,
744 Motooka, Fukuoka 819-0395, Japan
九州大学大学院工学研究院エネルギー量子工学部門、 〒819-0395 福岡市西区元岡 744*Institute of Nuclear Physics, Mocow State University, Moscow 119991, Russia*モスクワ大学核物理学研究所、モスクワ 119991、ロシア連邦
A plasma-kinetic model capable of properly describing the behavior of neutrons in the primordial
plasma during the epoch of big bang nucleosynthesis (BBN) is formulated in order to exactly analyze thenonthermal reactions induced by these neutrons. After calculating the realistic neutron energy distribution,
the nonthermal influence on individual reactions is examined on the example of the threshold D (n, 2n) p,
7
Li (n, n t) 4He, and reverse 3He (n, d) D processes. It is shown that at plasma temperatures T9 ≤ 1.2 thenonthermal neutrons strongly maintain these reactions, increasing their rate parameters by orders ofmagnitude as compared with the respective Maxwellian estimates.

1. Introduction
In the standard model of BBN, the nuclear
reaction network is operated with thermal reaction
rates in Maxwellian plasma [1]. In the primordial
plasma, however, a number of nonthermal
processes triggered by various energetic particles
can occur. The sources producing such particles areexoergic reactions in the plasma and up-scatteringof thermal background species by non-thermalized
products of these reactions. All these energetic
particles form several groups of non-Maxwellian
plasma species (n, p, t, 3He, 4He) which can undergo
nonthermal reactions. The most abundant andimportant nonthermal species are neutrons
generated in the D-T and D-D fusion reactions [2].
Most part of the present paper is based on ourrecent studies [3] and focused on examining the rate
parameters of nonthermal reactions induced bythese neutrons. A rigorous plasma-kinetic approachis adopted to obtain realistic neutron distributionfunction.
2. Plasma-Kinetic ModelIn the primordial plasma, fast neutrons slow
down due to nuclear and electromagnetic scattering
processes. The dominant mechanism is nuclear
elastic scattering off bulk protons; the next
contribution comes from elastic collisions with bulk
α-particles [2].
Our model starts from an equation of evolution
for the velocity distribution function of fastneutrons fn, fast (vn, t):(1)where (∂fn, fast /∂ t) C represents the scattering collision
term, L (vn, t) is the loss rate due to nuclear reactions,and S (vn, t) is the source at an arbitrary time t. The
main sources of fast neutrons are fusion reactions
and close scattering collisions between bulk thermal
neutrons and some energetic particles.
Because of the homogeneity and isotropy of
the Universe, velocity distributions of neutrons andother species can be assumed isotropic. This enables
us to use the neutron energy En instead of vn as anindependent variable and adopt the fast neutron flux
defined by Ψ = vn fn, fast (En, t), where fn, fast (En, t) isthe energy distribution function of fast neutrons.
Then, Eq. (1) is reduced to its final form:(2)
where nj is the number density of background
species j; σt jeff (En) and σS jeff (E′n → En) are the total(scattering + absorption) and differential scatteringcross sections, respectively, averaged over theenergy distributions of background species j.
Equation (2) retains the time variable t. In mostcases, however, the neutron thermalization time ismuch shorter than a typical time scale of plasma
evolution in the BBN epoch. This implies that theplasma temperature and density can be assumed to‘freeze out’ during the time needed for the slowing
down and thermalization of fast neutrons. In such acase, we can make ‘steady-state’ calculations toobtain the neutron distribution function at each time
step tn of plasma evolution. For a full detail, see [3].

Fig.1. Neutron distribution function at T9 = 0.7.

From the realistic distributions, the fraction ofnonthermal neutrons η′n in the total neutroncomponent is evaluated to be at a level of 10-2～
10-3 %, while their effective temperature T′n reaches
several MeV and exceeds the plasma temperature in
the BBN epoch by about a factor of 102.
The values of η ′n and T ′n can be used tosimplify a computational procedure by using a
two-temperature Maxwellian model for the neutrondistribution.
Now we examine how the non-Maxwellian tailof the realistic neutron distribution affects the rate
parameters of individual n-induced reactions. Herewe consider the n + X breakup (X = D, 7Li) andreverse 3He (n, d) D reactions which might haveinfluences on some primordial element abundances.
Figure 2 shows the astrophysical rate coefficientsNA< σ v > for these reactions. The solid curves show
the rate coefficients obtained for the realistic
neutron energy distribution. These realistic ratecoefficients are compared with the Maxwellian ones
given by the dashed curves. As seen, thenonthermal neutrons strongly support the breakup
reactions as the Universe cools down. The
enhancement factor obtained here is a few orders ofmagnitude.

Rate coefficient (cm3s-1mol-1)

3. Numerical Results and Discussions
The realistic neutron distribution function fn(En) at a cosmic time t can be reasonably defined as
fn (En) = fn, fast (En) + fn, bulk (En), where fn, bulk is thethermal distribution of bulk neutrons populating theprimordial plasma at that time.
Figure 1 presents, as an example, the neutronenergy distribution at a plasma temperature T9 = 0.7.
The solid curve shows the realistic distributionfunction allowing for the fast neutron component.
For comparison, the Maxwellian distribution isindicated by the dashed curve. It is clearly seen thatthe high-energy tail of realistic distribution isappreciably enhanced and deviates from theMaxwellian function.

n + 3He --> d + d105
103
101
10-1
10

realistic
Maxwellian-3

10-5
2.0

1.6

1.2

0.8

0.4

0.0T9Fig.2. Astrophysical rate coefficients as a function ofthe Universe temperature.

4. Concluding Remarks
Based on the rigorous kinetic calculations, wehave demonstrated that nonthermal neutrons canappreciably enhance rate parameters of endoergic
processes, such as D, 7Li breakup and reverse 3He(n, d) D reactions.
An important question still remains― to what
extent the nonthermal neutrons could affect thereaction kinetics in the early Universe and change
the predictions of standard BBN. To this end, anumber of nonthermal forward as well as reverse
reactions should be incorporated in the BBN
network. We address this in a future publication.
References[1] L. Kawano, Rep. No. FermiLab-Pub-92/04-A, 1992.
[2] V. T. Voronchev, et al., Astrophys. J. 725 (2010) 242;
J CAP 05 (2009) 001; ibid. 05 (2008) 010.
[3] Y. Nakao, et al., Phys. Rev. D. 84 (2011) 063016.