Primordial nucleosynthesis and radioactive beams

Nuclear Instruments and Methods in Physics Research B56/57 (1991) 564-567 North-Holland

Primordial nucleosynthesis and radioactive beams T. Kajino Department

of Physics, Tokyo Metropolitan

Vniuersity,

Setagaya,

Tokyo 158, Japan

The role of radioactive nuclear reactions in the inhomogeneous primordial nucleosynthesis models is discussed. The cosmic phase transition in quantum chromodynamics (QCD) as the source of forming an inhomogeneous baryon-number density distribution is reviewed. Several impacts of primordial nucleosynthesis on the dark matter problem and the Q problem are briefly summarized.

1. Introduction Recent progress in the physics of radioactive beams is opening a new field in nuclear astrophysics. Although only the light elements 2H, 3’4He, and ‘Li were presumed to be primordial in the standard homogeneous big-bang model [1,2], it has recently been shown in theoretical studies of baryon inhomogeneous cosmologies [3-lo] that the rare nuclides 9Be and l”‘llB and CNO and the heavier elements also could have been created in the early universe by radioactive nuclear reactions. In this new cosmological model there are two different sites of proton-rich high density zones and neutron-rich low density zones, which are the remnants of the cosmic QCD phase transition which took place before the onset of primordial nucleosynthesis. A lot of radioactive nuclei can seed heavy element production in an inhomogeneous universe. The first purpose of the present paper is to briefly review the inhomogeneous cosmology and discuss the role of radioactive beams in primordial nucleosynthesis. The second purpose is to discuss their impacts on several cosmological problems such as the dark matter problem and the D problem in the context of the inflationary universe.

MeV3, where T, is the coexistence temperature of quark-gluon and hadron phases and o is the surface tension of the phase boundaries. Although precise values of these QCD parameters are not known very well, the upper ranges are consistent with the result suggested from recent lattice QCD simulations. We also found [12] that the strange quark matter could be formed if 80 MeV I T, 5 150 MeV and 0 I 5 x lo5 MeV3. Very little strange matter evaporates into baryons and contributes to inhomogeneous nucleosynthesis.

3. Inhomogeneous

The big-bang nucleosynthesis code of Wagoner [l] was used with a number of nuclear reaction rates updated [13]. Because of the unique history of the neutron -rich and proton-rich environments in the inhomogeneous models, it is necessary to include a number of

STRANGE

PROTON

2. Baryon inhomogeneities phase transition

QUARK

MATTER

GAS

in first order cosmic QCD

The formation mechanism of the inhomogeneous baryon-number density distribution at the time of the cosmic QCD phase transition’has been studied theoretically [ll] in isothermal fluctuation theory. We found that the baryon inhomogeneities become large enough, as displayed in fig. 1, for primordial nucleosynthesis to proceed in an interesting and different way from that in the homogeneous universe if T, I 150 MeV and (I - 10’ 0168-583X/91/$03.50

nucleosynthesis

NEUTRON

GAS

SPACE Fig. 1. Inhomogeneous baryon-number density distribution as a remnant of the first order cosmic QCD phase transition and following neutron diffusion.

0 1991 - Elsevier Science Publishers B.V. (North-Holland)

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nucleosynthesis R-PROCESS

Fig. 2. Nuclear reaction network used for primordial nucleosynthesis calculations.

new reaction rates for unstable nuclei [7]. The network used in the present calculation is displayed in fig. 2. We solve the rate equation for the change of nuclear abundances:

temperatures as low as T = lo6 K. ‘Li is created directly 4He(3H, y)‘Li in neutron-rich zones and by 4He(3He, y)‘Be(e-, u)7Li in proton-rich zones. Measured low energy (E 5 1 MeV) cross sections for 4He(3H, y)‘Li are still uncertain by a factor of 2-3. It was found [9] that the new but unmeasured reaction path

where N, is the number density of a given nuclear species i, ,oB is the baryon mass density in each zone, NA is Avogadro’s number, and (a~)~~,~~ is the thermally averaged reaction rate. The third and fourth terms denote the weak decay rates. Three- and four-body processes are also included, if they are relevant, as 4He( 0101,y)i2C, to nucleosynthesis.

in neutron-rich zones provides extremely enhanced 9Be and “B abundances. These nuclear abundances, instead of 7Li, could be a good indicator of cosmological models because they are more robust than 7Li and relatively unaffected by astration. From calculations [lo] of the galactic chemical evolution of Be-B after their creation in the big-bang we predicted that the metal weak stars, having a metallicity lower than -3, are not polluted very much by cosmic ray production of these nuclides and could show the primordial abundances. The inhomogeneous models predict N( 9Be)/N(H) = lO_ 14-10 i2 which is 4 orders of magnitude larger than the standard model prediction. The recent observed data of the 9Be abundance of Ryan et al. [17] are approaching the sensitivity required to test the two models. Quite recently, the 7Li(3H, n)‘Be reaction cross section has been measured directly [18] and indirectly [19]. It is important to reexamine the measured cross sections by another experiment for a better prediction of the theoretical 9Be abundance. The ‘Li( 3H, n)gBe * cross

3.1. Light elements:

7Li, 9Be and 10’llB

It was found [3-51 that the inhomogeneous models predict a larger ‘Li abundance by at least an order of magnitude that the standard model prediction, N(‘Li)/N(H) - 10V1’. The effect of neutron backdiffusion [6,14,15] does not decrease ‘Li very much. Although late-time hydrodynamical mixing of matter [16] destroys ‘Li, this needs fine tuning of the time of the onset temperature of mixing. The observed primordial abundance of 7Li is quite controversial with the uncertain chemical evolution of this nucleus which is easily destroyed by the (p, cl) reaction in astration at stellar

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sections are also important. The reaction could destroy ‘Li which is another key nucleus, though stable, in primordial nucleosynthesis as discussed above.

lo+ -

3.2. CNO and heavier elements In the standard homogeneous big-bang model the nuclear reaction flow stops at the A = 5 and 8 nuclear systems due to the instability of these nuclei. Almost no heavy nuclei are created. The situation is quite different in the inhomogeneous models. The circumstance of the proton-rich regions is very similar to that inside the stars, but since the temperature is forced to decrease with the universal expansion as the time goes by, the nuclear reaction flow must stop at some hydrogen-burning stage. The most significant heavy element production in these regions is for the elements 12C, 13C and t4N which are produced via the CNO or beta-limited CNO cycle: 4He(24He,

y)r’C(p,

y)13N(p, ~)l’N(p,

r4N(p, y)150(e+

y)140(eC 4He)‘2C.

‘Li(n,

y)8Li(4He,

n)“B(n,

r3C(n, y)14C(n, 16N(e-

or

(3)

y)12B(e-

y)r’C(e-

v)160(n,

7Li(4He, y)llB

y )l’O(n,

v)r2C(n,

v)15N(n,

y)

y)lxO(n,

y)190.

or y)

... (4)

Although there are several reaction chains to create “B, the strongest is the neutron capture flow triggered by

1

18

10' TIME

103

lcp

(set)

Fig. 3. Evolution in time of light element neutron-rich zones of the inhomogeneous models.

2 10-15 .!2

mass fractions in nucleosynthesis

lNHOMOGENEOUS

\ h I ,I’ \ :: \ b :

/

_

I

l’s,

1 0

I

10 MASS

V)

In the neutron-rich regions neutron and triton induced reactions bypass unstable ‘Be to build up heavy elements: 7Li(3H, n)gBe(3H, n)l*B

5

STANDARD

\

I

20

,

30

NUMBER A

Fig. 4. Calculated primordial abundances of light-to-intermediate mass nuclei, compared with observations in a metal weak giant star [20].

7Li(n, y)‘Li which seeds the heavier nuclei 12 I A. This flow is extremely strong at times - 102-lo3 s, as shown in fig. 3, regulated by *Li decay. It is clear that the neutron-rich radioactive nuclei play significant roles in several places of the main reaction chain shown above. Fig. 4 displays the theoretical prediction [7,8] of the nuclear abundances calculated in two different models. We adopted here the same inhomogeneous density model as in ref. [4], assuming a 9, = 1 closed universe. The calculated abundances of heavy elements are enhanced very much approaching the observed values in a metal weak Population II star [20]. The observed abundances are 3 or 4 orders of magnitude smaller than the solar system values. Since this star is a giant which has been processed at the subgiant branch, the primordial abundance is less that that. The theoretical ambiguity comes from the lack of our knowledge on QCD physics and unmeasured nuclear input data. Most important unmeasured or poorly measured reaction cross sections are those for ‘Li(n, y)‘Li, 8Li(4He, n)‘rB, 12C(n, y)13C, 14C(n, y)15C, and all reactions which break the main reaction flow such as ‘Li(d, n)‘Be, ‘Li(d, p)gLi, ‘Li(d, t)‘Li, *Li(p, n)24He and others [21]. We predict [S] several observational signatures characteristic of the inhomogeneous models. For one, the 13C/12C ratio approaches unity in the large density fluctuation models. This is independent of y2 and is C. The due to the effects of neutron capture on r5N/14N isotopic ratio, however, is only slightly enhanced relative to the solar ratio so that one important observational signature could be CN molecular lines with a large contribution from r3C. Similar possible

T. Kajino / Primordial

isotopic signatures are the i70/r60 ratio (which is enhanced for large Q2, inhomogeneous models independent of the density fluctuation shape), the *lNe/*‘Ne ratio (which is particularly enhanced in the small fluctuation models due to the effects of neutron capture on 20Ne), and the 2sMg/24Mg ratio which is in excess of the solar ratio such that elemental magnesium becomes 85% 25Mg. As in the case of 13C/‘2C, this enhancement is largely independent of the value for Pa.

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is necessary for constraining the dark matter component and testing the inflationary cosmology. Future experiments of measuring the key nuclear reaction cross sections by the use of radioactive nuclear beams will provide many useful data of the reaction rates for these challenging problems in astrophysics and cosmology.

References

VI R.V. Wagoner, W.A. Fowler and F. Hoyle, Astrophys. J. 4. The dark matter problem and the D problem Primordial nucleosynthesis provides a test for the dark matter problem and the 52 problem. The present value of 0, the total universal mass density, in astronomical observations is - 0.2. The standard homogeneous model infers 9, = 0.04 and needs unknown dark matter. The inhomogeneous models give a constraint 0, I 0.15-0.4 from primordial nucleosynthesis, shedding light on solving the dark matter problem without introducing them (except for baryonic dark matter like black holes, neutron stars, brown dwarfs and strange quark matter). Inflationary cosmology resolves many fundamental difficulties of hot big-bang expansion, i.e. the horizon problem, the flatness problem, the monopole problem, and many others, but requires a marginally closed universe D + A = 1. The cosmological constant, A, is completely unknown. The inhomogeneous models will provide a crucial test for or against inflation with the future observation of A by using the gravitational microlensing effect and galaxy number counting.

5. Conclusion The primordial nuclear products in inhomogeneous cosmological models are not only the light elements 2H, 3,4He and 7Li but also the rare elements 9Be, “‘*‘B and even intermediate-mass nuclei *2C-28Si which could be created by nuclear reactions of radioactive nuclei. Several observational tests are proposed for these elemental abundances which are to be observed in the main sequence metal weak Population II stars. A better theoretical prediction of primordial nuclear abundances

148 (1967) 3.

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