# High-energy breakup of 6Li as a tool to study the Big Bang nucleosynthesis reaction 2H(α,γ)6Li

**ABSTRACT** The recently claimed observations of non-negligible amounts of 6Li in old halo stars have renewed interest in the Big Bang nucleosynthesis (BBN) of 6Li. One important ingredient in the predicted BBN abundance of 6Li is the low-energy 2H(α,γ)6Li cross section. Up to now, the only available experimental result for this cross section showed an almost constant astrophysical S factor below 400 keV, contrary to theoretical expectations. We report on a new measurement of the 2H(α,γ)6Li reaction using the breakup of 6Li at 150 A MeV. Even though we cannot separate experimentally the Coulomb contribution from the nuclear one, we find clear evidence for Coulomb-nuclear interference by analyzing the scattering angular distributions. This is in line with our theoretical description, which indicates a drop of the S24 factor at low energies as predicted also by most other models. Consequently, we find even lower upper limits for the calculated primordial 6Li abundance than before.

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**ABSTRACT:**STARLIB is a next-generation, all-purpose nuclear reaction-rate library. For the first time, this library provides the rate probability density at all temperature grid points for convenient implementation in models of stellar phenomena. The recommended rate and its associated uncertainties are also included. Currently, uncertainties are absent from all other rate libraries, and, although estimates have been attempted in previous evaluations and compilations, these are generally not based on rigorous statistical definitions. A common standard for deriving uncertainties is clearly warranted. STARLIB represents a first step in addressing this deficiency by providing a tabular, up-to-date database that supplies not only the rate and its uncertainty but also its distribution. Because a majority of rates are lognormally distributed, this allows the construction of rate probability densities from the columns of STARLIB. This structure is based on a recently suggested Monte Carlo method to calculate reaction rates, where uncertainties are rigorously defined. In STARLIB, experimental rates are supplemented with: (i) theoretical TALYS rates for reactions for which no experimental input is available, and (ii) laboratory and theoretical weak rates. STARLIB includes all types of reactions of astrophysical interest to Z = 83, such as (p,g), (p,a), (a,n), and corresponding reverse rates. Strong rates account for thermal target excitations. Here, we summarize our Monte Carlo formalism, introduce the library, compare methods of correcting rates for stellar environments, and discuss how to implement our library in Monte Carlo nucleosynthesis studies. We also present a method for accessing STARLIB on the Internet and outline updated Monte Carlo-based rates.The Astrophysical Journal Supplement Series 04/2013; 207(1). · 16.24 Impact Factor - SourceAvailable from: arxiv.org
##### Article: Primordial Nucleosynthesis

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**ABSTRACT:**Primordial nucleosynthesis, or Big-Bang Nucleosynthesis (BBN), is one of the three evidences for the Big-Bang model, together with the expansion of the Universe and the Cosmic Microwave Background. There is a good global agreement over a range of nine orders of magnitude between abundances of 4He, D, 3He and 7Li deduced from observations, and calculated in primordial nucleosynthesis. This comparison was used to determine the baryonic density of the Universe. For this purpose, it is now superseded by the analysis of the Cosmic Microwave Background (CMB) radiation anisotropies. However, there remain, a yet unexplained, discrepancy of a factor 3-5, between the calculated and observed lithium primordial abundances, that has not been reduced, neither by recent nuclear physics experiments, nor by new observations. We review here the nuclear physics aspects of BBN for the production of 4He, D, 3He and 7Li, but also 6Li, 9Be, 11B and up to CNO isotopes. These are, for instance, important for the initial composition of the matter at the origin of the first stars. Big-Bang nucleosynthesis, that has been used, to first constrain the baryonic density, and the number of neutrino families, remains, a valuable tool to probe the physics of the early Universe, like variation of "constants" or alternative theories of gravity.Acta Physica Polonica Series B 08/2012; · 1.01 Impact Factor - SourceAvailable from: Matthias JunkerM. Anders, D. Trezzi, A. Bellini, M. Aliotta, D. Bemmerer, C. Broggini, A. Caciolli, H. Costantini, P. Corvisiero, T. Davinson, [......], A. Lemut, M. Marta, C. Mazzocchi, R. Menegazzo, P. Prati, C. Rossi Alvarez, D. Scott, E. Somorjai, O. Straniero, T. Szücs[Show abstract] [Hide abstract]

**ABSTRACT:**The production of the stable isotope Li-6 in standard Big Bang nucleosynthesis has recently attracted much interest. Recent observations in metal-poor stars suggest that a cosmological Li-6 plateau may exist. If true, this plateau would come in addition to the well-known Spite plateau of Li-7 abundances and would point to a predominantly primordial origin of Li-6, contrary to the results of standard Big Bang nucleosynthesis calculations. Therefore, the nuclear physics underlying Big Bang Li-6 production must be revisited. The main production channel for Li-6 in the Big Bang is the 2H(alpha,gamma)6Li reaction. The present work reports on neutron-induced effects in a high-purity germanium detector that were encountered in a new study of this reaction. In the experiment, an {\alpha}-beam from the underground accelerator LUNA in Gran Sasso, Italy, and a windowless deuterium gas target are used. A low neutron flux is induced by energetic deuterons from elastic scattering and, subsequently, the 2H(d,n)3He reaction. Due to the ultra-low laboratory neutron background at LUNA, the effect of this weak flux of 2-3 MeV neutrons on well-shielded high-purity germanium detectors has been studied in detail. Data have been taken at 280 and 400 keV alpha-beam energy and for comparison also using an americium-beryllium neutron source.European Physical Journal A 01/2013; 49(2). · 2.04 Impact Factor

Page 1

arXiv:1011.6179v1 [nucl-ex] 29 Nov 2010

High-energy break-up of6Li as a tool to study the Big-Bang nucleosynthesis reaction

2H(α,γ)6Li

F. Hammache1,2, M. Heil2, S. Typel2,3, D. Galaviz4∗, K. S¨ ummerer2†, A. Coc5, F. Uhlig2,

F. Attallah2, M. Caamano6, D. Cortina6, H. Geissel2, M. Hellstr¨ om2, N. Iwasa7, J. Kiener5,

P. Koczon2, B. Kohlmeyer8, P. Mohr4‡, E. Schwab2, K. Schwarz2, F. Sch¨ umann9, P. Senger2,

O. Sorlin1§, V. Tatischeff5, J.P. Thibaud5, E. Vangioni10, A. Wagner11, and W. Walus12

1Institut de Physique Nucl´ eaire, UMR-8608, CNRS/IN2P3 and Universit´ e Paris Sud XI, F-91406 Orsay, France

2GSI Helmholtzzentrum f¨ ur Schwerionenforschung GmbH, D-64220 Darmstadt, Germany

3Excellence Cluster “Origin and Structure of the Universe”,

Technische Universit¨ at M¨ unchen, D-85748 Garching, Germany

4Technische Universit¨ at Darmstadt, D-64220 Darmstadt, Germany

5Centre de Spectrom´ etrie Nucl´ eaire et de Spectrom´ etrie de Masse (CSNSM), UMR-8609,

CNRS/IN2P3 and Universit´ e Paris Sud XI, F-91405 Orsay Campus, France

6Universidade Santiago de Compostela, E-15786 Santiago, Spain

7Tohoku University, Aoba, Sendai, Miyagi 980-8578, Japan

8Fachbereich Physik, Philipps Universit¨ at, D-3550 Marburg, Germany

9Ruhr-Universit¨ at Bochum, D-44780 Bochum, Germany

10Institut d’Astrophysique de Paris, UMR-7095, CNRS and Universit´ e Pierre et Marie Curie, F-75014 Paris, France

11Forschungszentrum Rossendorf, D-01314 Dresden, Germany and

12Institute of Physics, Jagiellonian University, PL-30-059 Krakow, Poland

(Dated: November 29, 2010)

The recently claimed observations of non-negligible amounts of6Li in old halo stars have renewed

interest in the Big-Bang Nucleosynthesis (BBN) of6Li. One important ingredient in the predicted

BBN abundance of6Li is the low-energy2H(α,γ)6Li cross section. Up to now, the only available

experimental result for this cross section showed an almost constant astrophysical S-factor below

400 keV, contrary to theoretical expectations. We report on a new measurement of the2H(α,γ)6Li

reaction using the break-up of6Li at 150 A MeV. Even though we cannot separate experimentally the

Coulomb contribution from the nuclear one, we find clear evidence for Coulomb-nuclear interference

by analyzing the scattering-angular distributions. This is in-line with our theoretical description

which indicates a drop of the S24-factor at low energies as predicted also by most other models.

Consequently, we find even lower upper limits for the calculated primordial

before.

6Li abundance than

PACS numbers: 25.40.Lw,25.60.-t, 25.70.De, 26.65.+t

I.INTRODUCTION

The Big–Bang model of the Universe is mainly sup-

ported by three observational evidences:

sion of the Universe, the Cosmic Microwave Background

(CMB), and the primordial or Big-Bang Nucleosynthe-

sis (BBN) of light nuclei like2H,3,4He, and7Li with

one free parameter, the baryonic density of the Universe,

Ωb.Recently, a precise value for this free parameter

(Ωbh2=0.02260±0.00053) has been deduced from the a-

nalysis of the anisotropies in the CMB as observed by

the WMAP satellite [1]. Using the best available nuclear

reaction rates, this now allows to make precise predic-

tions for the primordial abundances of these light nuclei.

the expan-

∗present address: Centro de F´ ısica Nuclear, Universidade de Lis-

boa, P-1649-003 Lisboa, Portugal

†Electronic address: k.suemmerer@gsi.de

‡present address: Diakonie-Klinikum Schw¨ abisch-Hall, D-74523

Schw¨ abisch-Hall, Germany

§present address:GANIL, BP 55027, F-14076 Caen Cedex 5,

France

A comparison between calculations and observations re-

veals good agreement for helium, excellent agreement for

deuterium, and a discrepancy (by a factor of ≈ 4) for

7Li [2–4]. Possible reasons for this discrepancy for7Li

have recently been discussed e.g. by Spite and Spite [5].

In 2006, high-resolution observations of Li absorption

lines in some very old halo stars have led the authors

to claim evidence for large primordial abundances also

of the weakly-bound isotope6Li [6].

tios of ∼ 5 × 10−2were found to be about three orders

of magnitude larger than the BBN-calculated value of

6Li/7Li ∼ 10−5. This observation has triggered many

studies to resolve the discrepancy either by considering

an early6Li formation in primitive dwarf galaxies at high

redshift in a hierarchical-structure formation context [7],

in situ by solar-like flares [8], or in terms of physics be-

yond the standard model of particle physics (see, e.g.,

Refs. [9–11]). More recently, however, Cayrel et al. [12]

and Steffen et al. [13] have pointed out that line asym-

metries similar to those created by a6Li blend could also

be produced by convective Doppler shifts in stellar at-

mospheres. Similarly, a recent study of Garcia Perez et

al. [14] could not claim any significant detection of6Li in

The6Li/7Li ra-

Page 2

2

metal-poor stars. So, presently the debate is open. More

stellar observations are required to solve this question

(see Asplund and Lind [15]).

Predictions for the production of6Li in BBN require

precise measurements of the2H(α,γ)6Li reaction rate, the

key production mechanism. In BBN, this reaction occurs

at energies in the range 50 keV ≤ Ecm≤ 400 keV [16]. At

higher energies, this reaction has been studied carefully

in direct kinematics: at energies above 1 MeV by Robert-

son et al. [17], and by Mohr et al. [18] in the energy range

around the dominant 3+resonance at Ecm= 0.711 MeV.

At BBN energies, however, direct measurements are dif-

ficult due to extremely low cross sections (about 29 pb

at Ecm = 100 keV). An attempt by Cecil et al. [19] at

Ecm= 0.053 MeV yielded only an upper limit for the S-

factor of 2.0×10−7MeV b which is more than an order of

magnitude higher than present estimates. A straightfor-

ward solution to overcome this problem is offered by the

indirect method of Coulomb dissociation (CD). As will

be shown below, the dominant multipolarity involved is

E2. When bombarding a high-Z target like208Pb with a

medium-energy (≈ 150 A MeV)6Li beam, an intense flux

of virtual E2 photons is created that dissociates6Li into

2H and α with a greatly enhanced cross section. From

the energy-differential CD cross section, the radiative-

capture one can be calculated easily [20] provided that

the multipolarity of the respective transition is known

and that higher-order electromagnetic or nuclear contri-

butions can be either ignored or taken into account quan-

titatively.

Kiener et al. [21] have investigated the2H(α,γ)6Li re-

action by means of the CD method employing 26 A MeV

6Li projectiles breaking up into D+α in the Coulomb field

of a208Pb nucleus. Referring to a theoretical paper by

Shyam et al. [22], Kiener et al. have claimed that their

measurement is largely free from nuclear background (the

same assumption was made in a later reevaluation of the

same dataset [23]). While the astrophysical S-factor de-

rived in Ref. [21] seems to agree well with theoretical

predictions at and above the resonance, a puzzling result

emerged below the resonance: the experimental data sug-

gest a rather constant S-factor in the astrophysically in-

teresting region below 400 keV; most theoretical curves,

however, drop with decreasing energy [24]. As we will

show in the present paper, it is likely that this constant

S-factor is due to nuclear processes that cannot be ig-

nored.

We report in this article on a new break-up mea-

surement performed at the SIS-18 heavy-ion synchrotron

at GSI (Helmholtzzentrum f¨ ur Schwerionenforschung in

Darmstadt, Germany) using a higher-energy (150 A

MeV)6Li beam. This higher beam energy should have

several advantages compared to the one used by Kiener

et al.: (i) the stronger forward focusing allows for a more

complete angular coverage; (ii) CD should be enhanced

relative to the nuclear contribution. In addition, we have

developed a comprehensive theoretical model of electro-

magnetic and nuclear break-up processes that allows to

interprete the measured data in detail. We will show be-

low, however, that it is unfortunately not possible to sep-

arate experimentally electromagnetic and nuclear contri-

butions. Nevertheless, most of the features of the mea-

sured data can be well explained by our model, thus giv-

ing our calculated2H(α,γ)6Li cross sections a firm ex-

perimental basis.

II. THEORETICAL PREDICTIONS

A.Radiative-capture reaction

The cross section of the2H(α,γ)6Li reaction at ener-

gies Ecm< 1 MeV is dominated by radiative E2 capture

from d waves in the α+2H channel into the Jπ= 1+

ground state of6Li via a prominent 3+resonance at

Ecm= 0.711 MeV. In comparison, E1 transitions from p

waves to the6Li ground state are strongly suppressed by

the isospin selection rule for N = Z nuclei due to the al-

most equal charge-to-mass ratio of the deuteron and the

α particle. Only at very low energies (Ecm≤ 150 keV),

the E1 contribution is expected to become larger than

the E2 capture since the penetrabilities in p and d waves

exhibit a different energy dependence [17].

In the past, a number of different theoretical ap-

proaches were considered for the calculation of the low-

energy2H(α,γ)6Li capture cross section, see [24] and re-

ferences therein. They comprise, e.g., simple potential

models and microscopic cluster models using the resona-

ting group method (RGM) or the generator coordinate

method (GCM). Provided that the parameters of these

models are well fitted to observable quantities like the

binding and resonance energies in the6Li system and

that the asymptotic form of the bound state wave func-

tion is correctly taken into account, good agreement be-

tween the predictions for the low-energy cross section is

found. This shows that the radiative capture at energies

below the 3+resonance is essentially an extranuclear pro-

cess and that details of the interior wave function are less

important.

In the present work we employ a potential model

for the

2H(α,γ)6Li reaction and, at the same time, can be used

in modelling the breakup reaction when6Li is scattered

on a Pb nucleus at 150 A MeV. This model assumes that

6Li is described by two interacting clusters, α and2H,

without internal structure. Bound and scattering wave

functions in the relevant partial waves, characterized by

orbital angular momentum l and total angular momen-

tum J, are obtained by solving the appropriate radial

Schr¨ odinger equation with α-2H potentials that contain

a central part of Woods-Saxon form

6Li system that provides the S-factor for the

Vl,J

c

(r) = −Vl,J

c

?

1 + exp

?r − R

a

??−1

(1)

Page 3

3

024

6

Erel [MeV]

-50

0

50

100

150

200

250

Phaseshifts [deg]

Jenny et al. (1983)

McIntyre et al. (1967)

Gruebler et al. (1975)

calculation

δ2

2

δ3

2

δ1

2

δ1

0

δ2

1

δ1

1

δ0

1

FIG. 1: (Color online) Phase-shift data measured for low-

energy α-2H scattering as a function of the relative α-2H en-

ergy in the c.m. system, Erel. Data points are from Jenny et

al. (circles, [25]), McIntyre et al. (squares, [26]), and Gr¨ uebler

et al. (diamonds, [27]). The results of the model calculations

(full lines) were obtained with the potential parameters de-

scribed in the text.

and a spin-orbit part of derivative Woods-Saxon form

Vl,J

so(r) = Vl,J

soλ2?L ·?S

¯ h2r

d

dr

?

1 + exp

?r − R

a

??−1

(2)

with λ = 2 fm.

1.25 A1/3fm with A = 6; a = 0.65 fm denotes the dif-

fuseness parameter. The depths Vl,J

MeV for the ground state (l = 0) and 56.7 MeV for all

other partial waves (l = 1,2). For the spin-orbit part

Vl,J

soa depth of 2.4 MeV was used for the relevant partial

waves l = 1,2. These values were obtained by adjusting

the parameters as to reproduce the experimental values

for the binding energy EB= 1.474 MeV of6Li and the

3+resonance energy with respect to the α+2H threshold.

This choice of parameters also describes the low-energy

α-2H experimental scattering phase shifts very well, see

Fig. 1. The cross section of the radiative capture reac-

tion is calculated in the present model with the usual

long-wavelength approximation of the E1 and E2 mul-

tipole operators M(Eλµ) = Z(λ)

denotes the electron charge and ? rαdis the radius vector

between α and deuteron. The effective charge numbers

The radius R is given by R =

c

were set to 60.712

efferλ

αDYλµ(ˆ rαd) where e

Z(λ)

eff= Zd

?

mα

md+ mα

?λ

+ Zα

?

−

md

md+ mα

?λ

(3)

depend on the charge numbers Ziand masses miof the

two clusters. The E1 effective charge number does not

vanish since experimental values for the masses are used.

However, the E2 contribution dominates over most of the

range of energies with a pronounced peak at the position

of the 3+resonance. Only at energies below 110 keV

the E1 contribution exceeds the E2 contribution. We

display the energy dependences of the two relevant mul-

tipole contributions to the S-factor below in Fig. 9 of

Sect.IV.

B. Breakup reaction

The theoretical description of the breakup reaction

208Pb(6Li,α2H)208Pb is considerably more involved than

that of the radiative capture reaction, in particular if

both electromagnetic and nuclear breakup have to be

included. The differential breakup cross section in the

6Li-208Pb c.m. system can be written in the general form

d3σ

dΩLiPbdEαddΩαd

µ2

LiPb

(2π)2¯ h4

(4)

=

pf

pi

LiPb

LiPb

1

2JLi+ 1

?

MLi

?

Md

|Tfi|2µαdpαd

(2π¯ h)3

with reduced masses µij = mimj/(mi+ mj) and rela-

tive momenta ? pij = µij(? pi/mi− ? pj/mj). Ωij denotes

the solid angle for the scattering of particles i and j in

their c.m. system and Eαd= p2

ergy in the fragment system after the breakup. In the

initial state,6Li is in the ground state with total angular

momentum JLi= 1 and MLi= ±1,0. In the final state,

the deuteron carries spin 1 with projections Md= ±1,0.

The cross section (4) determines the relative probability

to find the two fragments with given momenta in the fi-

nal state und thus can be used directly in a Monte-Carlo

simulation of the breakup reaction.

The main task is to calculate the T-matrix element

that contains all the relevant information on the breakup

process. In distorted wave Born approximation (DWBA)

it is given by

αd/(2µαd) is the c.m. en-

Tfi = ?χ(−)(? pf

×(VLiPb− ULiPb)|ΦLi(JLiMLi)χ(+)(? pi

LiPb)Ψ(−)

αd(? pαdMd)| (5)

LiPb)?

with the6Li ground state wave function ΦLiand the wave

function Ψ(−)

αdfor the relative motion of the fragments in

the continuum. These two functions are given by the

solutions of the Schr¨ odinger equation as in the calcula-

tion of the radiative-capture cross section. The distorted

waves χ(±)describe the scattering of the projectile on

the target. They can be found by solving the Schr¨ odinger

equation for the Li-Pb scattering with the optical poten-

tial ULiPbthat only depends on the distance between Li

and Pb. In contrast, VLiPbis the full many-body inter-

action potential. It is approximated by

VLiPb ≈

ZαZPbe2

|? rα−? rPb|+ZdZPbe2

+UN

|? rd−? rPb|

(6)

αPb(|? rα−? rPb|) + UN

dPb(|? rd−? rPb|)

separating Coulomb and nuclear contributions and intro-

ducing nuclear optical potentials UN

αPband UN

dPbfor the

Page 4

4

α-Pb and2H-Pb interaction, respectively. Similarly we

have

ULiPb(? rLiPb) ≈ZLiZPbe2

|? rLiPb|

+ UN

LiPb(|? rLiPb|) (7)

with ? rLiPb = ? rLi− ? rPb. Since both potentials contain

Coulomb and nuclear contributions additively, it is pos-

sible to separate the T-matrix element into a Coulomb

and a nuclear part as

Tfi= TC

fi+ TN

fi. (8)

In general, Coulomb and nuclear contributions to the

breakup amplitude can interfere.

In the breakup experiment, the projectile velocity

vLiPb relative to the target is large and the fragments

are observed at small forward scattering angles with res-

pect to the beam axis. Thus it is sufficient to replace

the distorted waves appearing in Eq. (5) by their eikonal

approximation, i.e.

χ(−)∗(? pf

LiPb)χ(+)(? pi

?

LiPb)

?

(9)

= exp i? q ·?b

?

expiSLiPb(?b)

?

with the momentum transfer

? q =1

¯ h

?

? pi

LiPb− ? pf

LiPb

?

(10)

and the phase function

SLiPb(?b) = −

1

¯ hvLiPb

?∞

−∞

dz ULiPb(? rLiPb) (11)

where the coordinate vector has been decomposed as

? rLiPb=?b + zˆ ebeam

?b ⊥ ˆ ebeam

(12)

and ˆ ebeam denotes the beam direction. The Coulomb

part of the phase function can be calculated analytically.

In order to avoid a divergent result at small impact pa-

rameters, b, the Coulomb potential of a point-like target

charge in Eq. (7) is replaced by that of a homogeneous

sphere. In the eikonal approximation, the Coulomb and

nuclear T-matrix elements can be written as

TC/N

fi

= ?Ψ(−)

αd(? pαdMd)|FC/N(? rαd)|ΦLi(JLiMLi)? (13)

with the Coulomb form factor

FC(? rαd) =(14)

ZPbe

?

Zαe

|? rαPb|+

d3rLiPb exp

?

i? q ·?b

?

exp

?

iSLiPb(?b)

?

×

?

Zde

|? rdPb|−

ZLie

|? rLiPb|

?

and the nuclear form factor

FN(? rαd) =

?

×?UN

(15)

d3rLiPb exp

?

i? q ·?b

?

exp

?

iSLiPb(?b)

?

αPb+ UN

dPb− UN

LiPb

?

that can be both decomposed into multipoles L =

0,1,2,.... Using the method of steepest descent, the mul-

tipole components of the Coulomb form factor (14) are

easily calculated. Neglecting the nuclear contribution in

the phase function SLiPbone obtains in lowest order the

well-known Coulomb excitation functions in the semiclas-

sical approximation. The nuclear optical potential UN

in (11) leads to corrections that take, e.g., the absorp-

tion by the target nucleus into account; also, relativistic

corrections are easily included, see Ref. [28] for details.

LiPb

Since the E2 virtual photons are orders of magnitude

more abundant than the E1 ones, the Coulomb contri-

bution to the breakup is essentially sensitive only to the

quadrupole contribution.(There is no monopole con-

tribution in this case.) Contrary to electromagnetic E1

excitations, nuclear L = 1 excitations are not suppressed

by isospin selection rules. Nuclear processes for all multi-

polarities have, therefore, to be taken into account when

modelling the break-up of6Li into α+2H at about 150 A

MeV. In the present work, we included nuclear L = 0,1,2

excitations because higher multipoles are expected to

give only small contributions to the total breakup am-

plitude.

In order to obtain numerical results for the T-matrix

elements, one has to specify the nuclear optical potentials

that enter into the calculation. Unfortunately, there are

no systematic optical- model potentials available descri-

bing the elastic scattering of α,2H and6Li on a Pb tar-

get at 150 A MeV. Therefore, we generated the optical

potentials from systematic optical-model potentials for

nucleon-Pb elastic scattering and folded them with the

matter distribution of the projectile and the fragments,

respectively. These potentials were tuned to reproduce

published elastic-scattering data at incident energies as

close to 150 A MeV as possible by multiplying the real

and imaginary parts by scaling factors not too far from

unity. Literature data have been used for the elastic scat-

tering of2H +208Pb at 55 and 70 A MeV [29, 30], of α

+208Pb at 120 A MeV and 175 A MeV [31], and of6Li

+208Pb at 100 A MeV [32].

We found that deuteron and α scattering on Pb were

best described starting with the relativistic nucleon-

nucleus potentials of Ref. [33].

Pb scattering the non-relativistic optical-model poten-

tial from Ref. [34] for nucleon-nucleus scattering worked

best. Fig. 2 shows measured and fitted elastic-scattering

data for the three cases. The optical-model potentials,

obtained by the procedure described above for the actual

energy of the breakup experiment, are well fitted by a

Woods-Saxon shape. Since mostly the outer region of

the potential is important the fits were started at a ra-

dius of 7 fm. In Table I we give the numerical values of

the depth, radius and diffuseness parameters for the real

and imaginary parts.

In the case of

6Li-

Page 5

5

0 10 2030 40

50 60

10-5

10-4

10-3

10-2

10-1

100

σel / σRutherford

0

5

10

15

20

10-5

10-4

10-3

10-2

10-1

100

σel / σRutherford

0

5

10

15

20

θc.m. [deg]

10-5

10-4

10-3

10-2

10-1

100

σel / σRutherford

208Pb(d,d)208Pb

Ed = 110 MeV

208Pb(α,α)208Pb

208Pb(6Li,6Li)208Pb

Ed = 140 MeV

Eα = 480 MeV

E6Li = 600 MeV

Eα = 699 MeV

(a)

(b)

(c)

FIG. 2: (Color online) Center-of-mass angular distributions

for (a) 55 and 70 A MeV

and (c) 100 A MeV6Li on208Pb. The full lines represent fits

to the measured data using the optical-model potentials as

described in the text. Note that the angular distributions for

Ed = 140 MeV in panel (a) and for Eα = 699 MeV in panel

(b) have been scaled by a factor of 10−2.

2H, (b) 120 and 175 A MeV α,

C. Predicted observables

The most meaningful observable that can illustrate the

predictions from the above-sketched model of6Li break-

up is the scattering angle, θ6, of the excited6Li∗before

break-up, relative to the incoming6Li beam. Fig. 3 de-

picts the expected θ6distribution.

The figure clearly shows that pure nuclear, pure

TABLE I: Woods-Saxon potential parameter used to describe

the scattering of6Li, α, and2H on a Pb target.

System

Vreal

Rreal

areal

Vimag

Rimag

aimag

6Li+208Pb α+208Pb

55.0407

7.4979

0.8665

84.1720

7.3633

0.8693

2H+208Pb

23.6250

7.9057

0.8984

28.3867

7.3712

0.9391

[MeV]

[fm]

[fm]

[MeV]

[fm]

[fm]

48.0315

7.9014

0.8542

45.4504

7.3763

0.9020

01234

5

θ6 (deg)

0

1000

2000

3000

4000

dσ/dθ6 (arbitrary units)

CD+Nuclear

CD

Nuclear

FIG. 3: (Color online) Expected distribution of the differen-

tial cross section, dσ/dθ6, as a function of the scattering angle,

θ6, of the excited6Li∗before break-up, in arbitrary units. The

full (red) curve represents the total distribution, whereas the

nuclear and Coulomb contributions are depicted by the dot-

dashed (blue) and dashed (green) histograms, respectively.

Note that the different curves have been normalized to the

same total cross section. All distributions were summed over

2H-α c.m. energies, Erel, up to 1.5 MeV.

Coulomb, and total (CD+nuclear) distributions exhibit

distinctly different peak structures. Pure Coulomb in-

teraction has its most prominent peak where the other

contributions show a minimum.

(CD+nuclear) distribution can be distinguished from a

nuclear-only theory by the large amplitude of the most

prominent peak (due to constructive CD-nuclear interfe-

rence), and by the disappearance of the third maximum

(due to destructive interference). In principle, these fea-

tures should allow to separate the contributions from the

individual interactions. However, the theoretical predic-

tions have to be folded with the resolution and the ac-

ceptance of the experimental apparatus using the Monte-

Carlo simulations described below in subsection IIIB.

Likewise, the total

Page 6

6

III. EXPERIMENTAL PROCEDURE

A.Apparatus

A schematic view of the set-up used is given in Fig. 4.

A208Pb target with 200 mg/cm2thickness was bom-

barded by a primary6Li beam of 150 A MeV energy.

The6Li beam was produced by the SIS-18 synchrotron

at GSI, separated from possible contaminant ions by us-

ing the FRS FRagment Separator [35] and transported

to the standard target position of the kaon spectrometer

KaoS [36]. The average6Li beam intensity at the break-

up target was of the order of 5x104per 4 sec spill. The

beam had a width of 0.17(0.12) cm and an angular di-

vergence of 4.4(4.4) mrad in x(y) direction at the target

(1σ widths).

The angles and positions as well as the energy losses of

the outgoing particles,2H and α, were measured by two

pairs of single-sided silicon strip detectors (SSD, 300 µm

thick, 100 µm pitch) [37] placed at distances of 15 and

30 cm, respectively, downstream from the target. From

the detector pitch one can calculate a resolution of the

2H-α opening angle in the laboratory, θ24, of about 1%.

Non-interacting6Li beam particles were identified event

by event with a 16-strip ∆E detector located directly be-

hind the SSD and stopped in a cylindrical Ta absorber

(12 mm diameter, 20 mm length) placed behind the de-

tector. Break-up events were discriminated from non-

interacting6Li-beam events by their energy-loss signals

in the 16-strip ∆E detector; an energy loss correspond-

ing to6Li was used as a trigger veto signal. Deuteron

and α momenta were analyzed with the large-acceptance

KaoS spectrometer and were detected in two consecutive

multi-wire proportional chambers (MWPC [37]) followed

by a plastic-scintillator TOF wall consisting of 30 ele-

ments (each 7 cm wide and 2 cm thick). This plastic

wall was used as a trigger detector for the data acquisi-

tion system. The KaoS magnets’ volume was filled with

He gas at atmospheric pressure to reduce multiple scat-

tering.

The coincident

break-up in the208Pb target were identified by recon-

structing their vertex at the target. This removed all

break-up events in layers of matter other than the target.

The2H and α momenta were determined from tracking

them with GEANT through the MWPC and TOF wall

behind KaoS. The incident angles in front of the magnets

were known unambiguously from the SSD hits. While in

the SSD each hit could be attributed to either2H or

α by its energy deposition, the corresponding hits in the

MWPC were attributed to the respective particle type by

finding the optimum trajectory through the MWPC and

the TOF wall. This was done in an iterative procedure

that started with a test assignment of each hit to either

α or2H and a test momentum for each of them. Both

the momentum values and the assignments were then it-

eratively changed until the minimum squared deviation

from the observed hits in all detectors downstream from

2H and α fragments resulting from

the KaoS magnet were reached. This momentum recon-

struction could be shown to be accurate within about

10−3. From the opening angles between the fragments

and from their momenta, the relative energies, Erel, be-

tween the2H and α particles in the c.m. system could

be reconstructed.

B.Monte-Carlo simulations

It is obvious that the experimental apparatus imposes

strong restrictions on the detection of the break-up par-

ticles, α and2H. This applies in particular to the angular

acceptance, the energy and position resolution, and the

detection efficiency. As a consequence, a meaningful com-

parison between theoretical predictions and experimental

data can only be made using theoretical data filtered by

the experimental set-up. To this end, we have modelled

the entire set-up, starting in front of the208Pb break-up

target, in GEANT3 [38]. As an event generator, the the-

oretical model described in the previous section was used.

Input data were generated as statistically-distributed en-

sembles of 100,000 break-up“events” each that were dis-

tributed according to the calculated differential cross sec-

tions. The emittance of the6Li beam (as measured with-

out break-up target and without absorber) was imposed.

Each break-up particle, α and2H, was followed through

the remainder of the Pb target after the reaction vertex,

the SSD detectors, the beamline exit window, the He-

filled interior of the magnets with the magnetic field and

the air behind KaoS before hitting the MWPC volumes

and the TOF wall.

The Monte-Carlo simulations were used to obtain esti-

mates of the resolution and the efficiency of our setup. As

an example, we plot in Fig.5(a) the 1σ-resolution of Erel.

The data points were obtained by sending 10,000 events

each with different values of Erel (within a narrow bin

of 0.1 MeV width for each case) into our setup and an-

alyzing the outgoing particles with the same routines as

in the experiment. From the same data sets, the number

of counts gave an approximate estimate of the detection

efficiency, shown in Fig.5(b). In the experiment, how-

ever, the detection efficiency is additionally limited by

the small and strongly fluctuating energy deposition of

deuterons in the MWPC. This latter quantity cannot be

simulated easily, such that we had to normalize the num-

ber of observed and simulated counts. Therefore, our

experiment does not allow to determine absolute cross

sections, despite the fact that all incident6Li ions were

counted.

IV.EXPERIMENTAL RESULTS

A relatively unbiased observable, based only on high-

resolution SSD measurements, is the opening angle, θ24,

between the outgoing fragments2H and α. Fig. 6 shows

this distribution, summed over Erel values up to 1.5

Page 7

7

FIG. 4: (Color online) The experimental setup shows the fragment-tracking SSD behind the Coulomb-break-up target followed

by a 16-strip ∆E detector and a beam stopper. Deuteron and α positions were measured near the focal plane of the KaoS

QD-spectrometer by two successive large area multi-wire proportional chambers (MWPC) followed by a scintillator-paddle

TOF wall used for trigger purposes.

0

0.5

1

1.5

0

0.05

0.1

0.15

0.2

0.25

Resolution (MeV)

0

0.5

1

1.5

Erel (MeV)

0.3

0.4

0.5

0.6

Efficiency

(a)

(b)

FIG. 5: (a) Relative-energy resolution (1σ widths) as deter-

mined by simulating

points can be approximated by the fitted function σE =

0.1645 ×√Erel. (b) Combined geometrical and analysis ef-

ficiency of determining Erel from the2H and α momentum

vectors. The intrinsic efficiency of the MWPC detectors has

been assumed to be unity in this graph.

6Li breakup with GEANT. The data

MeV; this condition was also set for all other spectra

shown below. The experimental data points are com-

pared with the corresponding Monte-Carlo simulations

for pure Coulomb (CD) and pure nuclear interactions as

well as combined (CD+nuclear) interactions. Each sim-

ulated histogram was normalized to contain the same

number of counts as the experimental spectrum, thus

providing the single scaling factor used to normalize all

simulated distributions.

01234

5

θ24 (deg)

0

100

200

300

400

counts

Experiment

CD+Nuclear

CD

Nuclear

FIG. 6: (Color online) Opening angles, θ24, between the out-

going fragments

sured data. The dash-dotted histogram (blue) denotes sim-

ulations with pure nuclear interaction, whereas the pure CD

contribution is shown by the dashed histogram (green). Com-

bined (CD+nuclear) contributions are shown by the full red

line. Note that the numbers of simulated counts in each spec-

trum were normalized to the experimental ones.

2H and α. Full circles correspond to mea-

As seen in Fig. 6, the data are reasonably well repro-

duced by the simulations over their entire range. The

3+resonance peak is clearly visible around 3 degrees; its

angular width is well reproduced indicating that the sim-

ulation takes both the scattering and the finite angular

resolution well into account. It is obvious, however, that

one cannot distinguish between the different interactions

on the basis of this angular distribution. We have there-

fore to search for an observable that is more sensitive to

the type of interaction. In Fig. 3 above, we have shown

that the observable θ6 should be very sensitive to the

Page 8

8

0

10

20

30

40

counts

Experiment

CD+Nuclear

CD

Nuclear

0

50

100

150

counts

01234

5

θ6 (deg)

0

20

40

60

80

counts

(a)

(b)

(c)

FIG. 7: (Color online) Angular distribution of the excited

6Li∗nuclei after the reaction (θ6).

three different bins of Erel: (a) 0.0 ≤ Erel < 0.5 MeV; (b)

0.5 ≤ Erel < 0.9 MeV; (c) 0.9 ≤ Erel < 1.5 MeV. The mea-

sured data points are shown in comparison with simulations

with pure nuclear and pure CD as well as with (CD+nuclear)

interactions. Line types and color codes are identical to the

ones in Fig. 6.

The panels represent

type of interaction.

The experimental data for this observable are pre-

sented in Fig. 7.Panel (a) of Fig. 7 shows data for

Erel values below the resonance; panel (b) covers the

resonance region, whereas panel (c) has been plotted for

0.9 ≤ Erel< 1.5 MeV. The finite KaoS acceptance cuts

the distributions at about 4 degrees. The figure shows

clearly that the observable θ6is sensitive to the type of

interaction. In all panels, the combined (CD+nuclear) in-

teraction, including interference, reproduces most of the

structures observed in the data points (red histograms).

This is particularly true for the sub-resonance region,

panel (a). The green histograms (CD-only) show sin-

gle peaks at larger angles. The pure nuclear interaction

(blue histograms) rises rapidly at small values of θ6, in

agreement with the measured data, but lacks the struc-

tures visible in the data points. The narrow peaks visible

in the on-resonance data, panel (b), at values of θ6 of

≈ 1.5,2.6 and 3.3 degrees, are not perfectly reproduced

by the (CD+nuclear) model and point to small deficien-

cies of the theoretical model. Nevertheless, Fig. 7 demon-

strates that Coulomb-nuclear interference is at work and

that the signs of the interference terms are correct. We

also conclude that even at our incident energy of 150 A

MeV the nuclear break-up is dominant.

The angle-integrated energy-differential cross sections

as a function of Erel are shown in Fig. 8. The full his-

0

0.5

1

1.5

Erel (MeV)

0

200

400

600

800

counts

Experiment

CD+Nuclear

FIG. 8: (Color online) Differential cross sections as a function

of the energy, Erel, in the α-2H c.m. system. Black points

indicate the experimental data; the histogram corresponds to

the GEANT simulation using the (CD+nuclear) interaction

as described in the text and a binning of 100 keV (note that

the vertical error bars result from a quadratic sum of statis-

tical and systematical uncertainties).

togram was obtained from the (CD+nuclear) calculation

convoluted by our GEANT simulation and normalised to

the experimental yield. The points and the histogram

represent the measured and predicted differential cross

sections, respectively, as a function of Erel. Our Erel

distribution is in very good agreement with the simula-

tion in particular in the energy region below 400 keV.

As we will show below (see Fig.10), the differential cross

sections in this energy regime result mostly from nuclear

interactions.

The astrophysically important quantity is the astro-

physical S-factor, S24, for the2H(α,γ)6Lireaction. Since

nuclear processes dominate, in particular for low Erel,

the determination of this quantity via an evaluation of

Page 9

9

10-9

10-8

10-7

10-6

S factor (MeV barn)

Kiener et al.

Mohr et al.

Robertson et al.

This work E1

This work E2

This work total

0

0.5

1

1.5

Erel (MeV)

10-9

10-8

10-7

10-6

S factor (MeV barn)

This work total

Mukhamedzhanov et al.

Mohr et al.

Kharbach et al.

Nollett et al.

Langanke et al.

(a)

(b)

FIG. 9: (Color online) (a) Theoretical E1, E2, and total S24-

factors that describe well the present experimental data, to-

gether with data points from the previous CD experiment by

Kiener et al. [21] and from direct measurements (Robertson

et al. [17] and Mohr et al. [18]). See Sect.V for an inter-

pretation of the data of Ref. [21]. (b) Comparison of various

theoretical predictions for the summed E1- and E2 contribu-

tions to S24(E) [18, 24, 39–41].

the CD component in our break-up data is not feasible

since. However, we have demonstrated above that our

theoretical model describes well the measured cross sec-

tions, hence the astrophysical S-factors from the present

work are those from our theoretical model.

The resulting E1-, E2-, and total S24-factors are vi-

sualized in the upper part of Fig. 9 together with the

previous CD data of Kiener et al. [21] and the direct data

of Mohr et al. [18] and Robertson et al. [17]. The present

results for the E2-component are in good agreement with

the direct measurements of Refs. [17, 18] in the resonance

region and above which gives confidence in our model.

Another check of the validity of our treatment of the

Coulomb part of the break-up reaction, described in

Sect.IIA, can be done by comparing our calculated res-

onance parameters for the 3+resonance with the exper-

imental ones. In order to determine those parameters,

we have calculated the theoretical capture cross section

around the resonance in 1 keV steps and fitted a Breit-

Wigner parametrization to the resonance. We obtain Γ-

widths of Γα= 22.1 keV and Γγ= 0.437 meV, in good

agreement with the literature values of Γα= 24 ± 2 keV

and Γγ= 0.440±0.030 meV as cited by Mohr et al. [18].

Note that we have used a spectroscopic factor of unity.

We will comment on the data points from the previous

CD experiment [21] in the following section.

The direct2H(α,γ)6Lireaction at very low energies is

sensitive also to the E1 amplitude. In our experiment,

this component cannot be constrained experimentally

due to the weak flux of virtual E1 photons. We have

therefore to rely exclusively on the theoretical model. At

higher energies, however, Robertson et al. [17] could sep-

arate E1- and E2-components on the basis of measured

angular distributions. Fig.1 in [17] shows that their the-

ory seems to overestimate the E1 component. Our E1

curve is very close to Robertson’s so that we also seem

to overestimate this component.

Several theoretical models for

posed to determine the shape and the magnitude of

the S24 energy dependence, such as potential models

[18, 28, 39], cluster-model calculations [24], or ab-initio

calculations [40]. Those predicted curves for S24 which

include both E1- and E2-contributions are displayed to-

gether with the theoretical curve from this work in the

lower panel of Fig. 9. As one can see in this figure, all

the calculations shown –independent of their very diffe-

rent model assumptions– yield very similar curves. We

have not included the theory of Blokhintsev et al. [42])

because it was specifically tuned to approach the exper-

imental data of Ref. [21].

6Li have been pro-

V. COMPARISON WITH OTHER CD

EXPERIMENTS

As visible in the upper panel of Fig. 9, the low-energy

data points derived for the S24-factor from the work of

Kiener et al. [21] disagree with the theoretical curve that

we have deduced from the present work. We believe that

this is most likely due to a strong nuclear contribution

at the lower incident energy of 26 A MeV, which was not

considered in their analysis in view of the theoretical pre-

diction [22]. We have performed a calculation with the

theoretical model of this work at an incident energy of

26 A MeV and have calculated CD and nuclear cross sec-

tions for the laboratory-angular range between 1.5 and 6

degrees, which should correspond approximately to the

acceptance of the setup of Ref. [21]. Fig. 10 displays the

ratio of nuclear to Coulomb break-up cross sections as a

Page 10

10

function of Erel for the two bombarding energies. Our

theory predicts that at 150 A MeV the nuclear cross sec-

tions are about a factor of 3 larger than the CD ones at

and above the resonance, whereas the nuclear component

dominates strongly at the lowest energies. At 26 A MeV,

the ratio of nuclear to CD cross sections is predicted to

be about a factor of ten larger than at 150 A MeV over

the entire range of Erel.This suggests that the data

points shown in Ref. [21] result almost exclusively from

nuclear interactions, contrary to the assumptions under-

lying their analysis. It is therefore not very meaningful to

tune theoretical models in order to improve their agree-

ment with the 26 A MeV data as was done in Ref. [42].

0 0.20.4

0.6

0.811.2 1.4

Erel (MeV)

10-1

100

101

102

103

104

Ratio Nuclear/Coulomb dissociation

26 A MeV

150 A MeV

FIG. 10: (Color online) Ratio of nuclear and Coulomb differ-

ential dissociation cross sections for6Li at 150 A MeV (full

line) and at 26 A MeV (dashed line). Both curves were calcu-

lated with the same model described in detail above in section

II.B.

VI. PRODUCTION OF6LI IN THE BIG BANG

The

2H(α,γ)6Li reaction is the main path for

BBN production while destruction proceeds via the

6Li(p,α)3He one. Both rates are available in the

NACRE [43] compilation. While the latter reaction rate

is reasonably well known at BBN energies, prior to this

experiment the former suffered from a large uncertainty.

This was mainly due to the fact that the published error

margins were aimed at including the Kiener et al. [21]

measurement [44]. As a result from the present study,

we can now propose a more reliable central value based

on a successful theoretical model, and a safe upper limit

that is even somewhat smaller than the previous NACRE

upper limit.

In Fig. 11, the BBN abundances of7Li and6Li are dis-

played as a function of the baryonic density. (It is usual

6Li

10

-15

10

-14

10

-13

10

-12

10

-11

10

-10

10

-9

1234567 8 9 10

1010η

Li/H

HD 84937

WMAP

GSI New

GSI Upper limit

7Li

6Li

10

-2

ΩBh2

FIG. 11: (Color online) Predicted BBN production ratios for

6,7Li over hydrogen as a function of η, the baryon-to-photon

ratio in the early Universe. The solid red line represents the

result for

work, based on theoretical values for the E1 and E2 com-

ponents. The dashed red line represents a very conservative

but safe upper limit where all observed events are assumed

to result from Coulomb break-up. The blue band denotes

the range of predicted7Li yields [4]. Observational data are

indicated by horizontal green-hatched areas: the upper one

has been derived from the recent review of lithium observa-

tions by Spite and Spite [5]; the lower one corresponds to the

largest

yellow vertical band shows the WMAP η-value [1].

6Li from the S24-values obtained in the present

6Li yield reported for the star HD 84937 [13]. The

to introduce another parameter, η, the ratio of the num-

ber of baryons over the number of photons which remains

constant during the expansion, and which is directly re-

lated to Ωbby Ωbh2=3.65×107η). The blue7Li band is

the result of a Monte Carlo calculation taking into ac-

count nuclear uncertainties as described in Ref. [4]. The

upper hatched horizontal area in the figure shows the pri-

mordial lithium (6Li+7Li) abundance derived from the

“Spite plateau”, i.e. from the practically metallicity-

independent Li observations in metal-poor stars [5].

The solid red line for6Li has been calculated within the

same physical model, using the theoretical reaction rate

from this work for2H(α,γ)6Li. Both E1 and E2 contri-

butions have been included. At WMAP baryonic density,

a value for the6Li/H production ratio of ≈ 1.3 × 10−14

results. The dashed red line represents a very conserva-

tive upper limit for2H(α,γ)6Li that would hold if the

low-energy S24data points from this work would result

from CD only. Fig. 7 demonstrates clearly that this is

not the case. But even this extremely conservative limit

is about two orders of magnitude smaller than the only

Page 11

11

T9

Na?σv?

cm3mol−1s−1

0.9153 × 10−29

0.2610 × 10−22

0.3458 × 10−19

0.3190 × 10−17

0.7929 × 10−16

0.9163 × 10−15

0.7672 × 10−14

0.4990 × 10−13

0.2100 × 10−12

0.6547 × 10−12

0.1655 × 10−11

0.3612 × 10−11

0.7142 × 10−11

0.1325 × 10−10

0.2363 × 10−10

0.4103 × 10−10

0.1157 × 10−09

0.2965 × 10−09

0.2014 × 10−08

0.8452 × 10−08

0.6594 × 10−07

0.2827 × 10−06

0.8598 × 10−06

0.2094 × 10−05

0.4372 × 10−05

0.8156 × 10−05

0.1397 × 10−04

0.2240 × 10−04

0.3406 × 10−04

0.4959 × 10−04

T9

Na?σv?

cm3mol−1s−1

0.6967 × 10−04

0.9495 × 10−04

0.1261 × 10−03

0.2090 × 10−03

0.3237 × 10−03

0.7846 × 10−03

0.1557 × 10−02

0.2715 × 10−02

0.4325 × 10−02

0.6453 × 10−02

0.9169 × 10−02

0.1674 × 10−01

0.2813 × 10−01

0.4502 × 10−01

0.6944 × 10−01

0.1033 × 10+00

0.2359 × 10+00

0.4350 × 10+00

0.6839 × 10+00

0.9623 × 10+00

0.1549 × 10+01

0.2132 × 10+01

0.2705 × 10+01

0.3280 × 10+01

0.4476 × 10+01

0.5754 × 10+01

0.7088 × 10+01

0.8438 × 10+01

0.9773 × 10+01

0.1107 × 10+02

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.010

0.011

0.012

0.013

0.014

0.015

0.016

0.018

0.020

0.025

0.030

0.040

0.050

0.060

0.070

0.080

0.090

0.100

0.110

0.120

0.130

0.140

0.150

0.160

0.180

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.600

0.700

0.800

0.900

1.000

1.250

1.500

1.750

2.000

2.500

3.000

3.500

4.000

5.000

6.000

7.000

8.000

9.000

10.00

TABLE II: Recommended

theoretical E1− and E2−S-factors from the present work for

the temperature range 106K ≤ T ≤ 1010K (10−3≤ T9 ≤ 10).

2H(α,γ)6Li reaction rates using

positive observation of6Li surviving after the reanalysis

of Li lines by Steffen et al. [13], indicated in Fig. 11 by

the lower hatched horizontal band. This finding corrobo-

rates earlier statements (e.g. [4, 5]) that observations –if

confirmed– of6Li primordial yields around a few percent

of the Spite plateau would require astrophysical sources

other than BBN.

In order to facilitate astrophysical calculations of stel-

lar6Li synthesis with our new theoretical E1 and E2

S-factors, we list in Table II the reaction rates for the

temperature range 106K ≤ T ≤ 1010K.

VII.CONCLUSIONS

A kinematically complete measurement of the high-

energy break-up of6Li at 150 A MeV has shown that

Coulomb and nuclear contributions and their interferen-

ces have to be taken into account when interpreting the

measured angular distributions. Though it was not possi-

ble to extract the Coulomb part experimentally, we were

able to infer the E2 component of the astrophysical S24-

factor for the2H(α,γ)6Li reaction from a theoretical re-

action model that describes well in particular the low-

energy break-up data. The model predicts a drop of S24

with decreasing relative2H-α energy, Erel, as predicted

also by most other nuclear models for6Li, contrary to

conclusions from an earlier CD experiment performed at

the lower energy of 26 A MeV. We have presented evi-

dence that this earlier experiment probably has measured

mostly nuclear break-up of6Li. Our findings allow to

make new predictions for the6Li/H production ratio in

Big-Bang nucleosynthesis (BBN) which is orders of mag-

nitudes smaller than the one derived from claimed obser-

vations of6Li in old metal-poor stars. Sources other than

BBN have therefore to be invoked for6Li production if

those observations are confirmed.

Acknowledgments

We thank N. Kurz for his tireless help with the data ac-

quisition. Thanks go to P. Descouvemont and K. Nollett

for kindly providing numerical results from their theore-

tical calculations. This research was supported by the

DFG Cluster of Excellence “Origin and Structure of the

Universe”.

[1] E. Komatsu et al., (WMAP) arXiv:1001.4538 (2010); As-

trophys. J. Suppl. Ser. 5, in press.

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