States in 12B and primordial nucleosynthesis

NUCLEAR PHYSICS A

Nuclear Physics A567 (1994) 125-145 North-Holland

States in 12B and primordial nucleosynthesis * (II). Resonance properties and astrophysical aspects Z.Q. Mao ‘, R.B. Vogelaar Department of Physics, Princeton University, Princeton, NJ 08544, USA

A.E. Champagne, J.C. Blackman, R.K. Das aDepartment of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA ’ Triangle Vnicersities Nuclear Laboratory, Duke Vniuersity, Durham, NC 27706, USA

K.I. Hahn * A. W. Wright Nuclear Structure Laboratory, Yale University, New Hare,

CT 06511, USA

J. Yuan Institute of Atomic Energy, Beijing 102413, People’s Republic of China

Received (Revised

30 March 1993 23 June 1993)

Abstract The ‘Be(ru, p)‘*B has been used to populate states which could correspond to astrophysically significant resonances in the ‘Li(cu, n)“B reaction. The branching ratios for neutron decays have been measured and the neutron angular distributions have been used to determine J” for these states. This information, combined with previous measurements of excitation energies and total widths, allows us to extract the resonance strengths for these states. The astrophysical significance of these results is discussed.

Key words: NUCLEAR REACTIONS ‘Be(o, deduced I-,,, r,, J, r, resonance strengths.

Work supported Energy. ’ Present address: 2 Present address:

l

0375-9474/94/$07.00

in part by the National

Science

Department of Physics, W.K. Kellogg Radiation

0 1994 - Elsevier

SSDI 0375-9474(93)E0391-K

p), E = 29 MeV;

Foundation

measured

pn-,

py-coin.

and in part by the U.S. Department

“B

of

University of Pennsylvania, Philadelphia, PA 19104, USA. Laboratory, Caltech, Pasadena, CA 91125, USA.

Science

B.V. All rights reserved

Z.Q. Mao et al. / States in 12B (II)

126

1. Introduction Recent primordial

studies

of inhomogeneous

production

from a standard

cosmologies

of A & 12 elements

(homogeneous)

big bang.

[l-51

in excess Although

suggest

of what

the possibility might

observations

of

be expected

would

be chal-

lenging in the presence of a large foreground of heavy elements produced via stellar evolution, they could provide clear evidence for inhomogeneities in baryon density in the early universe. Nucleosynthesis is expected to start near a temperature T= 1.2 x 10'K (Ty= 1.2) and any accompanying heavy-element production is thought to be a consequence of the sLi(a, n)“B reaction which will occur in regions of comparatively high neutron density. At Ty= 1.2, the most effective center-of-mass energy for this reaction (i.e. the region of the Gamow peak) will lie in the range 330-930 keV. A direct measurement of the reaction cross section at these (or any) energies is complicated by the short half-life of sLi (840 ms) which necessitates the use of radioactive-beam techniques. Measurements of the inverse reaction, “B(n, cu)‘Li have been carried out by Paradellis et al. [6] and show the presence of several broad resonance structures in the (a, no) cross section over this energy range. Although the locations of these resonances seem to coincide with known states in “B, their widths appear to be too large to correspond to any individual, known state [7]. As a result, their reaction rate may be overestimated. At higher energies (EC.,, 2 1.5 MeV), the ‘Li(a, n)“B reaction has been measured directly by Boyd et al. [Sl. Their cross section is about 5 times larger than that for the (a, no> branch alone which is attributed to the contributions of neutron decays or not this enhancement persists to lower to excited states in “B . Whether energies depends upon the structure of the low-energy resonances. However, if the (a, no> results are erroneous, then such an extrapolation to lower energies is not valid in any case. In an earlier article [7] we reported on measurements of excitations energies and widths, and on delimitations of spins and parities for states in 12B located between the sLi + (Y threshold (E, = 10.001 MeV 191 and EC,,,= 1.570 MeV. These results are summarized in Fig. 1 and Table 1. Of the six states lying in this region, the four lowest, located at E, = 10.199, 10.417, 10.564 and 10.880 MeV, are of the most immediate interest because as ((Y, n> resonances they would lie within the Gamow peak at To= 1.2. To determine if these states might make resonant contributions to the (a, n) cross section, we require a knowledge of their neutron and alpha partial widths CT, and r,, respectively), and their spins. The total widths of these states vary between 9 to 61 keV (ref. [7] and Table 1). At these energies, r, might be at least several keV at most whereas the widths for gamma emission, lY, are on the order of eV. Thus r = r, + r, and since r has been measured, a measurement of one decay branch determines the other. A neutron-decay measurement has been performed for the 10.564 MeV state [lo], but we are also interested in the other states mentioned above. Therefore in the present study, we

Z.Q. Mao et al. / States in 12B (II)

127

1.570, 1.327:\ 11.571

11.328

<8

<&

(O-3p

10.880

4,7 (0-e) 12, (2,3)-

10.564 10.199

8Li+a

28 LlEb ‘ELS

3.76

t

3.388 o+ ,‘

2.621 2.72

2-

1.674

12 Fig. 1. Level structure

Table 1 Summary

of previous

EX (MeV + keV) 10.199 f 3 f 14 f 3 * 3 f 10 + 6

10.417 10.564 10.880 11.328 11.571

a Ref. [7].

of “B.

“8

B

The information shown for states above the ‘Li + (Y threshold [7]. Other information is from ref. [9].

experimental

results

a

r

J”

CkeV) 9*

3

61 f 25 11+ 3 17* 4 75 * 25 45* 15

(2-3) (O-8) (2-3) (o-3)+ J98 J98

is from ref.

Z.Q.

128

Mao et al. / States in 12B (II)

have used the “Be(a, p)‘2B*(n)“B*(y11’B states of interest. Measurements of neutron

reaction to determine T,/T for the angular distributions also provided J”

for

an

‘Li(a,

these n)“B

states.

From

reaction

2. Experimental

this

has been

information,

improved

reaction

rate

for

the

obtained.

details and results

2.1. General considerations The “Be(a, p)‘*B reaction was produced at E, = 29 MeV using beams provided by the Yale ESTU tandem Van de Graaff accelerator. Two considerations lead to the choice of this beam energy: In general, energies below E, = 40 MeV were deemed preferable because decay neutrons at forward angles would be travelling slowly enough so that energy measurements (via time of flight) could be made with acceptable resolution with the detectors close to the target (so as to increase efficiency). Spectra taken at E, > 29 MeV showed a sizable yield of decay protons from highly excited states in ‘“N and 19F (populated via (a, p) reactions on 12C and IhO, respectively). Hence, E, = 29 MeV was chosen in order to maximize counting efficiency as well as signal-to-noise. A self-supporting target of about 100 bg/cm2 was used. Outgoing protons were detected using a 1 cm x 1 cm Si detector telescope mounted at f3,,, = 32” and at a distance of 5.2 cm from the target. In order to maximize count rate, the detector covered a large angular range co,,, = 26.5”-37.5” in the horizontal direction). Thus to preserve energy resolution, it was necessary to correct for the kinematic energy spread across the counter by measuring position (angle) as well as energy. The front element of the telescope was a 100 km-thick position-sensitive AE detector. This was backed by two 1000 km-thick E detectors. The first of these was thick enough to stop protons corresponding to states with E, < 4.2 MeV. The second E detector was used to veto any events which did not deposit their full energy in the first two detectors. In this way, background in the region of interest from partial stopping of higher-energy protons was reduced. A proton spectrum obtained after kinematic corrections is shown in Fig. 2. Outgoing neutrons were measured in coincidence with protons using a pair of heavily shielded 12.7 cm diameter X 5.2 cm NE213 liquid scintillators. The energies of these neutrons were derived via time of flight with respect to the proton AE detector. Two runs were taken, covering 13,~~= 60”, 90”, 105” and 120”. Target-to-detector distances were 81, 45, 46 and 47 cm, respectively. The first distance was chosen in order that the individual neutron groups could be distinguished from one another. The other distances were dictated by the size of the scattering chamber (90 cm in diameter). Because we interpret a deficit of decay neutrons as a measure of the alpha-decay branching ratio, a good measurement of

Z.Q. Mao et al. / States in 12B (II)

gBe(a,p)‘2B

9000

Em=29

MeV

129

8,,,=32°+5.50

8000 i 7000

6000

5000

i

i

CHANNEL

Fig. 2. Proton spectrum (corrected for kinematics) for the ‘Be(cy, p)“B reaction at E, = 29 MeV and I9,.&= 32” + 5.5”.

the absolute neutron-detection efficiency is of critical importance. The relutille efficiencies of the two detectors were measured with the aid of an Am-Be source located in the target position. Absolute efficiencies were obtained to an accuracy of about 20% by measuring the decays of the E, = 5.00 and 9.582 MeV states which were populated along with the states of interest. These data combined involve several neutron groups with known branches and energies ranging from about 1 to 8 MeV. The low-energy neutrons are of particular value because the efficiency decreases abruptly with decreasing energy below E, = 1 MeV. A Monte Carlo simulation, calculated using the code KSUEFF 1111 accurately reproduced the observed variation of efficiency with energy. Gamma rays were detected in coincidence with protons using a shielded 12.7 cm diameter X 10.2 cm NaI crystal, located at blah = 90” and at 7 cm from the target. The absolute detection efficiency was obtained from a simulation of the detector’s response using the code EGS4 (ref. [12]). This calculation accurately reproduced measurements taken with a calibrated is2Eu source and using the ‘Be(a, dy)“B reaction [measured concurrently with the “Be(a, p)‘*B reaction]. 2.1. Neutron-decay data Clean time-of-flight data were obtained for the 10.199, 10.564 and 10.880 MeV states (Figs. 3-5). The 10.417 MeV state appeared as a weak shoulder on the 10.564 MeV state and this prevented us from obtaining more than a rough measure of its neutron-decay strength. A time calibration of these spectra indicates

KJ

0

'

110

120

130

140

150

160

170

10 0

0

80

SO

ti:i
ii0

120 130

1050

80

90

100

120

130

e,,,= 1 2o”

CHANNEt

110

140

,kO

150

150

,f.l.i

160

160

170

!fCl

Fig. 3. Time-of-flight spectra for the decay of the 10.199 MeV state. The expected locations of individual neutron groups are shown.

e,,,=

CHANNEL

20

20

30

v

60

o

40

50 40

II 0

60

:

60

v, tz

Pa

ZIOO

60

100

170

70

90

160

140

80

150

ej,,=90°

140

eiob= 600

130

CHANNEL

123

CHANNEL

110

SO

133

160

SO

180

80

DI,,l,,,,.,.,,,,l,,.!

2.0

40

8o

z

t

~100

120

Z.Q. Mao el

al. /

States in 12B (II)

r

SlNfl03

SiNnO:,

131

132

Z.Q. Mao et al. / States in 12B (Ii)

.

”

f

SlNfl03

N

_

0

m

7

SINnO

SlNf-103

(D

,

0

O.OlO-

0.020 -

0.030-

0.060-

”

70

t

I

of

no

.

”

90

100

’

I

distribution

,

e

110

ecm

”

of

* I,

cm

,

J"=2-

---

130

'.

------c

Jn=l"

J"=2Jn__z+

a I

-

lb0

t

a

' 140

,.' 'x' . . *.-..___-

-----

-

I

40 ’ IlO

~

*. .,._

I

“‘I 120

n2

I30 do I(;0 ll0

distribution

,*=------=.

1’

60

Angular

0.070-

I,.

,

0.080

?5i ;o

0.005 -

0.010:

0.0151

0.020

Angular

,

I,

90 e

/

1

distribution

/

60

,

distribhon

,

,

,

cm

100

,

,

of

2

“3

I

110

,

of nl

,

1

I

I

120

_

I

so

0.0020 -

0.0040 --

I 60

j 90

1 100

8 cm

1 110

‘

I 120

8

I

130

,

T

,

I ;, **

'

, i,

Jn=2_

I

I 130

1 140

5

150

_

J"=3---

-

J"=3+

J"=2-

<* ” 4’ ) _ w--z

’

1

_____

,’ 0.0120,* Cl c <, ~0.0100 =--------yy , i I :, _._ ’ __=;, ~0.0080~.._ . _-i___________*-. /fl --_____* ~0.0060 -

0.0140-

Angular

0.0160-

/

I,,

70

i

Angular

1

0.0160

:_:i,

0.016-

O~ol*-

,

Fig. 6. Angular distributions of decay neutrons associated with the 10.19YMeV state. The solid lines are theoretical predictions for the value of J” that was judged to produce the best fits to the data. Examples of inferior fits are represented by the dashed cumes.

z=

-

g,

rr,

2

c

0.025

0.020

E

e

2

134

Z.Q. Mao et al. / States in I23 (Ii)

E

CCY

UP/(&M

E

m”

Z.Q. Mao et a/./

Staresin 12B(111

E

s”

tJP/(B)M

135

Z.Q. Mao et al. / States in “B (II)

136

that the groups observed correspond to neutrons populating the ground state (n,) and first three excited states (n,--nJ of “B. The individual yields were obtained via a peak-fitting procedure in which the location of each group was fixed according resolution Therefore,

to its time

of flight.

The peak

widths

of the detectors rather than by the we used the width of the gamma-ray

were

dominated

by the timing

time of flight through them. time-of-flight peak to fix the

widths of the neutron peaks. Proton-neutron angular correlations are shown in Figs. 6-8. These data were fit using the standard functional form of the angular distribution for decay from an oriented state:

w(e)

= g

; a,P,(c0s k=O

e),

(1)

where k is an even integer, 1 is the neutron orbital momentum, ak is an expansion coefficient and P,(cos 0) is a Legendre polynomial. The angle f3 is measured between the outgoing neutron and the recoiling 12B. The series was truncated at I= 3 because calculations indicate only a weak correlation for 1 > 3. Final values

-

~~1_ --: Nd

\:

( ‘%,Ip J;,

Fig. 9. Gamma rays collected in coincidence with outgoing protons for the 10.199, 10.564 and 10.880 MeV states. Gamma rays following neutron decay are labelled according their respective neutron groups.

Z.Q. Mao et al. / States in 12B (II)

137

for 1” were chosen by requiring an acceptable fit to the data for each of the four decay branches as well as consistency with the 1” values allowed by our previous results (Table 1 and ref. [7]). These are listed in Table 2. The total number of neutrons emitted was obtained by integrating Eq. (1) and was found to be quite insensitive to the range of values for ak allowed by our fits. After corrections for detector efficiencies, the ratio of neutrons to protons determined T,/T (also summarized in Table 2). 2.2. Gamma-ray data The gamma-ray spectra for the states of interest (displayed in Fig. 9) show strong peaks representing the de-excitation of “B following neutron decay. Although these measurements were performed at a single angle, the solid angle subtended by the NaI detector was large (12% of 4a) and in this geometry, our calculations show that essentially no proton-gamma angular correlation should be expected: For all decay branches, the deviation from isotropy is G 3%. Thus these data provide an independent measure of T,/T for the ni, n2 and n3 branches. These branching ratios are listed in Table 2 and are generally consistent with those derived from the neutron data. However, our branching ratio for the 10.564 MeV state are markedly different from those of Kubono et al. [lo]. The reason for this inconsistency is not obvious, but the present results were obtained using two independent techniques which produced similar results. Although the gamma-ray data could not provide a check of the no branching ratios, the general agreement between the neutron and gamma-ray measurements does indicate that the neutron results are reliable.

Table 2 Summary

of experimental J”

results “0

n1

a

r,/r

%eV) 10.199 10.417

“2

2<4-

10.564 d

2-

10.880

3+

a ’ ’ d

0.19 * 0.02 =

0.15 * 0.08 f no + n, = 0.78 f 0.24 0.25 5 0.15 f 0.03 0.12 i 0.11 5 0.12 f 0.02 0.07 * 0.11 f

0.02 0.02 0.07 0.02 0.02 0.01 0.02

a

n3

a

0.50 f 0.06 0.13 * 0.02 0.52 k 0.06 0.13 f 0.02 nz + n3 = 0.58 f 0.23 0.25 f 0.06 0.22 f 0.05 0.47 + 0.05 0.16 k 0.05 0.41 f 0.04 0.10 f 0.02 0.58 + 0.08 0.14 + 0.02 0.43 f 0.05 0.11 f 0.02

Total ’

0.85 f 0.05 1.25 + 0.25 0.80 + 0.05 0.80 f 0.05

The first entry is derived from the neutron data and the second is from the gamma-ray From a weighted average of the neutron and gamma results. Limit based on the strength of the nt branch. From ref. [lo], no = 0.34, n, = 0.04, n2 = 0.17, n3 = 0.12 and T,/T= 0.67.

data.

2.Q. Mao et al. / States in “B (II)

138

3. Determination

of the reaction

rate

The thermonuclear reaction rate is the product of the cross section CT and center-of-mass velocity U, averaged over a maxwellian velocity distribution:

(uv)=

(g2

(kr)-““/o(E)E

exp( -E/W)

(2)

dE.

For isolated, narrow resonances, the rate may be approximated

by

had y exp( - E,/kT),

(3)

where oy is the resonance strength defined by

Gr,

(2Jf + 1) “=(2Ji+1)(2J,+1)’

‘=

r

(4)

.

Here Jf, Ji and J, refer to the spins of the final state, initial state and transferred particle, respectively. For the ‘Li((u, n)“B reaction, w = 5(2J, + 1). The strengths derived from our results are discussed below and are summarized in Table 3. 3.1. Contributions

of individual

3.1.1. The 198 kevresonance

resonances (E, = 10.199 Mel/; J*=2-_)

Our measurements of r = 9 f 3 keV [7] and T,,/T = 0.95 k 0.05 imply r, = 0.5 + 0.5 keV or r, G 1 keV. In general, r, may be approximated by

r, = $f9:Pt( E),

Table 3 Parameters

for narrow

(5)

resonances .I”

r (keV)

10.199 10.564 10.880 11.328 11.571 ’ Calculated b Assuming ’ Assuming

198 f3 563 f 3 879 f 3 1.327 k 10 1.570 f 6

223+ JG8 .I<8

assuming 0: = 1. J = 4 and r = 100 keV. J= 5 and r= 60 keV.

9+ 3 11* 3 17+ 4 75 f 25 45 * 15

8.6 + 2.9 8.8 f 2.5 13.6 f 3.3

< 2.1 x 1o-3 a 2.2 f 0.8 3.4 + 1.1

Q 2.1 x 1o-3 1.7 + 0.6 3.8 k 1.1 g45 b d33 c

2.Q. Mao

et al. /

139

States in -‘2B fIl1

where r is the channel radius, 19,”is the dimensioniess reduced width and P,(E) is the Coulomb penetrabihty. Assuming 0,” = 1 (i.e., the single-particle limit) and r = 4.5 fm, we would expect r, = 2.1 eV. Clearly our measurement of r,/r is not sensitive enough to provide more than a very crude upper limit on r,. Consequently, we adopt r, = 2.1 eV and wy = 2.1 eV as an upper limit. An analytic expression for the contribution of the 198 keV resonance to the thermonuclear reaction rate is NA(o.u)= [O-117.41 x 104T;3/2 exp( -2.298/T,)

cm3 s-’ mole-’

where NA is Avogadro’s number and the multiplicative factor [O-l] represents upper and lower limits.

(6) the

3.1.2. The 416 keV resonance [E, = 10.417 Mel/ J = (O-S)] The broad (r = 61 + 25 keV [7]) state at 10.417 MeV has T,/T= 1.25 t 0.25. This is consistent with r, IS=r,, but does not give a quantitative alpha width. On the basis of penetrability considerations, the comparatively strong nI branch to the 2.125 MeV (.P = i-j state in “B would seem to require J < 4 for this state. Therefore, it may be formed by s-wave ‘Li + (Y capture. For 1= 0 capture, the upper limit on the alpha width would be r, = 6 keV (evaluated at the resonance energy). However, because this resonance is broad, the variation of the partial widths over the width of the resonance can not be ignored and Eq. (2) must be integrated numerically in order to obtain the reaction rate. As an upper limit, we have assumed J = 2, r, = 6 keV and I’,, = 80 keV (the Iatter two quantities evaluated on resonance). An analytic approximation to our numerical results is N&W)=

8.20 x 107T,-0.s32 exp( -4.267/T,)

cm3 SK’ mole-‘.

(7)

This expression reproduces the numerical calculation to within 5% over most of the temperature range 0.1 G Ts G 2.0. 3.1.3. The 563 and 879 keV resonances (E, = 10.564 Met/: J” = 2 - and E, = 10.880 MeV, J==3’)

For the 563 keV resonance, we have measured r,,/r = 0.80 rt 0.05 and r = 11 rt 3 keV [7]. These results suggest r, = 2.2 f 0.8 keV. This alpha width imphes 0: = 0.18. The resonance strength corresponding to these partial widths is wy = 1.7 i 0.6 keV. Similarly, for the 879 keV resonance, we have r,/T = 0.80 + 0.05 and I’= 17 + 4 keV [7] which yields r, = 3.4 f 1.1 keV and wy = 3.8 + 1.1 keV. These resonances contribute &(a~)~~~ = (6.00 f 2.17) N,(~u)~,~

x

107T;3/2 exp( -6.534/T,),

= (1.34 + 0.39) x 10xT;3.2 exp( - 10.201/T,)

(8)

cm s-’ mole-’

Z.Q. Mao et al. / States in 12B (II)

140

to the reaction the resonance

rate.

For both

resonances,

the dominant

source

of uncertainty

is

strength.

3.1.4. The 1.327 and 1.570 MeV resonances (E, = 11.328 MeV J G 8 and E, = 11.571 Mel/; Ja8) Although

we did not measure

neutron

decays

for the 11.328 and 11.571 MeV

states, we can place limits on their contributions to the (a, n) reaction rate. The total widths of these states are 7.5 + 25 keV and 45 f 15 keV, respectively [7], and at these energies, the alpha branch can contribute a large fraction of the total width. To give an upper limit, we have chosen r, = r, and the largest values of J, that are consistent with these widths. For the 11.328 MeV state, this implies J = 4 and for the 11.571 MeV state, J = 5. Higher J-values require non-physical dimensionless reduced widths (i.e., 13,”> 1) for our assumed partial widths. The resulting resonance strengths are wy G 45 keV for the 1.327 MeV resonance and wy G 33 keV for the 1.570 MeV resonance. However, the narrow-resonance approximation to the reaction rate is only valid for temperatures T9 2 2. For the lower temperatures of interest, we must also consider contributions from the low-energy tails of these resonances which again necessitates a numerical integration of Eq. (2). The resulting analytic approximations to the reaction rates are:

4d41.327 = [O-112.67

X

108T;o.s’2

exp( -13.15/T,),

NA(~~),,570

x

10sT;0.741

exp( -16.702/T,)

= [0-113.11

(10) cm3 s-l

mole-‘.

(11)

3.1.5. Unobserved resonances In our earlier article [7], we discussed

the possibility

that our initial

measure-

ments failed to account for all of the states of interest in “B. In particular, states with r G 10 keV and r, G 1.5 keV, or r > 100 keV and r, < 20 keV might not have been detected in our “B(d, p)12B studies. In order to estimate the maximum effect that such a state would have on the reaction rate, we assume s-wave alpha capture with 0: = 1. Clearly, the value of r, will depend upon the location of the state. For example, at EC,,,= 200, 500 and 800 keV, r, = lo-‘, 20, and 230 keV, respectively. Hence, in the limit of r 6 10 keV and r, G 1.5 keV, we have < 350 keV and wy 6 1.5 keV at higher energies. The other = wT, for EC,,. WY extreme, namely r > 100 keV and r, G 20 keV implies r, B 80 keV. This alpha width is unphysically large unless EC.,,.,> 650 keV. In other words, we have not missed any broad states at lower energies. At higher energies, the strength of such a missing resonance would be wy G 20 keV. However, it is more likely that 0: < 1

Z.Q. Mao et al. / States in 12B (II)

141

in which case this resonance would be pushed to higher energies and out of the region of interest. 3.2. The non-resonant reaction rate Although we do not confirm the widths of the resonances in the ‘Li(a, n,)“B reaction reported by Paradellis et al. [61, their data for the astrophysical S-factor do suggest that the non-resonant contribution is small (G 10 MeV . b). In their direct (a, n> measurement at higher energies, Boyd et al. [S] observe that the contribution from neutron decays to excited states exceeds that from the ground state alone by about a factor of 5. Our measurements of I’,,/T support their assertion that this enhancement persists to lower energies (&,/I’,,, = 5.0, 2.6, 5.3 and 6.7 for the 10.199, 10.417, 10.564 and 10.880 MeV states, respectively). Therefore, we adopt a non-resonant S-factor of S G 50 MeV . b. We again approximate a numerical solution to Eq. (2) by &((Tu),,, = [O-115.13

X

1011T;2/” exp( -19.48/T,‘13)

cm3 s-r melee’.

(12) 3.3, The ‘Li((.u, n)“B reaction rate The individual contributions to the reaction rate are summarized in Table 4 and displayed in Fig. 10. The resulting upper limit on the total rate is given primarily by

1.0

0.1

TEMPERATURE

(10’K)

Fig. 10. Individual resonant and non-resonant contributions to the ‘Li(cu, n)“B reaction non-resonant part (NR), and 198,416, 1327 and 1570 keV resonances are shown as upper

rate. The limits.

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.20 1.50 1.70 2.00

T,

2.45e - 04 8.48e + 00 2.13e+02 9.37e + 02 2.12e+03 3.46e + 03 4.75e + 03 5.86e + 03 6.75e+03 7.44e + 03 8.31e+03 8.72e + 03 8.65e + 03 8.30e + 03

1.64e - 10 1.7Oe- 01 1.4Ye+O2 4.09e -t 03 2.87e f 04 1.02e + 05 2.49e t 05 4.76e + 05 7.81e + 05 1.15e + 06 2.01e + 06 3.40e + 06 4.29e + 06 5.4Se + 06

416 keV upper limit

(cm3 s-I mol-l)

198 keV upper limit

N,(rrc)

Table 4 Reaction rates for sLi(cu, n)“B

7.97e - 20 4.35e - 06 1.27e-01 1.91e+Ol 3.58e+02 2.41e+03 9.05e + 03 2.38e + 04 4.94e + 04 8.72e + 04 1.97e + 05 4.19e t-05 5.80e+05 8.09e + 05

563 keV

2.11e-35 1.06e - 13 1.39e - 06 4.45e - 03 5.23e - Oi l.l9e+Ol 1.07e + 02 5.43e + 02 1.88e + 03 4.98e + 03 2.07e + 04 8.12e + 04 1.50e + 05 2.89e + 05

879 keV

l.l8e-38 1.70e-20 4.55e - 11 2.25e - 06 1.44e -03 l.O5e-01 2.22e + 00 2.17e+Ol 1.27e + 02 5.19e +02 4.23e + 03 3.38e +04 8.89e + 04 2.61e + 05

1.327 MeV upper limit l.l8e-38 5.53e - 28 5.03e - 16 4SOe - 10 l.h2e-06 3.70e - 04 1.76e - 02 3.14e-01 2,93e+OO 1.73e + 01 2.45e + 02 3.36e + 03 1.14e+ 04 4.39e +04

1.570 MeV upper limit 1.46e - 06 5.22e - 03 2.67e - 01 3.14e+OO i.80e+Ol 6.75e + 01 1.93e + 02 4.59e + 02 9.52e + 02 2.78e+03 4.96e + 03 1.59e + 04 2.93e + 04 6.21e + 04

non-res upper limit Sum

7.97e - 20 4.3Se - 06 1.27e - 01 1.91e+Ol 3.59e + 02 2.42e + 03 9.16e + 03 2.43e + 04 5.13e+04 9.22e + 04 2.18e+O5 5 .OOe+ 05 7.30e + 05 l.lOe+06

low

2.45e - 04 8.65e t 00 3.61e+02 5.06e + 03 3.13e+04 l.O9e+05 2.66e + 05 5.15e+05 8.58e + 05 1.28e -t 06 2.32e + 06 4.09e + 06 5.28e+06 6.94e + 06

high

Z.Q. Mao et al. / States in 12B (II)

143

-6

0.1

1.0

TEMPERATURE

(log K)

Fig. 11. Thermonuclear reaction rate for the ‘Lib, n)“B reaction. The shaded area represents the present range of uncertainty. For comparison, the rates of Malaney and Fowler [14], and Boyd et al. (81 are shown as the dotted and dashed curves, respectively.

the rates of the 198 and 416 keV resonances (which assume 0: = 1) while the lower limit is due to the 563 keV resonance. All other resonant contributions (including those from unobserved

resonances)

are negligible

for 0.1 < Tg =G2.0.

4. Discussion

From our measurements of excitation energies, spin-parities, total widths and branching ratios, we have obtained a new rate for the sLi(a, n)“B reaction for temperatures characteristic of big-bang nucleosynthesis. This reaction would occur in low-density, neutron-rich regions once ‘Li is produced in quantity. By this time, the temperature would have dropped to T9 = 1 (ref. [51X Here our rate is a factor of 1.6-34 times smaller than that advocated by Boyd et al. [8]. At temperatures near T9 = 1, this latter rate is equivalent to the (a, n,) rate of Paradellis et al. [61 multiplied by a factor of 5 to account for branches to excited states. Our results show that this estimate of the excited-state enhancement is quite reasonable. The difference between these rates lies in the fact that we have measured widths which are much smaller than those of ref. [61. In contrast, several calculations [14-161 of

2.Q. Mao et al. / States in “B (II)

144

the rate fortuitous

do fall within our range of uncertainty. This agreement is perhaps because the different structure of i2B implicit in these calculations.

Unfortunately,

our range of possible

reaction

rates is larger than desirable.

For

example, at T9 = 1 the present uncertainty amounts to about a factor of 20 and is a consequence of our upper limits for the 198 and 416 keV resonances. Both of these limits

were

based

on the assumption

of 0: = 1. However,

it is more

likely

that

0: G 0.2, in which case the actual rate would lie closer to our present lower limit. Improved results may be difficult to obtain using our present techniques and will probably require further development of radioactive beams. Our uncertainty increases for temperatures T9 G 0.5. However, this uncertainty does not appear to be astrophysically significant: By T9 = 0.5, the mean free path of a proton could have increased to the point where they would no longer be trapped in the high-density regions [17]. Thereafter, the universe would rapidly homogenize and low-density, neutron-rich nucleosynthesis will cease. Even without homogenization, it appears that by T9 = 0.5, the ((Y, n) reaction may no longer be the most efficient means of destroying sLi. Recent measurements of the 8Li(p, X) (X = n + d + a) reactions [18] would seem to indicate that destruction of sLi through the (p, X) channel is comparable to (a, n) for 0.5 < T9 < 1.0 and dominates the (a, n> channel for lower temperatures. It is hoped that a signature of an inhomogeneous big bang may be found in elemental abundances. Boyd and Kajino [19] and Kajino and Boyd [20] argue that the abundance of “Be could provide this evidence because an inhomogeneous big bang would produce 9Be in far greater quantity level still presents an observational challenge

than in a standard big bang. This [21,22]. However, if the universe

homogenizes during nucleosynthesis, then “Be could be destroyed to a level compatible with a standard big bang [17]. A signature in the lighter elements would be difficult to detect. For example, standard and inhomogeneous models predict differing abundances of 4He [23]. However, these differences are small and may be within systematic observational uncertainties. Another possibility lies in the A > 12 elements. Malaney and Fowler [4] and Kawano et al. [5] have predicted a CNO mass fraction of x(CNO1 = lo-“-lo-‘* for baryon densities flnb G 0.2. This level is substantially higher than that from a standard big bang [X(CNO) = 10-‘61, but would be hard to detect in the presence of stellar CNO production. Our new rate may not change this situation much because it is consistent with that used in each calculation. Apparently, evidence for primordial inhomogeneities will prove to be difficult to acquire.

We would like to acknowledge the assistance of P.D. Parker, A.J. Howard and the staff of the A.W. Wright Nuclear Structure Laboratory. We also thank C.R. Howell and W. Tornow for their loan of the NE213 detectors and R. Sherr for some very helpful discussions.

Z.Q. Mao et al. / States in ‘IB (II)

145

References [l] [2] [3] [4] [5] [6] [7] [8] [9] [lo]

[ll] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]

J.H. Applegate, C.J. Hogan and R.J. Scherrer, Phys. Rev. D35 (1986) 1151 J.H. Applegate, C.J. Hogan and R.J. Scherrer, Astrophys. J. 329 (1988) 572 J.H. Applegate, Phys. Reports 163 (1988) 141 R.A. Malaney and W.A. Fowler, Astrophys. J. 333 (1988) 14 L.H. Kawano, W.A. Fowler, R.W. Kavanagh and R.A. Malaney, Astrophys. J. 372 (1991) 1 T. Paradellis, S. Kossionides, G. Doukellis, X. Aslanoglou, P. Assimakopoulos, A. Pakou, C. Rolfs and K. Langanke, 2. Phys. A337 (1990) 211 Z.Q. Mao, R.B. Vogelaar and A.E. Champagne, Nucl. Phys. A567 (1994) 111 R.N. Boyd, I. Tanihata, N. Inabe, T. Kubo, T. Nakagawa, T. Suzuki, M. Yonokura, X.X. Bai, K. Kimura, S. Kubono, S. Shimoura, H.S. Xu and D. Hirata, Phys. Rev. Lett. 68 (1992) 1283 F. Ajzenberg-Selove, Nucl. Phys. A506 (1990) 1 S. Kubono, N. Ikeda, M.H. Tanaka, T. Nomura, I. Katayama, Y. Fuchi, H. Kawashima, M. Ohura, H. Orihara, C.C. Yun, Y. Tajima, M. Yosoi, H. Ohnuma, H. Toyokawa, M. Miyatake, T. Shimoda, R.N. Boyd, T. Kubo, I. Tanihata and T. Kajino, Z. Phys. A341 (1992) 97 N.R. Stanton, code KSUEFF, unpublished (1971) W.R. Nelson, H. Hirayama and D.O. Rogers, SLAC Report 265 (1985) R.M. Steffen and K. Alder, The electromagnetic interaction in nuclear spectroscopy, ed. W.D. Hamilton (North-Holland, Amsterdam, 1975) R.A. Malaney and W.A. Fowler, Astrophys. J. 345 (1989) L5 F.-K. Thielemann, J.H. Applegate, J.J. Cowan and M. Wiescher, in Nuclei in the cosmos, ed. H. Oberhummer (Springer, Berlin, 1991) T. Rauscher, K. Grim, H. Krauss, H. Oberhummer and E. Kwasniewicz, Phys. Rev. C45 (1992) 1996 CR. Alcock, D.S. Dearborn, G.M. Fuller, G.J. Mathews and B.S. Meyer, Phys. Rev. Lett. 64 (1990) 2607 F.D. Becchetti, J.A. Brown, W.Z. Liu, J.W. Janecke, D.A. Roberts, J.J. Kolata, R.J. Smith, K. Lamkin, A. Morsad, R.E. Warner, R.N. Boyd and J.D. Kalen, submitted to Nucl. Phys R.N. Boyd and T. Kajino, Astrophys. J. 336 (1989) L55 T. Kajino and R.N. Boyd, Astrophys. J. 359 (1990) 267 G. Ryan, M.S. Bessel, R.S. Sutherland and J.E. Norris, Astrophys. J. 348 (1990) L57 G. Gilmore, B. Edvardsson and P.E. Nissen, Astrophys. J. 378 (1991) 17 G.M. Fuller, R.N. Boyd and J.D. Kalen, Astrophys. J. 371 (1991) Lll