States in 12B and primordial nucleosynthesis

NUCLEAR PHYSICS A

Nuclear Physics A567 (1994) 111-124 North-Holland

States in 12B and primordial nucleosynthesis (I). Spectroscopic measurements

*

Z.Q. Mao I, R.B. Vogelaar Department of Physics, Princeton Unicersity, Princeton, NJ 08544, USA

A.E. Champagne UDepartment of Physics and Astronomy, Unillersity of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA ’ Triangle Uniaersities Nuclear Laboratory, Duke Unicersity, Durham, NC 27706, USA Received (Revised

30 March 1993 23 June 1993)

Abstract The ‘Be(cu, p)“B and “B(d, p)“B reactions have been used to determine excitation energies, total widths and spin-parities for states which could correspond to astrophysically significant resonances in the sLi(a, n)“B reaction. Six such states are observed at E, = 10.199, 10.417, 10.564, 10.880, 11.328 and 11.571 MeV. None of these states corresponds to the broad resonance observed in the “B(n, u)sLi reaction. However, we find no evidence that such a resonance exists.

Key words: NUCLEAR REACTIONS ‘Be(a, p), E = 35.2, 39.7 MeV; “B(d, measured cr(6’,). ‘*B deduced levels, r, J, X-. Enriched target

p), E = 26.3 MeV;

1. Introduction

According to recent theoretical studies, a quark-hadron phase transition in the early universe may have given rise to inhomogeneities in the baryon density [ll. These non-uniformities could in turn lead to high-density, proton-rich regions and

* Work supported Energy. ’ Present address:

0375-9474/94/$07.00

in part by the National Department

of Physics,

0 1994 - Elsevier

SSDI 0375.9474(93)E0390-T

Science

Foundation

University

Science

and in part by the U.S. Department

of Pennsylvania,

B.V. All rights reserved

Philadelphia,

of

PA 19104, USA.

Z.Q. Mao et al. / States in “B (I)

112

low-density, segregation

neutron-rich of protons

abundances

of some

bang. Although

regions at the onset of nucleosynthesis [2-41. and neutrons could result in notable differences

elements

a successful

as compared

model

with a standard

of inhomogeneous

Such a in the

(homogeneous)

nucleosynthesis

big

must neces-

sarily reproduce the observed abundances of the light elements, neither current observations nor model parameters preclude the possibility of relics appearing in the abundances of, e.g. 4He [51, “Be [6-101 or the A 2 12 elements [ll]. Detection of these signatures would provide important evidence for inhomogeneity in the early universe. However, the reaction networks are not understood in sufficient detail to permit unambiguous predictions of these abundances. For example, in the case of 9Be, different reaction networks and different treatments of hydrodynamics lead to final abundances which span more than three orders of magnitude [7-101. The abundances of the A 2 12 elements are also ill determined, but it appears that the primary route to this mass region passes through ‘Li. The *Li(cy, n)“B reaction leads to the production of heavier elements [12], while competing reactions turn the reaction flow back towards lighter elements. Because of the short of the (a, n) reaction is half-life of sLi (T,,2 = 840 ms>, a direct measurement difficult at best. Such a measurement has been performed by Boyd et al. [13], but the data are limited to center-of-mass energies EC,,, 2 1.5 MeV that are somewhat higher than the energy range of astrophysical interest (nucleosynthesis starts at T = 1.2 x lo9 K, or T9 = 1.2, corresponding to a most effective energy in the sLi + (Y system of 330-930 keV). In addition, the inverse reaction “B(n, a)sLi has been measured by Paradellis et al. [14] and this work has provided information about the (a, n) cross section at lower energies, albeit for the ((.u, no) branch only. In particular, it shows that the astrophysical S-factor is dominated by a resonance at J%n.= 580 keV with a width r = 200 keV. Where these two studies overlap in energy, the ratio of the n,, branch to that for decays to excited states is about i and thus Boyd et al. [13] recommend that the lower-energy (a, no> data be scaled up by a factor of 5 to account for these unobserved branches. The resulting thermonuclear reaction rate at T9 = 1 is a factor of 10.6 larger than a previous estimate [8]. However, since the (a, n) reaction appears to proceed through a few, individual resonances (as well as via a non-resonant direct process), there is little reason to suppose that this factor of 5 normalization will apply to all of them. Additional information regarding the nature of these resonances may be obtained from spectroscopic studies. Several levels above the ‘Li + cy threshold (at E, = 10.001 MeV [15] have been identified in “BeC7Li, a)12B and ‘“B(t, p)12B measurements (refs. [16,17], see also Fig. 1 and Table 1). In both reactions, a state is observed near E, = 10.6 MeV, i.e. at the expected location of the resonance seen in the (n, cu) study [14]. However, in each instance, the total width is much less than 200 keV. More recent measurements [18,19], using the 9Be(a, p)12B reaction, have produced more precise excitation energies and some information regarding total widths. Furthermore, neutron-decay data [20] for a state at E, =

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

879-

-

3.388

3I

/ 2,62,2.72

O+

0

,-

/

3.370

“B+n

1+

12

Fig. 1. Level structure

113

B

of “B. The information shown for states above the “Li + CYthreshold present study. All other entries are from ref. [15].

is from the

10.572 MeV indicate that excited states would account for only about half of the (a, n) cross section through this state, rather than 83% as suggested by ref. [13]. In any case, none of these measurements have shown evidence for a state near E, = 10.58 MeV with r= 200 keV. Consequently, we have re-examined the “Be(cu, p)‘*B reaction at several energies and at different angles in order to study potential (cy, n) resonances and to further search for the state observed the (n, (Y)measurement [14]. In so doing, we have obtained accurate excitation energies, total widths and some spin delimitations for all of the observed states between the ‘Li + a: threshold and E,,,,= 1.5 MeV. In addition, “B(d p)12B angular-distribution data have been used to directly probe the “B + n’character of these states. Although the (a, p) reaction might not populate al1 of the states of interest, in principle a significant (n, (u) or ((u, n) resonance will be formed via the (d, p) reaction.

114

Z.Q. Mao et al. /

Statesin 12B (I)

Z.Q. Mao et al. / States in “B (I)

115

2. Experimental procedures and results 2.1. The ‘Be(a, p)“B reaction 2.2.1. Determination of excitation energies The ‘Be(cr, p)12B reaction provided

by the Princeton

was studied AVF

cyclotron

at E, = 35.2 and 39.7 MeV using beams (preliminary

runs

were

also taken

at

E, = 48 MeV). Reaction products were momentum-analyzed at elab = lo” and E, = 35.2 MeV, and at 5” G elab G 25” (in 2.5” steps), 30” and 35” with E, = 39.7 MeV using a QDDD magnetic spectrometer. Targets consisted of self-supporting “Be foils with thicknesses of 100 + 20 kg/cm*. A typical proton spectrum is shown in Fig. 2. Excitation energies were obtained from the E, = 39.7 MeV data using the following calibration procedure: The energy dispersion was measured using well-known states populated in the ‘“F(a, ‘He)*“F reaction at the same QDDD field settings as for the ((u, p) data. In order to determine absolute energies, it was necessary to establish a reference for the dispersion curve (which is equivalent to

CHANNEL Fig. 2. Proton

spectra,

corresponding

to three different momentum bites of the “Be(cy, p)"B reaction E, = 39.7 MeV and Olab = lo”.

at

an accurate measurement of the beam energy). This was accomplished by measuring the position of the 11.4376 MeV state in ‘“N which was populated using the 12C((u, p)‘“N reaction, again at the same field settings. This measured position was compared with a prediction based on the measured dispersion and a nominal beam energy. The energy was then varied in order to reproduce the measured position. This technique requires that the reaction used to calculate the dispersion curve [19F(~, ‘Hej2’F] and that used to determine the beam energy [12C(a, p)15N] have very different kinematics in order to ensure adequate sensitivity to beam energy. The resulting excitation energies (listed in Table 11 compare well with previous determinations, but are of higher precision. The quoted uncertainties include contributions from the reaction @values, the absolute energy calibration, corrections for target thickness, errors in obtaining the peak centroids, and estimated systematic effects (for example, drifts in the magnetic fields between measurements). The states observed are located at E, = 10.199, 10.417, 10.564, 10.880, 11.328 and 11.571 MeV and would correspond to *Li -t-a resonances at E,,,, = 198 & 3, 416 rfr 14, 563 + 3, 879 f 3, 1327 + 10 and 1570 + 6 keV, respectively. 2.1.2. Total widths The total widths of the lowest four states were extracted from the data collected at E,, = 35.2 MeV and elab = 10”. The E, = 39.7 MeV data were used for the 11.328 and 11.571 MeV states. The portion of the observed Iineshape arising from inst~mental effects was determined by measuring the widths of states populated in the 12C(a, p)‘“N reaction near E, = 9.5 MeV, and those located near E, = 1 MeV in “B. All of these states are known to have natural widths of < 1 keV, i.e. much smaller than the expected instrumental resolution. However, they are populated with somewhat different dp/d8 than are the states of interest. Although the QDDD has multipole elements which are designed to correct for kinematic broadening, the correction is complete at only one place in the spectrum. This raises the possibility of a systematic error in the instrumental width which could be difficult to quantify. Therefore, the horizontal entrance slits were closed from the nominal full aperture of i60 mr to only i 1.5 mr so that the effects of kinematic broadening would be negligibIe. The instrumental resolution was 10.9 + 1.5 keV for the data taken at E, = 35.2 MeV and 16.6 i 2.8 keV at E, = 39.7 MeV. The measured lineshapes were fit with a convolution of this (gaussian) width with a lorentzian of variable width. These fits are shown in Fig. 3 and the resulting natural widths are listed in Table 1. 2.1.3. Analyses of angular distributions Angular-distribution data were analyzed using the code DWUCK4 [21] in a (bound) cluster approximation. Optical-model parameters appropriate to this mass and energy region were selected from tabuiated 1221values and are listed in Table 2. Although the detailed mechanism for the (a, p) reaction is not completely

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

117

60

50

2 40 : s

30

20

10

01

’

I

260

’

’

300

260

320

1

’

340

36C

Channel

I

I

I

I

16.0

16.0

14.0

2

c

9‘*.O 10.0 6.0 ___+---L---L________’

i-‘---j

6.0 !

I

.I

520

500

I

540

,

560

,

560

600

Channel

Channel

120

[“““““““““‘J 200

,

,

.

’

8

,

,

,

,

,

llOloo-

0

420

440

460

460

500

520

540

560

560

600

401220’

240

’

260

’

280 Channel

’

300

’

320

’

340

’

Fig. 3. Lineshape analysis for the states of interest in 12B The long-dashed line represents a linear background while the short-dashed line shows the measured instrumental lineshape (corresponding to a gaussian with a width of 10.9 keV for E, G 10.880 MeV and 16.6 keV for the remaining two states). Fits to the data using a convolution of the instrumental lineshape and a lorentzian are shown as the solid lines.

understood, its gross features have been studied in enough detail so that we may infer some information concerning spins and parities from the shapes of the angular distributions (Fig. 4). In each case, several different combinations of

Z.Q. Mao et al. / States in 12B (1)

118 Table 2 Summary Channel ‘Be fru “B + d “B+p ‘Be+t “B+n

of optical-model

parameters

”

[:rn)

alI (fm)

(MeV)

67.15 109 48.3 ’ h

1.669 0.90 1.15 1.25 1.26

0.653 0.822 0.4 0.65 0.6

22.44 8.39 6.5 _

a Ref. [23]. h Varied to give correct

binding

V*.o. (MeV)

W

V,, (MeV)

or resonance

1.066 1s45 1.os _ _

0.72 0.729 0.4 _ _

5.0 7.5 6.0

_ _ 1.2 1.25 1.26

_ _ 0.4 0.65 0.6

1.2 1.25 1.25

1.20 -

energy.

transferred orbital and total angular momenta produced acceptable fits and therefore it was only possible to place rather crude limits on J”. These values are listed in Table 3. Astrophysically significant states will most likely be formed via s-,

gBe(a,p)‘2B

E,=39.7

MeV

/:c;i-_‘~~ t

Fig. 4. ‘Be(a, p)“B angular-distribution data for the states of interest. The individual calculations are labelled by (I, 2j) where I and j are the transferred orbital and spin angular momenta, respectively. The solid and short-dashed curves represent fits judged to be acceptable. Examples of inferior fits are shown by the long-dashed curves.

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

Table 3 Summary

of spin-parity

119

information

EX (MeV)

(CI, p) reaction

Cd, p) reaction

(I, 2j)

J”

1

J” (DWBA)

K 1s

J” (decay method)

10.199

(1, 1) (2, 3)

2+4 4

(2-4)(2-6) -

0.50-0.90 1.3 -3.3

(2-6)-

(2-3)-

10.417

(3, (6, (1, (2,

(1, 2)+ (O-3)_ (o-5)+ (o-S)(1, 2)+ (O-3)_

0+4 2+4 4 1 lf3

(1, 2)_ (2-4)(2-6) (o-3)+ (l-3)+

0.84 0.75-1.4 1.5 -3.9 0.04-0.27 1.X -4.2

(2-6)-

(O-8) (2-3)-

(O-3) +

(o-3)+

10.564

10.880 11.328 11.571 a Defined

5) 13) 1) 3)

(3, 5) (6, 13) 1~6 166

(o-5)+ (O-8) .I<8 .I<8

.I” (adopted)

.I<8 J<8

as T/ST,,

p- or d-wave alpha transfer and consequently we are interested in states possessing J” = Of and (l-4)‘. Our present results do not exclude any state from being an important resonance on the basis of its J”.

2.2. The “B(d, p)12B reaction

2.2.1. Excitation energies and total widths The “B(d, p)‘*B reaction was produced at E, = 26.3 MeV, again using the Princeton AVF cyclotron and QDDD spectrometer. A self-supporting, enriched “B target of 110 + 20 ug/cm* thickness was used. Protons were detected at 10” G elab G 45”, in 5” steps. The elab = 20” spectrum is shown in Fig. 5. A notable feature of the spectrum is the rapidly rising background which is caused by projectile breakup and by decay protons from highly excited states produced in reactions involving carbon and oxygen contaminants. However, it showed a smooth variation with energy and did not interfere with the more strongly populated states at E, = 10.199, 10.564 and 10.880 MeV. The energy dispersion was calculated from the known excitation energies and measured positions of states in 13C 22Ne and 34S which were populated by (d, 3He) reactions on 14N, 23Na and 3sC1, respectively, at the same field settings as for the (d, p) data. However, unlike the procedure described above for the (a, p) reaction, it was not possible to find a suitable set of reactions in order to determine accurate absolute energies. As a result, we have used the (d, p> data to check the energy differences obtained from the (a, p) calibration. The difference obtained from the (d, p) measurement are 361 k 2 keV between the 10.199 and 10.564 MeV states, and 314 + 3 keV between the 10.564

Z.Q. Mao et al. / States in t2B (I)

120

E,=26.3

400

300

L 0

1

200

MeV,

01ab=200

I

1

400

600

I

800

>

1000

CHANNEL

Fig. 5. Proton spectrum from the “B(d, p)‘*B reaction at 17, = 26.3 MeV and B,,, = 20”. The dashed curve shows the expected yield from a state at E, = 10.58 MeV with I’, = 200 keV. The states observed in the (a, p) reaction are indicated. In addition there is a suggestion of a state near E, = 10.6 MeV.

and 10.880 MeV states. These values are in good agreement with the ((Y, p) energy differences of 365 t- 4 and 316 k 4 keV, respectively. Total widths were obtained for the 10.199, 10.564 and 10.880 MeV states via a procedure similar to that used for the ((u, p) reaction. These are listed in Table 1 and are in excellent agreement with the ((Y, p) results.

2.2.2. Spins and parities The DWBA code DWUCK4 [21] was used to analyze the angular-distribution data shown in Fig. 6. Potential parameters are listed in Table 2. Since the states of interest are unbound to neutron emission by 6.83-7.51 MeV, an unbound form factor was employed and angular-momentum transfers up to and including I= 4 were considered. Unfortunately, the high excitation energies of these states also ensured

that the characteristic

diffractive

shapes

of the angular

distributions

were

largely washed out. Consequently, it was impossible to deduce a unique f-transfer when fitting these data. However, both the 10.199 and 10.564 MeV states are best fit by even l-transfer whereas the 10.880 MeV state is best fit by odd-l. This implies positive parity for the latter state and negative parity for the remaining two. It was possible to place more restrictive bounds on the spins of these states by comparing those obtained by angular-distribution fits to those obtained through the use of the particle-decay method of Fortune and Vincent [231. This latter technique makes use of the relationship l-Jr,, = S where r, is the neutron width, c,, is the width of a (fictitious) pure, single-neutron state, and S is the neutron spectroscopic factor. Single-particle widths were calculated from the unbound form factors used in the DWBA calculations and spectroscopic factors were extracted

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

121

ecm(ded Fig. 6. “B(d,

p)“B

angular-distribution data for the 10.199, 10.564 and 10.880 MeV states. show all of the fits that were judged to be acceptable.

using the relationship calculation, frownA:

u ‘=P

between

=N(2Jf+I) (2Ji + 1)

the experimental

cross section,

The curves

ueexPand the DWBA

c2sa DWBA’

Here Ji and Jf are, respectively, the spins of the target and final state, N is an overall normalization (equal to 1.53 for the (d, p) reaction [21]) and C” is the isospin Clebsch-Gordan coefficient. For convenience, we define the quantity K = (&/Srsp> and we tacitly assume r,, = r. The values of K associated with 1 transfers producing acceptable fits to the angular distributions are listed in Table 3. In most cases, a range of values are listed and this reflects uncertainties associated with extracting S from these data. In principle, a proper choice of 1 would result in K = 1. However, because of uncertainties in the calculations of r,, and the fact that a significant a-decay branch would imply r, < r, this condition must be relaxed somewhat. Thus it is likely that we can not rule out any 1 transfer resulting in a K within about a factor of 3 of unity. The adopted values of J” in

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

122

Table 4 Summary

of experimental

results I‘ ” (keV)

E, (MeV + keV) 10.199 + 10.417 10.564 10.880 11.328 11.571

3

Y?

* 4 k 3 * 3 f 10 k 6

a Average

J”

3

(2-3)-

61 +25 11* 3 17* 4 75 * 25 45 + 1s

(O-8) (2-3)(o-3)+ J<8 .I<8

of (LY,p) and Cd, p) results

Table 3 were obtained using values of I producing 0.3 < K 6 3 and which also were consistent with the results obtained from the ((w, p> reaction.

3. Discussion We have identified 6 states in 12B which, by virtue of their excitation energies and possible values of J”, could correspond to astrophysically significant ‘Li + (Y resonances. Our results are summarized in Table 4. Further information regarding the roles of these states in the “Li(cu, n)“B reaction may be obtained via measurements of their partial decay widths. These studies are the subject of another article [24]. However, from our measurements of total widths, it is clear that we have not observed a state near E, = 10.58 MeV with r = 200 keV as is implied by the S-factor curve of Paradellis et al. [14]. This inconsistency can be the result of either (i) a bias against populating this state in our measurements, or (ii> a resolution effect in the data of ref. [14]. Because the (cu, p) reaction is angular-momentum mismatched (Q = - 16.886 MeV at E, = 10.000 MeV), it might tend to preferentially populate high-spin states at these excitation energies. However, our spin results do not show that this effect

is particularly

strong.

Since

the mechanism

for the ((u, p> reaction

is not

well-understood, it could be more likely that an interference effect has prevented us from observing all of the states that might be populated via the (a, n) reaction. There are striking examples of compound-nuclear interference processes for much simpler reactions (e.g. in 26Mg( (Y, (~‘1, [25]), but it also clear that these effects vary quite dramatically with reaction kinematics. The “Be(cu, p) reaction has now been observed at E, = 29, 35.2, 39.7, 48, 50.3, 64 and 65 MeV (this study and refs. 118,19,20,241) without producing any evidence for a broad state at E, = 10.58 MeV. In fact, such a state would have been readily discernable in our (d, p) spectra: If it were a strong neutron-capture resonance, then it must a priori be a strong single-neutron state. Since it would be about 580 keV above the (Y threshold, a typical (Y width would be no more than approximately 15 keV and thus r, = r.

Z.Q. Mao et al. / States in “B (0

123

This large neutron width in turn implies a large neutron spectroscopic factor. For example, if this state were formed with the same angular-momentum transfer as was the 10.564 MeV state, then it would have been populated about 17 times more strongly than the 10.564 MeV state (see Fig. 5). It is conceivable that the single, broad structure in the (n, a) cross section is rather a superposition of several narrow states (presumably including the 10.564 MeV state. This possibility has been advocated by Boyd et al. [19] on the basis of the inconsistency between their width measurements and those of the earlier c7Li, cu>study [16]. Consideration of the entries in Table 1 might suggest that this is an instrumental artifact: Widths have decreased as experimental resolution has improved. Nonetheless, if r = 200 keV is not the result of instrumental resolution, then this “state” must be a combination of narrower states, simply because the 10.564 MeV state does correspond to a strong (cu, n) resonance [20,24] and thus contributes a significant portion of the (n, a) yield. Although our (d, p> spectra (Fig. 5) do not indicate the presence of a nearby level to combine with the 10.564 MeV state, they exhibit a rather large background and thus it is possible that one or more weak states could have gone undetected. Specifically, a narrow state (i.e. a state with a width of no more than the instrumental resolution) could have escaped detection if it had G 15% of the strength of the 10.564 MeV state. On the other hand, a broad state could be relatively strong and still be unobserved. For example, if I’= 100 keV, then a (d, p) strength of G 30-50% of that for the 10.417 MeV state would be difficult to detect. In fact some of the (d, p) spectra suggest such a state near E, = 10.6 MeV. In terms of widths, these two extremes correspond to I’< 10 keV and r, G 1.5 keV, or r > 100 keV and r, G 20 keV. The latter extreme may well imply unphysically large alpha widths. Although we do not confirm the existence of the resonant structure observed [14] in the “B(n, cy)sLi reaction, we believe [primarily on the basis of our (d, p) data] that we have identified the states of astrophysical interest in i2B. Further discussion of the astrophysical significance of these states will be found in a forthcoming article [241.

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

E. Witten, Phys. Rev. D30 (1984) 272 C. Alcock, G.M. Fuller and G.J. Mathews, Astrophys. J. 320 (1987) 439 J.H. Applegate, C.J. Hogan and R.J. Scherrer. Astrophys. J. 329 (1988) 572 G.M. Fuller, G.J. Mathews and CR. Alcock, Phys. Rev. D37 (1988) 1380 G.M. Fuller, R.N. Boyd and J.D. Kalen, Astrophys. J. 371 (1991) Lll R.N. Boyd and T. Kajino, Astrophys. J. 336 (1989) L55 T. Kajino and R.N. Boyd, Astrophys. J. 359 (1990) 267 R.A. Malaney and W.A. Fowler, Astrophys. J. 345 (1989) L5 C.R. Alcock, D.S. Dearborn, G.M. Fuller, G.J. Mathews and B.S. Meyer, Phys. Rev. Lett 64 (1990) 2607

Z.Q. Mao et al. / States in

“‘3 (11

123

This large neutron width in turn implies a large neutron spectroscopic factor. For example, if this state were formed with the same angular-momentum transfer as was the 10.564 MeV state, then it would have been populated about 17 times more strongly than the 10.564 MeV state (see Fig. 5). It is conceivable that the single, broad structure in the (n, a> cross section is rather a superposition of several narrow states (presumably including the 10.564 MeV state. This possibility has been advocated by Boyd et al. [19] on the basis of the inconsistency between their width measurements and those of the earlier (‘Li, a) study 1161.Consideration of the entries in Table 1 might suggest that this is an instrumental artifact: Widths have decreased as experimental resolution has improved. Nonetheless, if r = 200 keV is not the result of instrumental resolution, then this “state” must be a combination of narrower states, simply because the 10.564 MeV state does correspond to a strong ((Y, n) resonance 120,241 and thus contributes a significant portion of the (n, a) yield. Although our (d, p) spectra (Fig. 5) do not indicate the presence of a nearby level to combine with the 10.564 MeV state, they exhibit a rather large background and thus it is possible that one or more weak states could have gone undetected. SpecificaIly, a narrow state (i.e. a state with a width of no more than the instrumental resolution) could have escaped detection if it had G 15% of the strength of the 10.564 MeV state. On the other hand, a broad state could be relatively strong and still be unobserved. For example, if Z- = 100 keV, then a (d, p> strength of < 30-50% of that for the 10.417 MeV state would be difficult to detect. In fact some of the (d, p) spectra suggest such a state near E, = 10.6 MeV. In terms of widths, these two extremes correspond to r G 10 keV and r,, G 1.5 keV, or r > 100 keV and r,, =G20 keV. The latter extreme may well imply unphysically large alpha widths. Although we do not confirm the existence of the resonant structure observed [14] in the “B(n, a)‘Li reaction, we believe [primarily on the basis of our (d, p) data] that we have identified the states of astrophysical interest in “B. Further discussion of the astrophysical significance of these states will be found in a forthcoming article [24].

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

E. Witten, Phys. Rev. D30 (1984) 272 C. Alcock, G.M. Fuller and G.J. Mathews, Astrophys. J. 320 (1987) 439 J.H. Applegate, C.J. Hogan and R.J. Schemer, Astrophys. J. 329 (1988) 572 G.M. Fuller, G.J. Mathews and C.R. Alcock, Phys. Rev. D37 (1988) 1380 G.M. Fuller, R.N. Boyd and J.D. Kalen, Astrophys. J. 371 (1991) Lll R.N. Boyd and T. Kajino, Astrophys. J. 336 (1989) LS5 T. Kajino and R.N. Boyd, Astrophys. J. 359 (1990) 267 R.A. Malaney and W.A. Fowler, Astrophys. J. 345 (1989) I.5 C.R. Alcock, D.S. Dearborn, G.M. Fuller, G.J. Mathews and B.S. Meyer, Phys. Rev. Lett 64 (1990) 2607

124

[lo] [ll] [12] [13] [14] [15] [16] [17] [18]

[19] [20]

[21] [22] [23] [24] [25]

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

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