The ^(26)Al(^3He,d)^(27)Si reaction was measured from 0°≤θ_(c.m.)≤35° at E(^3He)=20 MeV using a quadrupole-dipole-dipole-dipole magnetic spectrometer. States in ^(27)Si were observed above the background at 7652 and 7741 keV and upper limits were set for the state at 7592 keV. Implications for the ^(26)Al(p,γ)^(27)Si stellar reaction rate are discussed

Champagne, A. E.

Howard, A. J.

Kavanagh, R. W.

Magnus, P. V.

Mitchell, L. W.

O'Brien, H. A.

Parker, P. D.

Smith, M. S.

Vogelaar, R. B.

English

The 26Al(3He,d)27Si reaction was measured from 0°≤θc.m.≤35° at E(3He)=20 MeV using a quadrupole-dipole-dipole-dipole magnetic spectrometer. States in 27Si were observed above the background at 7652 and 7741 keV and upper limits were set for the state at 7592 keV. Implications for the 26Al(p,γ)27Si stellar reaction rate are discussed

Vogelaar, R.B.

Mitchell, L.W.

Kavanagh, R.W.

Champagne, A.E.

Magnus, P.V.

Smith, M.S.

Howard, A.J.

Parker, P.D.

O&apos

Carolina Digital Repository

dPHYSICAL REVIEW C APRIL 1996VOLUME 53, NUMBER 40556-281Constraining 26Al1p resonances using26Al „3He,d…27SiR. B. Vogelaar,* L. W. Mitchell,† and R. W. KavanaghW. K. Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, California 91125A. E. Champagne‡Department of Physics, Princeton University, Princeton, New Jersey 08544P. V. Magnus,§ M. S. Smith,i A. J. Howard, and P. D. ParkerA. W. Wright Nuclear Structure Laboratory, Yale University, New Haven, Connecticut 06511H. A. O’BrienLos Alamos National Laboratory, Los Alamos, New Mexico 87545~Received 1 November 1995!The 26Al ~3He,d!27Si reaction was measured from 0°<uc.m.<35° atE~3He!520 MeV using a quadrupole-dipole-dipole-dipole magnetic spectrometer. States in27Si were observed above the background at 7652 an7741 keV and upper limits were set for the state at 7592 keV. Implications for the26Al ~p,g!27Si stellar reactionrate are discussed.PACS number~s!: 25.55.Hp, 26.20.1f, 27.30.1taral-t,-atanrtnI. INTRODUCTIONInterest in the origin of26Al following observation of itsdecay radiation in the galactic plane@1–6# and its isotopicresidues in meteorites@7,8# has prompted measurements ofthe reactions involved in its production and destruction. Prioto the present work, resonances in the26Al ~p,g!27Si destruc-tion reaction as low asEp5288 keV had been observed di-rectly @9#. Spectroscopy of transfer reactions on stable targeby Wanget al. @10# and others@11# has revealed seven statesin 27Si at lower energies~Fig. 1!. Some of the proposed26Alproduction sites involve temperatures below 108 K ~T950.1!at which one of these lower states could dominate the reation rate. Since theJp551 ground state of26Al stronglyfavors formation of high-spin states in27Si, the spins~as wellas spectroscopic strengths! of the observed states are neededBecause Wanget al. @10# could not extract this informationdirectly from their data, they identified low-spin states in theanalogous region in27Al in an effort to eliminate from fur-ther consideration states in27Si which could not correspondto astrophysically interesting resonances.To avoid this dependence on uncertain analog assigments, we developed a thin target of radioactive26Al to ex-*Present address: Physics Department, Princeton University, Prceton, NJ 08544.†Present address: Department of Physics, Flinders UniversiBedford Park 5042, Australia.‡Permanent address: Department of Physics and Astronomy, Uversity of North Carolina at Chapel Hill, Chapel Hill, NC 27599and Triangle Universities Nuclear Laboratory, Duke UniversityDurham, NC 27706.§Present address: Department of Physics, University of Washinton, Seattle, WA 98195.iPresent address: Oak Ridge National Laboratory, Oak Ridge, T37831.533/96/53~4!/1945~5!/$10.00rtsc-.n-amine the26Al ~3He,d!27Si reaction. This reaction is expectedto proceed by direct proton transfer in which the anguldistribution of the outgoing deuteron reflects thel transfersinvolved, and the flux of each deuteron group is proportionto the proton width,Gp , of the residual state. The thermonuclear reaction rate for an isolated narrow resonance atEris given in the center-of-mass system by^sv&5S 2pmkTD3/2\2~vg!expS 2ErkT D .The quantitym is the reduced mass andvg is the resonancestrength, which is defined byvg52J11~2Jt11!~2Jp11!GpGgG.Here,J, Jt , andJp refer to the spins of the final state, targeand incident proton, respectively, andGp , Gg , andG are theproton andg-ray partial widths, and the total width, respectively. Since the energies of interest are sufficiently low ththe Coulomb barrier makes the proton width much less ththe g-ray width, vg'(2J11)Gp/22 for the26Al ~p,g!27Sireaction. The proton width may be obtained from the familiarelationGp5C2SGs.p.whereC2S is the proton spectroscopicfactor measured via the~3He,d! reaction, andGs.p. is thesingle-particle width. The results of the presen26Al ~3He,d!27Si work indicated the probable existence of a26Al ~p,g!27Si resonance nearEp5195 keV, and prompted asubsequent sensitive search@13# which succeeded in directlymeasuring its energy and strength~see Sec. V!.II. TARGETThe production and purification of the26Al target materialis described elsewhere@13,14#. A transmission target on athin carbon foil was made by evaporation of Al2O3~26Al/ 27Al56.360.1%! from a graphite boat brought to 2475in-ty,ni-,g-N1945 © 1996 The American Physical Societyindleorerl-re-dpseers-k-et1946 53R. B. VOGELAAR et al.K for 15 sec six times, allowing a cooling period betweeeach heating. Attempts using premounted self-supportcarbon foil backings failed owing to poor adhesion of thAl2O3, whereas successful targets were obtained by fievaporating a 40mg/cm2 carbon film directly onto a lightlyetched 76mm Cu foil which was itself clamped to a largeCu heat sink. After the Al2O3 was deposited, a 10mg/cm2overlay of carbon was then added in order to further stabilthe target against mechanical or other loss mechanisms.The four-layer foil ~Cu, C, Al2O3, C! was laid, carbonface down, over a tantalum frame coated with a thin filmvacuum grease and having a 6.4 mm diameter centered hThe excess foil was folded over the edges of the framesupport. An etching solution~1 ml H2O:1.1 ml 13M NH4OH:1 g trichloroacetic acid! was made to flow gently overthe Cu side of the target to remove the copper foil.The energy resolution of the deuteron group to bsearched for is determined by beam-energy resolution, detor resolution, energy straggling in the target, and, fforward-angle detection, the difference in energy loss btween 3He and deuterons passing through the target. Tknown level density in27Si necessitated a resolution of<15keV which placed an upper limit on the target thickness. Tfinal target was analyzed using Rutherford backscatter~Fig. 2!, and by integrating the yield of the 992 keV resonance in27Al ~p,g!28Si. The total surface density was'55mg/cm2, with ~0.6060.03! mg/cm2 of 26Al and the observedFIG. 1. Excitation energies in27Si near the26Al1p thresholdand their corresponding resonance energies in26Al ~p,g!27Si. Ener-gies are in keV@12#.ningerstrzeofole.foretec-ore-heheing-resolution was'12 keV. A reference target of natural Al~27Al ! was made in an identical fashion.III. EXPERIMENTAL PROCEDUREA 20 MeV 3He beam was supplied by the PrincetoAVF cyclotron, and the outgoing deuterons were analyzeusing a dispersion-matched quadrupole-dipole-dipole-dipo~QDDD! magnetic spectrometer. The focal-plane detectconsisted of a position-sensitive gas proportional count(DE), followed by a plastic scintillator (E-DE) that allowedfor standard particle identification.The momentum bite afforded by the 60-cm-long focaplane detector allowed us to study deuteron groups corsponding to population of states in27Si between about 7.25and 8.25 MeV excitation. Deuteron-energy calibration anabsolute yields were determined from known particle grouarising from27Al ~3He,d!28Si reactions on the27Al in the tar-FIG. 3. Deuteron groups identified by the excited state of thresidual nucleus. Those from28Si are labeled above the curve, whilethose from27Si states are labeled below.FIG. 2. Rutherford backscattering of 2 MeVa particles. Thedouble carbon peak reflects the target’s layered structures. Reving the target shifts the Al and O peaks by the difference in thicness of the two carbon films. Other structure comes from targcontaminants and pin holes in the carbon.to53 1947CONSTRAINING 26Al1p RESONANCES USING26Al1~3He,d!27SiFIG. 4. Examples of~a! subtraction and~b! fitting analyses described in the text. In~a! the dashed line corresponds to the27Al calibrationtarget while the upper solid line corresponds to the 6.3%26Al target; the low solid line corresponds to the net26Al ~3He,d!27Si yield aftersubtraction. Notice the difference in line shape between the Si and F groups in the 17.5° spectrum. Residual groups attributed27Si arelabeled below the curves.oerlouooteetfornd,toksre01theelal-gs.s-ully-wnrmet.get @15#. Data were collected atulab50, 5, 10, 13, 15, 17.5,20, 30, and 35 deg.IV. ANALYSESA representative deuteron spectrum atulab55° is pre-sented in Fig. 3. The spectrum is clearly dominated by pructs of the27Al ~3He,d!28Si reaction, as well as by deuteronarising from reactions on12C, 16O, and14N ~the 14N perhapscoming from ammonia in the copper etch!. Spectra takenwith the reference27Al target were gain matched and normaized ~using strong, isolated peaks arising from27Al ! to thoseof the 26Al target, and then subtracted from the26Al spectra.Two residual peaks were observed and their kinematicergy change with angle was consistent with production aing from theA526 component of the target. An energy cabration, based upon the well-known states in28Si indicatedthat these peaks corresponded to the 7652 and 7741states in27Si. Additionally, at several angles the regioninterest for the 7592 keV state was clear of background,an upper limit on its strength could be established. Absolcross sections were then obtained from the26Al/ 27Al ratioand the known27Al ~3He,d!28Si cross sections@15#. Becauseof the large background elsewhere, no information wastained for other states in27Si.This straightforward approach assumed that contributifrom contaminants were the same for each target and thaline shapes did not vary between runs. To avoid relyingtirely upon these assumptions, we developed a fitting produre in which isolated deuteron groups from28Si states wereused to define a single ‘‘Si’’ line shape for each spectrum ayields from 28Si states were held to their known relativstrengths@15#. Other contaminant line shapes were takfrom fits to the reference target data, and the ratio ofd-sl-n-is-i-keVfsoteb-nsthen-ce-ndenheyields obtained with the two targets was indeed constantall angles. Remaining parameters, viz., a linear backgroucentroids, and independent amplitudes, were then variedminimizex2. The fits included the nearest two or three peato the one of interest~Fig. 4!.The particle-group centroids returned by this proceduare presented in Fig. 5. Centroids of the 11780 and 119keV 28Si groups were used as calibration points, and thendifference of each centroid from that of the 11901 keV levwas plotted against exit angle. The curves shown were cculated using known kinematic relations and level spacinThe background15O group, whose line shape changed dratically with angle, appears to have been handled successfbased on the kinematic shift of its centroid. More signifiFIG. 5. Expected kinematic shifts of deuteron groups are shoby smooth curves. Actual observations are indicated and confithat the 7741- and 7652-keV groups come from a mass 26 targ1948 53R. B. VOGELAAR et al.TABLE I. DWBA parameters@15,19#.ChannelV~MeV!r~fm!a~fm!W~MeV!W8~MeV!r 8~fm!a8~fm!VSO~MeV!r c~fm!26Al13He 159 1.15 0.68 17.86 1.57 0.88 1.2527Si1d 39 1.30 0.88 89 1.48 0.54 1.3026Al1p varieda 1.25 0.65 l525 1.25aAdjusted to give the correct resonance energy.ane-.ac-gthe-ec---,.en-tor.isrcs-stFIG. 6. Angular distributions and DWBA fits for the states ointerest.cantly, the two peaks of interest are again consistent withA526 target. At some angles fitting became impractical bcause of background peaks that moved into the fit regionThe yields of the27Si groups obtained by this fitting pro-cedure were consistent with those obtained by direct subtrtion, and the two sets of results were combined by takinweighted averages for the cross sections and errors usingmethod of Wohlet al. @16#. Spectroscopic factors were obtained from the relationship between the measured cross stion, ds/dV~expt!, and that calculated using the distortedwave Born approximation~DWBA! codeDWUCK4 @17#:dsdV~expt!5N C2SS 2J11~2Jt11!~2Ji11! D dsdV ~DWBA!,whereN is an overall normalization~equal to 4.42 for thisreaction@18#!; C2S is the aforementioned spectroscopic factor; andJt and J are the spins of the target and final staterespectively, whileJi is the transferred angular momentumOptical-model parameters appropriate for this mass andergy region were used@19# ~summarized in Table I! and thetransferred proton was treated using an unbound form facSinceJi is not uniquely determined byl , we have chosen2s1/2, 2p3/2, 1d3/2, and 1f 7/2 transfers. The uncertainty result-ing from this ambiguity in the angular-momentum transfersmall compared to the other uncertainties that enter invg.The angular distributions~shown in Fig. 6! are not particu-larly distinctive, and the nonzero spin of the target allows fothe possibility of mixedl transfers. Consequently, we werenot able to deduce uniquel assignments. The spectroscopifactors shown in Table II were obtained under various asumptions for purel transfers, and this represents the largesource of uncertainty invg. Single-particle widths were thenfTABLE II. Spectroscopic factors and resonance strengths.Ep~keV!Ex~27Si!~keV! l (2J11)C2S avg~meV!vg~lit ! b~meV!133 7592 0 ,0.02 ,5.931026 ,5.731023195 7652 0 2.1 0.29 ,0.0421 1.9 0.064 0.055c2 4.2 ,3.2310233 5.9 ,9.931025288 7741 0 0.87 19.0 2.9c1 0.64 3.602 1.24 0.173 1.99 ,7.031023aAssuming 2s1/2, 2p3/2, 1d3/2, and 1f 7/2 transfer.bReference@10# unless noted.cReference@13#.ew-ea-rerte.53 1949CONSTRAINING 26Al1p RESONANCES USING26Al1~3He,d!27Sicalculated using the same form factors employed inDWBA calculations. The resulting resonance strengthspure l transfers are also listed in Table II.V. CONCLUSIONSOur upper limit for the resonance strength correspondto the 7592 keV state in27Si is at least 200 times weaker thathe limit obtained by Wanget al. @10# under the assumptionthat this was a pure single-particle state. On the other hathe 7652 keV state is found to be a strong single-partistate and with a maximuml transfer of 3~estimated fromFig. 6!, it increases the experimental limit on̂sv& atT9'0.1 by more than two orders of magnitude. This mesurement exemplifies the general role of spectroscopic sies in identifying states that warrant further study throudirect observation of the reaction in question, where coplete excitation functions are frequently impossible becaof the low rates involved. In this case, the large spectroscofactors found here for the 7652 keV state prompted furtdirect (p,g) measurements described elsewhere@13# whichtheforingnnd,clea-tud-ghm-usepicherdid, in fact, observe a resonance at 195 keV in26Al ~p,g!27Sihavingvg55569 meV. The 7741 keV state is also a strongsingle-particle state. In this case, (p,g) measurements hadalready been performed@9,13# and the measured resonancstrength falls within the range listed in Table II.Since we were not able to observe any states beloEp5195 keV in the26Al1p system, there are sizable uncertainties in the reaction rate forT9,0.1. Although the 7592keV state was too weak to be observed in the present msurement, our upper limit onvg is still sufficient for it to beastrophysically important: A recent theoretical study@20# re-ported a resonance strength similar to our limit, with a majocontribution to the reaction rate at low temperatures. Furthinformation on the low-energy states will require a targewith a significantly higher26Al enrichment.ACKNOWLEDGMENTSThis work was supported in part by National SciencFoundation Grant No. PHY88-17296 and in part by the U.SDepartment of Energy.M.ar,l.ol-ndys.@1# W. A. Mahoney, J. C. Ling, W. A. Wheaton, and A. S. Jacobson, Astrophys. J.286, 578 ~1984!.@2# G. H. Share, R. L. Kinzer, J. D. Kurfess, E. L. Chupp, and ERieger, Astrophys. J.292, L61 ~1985!.@3# C. J. MacCallum, A. F. Huters, P. D. Stang, and M. LeventhaAstrophys. J.317, 877 ~1987!.@4# P. von Ballmoos, R. Diehl, and V. Scho¨nfelder, Astrophys. J.318, 654 ~1987!.@5# R. Diehl, C. Dupraz, K. Bennett, H. Bloemen, H. de Boer, WHermsen, G. G. Lichti, M. McConnell, D. Morris, J. Ryan, VSchönfelder, H. Steinle, A. W. Strong, B. N. Swanenburg, MVarendorff, and C. Winkler, Astrophys. J. Suppl.92, 429~1994!.@6# R. Diehl, K. Bennett, H. Bloemen, C. Dupraz, W. Hermsen,Knödlseder, G. G. Lichti, D. Morris, U. Oberlack, J. Ryan, VSchönfelder, H. Steinle, M. Varendorf, and C. Winkler, AstronAstrohys.298, L25 ~1995!.@7# T. Lee, D. A. Papanastassiou, and G. J. Wasserburg, AstrophJ. 211, L107 ~1977!.@8# P. Hoppe, S. Amari, E. Zinner, T. Ireland, and R. S. LewiAstrophys. J.430, 870 ~1994!.@9# L. Buchmann, M. Hilgemeier, A. Krauss, A. Redder, C. Rolfs-.l,...J...ys.s,,and H. P. Trautvetter, Nucl. Phys.A415, 93 ~1994!.@10# T. F. Wang, A. E. Champagne, J. D. Hadden, P. V. Magnus,S. Smith, A. J. Howard, and P. D. Parker, Nucl. Phys.A499,546 ~1989!.@11# P. Schmalbrock, T. R. Donoghue, M. Wiescher, V. WijekumC. P. Browne, A. A. Rollefson, C. Rolfs, and A. Vlieks, NucPhys.A457, 182 ~1986!.@12# P. M. Endt, Nucl. Phys.A521, 1 ~1990!.@13# R. B. Vogelaar, Ph.D. thesis, California Institute of Technogy, 1989.@14# K. W. Thomas, Radiochim. Acta33, 213 ~1983!.@15# A. E. Champagne, M. L. Pitt, P. H. Zhang, L. L. Lee, Jr., aM. J. LeVine, Nucl. Phys.A259, 239 ~1986!.@16# C. G. Wohlet al., Rev. Mod. Phys.56, S1 ~1984!.@17# P. D. Kunz, University of Colorado report, 1974~unpublished!;programDWUCK4, P.D. Kunz~unpublished!; extended versionof J. R. Comfort~unpublished!.@18# R. H. Bassel, Phys. Rev.149, 791 ~1966!.@19# C. M. Perey and F. G. Perey, At. Data Nucl. Data Tables17, 1~1976!.@20# A. E. Champagne, B. A. Brown, and R. Sherr, Nucl. PhA556, 123 ~1994!.

Constraining 26Al+p resonances using 26Al(3He,d)27Si

Caltech Authors - Main

Constraining ^(26)Al+p resonances using ^(26)Al(^3He,d)^(27)Si

PHYSICAL REVIEW C APRIL 1996VOLUME 53, NUMBER 4
0556-2813Constraining 26Al1p resonances using 26Al3He,d27Si
R. B. Vogelaar,* L. W. Mitchell,† and R. W. Kavanagh
W. K. Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, California 91125
A. E. Champagne‡
Department of Physics, Princeton University, Princeton, New Jersey 08544
P. V. Magnus,§ M. S. Smith,i A. J. Howard, and P. D. Parker
A. W. Wright Nuclear Structure Laboratory, Yale University, New Haven, Connecticut 06511
H. A. O’Brien
Los Alamos National Laboratory, Los Alamos, New Mexico 87545
~Received 1 November 1995!
The 26Al~3He,d!27Si reaction was measured from 0°<uc.m.<35° at E~3He!520 MeV using a quadrupole-
dipole-dipole-dipole magnetic spectrometer. States in 27Si were observed above the background at 7652 and
7741 keV and upper limits were set for the state at 7592 keV. Implications for the 26Al~p ,g!27Si stellar reaction
rate are discussed.
PACS number~s!: 25.55.Hp, 26.20.1f, 27.30.1tI. INTRODUCTION
Interest in the origin of 26Al following observation of its
decay radiation in the galactic plane @1–6# and its isotopic
residues in meteorites @7,8# has prompted measurements of
the reactions involved in its production and destruction. Prior
to the present work, resonances in the 26Al~p ,g!27Si destruc-
tion reaction as low as Ep5288 keV had been observed di-
rectly @9#. Spectroscopy of transfer reactions on stable targets
by Wang et al. @10# and others @11# has revealed seven states
in 27Si at lower energies ~Fig. 1!. Some of the proposed 26Al
production sites involve temperatures below 108 K ~T950.1!
at which one of these lower states could dominate the reac-
tion rate. Since the Jp551 ground state of 26Al strongly
favors formation of high-spin states in 27Si, the spins ~as well
as spectroscopic strengths! of the observed states are needed.
Because Wang et al. @10# could not extract this information
directly from their data, they identified low-spin states in the
analogous region in 27Al in an effort to eliminate from fur-
ther consideration states in 27Si which could not correspond
to astrophysically interesting resonances.
To avoid this dependence on uncertain analog assign-
ments, we developed a thin target of radioactive 26Al to ex-
*Present address: Physics Department, Princeton University, Prin-
ceton, NJ 08544.
†Present address: Department of Physics, Flinders University,
Bedford Park 5042, Australia.
‡Permanent address: Department of Physics and Astronomy, Uni-
versity of North Carolina at Chapel Hill, Chapel Hill, NC 27599
and Triangle Universities Nuclear Laboratory, Duke University,
Durham, NC 27706.
§Present address: Department of Physics, University of Washing-
ton, Seattle, WA 98195.
iPresent address: Oak Ridge National Laboratory, Oak Ridge, TN
37831.53/96/53~4!/1945~5!/$10.00amine the 26Al~3He,d!27Si reaction. This reaction is expected
to proceed by direct proton transfer in which the angular
distribution of the outgoing deuteron reflects the l transfers
involved, and the flux of each deuteron group is proportional
to the proton width, Gp , of the residual state. The thermo-
nuclear reaction rate for an isolated narrow resonance at Er
is given in the center-of-mass system by
^sv&5S 2pmkT D
3/2
\2~vg!expS 2ErkT D .
The quantity m is the reduced mass and vg is the resonance
strength, which is defined by
vg5
2J11
~2Jt11 !~2Jp11 !
GpGg
G
.
Here, J , Jt , and Jp refer to the spins of the final state, target,
and incident proton, respectively, and Gp , Gg , and G are the
proton and g-ray partial widths, and the total width, respec-
tively. Since the energies of interest are sufficiently low that
the Coulomb barrier makes the proton width much less than
the g-ray width, vg'(2J11)Gp/22 for the 26Al~p ,g!27Si
reaction. The proton width may be obtained from the familiar
relation Gp5C2SGs.p. where C2S is the proton spectroscopic
factor measured via the ~3He,d! reaction, and Gs.p. is the
single-particle width. The results of the present
26Al~3He,d!27Si work indicated the probable existence of an
26Al~p ,g!27Si resonance near Ep5195 keV, and prompted a
subsequent sensitive search @13# which succeeded in directly
measuring its energy and strength ~see Sec. V!.
II. TARGET
The production and purification of the 26Al target material
is described elsewhere @13,14#. A transmission target on a
thin carbon foil was made by evaporation of Al2O3
~26Al/27Al56.360.1%! from a graphite boat brought to 24751945 © 1996 The American Physical Society
1946 53R. B. VOGELAAR et al.K for 15 sec six times, allowing a cooling period between
each heating. Attempts using premounted self-supporting
carbon foil backings failed owing to poor adhesion of the
Al2O3, whereas successful targets were obtained by first
evaporating a 40 mg/cm2 carbon film directly onto a lightly
etched 76 mm Cu foil which was itself clamped to a larger
Cu heat sink. After the Al2O3 was deposited, a 10 mg/cm2
overlay of carbon was then added in order to further stabilize
the target against mechanical or other loss mechanisms.
The four-layer foil ~Cu, C, Al2O3, C! was laid, carbon
face down, over a tantalum frame coated with a thin film of
vacuum grease and having a 6.4 mm diameter centered hole.
The excess foil was folded over the edges of the frame for
support. An etching solution ~1 ml H2O:1.1 ml 13M NH4
OH:1 g trichloroacetic acid! was made to flow gently over
the Cu side of the target to remove the copper foil.
The energy resolution of the deuteron group to be
searched for is determined by beam-energy resolution, detec-
tor resolution, energy straggling in the target, and, for
forward-angle detection, the difference in energy loss be-
tween 3He and deuterons passing through the target. The
known level density in 27Si necessitated a resolution of <15
keV which placed an upper limit on the target thickness. The
final target was analyzed using Rutherford backscattering
~Fig. 2!, and by integrating the yield of the 992 keV reso-
nance in 27Al~p ,g!28Si. The total surface density was '55
mg/cm2, with ~0.6060.03! mg/cm2 of 26Al and the observed
FIG. 1. Excitation energies in 27Si near the 26Al1p threshold
and their corresponding resonance energies in 26Al~p ,g!27Si. Ener-
gies are in keV @12#.resolution was '12 keV. A reference target of natural Al
~27Al! was made in an identical fashion.
III. EXPERIMENTAL PROCEDURE
A 20 MeV 3He beam was supplied by the Princeton
AVF cyclotron, and the outgoing deuterons were analyzed
using a dispersion-matched quadrupole-dipole-dipole-dipole
~QDDD! magnetic spectrometer. The focal-plane detector
consisted of a position-sensitive gas proportional counter
(DE), followed by a plastic scintillator (E-DE) that allowed
for standard particle identification.
The momentum bite afforded by the 60-cm-long focal-
plane detector allowed us to study deuteron groups corre-
sponding to population of states in 27Si between about 7.25
and 8.25 MeV excitation. Deuteron-energy calibration and
absolute yields were determined from known particle groups
arising from 27Al~3He,d!28Si reactions on the 27Al in the tar-
FIG. 3. Deuteron groups identified by the excited state of the
residual nucleus. Those from 28Si are labeled above the curve, while
those from 27Si states are labeled below.
FIG. 2. Rutherford backscattering of 2 MeV a particles. The
double carbon peak reflects the target’s layered structures. Revers-
ing the target shifts the Al and O peaks by the difference in thick-
ness of the two carbon films. Other structure comes from target
contaminants and pin holes in the carbon.
53 1947CONSTRAINING 26Al1p RESONANCES USING 26Al1~3He,d!27SiFIG. 4. Examples of ~a! subtraction and ~b! fitting analyses described in the text. In ~a! the dashed line corresponds to the 27Al calibration
target while the upper solid line corresponds to the 6.3% 26Al target; the low solid line corresponds to the net 26Al~3He,d!27Si yield after
subtraction. Notice the difference in line shape between the Si and F groups in the 17.5° spectrum. Residual groups attributed to 27Si are
labeled below the curves.get @15#. Data were collected at ulab50, 5, 10, 13, 15, 17.5,
20, 30, and 35 deg.
IV. ANALYSES
A representative deuteron spectrum at ulab55° is pre-
sented in Fig. 3. The spectrum is clearly dominated by prod-
ucts of the 27Al~3He,d!28Si reaction, as well as by deuterons
arising from reactions on 12C, 16O, and 14N ~the 14N perhaps
coming from ammonia in the copper etch!. Spectra taken
with the reference 27Al target were gain matched and normal-
ized ~using strong, isolated peaks arising from 27Al! to those
of the 26Al target, and then subtracted from the 26Al spectra.
Two residual peaks were observed and their kinematic en-
ergy change with angle was consistent with production aris-
ing from the A526 component of the target. An energy cali-
bration, based upon the well-known states in 28Si indicated
that these peaks corresponded to the 7652 and 7741 keV
states in 27Si. Additionally, at several angles the region of
interest for the 7592 keV state was clear of background, so
an upper limit on its strength could be established. Absolute
cross sections were then obtained from the 26Al/27Al ratio
and the known 27Al~3He,d!28Si cross sections @15#. Because
of the large background elsewhere, no information was ob-
tained for other states in 27Si.
This straightforward approach assumed that contributions
from contaminants were the same for each target and that the
line shapes did not vary between runs. To avoid relying en-
tirely upon these assumptions, we developed a fitting proce-
dure in which isolated deuteron groups from 28Si states were
used to define a single ‘‘Si’’ line shape for each spectrum and
yields from 28Si states were held to their known relative
strengths @15#. Other contaminant line shapes were taken
from fits to the reference target data, and the ratio of theyields obtained with the two targets was indeed constant for
all angles. Remaining parameters, viz., a linear background,
centroids, and independent amplitudes, were then varied to
minimize x2. The fits included the nearest two or three peaks
to the one of interest ~Fig. 4!.
The particle-group centroids returned by this procedure
are presented in Fig. 5. Centroids of the 11780 and 11901
keV 28Si groups were used as calibration points, and then the
difference of each centroid from that of the 11901 keV level
was plotted against exit angle. The curves shown were cal-
culated using known kinematic relations and level spacings.
The background 15O group, whose line shape changed dras-
tically with angle, appears to have been handled successfully
based on the kinematic shift of its centroid. More signifi-
FIG. 5. Expected kinematic shifts of deuteron groups are shown
by smooth curves. Actual observations are indicated and confirm
that the 7741- and 7652-keV groups come from a mass 26 target.
1948 53R. B. VOGELAAR et al.TABLE I. DWBA parameters @15,19#.
Channel
V
~MeV!
r
~fm!
a
~fm!
W
~MeV!
W8
~MeV!
r8
~fm!
a8
~fm!
VSO
~MeV!
rc
~fm!
26Al13He 159 1.15 0.68 17.86 1.57 0.88 1.25
27Si1d 39 1.30 0.88 89 1.48 0.54 1.30
26Al1p varieda 1.25 0.65 l525 1.25
aAdjusted to give the correct resonance energy.FIG. 6. Angular distributions and DWBA fits for the states of
interest.cantly, the two peaks of interest are again consistent with an
A526 target. At some angles fitting became impractical be-
cause of background peaks that moved into the fit region.
The yields of the 27Si groups obtained by this fitting pro-
cedure were consistent with those obtained by direct subtrac-
tion, and the two sets of results were combined by taking
weighted averages for the cross sections and errors using the
method of Wohl et al. @16#. Spectroscopic factors were ob-
tained from the relationship between the measured cross sec-
tion, ds/dV~expt!, and that calculated using the distorted-
wave Born approximation ~DWBA! code DWUCK4 @17#:
ds
dV ~expt!5N C
2SS 2J11~2Jt11 !~2Ji11 ! D dsdV ~DWBA!,
where N is an overall normalization ~equal to 4.42 for this
reaction @18#!; C2S is the aforementioned spectroscopic fac-
tor; and Jt and J are the spins of the target and final state,
respectively, while Ji is the transferred angular momentum.
Optical-model parameters appropriate for this mass and en-
ergy region were used @19# ~summarized in Table I! and the
transferred proton was treated using an unbound form factor.
Since Ji is not uniquely determined by l , we have chosen
2s1/2, 2p3/2, 1d3/2, and 1 f 7/2 transfers. The uncertainty result-
ing from this ambiguity in the angular-momentum transfer is
small compared to the other uncertainties that enter in vg.
The angular distributions ~shown in Fig. 6! are not particu-
larly distinctive, and the nonzero spin of the target allows for
the possibility of mixed l transfers. Consequently, we were
not able to deduce unique l assignments. The spectroscopic
factors shown in Table II were obtained under various as-
sumptions for pure l transfers, and this represents the largest
source of uncertainty in vg. Single-particle widths were then
TABLE II. Spectroscopic factors and resonance strengths.
Ep
~keV!
Ex~27Si!
~keV! l (2J11)C2S a
vg
~meV!
vg~lit! b
~meV!
133 7592 0 ,0.02 ,5.931026 ,5.731023
195 7652 0 2.1 0.29 ,0.042
1 1.9 0.064 0.055c
2 4.2 ,3.231023
3 5.9 ,9.931025
288 7741 0 0.87 19.0 2.9c
1 0.64 3.60
2 1.24 0.17
3 1.99 ,7.031023
aAssuming 2s1/2, 2p3/2, 1d3/2, and 1 f 7/2 transfer.
bReference @10# unless noted.
cReference @13#.
53 1949CONSTRAINING 26Al1p RESONANCES USING 26Al1~3He,d!27Sicalculated using the same form factors employed in the
DWBA calculations. The resulting resonance strengths for
pure l transfers are also listed in Table II.
V. CONCLUSIONS
Our upper limit for the resonance strength corresponding
to the 7592 keV state in 27Si is at least 200 times weaker than
the limit obtained by Wang et al. @10# under the assumption
that this was a pure single-particle state. On the other hand,
the 7652 keV state is found to be a strong single-particle
state and with a maximum l transfer of 3 ~estimated from
Fig. 6!, it increases the experimental limit on ^sv& at
T9'0.1 by more than two orders of magnitude. This mea-
surement exemplifies the general role of spectroscopic stud-
ies in identifying states that warrant further study through
direct observation of the reaction in question, where com-
plete excitation functions are frequently impossible because
of the low rates involved. In this case, the large spectroscopic
factors found here for the 7652 keV state prompted further
direct (p ,g) measurements described elsewhere @13# whichdid, in fact, observe a resonance at 195 keV in 26Al~p ,g!27Si
having vg55569 meV. The 7741 keV state is also a strong
single-particle state. In this case, (p ,g) measurements had
already been performed @9,13# and the measured resonance
strength falls within the range listed in Table II.
Since we were not able to observe any states below
Ep5195 keV in the 26Al1p system, there are sizable uncer-
tainties in the reaction rate for T9,0.1. Although the 7592
keV state was too weak to be observed in the present mea-
surement, our upper limit on vg is still sufficient for it to be
astrophysically important: A recent theoretical study @20# re-
ported a resonance strength similar to our limit, with a major
contribution to the reaction rate at low temperatures. Further
information on the low-energy states will require a target
with a significantly higher 26Al enrichment.
ACKNOWLEDGMENTS
This work was supported in part by National Science
Foundation Grant No. PHY88-17296 and in part by the U.S.
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Constraining ^(26)Al+p resonances using ^(26)Al(^3He,d)^(27)Si

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