Table Of ContentEquilibrium and pre-equilibrium processes in the 55Mn(6Li,xp) and 57Fe(α,xp)
reactions
A.V. Voinov,1,∗ S.M. Grimes,1 C.R. Brune,1 A. Bu¨rger,2 A. G¨orgen,2
M. Guttormsen,2 A.C. Larsen,2 T.N. Massey,1 S. Siem,2 and C. Kalbach3
1Department of Physics and Astronomy, Ohio University, Athens, OH 45701, USA
2Department of Physics, University of Oslo, N-0316 Oslo, Norway
3Physics Department, Duke University, Durham, NC 27708-0305, USA
Spectra of outgoing neutrons and protons from the 6Li+55Mn reaction and protons from the
α+57Fe reaction have been measured with beams of 15 MeV 6Li ions and 30 MeV α particles.
Thesereactionsproceedthroughthesame61Ninucleusatthesameexcitationenergy,thusallowing
thedifference in reaction mechanism to bestudied. It is shown that spectra from thefirst reaction
1 measured at backward angles are due to emission from a traditional compound nucleus reaction,
1 in which the intermediate nucleus has reached statistical equilibrium; the spectra from the second
0 reaction contain a significant fraction of pre-equilibrium emission at all angles. Level density pa-
2 rameters of the residual nucleus 60Co have been obtained from the first reaction. Both emission
n spectraandangulardistributionshavebeenmeasuredforthesecondreaction. Itwasfoundthatthe
a pre-equilibriumcomponentexhibitsaforward-peaked angular distribution,asexpected,butwith a
◦
J steeper slope than predicted and with an unusual slight rise at angles above 120 . The backward-
angle rise is explained qualitatively by the dominance of the multi-step compound mechanism at
0
2 backward angles.
] PACSnumbers: 21.10.Ma,24.60.Dr,24.60.Gv,25.55.-e
x
e
- I. INTRODUCTION volving a single target-projectile interaction. Some di-
l
c rect reaction mechanisms are inlcuded in common pre-
u
equilibrium models and others are not, nor is their uni-
n Understanding the pre-equilibrium reaction mecha-
versal agreement as to which mechanisms are included
[ nism is one of the most challenging problems in nuclear
in which models. In some applications it is useful to
reactionphysics. Theterm“pre-equilibriummechanism”
1 further divide the pre-equilibrium component into two
refers to the process through which an incoming parti-
v
parts: multi-stepdirect(MSD)andmulti-stepcompound
4 cle’s energy is gradually redistributed among more and
(MSC). Here, however, it is important to recognize that
9 more nuclear degrees of freedom. Energy equilibration
the equilibrium component represents additional MSC
9 can be described as a chain of particle-hole excitations,
3 where the particle and hole degrees of freedom are re- crosssection, eventhoughit is typicallycalculatedusing
. traditionalequilibriummodels. The MSD/MSC division
1 ferred to collectively as excitons. As the exciton number
of the cross section is discussed later in connection with
0 increases, some particle-hole pairs will annihilate, and a
1 state of full steady-state energy equilibrium is reached. the interpretation of the experimental angular distribu-
1 An outgoing particle can be emitted at any stage during tions.
v: the equilibration process, and this is usually referred to Since the whole process is very complicated, there is
i as “pre-equilibrium” emission, whereas particle emission still no unified theory describing all aspects of it within
X
occurring after statistical equilibrium has been achieved the same framework. Instead, there are several ap-
r is referred to either as equilibrium emission or parti- proaches describing each stage separately. For a review
a
cle evaporation. Including the pre-equililbrium mecha- of this topic, see Ref. [1].
nism in calculations helps in interpreting the observed One factor hindering further development of the the-
enhancementsofhighenergyparticleemissioncompared ories is the lack of experimental data, especially double-
to predictions based solely on statistical evaporation at differential cross sections of outgoing particles. Most of
the equilibrium stage. In reality, however, there is no the data are available for forward angles, and detailed
sharpdividingline betweenthe twostages,since equilib- angulardistributions for backwardangles are often lack-
rium is approached very gradually. ing or have poor statistics. As a result, the most devel-
The situation becomes complicated when calculating oped theories are those related to the first stages of the
theenergyandangulardistributionsoftheemittedparti- equilibration process. These have the largest cross sec-
cles. Sometimes, especially in studying the spectroscopy tions and produce strongly asymmetric, forward-peaked
of low-lying energy states in the residual nucleus, it is angulardistributions. Angulardistributionsatbackward
convenient to consider only direct reactions—those in- anglesarestillnotwellunderstoodexceptforpurelyequi-
librium reactions, for which they are symmetric with re-
◦
spect to 90 in the center-of-mass system.
Although the angular distributions (pre-equilibrium
∗Electronicaddress: [email protected] and equilibrium) for nucleon-induced reactions can be
2
reasonablywelldescribedwiththepurelyphenomenolog- which the energy and the particle type were determined
ical Kalbachsystematics [2], there is a reported problem by the energydeposited in 1500µm Si detectorsand the
for α-particle-induced reactions, for which experimental flight time for the 2 m flight paths between the target
angulardependenciesareoftensteeperthanindicatedby and the detector. The measurement was carried out at
◦
the systematics. 157.5 .Theabsolutecrosssectionwasobtainedfromthe
Themoregeneralproblemdirectlyrelatedtothestudy knowntargetthickness,theintegratedbeamcurrent,and
of pre-equilibrium processes is to determine the relative the solid angle of the detectors. The target for all of the
fractionsofpre-equilibriumandequilibriumemissionrep- 55Mn measurements was a 1 µm thick manganese foil
resented in experimental energy spectra. Such a separa- coatedwith a thin (10 nm) carbonfoil. The background
tion is usually model dependent and relies on input pa- caused by the carbon layer has been determined from a
rametersusedintheHauser-Feshbachcompoundnucleus separate experiment on a carbon target and found to be
reactionmodel. The mostuncertainquantityis the level negligible.
density,whichstronglyaffectstheshapeofparticleevap- ◦ ◦
Theneutronspectrumwasmeasuredat125 and140
oration spectra. Therefore, the level density appears to
with the neutron time-of-flight spectrometer of the Ed-
becrucialfortheseparationofexperimentalspectrainto
wards Accelerator Laboratory. The 5 m flight path and
their pre-equilibrium and equilibrium components.
NE-213liquidscintillatorswereusedtodeterminetheen-
In this work we study inclusive proton spectra from
ergy of the outgoing neutrons. Detector efficiencies were
the 55Mn(6Li,xp) and 57Fe(α,xp) reactions experimen-
determined with the calibrated neutron spectrum from
tally. These reactions proceed through the same 61Ni
the27Al(d,n)reactionmeasuredwith7.5MeVdeuterons
intermediate nucleus, and our incident energies are cho-
[4]. Thespectraatthetwoangleswereidenticaltowithin
sen to produce it with very nearly the same excitation
their error bars and were averaged for comparison with
energy. We will show that the spectrum from the first
model calculations.
reactionmeasuredatbackwardangles canbe considered
entirely due to the compound nucleus (or equilibrium
evaporation) mechanism, whereas a large fraction of the
(α,xp)crosssectionisknowntobeduetopre-equilibrium
processes. Therefore, by comparing proton spectra from
these two reactions, the pre-equilibrium fraction in the B. The 57Fe(α,xp) reaction
latter reaction can be obtained in a nearly model inde-
pendentway. Inaddition,theleveldensityoftheresidual
nucleus 60Co can be obtained from the proton evapora- Protonsfromthe 30MeVα-particle-inducedreactions
tion spectrum of the lithium-induced reaction, and our on57Fehavebeenmeasuredwiththe∆E-E techniqueat
understandingofthisreactioncanbeverifiedbysimulta- the cyclotron laboratory of the University of Oslo. The
neouslyreproducingthe(6Li,xn)reactionusingthesame ∆E-Etelescopeconsistedofa200µmthick∆E Sidetec-
model calculations. tor and a 5000 µm thick Si(Li) detector. It was rotated
around the target to measure the angular distributions.
◦ ◦ ◦
Spectra were measured at nine angles: 30 , 45 , 70 ,
◦ ◦ ◦ ◦ ◦ ◦
II. EXPERIMENTS 90 , 104 , 120 , 135 , 150 , and 160 in the laboratory
system. A separate 1500 µm thick silicon detector was
◦
A. The 55Mn(6Li,xp) and 55Mn(6Li,xn) reactions placedat45 to monitor the beamcurrentbymeasuring
elastically scattered α particles. The 1.7 mg/cm2 thick
57Fe target was enriched to 95%.
The inclusive proton and neutron spectra from the
6Li+55Mn reaction have been measured with a 15 MeV In order to obtain absolute cross sections, the angular
6Li beam from the tandem accelerator of the Edwards dependence of the elastically scattered α particles was
AcceleratorLaboratory,atOhioUniversity. Theprotons measuredandscaledtotheresultsofopticalmodelcalcu-
have been registered with a ∆E-E telescope consisting lations. Onlythreedatapointsfromforwardangleswere
two silicon detectors. Their thicknesses were 150 µm usedforthescaling,becauseatbackwardanglesinelastic
for the ∆E detector and 3500 µm for the E detector. α particles populating the first excited level of 57Fe, at
The latter was able to stop protons with energies up to 14.4 keV,might contaminate the elastic-scatteringpeak.
28MeV,whichwassufficienttomeasuretheprotonspec- DifferentopticalmodelparameterstakenfromtheRIPL-
trum up to its maximum energy of around 25 MeV. The 2 compilation [5] were tested. The best parameters were
◦
telescopewasplacedatalaboratoryangleof150 , tore- found to be under number 9401 in the compilation. Fig-
duce or eliminate the contribution from non-equilibrium ure 1 presents the scaled experimental points along with
mechanisms. Because of the stopping power of the ∆E the results of the optical model calculations. The uncer-
detector, only protons with energies above about 7 MeV tainty in this scaling is mostly determined by the aver-
were registered. The low energy portion of the proton age deviation of the scaled experimental points from the
spectrum,withprotonenergiesuptoabout10MeV,was calculated ones, which is about 8% in our case. Uncer-
measured with the charged-particle spectrometer [3], in tainties due to counting statistics do not exceed 1%.
3
4 formula is -0.054. We also tested the functional form
10
experiment of the original Fermi-gas (Bethe) formula [12] (without
3
10 optical model the constant temperature part) and found it to be to-
)
sr 2 tally consistent with the HF-BCS level densities for the
b/ 10 residualnucleipopulatedinthisreaction. Wefoundthat
m
1
( 10 the experimental spectra are best reproduced with the
n
o 0 Gilbert-Cameron formula, which includes the constant-
cti 10 temperature energy dependence at low excitation ener-
e -1
s10 gies. ModelsusingonlytheFermi-gasenergydependence
s
s -2 do not reproduce the shape of the evaporation spectra.
o10
Cr This conclusion is in agreement with our previous re-
-3
10 sults [13] and the results of Ref. [14], where the authors
-4 showedtheimportanceoftheconstant-temperaturelevel
10
20 30 40 50 60 70 80 90 100 density in describing evaporation spectra in the A = 50
to 60 mass range.
Angle,lab system (degree)
We also compared results from the 55Mn(6Li,xp) pro-
. tonspectrumwithinformationfromthe58Fe(3He,xp)re-
action. The latter was measured with a 10 MeV 3He
FIG. 1: The angular dependence of elastically scattered α
beam, also at the Edwards Accelerator Laboratory [3].
particles. Points show the experimental data scaled to the
calculation. Error bars due to counting statistics are less In Fig. 3 we compare the experimental proton spectrum
than the size of the points. The line show the results of cal- fromthe3He-inducedreactionwithHauser-Feshbachcal-
culations with the optical model potential N-9401 from the culations using the same Gilbert-Cameron level densi-
RIPL-2database [5] ties that were used to calculate the spectrum from the
lithium-induced reaction (see Fig. 2). The conclusion is
that the Gilbert-Cameron level density is able to repro-
III. ANALYSIS OF EXPERIMENTAL SPECTRA duce the backward-angleprotonspectra from both reac-
tions.
The experimental proton and neutron spectra from The fact that proton spectra from both reactions are
both reaction systems were converted to the center-of- described with the same input level density function,
masssystemforcomparisonwithcalculations. Theusual even though the excitation energies in the intermedi-
assumptionthatallparticleswereemittedfromthefused ate nucleus were different, indicates the independence of
target+projectile nucleus was made. the proton emission spectra on the type of projectile.
We thereby conclude that at these incident energies, the
dominantreactionmechanismatbackwardanglesinboth
A. The 55Mn(6Li,xp) and 55Mn(6Li,xn) reactions reactions and for all proton emission energies is particle
emissionfromanenergy-equilibratedcompoundnucleus.
Theprotonandneutronspectrafromthe6Li+55Mnre-
action measured at backwardangles have been analyzed
with the empire computer code [6] using the Hauser- B. The 57Fe(α,xp) reaction
Feshbach compound-nucleus-reactionmodel [7] (see Fig.
2). No pre-equilibrium emission was allowed in the cal- Proton spectra from the 57Fe(α,p) reaction were mea-
culations, but sequential equilibrium emission of more sured at each of the nine experimental angles. The re-
thanone particle wasconsidered. Calculations wereper- sults are presented in Fig. 4, and the angle-integrated
formed with two sets of model level densities. One was energy spectrum is shown in Fig. 5. An unusual fea-
theGilbert-Cameroncompositeformula[8],whichusesa ture of the data is the concentration of measurements
constant-temperature dependence at low energies and a at angles in the backward hemisphere with very good
Fermi-gasdependenceathigherexcitationenergies,while statistics (especially at 160 degrees) even at the higher
the other was the microscopic model based on a statis- emissionenergies, where the cross sectionis overtwo or-
tical approach using the HF-BCS model [9]. Parameter ders of magnitude lower than in the evaporation peak.
systematics for the Gilbert-Cameronformula were taken This facilitates the study of the angular distributions at
from Ref. [10]. The Fermi-gas parameter a in the em- backwardangles. ThecalculatedspectrashowninFig.5
pire code is assumed to be energy dependent according were obtained using the talys [15] and empire [6] com-
to the Ignatyuk formula [11], which takes into account putercodes. Whilebothcodesdowellatreproducingthe
shelleffects. Theleveldensityparametersfortheresidual overallenergydistributionoftheemittedparticles,talys
60Co nucleus are as follows: the nuclear temperature T uses the more sophisticated two-component exciton pre-
is1.35MeV,theadjustableenergyshiftE is-3.39MeV, equilibrium model and gives better agreement with the
0
thepairingenergy∆is0.0MeV,theasymptoticparame- data, especially at the highest emission energies. There-
tera˜is7.95MeV−1 andtheparameterγ intheIgnatyuk forewewillusetalyscalculationstofurtheranalyzethe
4
3 3
10 10
2 2
10 10
V V
e 101 e 101
M M
b/ 100 b/ 100
m m
n 10-1 n 10-1
o o
cti 10-2 cti 10-2
e e
s s 10-3 s s 10-3
s -4 s -4
o 10 o 10
r r
C -5 C -5
10 10
-6 -6
10 10
0 5 10 15 20 25 0 5 10 15 20 25
Proton energy, c.m. system (MeV) Neutron energy, c.m. system (MeV)
FIG.2: Protonandneutronevaporationspectrafrom the6Li+55Mnreaction. Thepointsareexperimentaldatatakenat157◦
forthelowerprotonenergiesand150◦ forhigherprotonenergies. Thelinesaretheresultof empirecalculations withGilbert-
Cameron (top curve) and HF-BCS (bottom curve) input level density models. Experimental cross sections are multiplied by
4π sr tocompare with thecalculated, angle-integrated spectrum.
2 proton angular distributions. The small overall excess
10
experiment (25%) in the calculated cross sections relative to the ex-
V) 1 calculation perimentalones is well within the levelofagreementone
e 10 might expect from statistical models using a global in-
M
b/ put set. It can, in part, be explained by inadequacies in
m 100 the level density parameters for the residual nuclei pop-
(
n ulated by the competing proton and neutron emission
o
cti10-1 channels and/or by small contributions from direct pro-
e cesses not taken into account in the model calculations.
s
s Emission from the equilibrated compound nucleus was
s -2
o10 calculatedwiththeinputleveldensityobtainedfromthe
r
C 55Mn(6Li,xp) reaction, which thus forms a useful com-
-3 plement to the 57Fe(α,xp) reaction.
10
2 4 6 8 10 12 14 16 18
The angular distributions for several energy bins of
Proton energy, c.m. system (MeV) outgoing protons are presented in Fig. 6, along with
the results of talys calculations. These calculations as-
FIG.3: Theprotonevaporationspectrumfromthe3He+58Fe sume that the equilibrium component, calculated with
◦
reaction. Thepointsshowthe157 datafromRef.[3]normal- the Hauser-Feshbach-model part of the code, is emitted
izedto4πsr,andthelineshowstheangle-integratedresultsof isotropically. Thisisoftenagoodapproximation,butthe
empire calculations using the Gilbert-Cameron level density emission is better described as being symmetric about
model with theparameters from Ref. [10]. ◦
90 in the center-of-mass system, typically with a small
dip or minimum at that angle. For the pre-equilibrium
5
101 101
7-8 MeV
x0.5 r)
0 s
10 x0.25 b/
V/sr) -1 xx00..1055 on (m 100 15-17 MeV
Me10 cti
e
mb/ s s10-1 19-21 MeV
on (10-2 Cros
cti
e
s s10-3 10-2
s 0 20 40 60 80 100 120 140 160 180
o
r
C Angle,c.m. system (degree)
-4
10
FIG. 6: Angular distribution of outgoing protons from dif-
ferent energy intervals. The points show the experimental
10-5 results from the 57Fe(α,xp) reaction, and the lines are from
5 10 15 20 25 thecalculations with thecode talys.
Proton energy, c.m. system (MeV)
FIG. 4: Proton experimental spectra from the α+57Fe reac- thatevaporationfromthecompoundnucleusisthedom-
inant reaction mechanism. Because of the assumption
tionmeasuredatlaboratoryanglesof30,45,70,90,104,120,
135,150,and160degrees(fromtoptothebottom). Thefour of isotropic emission for the equilibrium component, the
◦
backward-angle spectra are scaled down for better visualiza- calculationsshowmuchlessofadiparound90 thanthe
tion. databutotherwisegivereasonableagreementwiththem.
For more energetic protons, the equilibrium component
decreases rapidly in intensity, and the angular distribu-
4
10
tions exhibit the forward-peaked behavior characteristic
Experiment
V) 103 Empire pre-equilibrium ofpre-equilibriumprocesses. Theseangulardistributions
Me 102 Talys pre-equilibrium are not well reproduced by the talys results, which are
mb/ 101 Empire compound mthuecflhalteossrfsolirgwhatlryd-inpceraekaesdintghacrnotshsesedcatitoanaantdafnagilletsoasbhoovwe
n ( 0 120◦.
o 10
cti -1 To better understand this discrepancy between exper-
e10 iment and the Kalbach angular-distribution systematics
s
ss 10-2 used in the model calculation, it is useful to try to di-
o vide the measured cross section into its equilibrium and
Cr10-3 pre-equilibrium components. Fortunately, this is possi-
10-4 blebecausetheequilibriumcomponentcanbecalculated
0 5 10 15 20 25 30 based on the data from the 55Mn(7Li,xp) reaction. Fig-
◦
ure 7 compares the experimental 160 proton spectrum
Proton energy, c.m. system (MeV)
withtheequilibriumcomponentcalculatedbytalys. By
subtracting the equilibrium component from the experi-
FIG. 5: The angle-integrated proton spectrum from the
α+57Fe reaction. The points show the experimental data, mentalspectraateachangle,thedouble-differentialcross
while the lines are the results of calulations using the em- sections and thus the angular distribution of the experi-
pire and talys codes. The curves labeled “pre-equilibrium” mental pre-equilibrium cross section can be determined.
also includecontributionsfrom theequilibrium orcompound The calculated evaporation component was normalized
component. downward by about 20% to reproduce the data at low
emission energies before doing the subtraction. Figure
8 shows the angular distribution of the resulting pre-
component, talys uses the phenomenological Kalbach equilibrium component from the 57Fe(α,xp) reaction in-
angular-distribution systematics [2]. These systematics tegratedoveremissionenergiesfrom16to25MeV,where
arebasedonexperimentalresultsforawidevarietyofre- pre-equilibrium emission is dominant and the subtrac-
actionchannels. Figure 6 shows that for low-energyout- tion is most accurate. If the pre-equilibrium component
goingprotons,theexperimentalangulardistributionsare werepure MSD,asisassumedinthe modelcalculations,
flat,andtheir near-symmetryabout90degreesindicates thenthisangulardistributionshouldcontinuetodecrease
6
2 1
10 10
experiment
sr) 101 calculation
V/ r)
b/Me1100-10 (mb/s 100
m n
on (10-2 ctio
ecti10-3 s se10-1
s -4 s
s 10 o
os -5 Cr
r10
C
-6 -2
10 10
0 5 10 15 20 25 30 0 20 40 60 80 100 120 140 160 180
Proton energy, c.m. system (MeV) Angle,c.m. system (degree)
FIG. 7: Energy spectrum of outgoing protons from the FIG.8: Experimentalangulardistributionofpre-equilibrium
57Fe(α,xp) reaction measured at a laboratory angle of 1600. outgoingprotonswithenergiesgreaterthan16MeVfromthe
The points show the data, and the line is the compound nu- 57Fe(α,p) reaction.
cleus reaction component calculated in thetalys code.
◦
sequent particle emission is symmetric about 90 in the
◦
withincreasingangle. Insteaditisagainflatabove120 , center-of-mass and contains exponentials in both cosθ
with a small increase at 160◦. The observed cross sec- and −cosθ. The MSC cross section is composed of the
tion at backward angles therefore implies that the pre- rest of the pre-equilibrium component plus the equilib-
equilibrium component is not pure MSD but contains rium cross section. Thus, the systematics, when applied
significant MSC pre-equilibrium cross section. This pre- to equilibrium emision, avoidthe assumption of isotropy
equilibrium MSC cross section, because its angular dis- used in talys and empire for that component.
◦
tribution is symmetric about 90 , produces the observed The angular distribution of the double-differential
rise in cross section at large angles in the figure. In this cross section has the form
regard, it is interesting to note that the data from Ref.
[f1o6r]osuhtogwoeindgapsriomtoilnasribnactkhwea5r6dF-ea(nαg,xlepr)isreeainctciornosastseacntiionn- ddΩ2dσǫb = 41π ddǫσb eaang −1e−aang (cid:2)(1+fmsd)eaangcosθ
cident energy of 23 MeV. All of this points to the need + (1−fmsd)e−aangcosθ(cid:3) (1)
toreexaminetheangulardistributionsystematicsforthe
(α,xp)reactionchannel,recognizingthatsomeofthepre- where ǫb is the channel energy for the exit channel in
equilibriumcrosssectionwillbe multi-stepcompoundin thereaction,f isthefractionofthecrosssectionthat
msd
nature. is MSD, and a is the angular distribution “slope pa-
ang
rameter,” used for both the forward-peaked MSD and
symmetric MSC components. A slope parameter of
IV. IMPLICATIONS FOR THE KALBACH zero would yield an isotropic angular distribution. The
SYSTEMATICS Kalbachsystematicsdefinetheslopeparameterasafunc-
tionofthe energiesofthe incidentandemittedparticles,
The Kalbach angular distribution systematics [2] uti- and its values have been set phenomenologically, based
lize the division of the cross section into its multi-step on comparisons with a broad database.
direct (MSD) and multi-step compound (MSC) parts. Inthe laterstagesofdevelopingthese systematicsand
Multi-step direct emission is defined as particle emission in their implementation in talys, it was assumed that
that occurs when the equilibrating nucleus has passed thepre-equilibriumcomponentispurelyMSD.Thecom-
throughasequenceofstatesallofwhichhaveatleastone parison of experimental angular distributions with the
particle-degree-of-freedom in an unbound single-particle systematicsat16and20MeV(seeFig.6),however,sug-
state [17]. It is made up of the direct and much of the gests that this assumption was inadequate and that the
pre-equilibrium cross section, and it exhibits a forward- systematics need to be revisedto be able to describe the
peaked angular distribution described by an exponential data, especially at the higher emission energies where
incosθ. Oncethesystempassesthroughatleastonecon- neither the amount of forward peaking nor the rise at
figuration in which all of the particle degrees-of-freedom backwardangles is reproduced.
are in bound single-particle states, “memory” of the di- Toquantifytheproblem,theexperimentalangulardis-
rection of motion of the projectile is assumed to be lost tributions from Fig. 6 were fit using Eq. (1) while vary-
andthemechanismistermedmulti-stepcompound. Sub- ing the parameters dσ/dǫ, f , and a . The results,
msd ang
7
shown in Fig. 9, demonstrate that the general form of
TABLE I: Comparison of parameters from fitting the exper-
the equation successfully reproduces the data. However
imental angular distributions with the parameters used in
the fitting process yields parameter values, summarized talys.
inTableI,whicharequite differentfromthe valuesfrom
Ref. [2] used in talys. As expected, the slope parame- Proton aang aang sys/fit fpre fmsd
ters at 16 and 20 MeV are much larger than indicated energy (sys.) (fit) (calc.) (fit)
by the Kalbach systematics. In addition, the values for 7.5 MeV 0.62 0.67(7) 1.1 0.05 0.18(3)
fmsd at these energies are lower than fpre, the fraction 16 MeV 0.98 2.10(8) 2.1 0.90 0.84(1)
of the cross section due to pre-equilibrium emission, ob- 20 MeV 1.15 2.75(9) 2.4 0.99 0.935(6)
tained from talys. This confirms that there is likely to
be an MSC contribution to the pre-equilibrium compo-
nent. Thefittedcurvesshowthatevenasmallamountof
proton particle-degrees-of-freedom are in single particle
MSCcrosssection(6%to7%at20MeV)cancauseasig- statesbelow theprotonbindingenergyandthatonesuch
nificantriseinthecrosssectionatbackwardangleswhen
degreeoffreedomthengetspromotedtoasingleparticle
a large slope parameter causes the main, MSD part of state 20 MeV above the proton binding energy, through
the angular distribution to fall off rapidly with increas-
one or more two-body interactions. This kind of MSC
ing angle. The existence of multi-step compound pre-
pre-equilibrium emission is clearly possible, because we
equilibrium emission is known, but for nucleon-induced
see equilibrium evaporation of such energetic particles,
reactions it is most often concentrated in the region of
but detailed calculations in a single, unified framework
the evaporation peak [18]. The enhanced MSC emission
will be needed to see if pre-equilibrium MSC emission
forhighenergyprotonsfromα-inducedreactionsisanew
can account for as much cross section as is indicated by
result which needs to be understood.
fits to the data.
The probable presence of MSC pre-equilibrium cross
section at such high emission energies (relative to the
spectral endpoint) suggests that too much weight was
giventobackward-angledata(frequentlywithsmallcross
sections and large error bars) in determining the slope
parameters in the Kalbach systematics for α-particle-
induced reactions, because that analysis assumed that
pre-equilibrium particle emission was pure MSD. For
α-particle induced reactions, the observed excess of
forward-angleexperimentalcrosssectionthatwasnotre-
produced by the resulting systematics was found in Ref.
[2] to be qualitatively consistent with the observation of
projectile-breakup fragments traveling with roughly the
projectile velocity. However, a new preliminary model
oflight-projectilebreakup[19]suggeststhatthebreakup
peaks should be less intense and have a narrowerenergy
distributionthantheexcesscrosssectionobservedinRef.
[2]. This is again consistent with the need to reconsider
the systematics for α-particle-induced reactions, putting
moreweightonintermediateandforwardanglesandless
on the very backward angles.
FIG.9: Comparisonbetweentheexperimentalangulardistri-
butions for the 57Fe(α,xp) reaction and the curves obtained VI. CONCLUSION
by fitting using Eq. (1). The results are displayed as a func-
tion of cosθ in order to show the exponential fall off of the The proton spectra from both the 55Mn(6Li,xp) and
cross section at forward angles at 16 and 20 MeV.
57Fe(α,xn) reactions have been measured and com-
paredwithcalculationsperformedusingthe excitonpre-
equilibrium model and a Hauser-Feshbach evaporation
model.
V. DISCUSSION The backward-angle spectrum from the first reaction
allows the level density parameters and the equilibrium
Physically, the results of the fitting process imply, for componentto be well determined, because the measured
instance, that for 6% to 7% of the pre-equilibrium cross cross section appears to be almost exclusively due to
section for 20 MeV proton emission, the system has particleevaporationfromanenergy-equilibratedsystem.
passed through one or more configurations where all the Here it is found that the Gilbert-Cameron level density
8
model with the input parametersof Ref. [10] works well. equilibrium component at these energies than one might
This was confirmed by comparisons with earlier results na¨ıvely expect, especially given the predicted predomi-
on the 58Fe(3He,xp)60Co reaction at 10 MeV. nance of direct nucleon-transfer (stripping) reactions at
Theangulardistributionsfromthe57Fe(α,xp)reaction proton energies of 16 and 20 MeV. This observation can
show two important effects. First, for emission energies helpguideare-evaluationoftheangulardistributionsys-
abovethemainevaporationpeak,theexperimentalcross tematics for incident α particles.
section exhibits a significantly more rapid decrease with
increasing angle than the calculated curves. This sug-
gests that the Kalbach systematics for the (α,xp) chan-
nelandperhapsforallreactionswithincidentα-particles
VII. ACKNOWLEDGMENTS
needtoberevised. Second,theexcellentdatastatisticsin
◦
the backward-anglespectra (in particular the 160 spec-
trum) show a distinct flattening of the angular distri- We greatly acknowledge the help of D. Jacobs, D.
butions and even a small rise in cross section at angles Carter,J.O’Donnellforrunningthe Edwardsaccelerator
◦
above 120 for the higher emission energies. Using the and for the computer and electronics support. We are
level-density parameters determined from the (6Li,xp) also very grateful to E.A. Olsen and A. Semchenkov for
reaction, it is shown that most of the cross section in running the Oslo Cyclotron. Financial support from the
thisdomainisnotduetoequilibriumevaporationofpro- ResearchCouncilofNorwayandU.S.DepartmentofEn-
tons,sotherearepre-equilibriumprocessesthatexhibita ergy grants numbers DE-FG52-06NA26187, DE-FG02-
backward rise in cross section. This suggests that there 88ER40387, and DE-FG02-97ER41033 (Duke Univer-
is more multi-step compound cross section in the pre- sity, for C.K.) is greatly appreciated.
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