Comparative study of the radius of sensitivity of the optical model potentials for $^6$Li+$^{58,64}$Ni and $^{16}$O+$^{58,64}$Ni

0.24 MB·English

by  Mili Biswas

APS/123-QED
A comparative study of the radius of sensitivity of the optical model
potentials for 6Li+58,64Ni and 16O+58,64Ni
∗
Mili Biswas
Saha Institute of Nuclear Physics, 1/AF, Bidhan Nagar, Kolkata-700 064, INDIA
(Dated: February 2, 2008)
8
0 Radii of sensitivity were estimated for the 6Li+58,64Ni system at energies near the Coulomb
0 barrier. Forcomparisonpurposes,suchradiiwerealsoestimatedforstable16Oscatteredfromsame
2 targetisotopes. Theelasticscatteringdatawereanalysedwithfoldedrealpotentialgeneratedfrom
DDM3Ynucleon-nucleoninteractionandanimaginarypotentialofvolumeWoods-Saxonform. The
n most sensitive radii for 16O+58,64Ni system are found to be energy independent and close to the
a
J strong absorption radius. For 6Li projectile, unlike its strongly bound counterpart, the crossing
radius increases with decreasing energy. However, no two crossing situation has been observed for
2 both 6Li+58,64Ni and 16O+58,64Nisystems at thetop of the barrier.

]
x PACSnumbers: 25.60.Bx,24.10.Ht,27.20.+n
e
-
l
c The threshold anomaly is a well known phenomenon
nu olobwsebrvoemdbianrdciansgeeonferhgeiaevs.y-Iitonrefsecrasttteoriangstsryosntgemvasri[a1t]ioant 6Li+58Ni, 12MeV 6Li+58Ni, 18MeV 100
[ 100
of the real interaction potential with incident energies
55v1 ccirnelrogeasacetstoiitonotnghteschtheirnaeCncnrongeuetahllssoimoninfgbttahbhveaeariirsmliaaebamrgi.leiiIntteyaniroseyfrcgplooyonctnadeeloncmettineaaedlirncgw.oyirtTrtheohsteephxoeccnoiinndte--- s/sRuth10-1 Eaaaaxwwwwp====e0000r.....45 66v8838a5555luffffmmmme Expearaaaa.w wwwwv===a==0l000u0...6.e.77889494955555fffmffmmmm 1100--21
3 40 80 120 160 40 80 120 160
nection is through a dispersion relation [2,3] that arises
0 from the causality in heavy ion collision. The disper- 6Li+64Ni, 13MeV 6Li+64Ni, 17MeV
1. sionintegralinvolvestherealandimaginarycomponents Ruth100 100
v:080 tipqnhuovataetensntnttiietgiaeiaedltssi.tnaogtTbtthheheeeegvseeatnrnluoeernargatgyeladcdboaesntpovreaepnnctdtieeoironntncareinaisodrfitauotdsh.ieuevHsapovlouwalalaeutrveeiezrwta,hthtieoihslneee s/s 1100--21 Eaaaaaxwwwwwp=====e00000r......76786 v16611a55555lufffffmmmmme Exapaaaawewwwwr=====. 000v00..a...66778l49u49444e444fffffmmmmm 10-1
i
X question is whether the so-called strong absorption ra- 40 80 120 160 40 80 120 160
dius corroborates with the most sensitive radius or not q c.m. (degrees) q c.m. (degrees)
r
a as the bombarding energy decreases? Roubos, et al., [4]
have recently studied the scattering of 6Li and 16O from
FIG.1: Elasticscatteringangulardistributionsforthesystem
heavymasstarget208Pbto investigatethe radiusofsen- 6Li+58,64Ni
sitivity for these systems. The authors observedthat for
thetightlyboundsystemstheappropriateradiusofeval-
uation of dispersion relation is the strong absorption ra- letron Facility over the energy range 13-26MeV [9]. We
dius but for weakly bound systems that is not the case. havereanalysedtheexistingdataofthesystem6Li+58Ni
It is therefore important to ascertain the radial region [10]. For 16O+58,64Ni system we have used the data of
of sensitivity of the potentials before making use of the Ref.[5,11]. In Fig.1 and Fig.2, the elastic angular distri-
dispersion relation. Work has also been carried out in butions at some of the energies have been shown.
this direction in Refs.[5-8]. In this context we present To investigate the radius of potential sensitivity and
a systematic study of the elastic data of 6Li and 16O its possible variation with incident energy, we have ana-
projectiles on two different isotopes of medium mass Ni lyzed the 12,14,16,18 and 20MeV data of 6Li+58Ni, and
targettodeterminetheradialregionofthepotentialsen- 13,14,17,19 and 26MeV data of 6Li+64Ni. The plots for
sitivity and to identify the difference in observation for crossing point radius at 14,19 and 26MeV for 6Li+64Ni
the weakly and strongly bound nature of the projectile are shown in Fig.3.
as the target mass decreases.
For comparison purpose the same plots at 44 and
The elastic angular distributions of the system 60MeV for 16O+64Ni have been shown in Fig.4. All
6Li+64Ni have been measured in an experiment per- the new and existing elastic scattering data were anal-
formed at TIFR, Mumbai using the BARC-TIFR Pel- ysedconsistentlyintermsoftheopticalmodelpotential.
ThemodelpotentialU (r)inthepresentstudyhasthe
mod
form
2
6Li+64Ni,14MeV
16O+58Ni, 42MeV 16O+58Ni, 60MeV E/EC.b.=1.014
100 100 eV) 1.0
s/sRuth Eaaaaxwwwwp===e=000r0.... .3334v469a1272l7uffffmemmm Eaaaaaaxwwwwwwp======e000000r....... 333444v368316a616611luffffffmmemmmm 10-1 W(r)(M 0.1 aaaaawwwww=====00000.....876672227744444fffffmmmmm
10-1 aw=0.442fm aw=0.486fm
16O+64Ni, 44MeV 16O+64Ni, 60MeV 6LEi+/E64N=i,119.3M7e7V
Ruth100 100 V) C.b.a=0.664fm
s/s 1100--21 Expaaaaaaaewwwwwwwr==.===== 0v000000a.......5554444lu5304538e9499944fffffffmmmmmmm Eaaaaaaaxwwwwwwwp=====e==00000r00....... .455556v685038a0305005l50ufffffffmmemmmmm 10-1 W(r)(Me 1 aaaawwwww====0000....887716614444ffffmmmm
40 80 120 160 30 40 50 60 70 6
qq cc..mm.. ((ddeeggrreeeess)) q c.m. (degrees) 5 6Li+64Ni, 26MeV
4 E/E =1.884
C.b.
V) 3
e
M
F16IOG+.258:,6E4lNasiticscatteringangulardistributionsforthesystem W(r)( 2 aaww==00..761666ffmm
a=0.766fm
w
a=0.816fm
aw=0.866fm
w
1
Vfold(r)isthedoublefoldedpotentialandWv istheimag- 8 9 10 11
R(fm)
inary volume Woods-Saxon potential. The renormaliza-
tionfactorλ simulates the effectof∆V, the realpartof
r
the polarization potential related to the imaginary com- FIG. 3: Crossing radii for the system 6Li+64Ni at different
ponent as energies. Coulomb barrieris13.8MeV inlabframeaccording
to Broglia and Winther[17]
′
P W(r;E )
′
∆V(r;E)= dE (2)
π Z E′−E
good fit to the elastic scattering angular distributions
where P denotes the principal value. shown in Fig.1 with different diffusivities.
The double-folded potentials were calculated with the It was observed that if we varied the diffusivities be-
nickelmassdensitiesobtainedfromRef.[12]and6Liden- yond the range of values shown, the different sets of po-
sity by unfolding the parametrized charge density from tential parameterswouldnot intersect provingthat they
Ref.[13]. Theneutrondensityof6Liwasassumedtohave are no good potentials describing the elastic scattering
thesameshapeastheprotondensity. Densityof16Owas angular distributions properly. The same procedure has
againtakenfromRef.[12]. The M3Ynucleon-nucleonin- beenperformedforthe system16O+58,64Ni. InFig.2,all
teraction in DDM3Y [14,15]conventionwas used for the the calculated angular distributions with different diffu-
calculation that includes an intrinsic energy dependence sivitieshavebeenshown. Thoughtheχ2/Nvaluesofthe
through a multiplicative factor of g(E)=(1-0.002E). fitsvarywithinthe rangeof2χ2 /N,thecorresponding
min
Toobtainthebestfitparametersofthepotentialsanal- fits are quite good. The observed departure at large an-
ysis was started with the highest energy data for all the glesare wellwithin the errorlimit ofthe data. For these
systems. At the highest energy with the model poten- systems the crossing points are close to the strong ab-
tial U (r) we performed an initial search over all the sorptionradius where the various reactions are expected
mod
fourparameters(λr,W0,rw,aw)simultaneously. Subse- to take place. The search code ECIS94 [16] was used to
quently, the imaginary radius parameter obtained from perform the model calculations. The optical model po-
theinitialsearchwaskeptfixed. Thebestfit,determined tential parameters obtained following the above search
by χ2 minimization, was found by searching over the procedure along with the χ2/N (N denotes the number
real renormalization factor and the imaginary strength of data points) values and the reactioncross sections σ
R
while gridding over the imaginary diffuseness a . Same with different diffusivities have been given in TablesI-II.
w
search procedure was adopted for all the incident ener- It is to be noted that with the chosen model poten-
gies. Theradiusparameterwasheldfixedthroughoutas- tial our search procedure will only provide the crossing
suming that the change in the value of r due to change point for the imaginary potential. No crossing will be
w
in incident energy is not so significant. The range of the observed in the real potentials as the shapes and fall-off
diffusivityparameterwasdeterminedbythe conditionof of these potentials are pre-fixed. Therefore, the crossing
similar χ2/N. For the systems 6Li+58,64Ni we have con- pointoftheimaginarypotentialswillbetreatedasthera-
3
TABLE III: Crossing radii with energy for 6Li+64Ni and
aaww==00..458005ffmm 16O+64Ni
aw=0.530fm E(MeV) Radius(fm) for E(MeV) Radius(fm) for
V) aaww==00..555850ffmm 6Li+64Ni 16O+64Ni
Me1.0 aaww==00..663005ffmm 13.0 10.80 44.0 10.10
W(r)( 14.0 10.25 60.0 10.05
16O+64Ni, 60MeV 17.0 9.60
E/EC.b.=1.54 19.0 8.90
0.1 26.0 8.43
10.0 aw=0.434fm
aw=0.449fm
aw=0.459fm
V) aaww==00..540894ffmm that the imaginary crossings are quite distinct and un-
Me1.0 aaww==00..555394ffmm ambiguous for these systems at all the energies studied.
W(r)( 16O+64Ni, 44MeV Agesnetrhaeteismtahgeinraeraylppooltaerniztaiatliotnhprooutgenhtidails,piterissiojunstriefilaedtiotno
E/EC.b.=1.13 use the imaginary crossing radius in the study of radius
0.1 of potential sensitivity.
9 10 11
R(fm) Theobservedphenomenonisthatatnearbarrierener-
gies, the tightly bound projectiles like 16O, in principle,
FIG. 4: Crossing radii for the system 16O+64Ni, EC.b. in probeauniqueradiusofthe potentialdeterminedbythe
lab=38.85MeV [17] crossing point radius, and it is very close to the strong
absorptionradius. The variationofcrossingpointradius
orsensitiveradiuswithincidentenergyisnotsignificant.
Thereforethe evaluationofthe dispersionintegralatthe
TABLE I: Potential parameters for 6Li+64Ni strongabsorptionradiusisquitejustified. Fortheweekly
E(MeV) NR WS Rw aw χ2/point σR(mb) boundprojectiles,thebehaviorisdifferent. Thecrossings
14.0 0.97 87.90 6.753 0.624 4.161 362.73 for 6Li+58,64Ni are located in the vicinity of the strong
0.85 58.52 6.753 0.674 4.065 365.54 absorption radius for higher bombarding energies, but
0.75 41.13 6.753 0.724 4.036 369.59 thevaluesarelargerby∼20%thanthestrongabsorption
0.67 29.95 6.753 0.774 4.063 374.60
radius at lower bombarding energy. Similar observation
0.60 22.71 6.753 0.824 4.155 379.22
for light targets has also been reported by Roubos, et
19.0 0.65 34.93 6.753 0.664 3.236 913.89
al.,[4]. Hence care should be taken while evaluating the
0.58 28.15 6.753 0.714 3.107 932.22
0.51 23.56 6.753 0.764 3.091 953.11 dispersion relation in the investigation of energy depen-
0.44 19.81 6.753 0.814 3.192 972.34 dence of effective potential for loosely bound projectiles.
0.38 17.29 6.753 0.864 3.431 997.94 The crossing radii obtained for 6Li+64Ni and 16O+64Ni
26.0 0.72 32.58 6.753 0.666 0.633 1401.56 are compared in TableIII.
0.67 27.70 6.753 0.716 0.574 1431.90 An interesting aspect of the work in Ref.[4] is the ob-
0.60 24.46 6.753 0.766 0.536 1467.47
servation of two crossing points at below or top of the
0.53 21.87 6.753 0.816 0.522 1504.00 6 208 16 208
barrier energies for Li+ Pb and O+ Pb systems.
0.45 19.31 6.753 0.866 0.522 1535.46
The authors have shown that the one at higher radius
valuecorrespondstonearsidescatteringandtheotherat
lower radius value corresponds to farside scattering. To
TABLE II:Potential parameters for 16O+64Ni identify the crossings associated with nearside and far-
E(MeV) NR WS Rw aw NORM χ2/point σR(mb) side scattering we followed the prescriptions of Ref.[4].
We have performed our analysis in two steps for all the
44.0 1.41 1452.50 6.846 0.434 0.976 1.248 500.95
1.37 1150.60 6.846 0.449 0.976 1.418 504.03 saidfour systems at top of the barrierenergies. First we
1.34 990.78 6.846 0.459 0.976 1.564 505.95 have fitted our elastic angular distributions considering
1.27 694.80 6.846 0.484 0.976 2.031 510.40 the forward angle data only that is, 15o ≤ θc.m. ≤ 125o
1.20 501.50 6.846 0.509 0.976 2.625 515.04 , angles up to the point where the ratio of the angu-
1.14 370.60 6.846 0.534 0.976 3.329 519.43 lar distribution to Rutherford drops to ∼0.5. Next we
1.08 280.27 6.846 0.559 0.976 4.133 523.67 have taken into account only the backward angle data,
60.0 1.26 597.10 6.846 0.480 1.001 4.522 1208.94 more specifically, 123o ≤ θ ≤ 176o, to obtain the
c.m.
1.22 433.30 6.846 0.505 1.001 3.424 1215.79
fit. We did not observe the ”two crossings” situation
1.18 323.30 6.846 0.530 1.001 2.756 1222.59 for both 6Li+58,64Ni and 16O+58,64Ni systems at near
1.15 246.40 6.846 0.555 1.001 2.531 1229.16
barrier energies. In Fig.5 crossings associated with two
1.11 192.35 6.846 0.580 1.001 2.769 1235.80
1.08 152.33 6.846 0.605 1.001 3.490 1242.00 different angular regions of the angular distributions for
1.05 122.99 6.846 0.630 1.001 4.706 1248.57 6Li+58Niand16O+58NiatnearCoulombbarrierenergies
4
10.0 14, 19 and 26MeV have been shown. As the energy goes
6Li+58Ni, 14MeV 16O+58Ni, 42MeV highertheradiusbecomessmallerwithenhancedabsorp-
E/EC.b.=0.992 E/EC.b.=1.045 10.00 tionstrength. Thesameenergydependencehasbeenob-
eV)1.0 (a) (c) 1.00 servedincaseof6Li+58Nisystemtoo. Interestinglythese
M crossing radii are closer to the interaction distances at
W(r)(0.1 aaawww===000...556383333fffmmm aaawww===000...333694722fffmmm 0.10 wThhiicshptohsesirbalytioinσd/iσcaRtuetshtfhoratthuonsleikeenetrhgeiesstdroronpgslytobo9u8n%d.
aaww==00..678333ffmm aaww==00..441472ffmm projectiles where fusion at relatively lower radius domi-
0.01
natestheabsorptionprocessatnearbarrierenergies,the
6Li+58Ni, 14MeV 16O+58Ni, 42MeV absorption for loosely bound projectile like 6Li is domi-
E/E =0.992 E/E =1.045
C.b. C.b. 10.0 nated by reactions at large separation. Breakup at large
1.0 (b) (d)
separationorsingle neutrontransfer leading to unbound
V)
e ejectiles could be possible reaction processes controlling
W(r)(M0.1 aaaaawwwww=====00000.....677888833833333fffffmmmmm aaaaawwwww=====00000.....444454169127727fffffmmmmm 01..10 tsheneInsaitbsivusoimtrypmtaiaornnya,olywnseiasphpaorvfoea1cp6heOirnf+ogr5tm8h,6ee4dNbaairrsaiyensrdt.em6Latii+c5r8a,6d4iNail
8 10 7 8 9 10 11 elasticscatteringdata. Two-crossingeffectatthebarrier
R(fm) R(fm)
has not been observed for any of the four systems
FIG. 5: Crossing points obtained from fits to the forward studied. However, as pointed out by Roubos, et al.[4],
angle data (15o ≤ θc.m. ≤ 125o) [(a)and(c)] and backward to probe the existence of two crossings requires more
angle data (123o ≤ θc.m. ≤ 176o) [(b)and(d)] of the elastic experiments emphasizing the backward angle data with
angular distributions of 6Li+58Niand 16O+58Ni good statistics in the light mass targets.
Acknowledgments
and backward angle data differ slightly but not enough
to identify as two distinct crossings. Possibly the said
decoupling between the nearside and farside scattering The author would like to thank Prof. Subinit Roy for
did not occur at this mass region. hisgeneroushelpandfruitfuldiscussionstocarryoutthis
The energy dependent nature of the crossingpoint ra- work. Inaddition,theauthorgratefullyacknowledgesN.
dius for weakly bound 6Li+58,64Ni systems has been de- Keeleyforprovidingwiththe16O+58,64Nidataintabular
picted in Fig.3 where the crossing radii for 6Li+64Ni at form.
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