Rutherford scattering and heavy-ion reaction study

Anushree Ghosh, Nitali Dash, Sudeshna DasGupta, Sumanta Pal & Vivek Singh

INO GRADUATE SCHOOL

1 Introduction:

To probe the properties of the nuclei and predict theirbehavior scattering of nuclei at different energies isdone. Study of nucleon-nucleon scattering above E>Ec opens the channel of nuclear reactions and inelas-tic scattering which provides an insight in the nuclearstructure. In this project, a study of Rutherford scatter-ing and angular distribution for 12C+209Bi below andabove Ec (at lab energies of 48MeV and 66MeV re-spectively) was carried out. While the first conformedto the ideal Rutherford scattering, the later was an-alyzed in the framework of the optical model. TheWood-Saxon potential volume parameters were ex-tracted for the same. At E >Ec apart from the usualelastic scattering, direct reactions and compound nu-clear reactions also take place. This is illustratedhere using 12C+27Al scattering, at 66MeV, where thelight particles produced in the reaction were identi-fied. The quantum effect of identical particle scatter-ing, which has no classical analogy, was also studied.The difference between the identical and distinguish-able particle scattering was illustrated by comparingthe 12C+12C with 13C+12C scattering at projectile en-ergy of 20MeV.

2 Experimental Setup

The beam was taken from 14MV TIFR-BARC Pel-letron accelerator facility at TIFR, Mumbai. The tar-gets used were in the form of self supporting foils. Thetarget and the detector were mounted inside the scat-tering chamber of 1m diameter for measuring the pro-jectile particles under high vacuum of ∼10−5mbar. Aschematic diagram of experimental set up is shown inFigure 1. The incident beam was collimated with a5mm diameter aperture. The detector was mounted ona movable arm inside scattering chamber and the tar-gets were mounted on an adjustable ladder. A 4E-Etelescope detector was used for energy measurementand particle identification. A Silicon surface barrierdetector of thickness 30µm (transmission mount) wasused as a4E detector while the E detector had a thick-

ness of 300µm (back mount). The detector system wascollimated with a 5mm diameter aperture for particleacceptance and was mounted at 21cm distance fromthe target ladder subtending a solid angle of 0.49 mradat the target.

Figure 1: Schematic of experimental setup.

Fast coincidence between4E and E was used to gen-erate an event trigger and energies of both the detec-tors were recorded using a CAMAC based acquisitionsystem (LAMPS). The gain and shaping time of ampli-fiers were adjusted to get the best signal to noise ratio.The CFD threshold were set just above the noise level.Typical counting time of 15-90 minutes were used toget reasonable statistics. Beam current was measuredusing a Faraday Cup. Typical beam current of 20-85nA was used. A schematic diagram of the electronicssetup is shown in Figure 2.

Figure 2: Schematic of electronics setup.

The typical accelerator parameters for a beam arelisted in Table 1.

1

Incident

ParticleCharge State

Voltage

(MV)

Magnetic

Field of

Analyzing

Magnet

(Gauss)

Beam Energy

(MeV)

12C 5+ 8.0 3459 48

12C 5+ 11.0 4059 66

13C 4+ 4.0 2905 20

12C 4+ 4.0 2792 20

Table 1: The typical accelerator beam parameters

3 Rutherford Scattering

The Rutherford scattering on 209Bi target was donewith 12C beam at 48MeV (E <Ec) and 66MeV (E >Ec).The targets were prepared using vacuum evaporationtechnique and the thickness was measured using thick-ness monitor. The thickness was independently mea-sured by the energy loss method with an 241Am α-source to be ≈275µg/cm2. The elastic scattering an-gular measurement was done in the range of θlab= 20o-150o with the angular resolution being about 0.5o. Co-incidence between 4E and E was set up to identifythe charge and mass separated products from 2D spec-trum of4E versus4E + E. The differential scatter-ing cross section, normalized to the Rutherford scat-tering, is shown in Figure 3. For forward scatteringangle and in angular range below and near the bar-rier the statistical error on the normalized cross sec-tion is about 1% while towards backward angles it is3%. The values of σel/σR at different scattering an-gles for Elab= 48MeV shows that below the coulombbarrier the nuclei can only undergo elastic scatteringunder the influence of nuclear force. On the other handfor Elab= 66MeV, σel/σR shows a sharp but continu-ous fall near the grazing angle. Strong nuclear forcesbetween the colliding nuclei causes significant distor-tion in all of the projectile trajectories and they are re-moved from the elastic channels because of nuclearabsorption. The 66MeV data set were fitted within theframework of optical model using FRESCO[1]. In thismodel, the incident particle in its encounter with thetarget nucleus, is acted upon by an average potentialwhich is complex. A volume Woods-Saxon potential

Vr = Uc(r, rc)− V (r) + iW (r) (1)

was used for analysis where V(r)=V0f0 andW(r)=W0f1. The strengths of the real and imaginarypotential are given by V0, W0 and

fi =1

1 + exp( r−Riai

)(2)

where i= 0 or 1. The real part of the potential givesthe elastic scattering while the imaginary part givesthe absorption term of the incident projectile insidethe nucleus. Ri gives the measure of the effectivenuclear potential width and is defined as distance be-tween the centers of the two colliding nuclei while aigives a measure of diffusiveness in the same. The termUc(r, rc) is the coulomb potential between the two nu-clei.

Figure 3: Normalized cross section for 12C+209Bi at 48MeV and

66MeV

The Optical model fit was obtained by minimizing theχ2for the fit by searching all the parameter space ofreal and imaginary potential function. The best fitvalue is shown in Table 2. The broad maxima nearthe grazing angle is due to the constructive interfer-ence between part of the incident particle wave func-tion scattered from the front surface of the nuclear po-tential well and part scattered from the back. Howeverthe data point near the maxima seems anomalous andneeds repeat of the measurement.

V0(MeV) R0(fm) a0(fm) W0(MeV) R1(fm) a1(fm)

81.48±0.91 1.255±0.002 0.444±0.001 22.49±2.76 1.294±0.006 0.290±0.012

Table 2: The optical model parameters for Woods Saxon volume Po-

tential for 12C+209Bi at Elab= 66MeV.

4 Nuclear Reaction

12C beam of Elab= 66MeV was bombarded on 27Altarget to study heavy ion reaction process. The tar-get thickness was 0.965mg/cm2. The4E -E telescopedetector was kept at a lab angle of 30o with respectto the beam. As before, the 2D spectrum of 4E

2

versus 4E + E was used to identify the charge andmass separated reaction products. The 2D spectrumis shown in Figure 4. The particle identification wasdone using the fact that4E ∝Z2

β2 ∼MZ2/Etotal whereEtotal is (4E + E) . The particles identified were14N7, 12C6 ,11B5, 10B5,9Be4,7Be4, 7Li3, 6Li3,4He2.It therefore, shows that for energies E > Ecoulomb theincident trajectories which can cross the barrier aretrapped in the nuclear potential pocket and fuse withthe scatterer to form a single, equilibriated compoundnucleus (CN). This nucleus subsequently decays eitherby evaporation of light particles or emission of inter-mediate mass fragments. The first and second excitedstates of 12C (4.438MeV and 7.654MeV respectively)were identified. The first, second and third excitedstates of 11B (2.124MeV, 4.444MeV and 5.02MeV re-spectively) were also observed.

Figure 4: 4E vs (4E + E) for particle identification

5 Identical Particle Scattering[2]

12C target was bombarded with 20MeV beam of 12Cand 13C respectively. The first is the collision of twoidentical spinless nuclei while the latter is collision be-tween distinguishable particles though the coulomb in-teraction due to charge Ze remain the same in both thecases. The targets were prepared using vacuum evapo-ration technique and the thickness was measured usingthickness monitor. The thickness was independentlymeasured by the energy loss method with an 241Am α-source to be ≈67µg/cm2. The scattering angular mea-surement was done in the range of θlab≈20o- 70o withthe angular resolution of about 0.5o. The normalizedcross section for both 12C+12C and 12C+13C scatter-ing shown in Figure 5. The cross sections are nor-

malized to the forward scattering angle of θlab=21.6o.For 12C+13C scattering Figure 5 shows the total crosssection due to detection of both 12C as well as 13C.Classicaly the differential scattering cross section fordistinguishable particle in central interaction potentialis defined as(

dσ

dΩ

)distinct

= |f (θ) |2 + |f (π − θ) |2 (3)

which is the sum total of the differential scatteringcross section of both the nuclei. 12C+13C clearly val-idates this as the cross section first decreases to aminima around θCM=90oand again increases. How-ever in case of identical particles scattering12C+12C,due to symmetry under the interchange of spatial co-ordinates of two particles, the differential cross sectionnow contains a interference term, which has no classi-cal analogy, and is given by(

dσ

dΩ

)identical

= |f (θ) + f (π − θ) |2 (4)

The interference term peaks at θCM=90o as can beseen from the 12C+12C cross section data. It shouldbe noted that the beam energy of 20MeV is higherthan the coulomb barrier of the respective systems andhence the nuclear forces between the two colliding nu-clei cannot be neglected.

Figure 5: Normalized cross section for 12C+12C and 12C+13C at

Elab= 20MeV.

The reduced elastic cross section above the grazing an-gle θCM≈103o strongly hints at the presence of nu-clear couplings which requires further investigation.

6 Conclusion

Elastic scattering measurements are reported for thesystem 12C+209Bi for energy scale of 48MeV and

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66MeV. The optical model (phenomenological) anal-ysis was done using FRESCO and the fitted values ofoptical model are nearly in agreement with Santra et.al[3]. The fact that nuclear reaction channels open upfor collision above Coulomb barrier was shown using12C+27Al. The interference term for identical particlescattering was clearly established and distinguishedwith the classical scattering of two particles.

7 References

1. FRESCO, I.J.Thompson, Version FRES 2.4, Dec2007

2. Treatise on Heavy-Ion Science, Vol-3, Chapter-3, Page-231, 12C+12C angular distribution andphase shift analysis of the MIT Group.

3. S. santra, P. singh, S. Kailas, A. Chatterjee, A.Navin, A. Shrivastava, A.M. Samant and K. Ma-hata, Phys. Rev. C, 60,034611(1999).

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