Study evolution of fragment energy spectrum in compound and elemental absorber with thickness via effective charge correction
Rajkumar Santra, V.G.Vamaravalli, Ankur Roy, Balaram Dey, Subinit Roy
aa r X i v : . [ nu c l - e x ] J a n Study evolution of fragment energy spectrum in compound andelemental absorber with thickness via effective charge correction
Rajkumar Santra a , b , V.G.Vamaravalli c , Ankur Roy d Balaram Dey a Subinit Roy a , ∗ , a Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata-700064, India b Homi Bhabha National Institute, Anushaktinagar, Mumbai-400094, India c Department of Physics, Andhra University, Visakhapatnam, India d Department of Physics, Jadavpur University, Kolkata - 700032, India
Abstract
The energy loss behaviour of fission fragments (FF) from
Cf(sf) in thin Mylar ( H C O ) and Aluminium absorberfoils have been revisited. The aim is to investigate the observed change in the well known asymmetric energy ofspontaneous fission of Cf as the fragments pass through increasingly thick absorber foils. Two different typesof absorbers have been used- one elemental and the outher an organic compound. The stopping powers have beendetermined as a function of energy for three fragment mass groups with average masses with < A > = 106.5, 141.8,125.8 corresponding to light, heavy and symmetric fragment of
Cf. Using the effective charge (Z eff ) in the stoppingpower relation in the classical Bohr theory best describes the stopping power data. Spectrum shape parameters,subsequently have been extracted from the energy spectra of fission fragments for different foil thickness. The effectivecharge (Z eff ) correction term determined from the stopping power data is then used in the simulation for the absorberthickness dependence of the shape parameters of the energy spectrum. The present simulation results are comparedwith the TRIM prediction. The trends of the absorber thickness dependence of the spectrum shape parameters, forboth Mylar and Aluminium are well reproduced with the present simulation.
1. Introduction
The energy loss mechanism of heavy charged par-ticles, e.g. the fission fragments, unlike the lightcharged particles, is much more complicated due tothe variation of effective charge of the heavy parti-cles as the velocity of the particles changes in themedium [1]. Also towards the end of the flight path,the energetic heavy particle loses major part of itsenergy in atom-atom collisions. Theories of specificenergy loss of charged particles in matter have beenpresented in seminal works of Bohr [2,3] and Lind-hard, et al. [4].The measurement of specific energy loss of heavyions in different media have also been performed ex- ∗ Corresponding author.
Email address: [email protected] (Subinit Roy). tensively in the past and compared with various the-oretical models [5–10]. Of different heavy projectiles,fragments from asymmetric fission of
Cf nucleusprovides an interesting domain for study of energyloss of heavy charged particles. The decay fragmentsare neutron rich, heavy in nature with velocities inthe range of 0.4 ≤ E/A ≤ Cfundergoes asymmetric fission, one gets two distinctgroups of heavy charged particles for a simultane-ous study of energy loss behaviour in a medium. Ina recent work, Biswas, et al. [11] have observed thatthe shapes of energy or velocity spectra of the twofragment groups change distinctly as the thicknessof absorber medium is increased. In their case theabsorber medium was Mylar, an organic polymer.In the present study, we investigated the distinc-tive change in the energy spectra of the two groups
Preprint submitted to Elsevier 26 January 2021 f fission fragments from
Cf in two different ab-sorber media.We used the organic compound Mylar along withthe elemental Aluminium as the two types of ab-sorber media.Mylar with its covalent bond structure for theelectrons has less number of free electrons comparedto Aluminium, which approaches the ideal metalliccondition of free valence electron gas surroundingthe array of metallic ions. The specific energy loss formost probable light , heavy and symmetric fragmentsin Mylar and Aluminium absorber foils of varyingthickness have been measured.The semi-empirical fit using Bethe-Bloch formulawith dynamic effective charge correction is used todescribe data and the parameters of an enparicalexpression for effective charge, Z eff , have been de-rived. Finally, we provided the explanation for theevolution of shapes of the energy distributions oflight and heavy fragment groups in two different ab-sorber media including the dynamic effective chargecorrection factor in Bethe-Bloch formula.
2. Experimental set-up
The setup consists of a vacuum chamber with asource holder and a detector mount. The absorberfoil can be placed in between the source holder andthe detector mount. The chamber is then evacuatedand maintained at a pressure ∼ − Torr duringthe measurements. An ORTEC Silicon Surface Bar-rier detector (Model No: BU-015-200-100, Serial No:3.3-271D.5) of effective thickness of 100 µ m at an op-erating bias of 50 volt is used in the experiment. Nor-mal electronics setup has been adopted for process-ing the signal.The signal is digitized through NIMbased Dual ADC in MPA3 data acquisition systemfrom FASTCOMTEC and stored in the desktop forsubsequent analysis.2.1. Comparison of FF pulse height spectra inMylar and Aluminium absorbers
In this work we studied the relative change in en-ergy distributions of light and heavy groups of fissionfragments with increasing thickness of the absorberfoil. Two different types of absorbers - organic com-pound Mylar and metallic Aluminum having verysimilar Z A ( ∼ . C oun t s
8 m
Channel (4k/1000)
3 m
1 mNo foil
Fig. 1.
Energy spectrum of fission fragments without foil andwith Mylar foils of different thickness. increased. The nature of evolution of the energy dis-tribution of fission fragments from
Cf with foilthickness is distinctly different for Mylar and Alu-minium. The variation with increasing thickness ofMylar and Aluminium foils are shown in Figs. 1 and2, To further investigate the changing nature, we fit-2 C oun t s Channel (4k/1000)
Fig. 2.
Energy spectrum of fission fragments without foil andwith Aluminium foils of different thickness. ted both heavy and light FF energy spectra by Gaus-sian functions and the ratio of area under the lightand the heavy fragment peaks have been estimated.It is observed that the ratio remains within a rangeof 10% relative to the value obtained without anyfoil. This ensures that while estimating the spec-trum parameters no counts under the peaks havebeen missed. 2.2.
Energy calibration of silicon detector for FF
The suitability of the detector used for FF de-tection is established following the prescriptionof Schmitt and Pleasonton [6,13,14]. The result-ing spectrum shape parameters corroborate nicelywith the expected values of Schmitt and Pleason-ton[6,13,14] that establishing the goodness of thedetector for the energy loss measurements of thefission fragments.In the next step, we used the mass-dependent en-ergy calibration equation from Ref. [15] to obtainthe fragment energy in terms of its mass ( m ) andthe corresponding pulse height ( x ) from the siliconsurface barrier detector. The relation is E ( x, m ) = ( a + a ′ m ) x + b + b ′ m (1)The constants in Eq.1 depend on the spectrumshape parameters and the required expressions aregiven as in Ref. [16] The values of the constants ofmass dependent calibration equation for the presentexperiment have been shown in Table 1. Table 1Estimated values of calibration constants.a a ′ b b ′ − Using calibration Eq. 1 with the constants given inTable 1, the energies of light, heavy and symmetricfragments are estimated. The average mass values ofthe fragments are taken from Ref. [17]. The energyvalues of respective fragments are given in Table 2.The estimated values of the fragment energies, with-out any absorber, compare well with those reportedin the literature. In Table 2, we have also presentedour estimation of pulse height defect (PHD) of eachfragment. The pulse height defect (PHD) has beenevaluated as a difference of expected energy from al-pha calibration and the actual observed energy forrespective fragments. A comparison of the resultantPHD values for the light and heavy fragments areshown in Column 4 of the table. The energy calibra-tion scheme is then followed in subsequent determi-nation of energy loss of fragments in the absorberfoil.3 able 2The energy and PHD values of light, heavy and symmetric FF.System Energy E(x,m) in MeV PHD in MeVFF Light Heavy symmetric Light Heavy symmetricPresent study 102.56 ± ± ± ± ± ± ± ± ±
3. FF energy loss in Mylar and Aluminumabsorbers
It is difficult to measure the energy loss of eachand every FF mass from the energy spectrum. Wemeasured instead the energy loss of most probablecomplimentary light and heavy fragments and thatof the symmetric fragments using the mass depen-dent energy calibration equation of FF for the peaklocations of light , heavy and symmetric fragments fordifferent thicknesses of the absorbers. Energy loss ismeasured as the difference of two energies viz. E foil ,the fragment energy after passing through the se-lected foil and E hole the fragment energy withoutany foil. The specific energy loss is then estimated atan effective particle energy E within the thickness∆ X as∆ E ∆ X ( E ) = E hole − E foil h (2)where h is the thickness of absorbing foil and E isthe effective particle energy. For thin absorber ( h less than ≈ µ m) with ∆ E ≪ E , the approxima-tion E = ( E hole + E foil ) / E ≪ E does not hold, weused a numerical approach with finite foil thicknesscorrection to estimate the effective E following theexpression given in Ref. [18].The estimated stopping power values as functionof incident energy are plotted in Figs. 3 and 4. Theplots are shown for three different average mass val-ues corresponding to the two peaks and the mini-mum in the mass spectrum.3.1. Estimation of uncertainty
In the determination of uncertainty associatedwith the measured specific energy loss, we used thestandard error propagation technique. The uncer-
40 60 80 1005075100 =141.8 =125.8=106.5
E [ MeV ] d E / d x [ M e V / m g / c m ] Fig. 3.
Stopping power data with Mylar foils, for heavy FFwith < A > =141.8 (top panel), light FF with < A > =106.5(middle panel) and symmetric FF with < A > =125.8 (bottompanel). Solid square points with error bar are the present ex-perimental data. Solid black lines show present semi-empir-ical fits and red dashed lines denote calculation with SRIM2013 code. tainty in specific energy loss primarily comes fromthe uncertainties in energy loss ∆ E of the frag-ments in the absorber and in the determination offoil thickness. Taking into consideration all the fac-tors the uncertainty of ∆ E varies from 0.6 to 1.9% and the accuracy of foil thickness is typically in4 =141.8 =106.5 E [ MeV ] d E / d x [ M e V / m g / c m ] =125.8 Fig. 4.
Stopping power data with Aluminium foils, for heavyFF with < A > =141.8 ( top panel), light FF with < A > =106.5(middle panel) and symmetric FF with < A > =125.8 (bottompanel). Solid square points with error bar are the present ex-perimental data. Solid black lines show the present semi-em-pirical fit and red dashed lines give the calculation withSRIM(no effective Z) 2013 code. the range of 10 to 16%. The thickness of each ab-sorber foil is determined separately by the α -energyloss technique, using a 3-line α -source. The over-all uncertainty of the specific energy loss value inthe present measurement is primarily determined bythe uncertainty in the foil thickness and is within10-17%. The error resulting from the use of the av-eraged mass and atomic number instead of the ac-tual values, estimated using the code SRIM 2013,is small compared to the overall uncertainty men-tioned above. Hence this contribution has not beenconsidered. The errors are shown in Figs 3 and 4.
4. Semi-empirical description of FF energyloss
According to classical theory of Bohr [3], elec-tronic stopping power of an ion with charge Z mov-ing with velocity v in a medium consisting of atomshaving charge and mass Z , A , is given as − dEdx = 3 . × Z A Z β ln( m e v I ) (3)in the non-relativistic limit and in the unit of M eV /mgcm − . Here β = v/c , c is the speed oflight. The mean ionization and excitation potential I = I Z with I ≈
10 eV. Now fast moving heavyions, depending on their velocities, can pick upelectrons from or lose electrons into the medium.Thus the effective ionic charge fluctuates around acertain equilibrium value of Z eff [2]. The resultingscreening of Coulomb field of the nuclear chargeaffects the stopping power. The effective charge isexpressed as Z eff = γZ where multiplicative fac-tor γ is the effective charge parameter which has acomplicated dependence on the atomic number Z of absorber foil and the energy or velocity of thefragment moving through the absorber medium.The general semi-empirical form for γ , as suggestedby Bohr, can be written as [22,23]. γ = 1 − a exp( − a vv Z / ) (4)where a and a are constants and v is the Bohrvelocity. We obtained three sets of values for a and a each by fitting the stopping power data in My-lar and in Aluminum foils is shown in Figs 3 and 4for light, heavy and symmetric FF to construct theeffective charge parameter γ . Since Mylar is an or-ganic compound, we used the average value of chargeand mass number for this material ( Z = 4 . A =9 .
09) [17]. The fitted parameters a , a are listed inTable 3. The soild lines in the figures are the fits us-ing the semi-empirical expression. The dashed linesrepresent the prediction of SRIM-2013 without thecorrection for effective Z.It is obvious from Figs 3 and 4 that the requiredcorrection for effective charge is significant in the co-valent organic absorber Mylar compared to metallicAluminium. The difference in reflected in the valuesof parameter a in the exponent of the relation inEq. 4.5 able 3The semi-empirical fitting parameters.Foil FF group a a Reduced χ Light 1.11 3.56 1.28Mylar Heavy 1.15 3.54 2.7Symmetric 1.06 3.13 2.78Light 1.05 5.81 0.57Al Heavy 1.00 3.98 0.74Symmetric 1.04 5.10 1.24
5. Results and Discussion
As mentioned earlier, in the current work, westudied the relative change in energy distributionpatterns of light and heavy groups of fission frag-ments with increasing thickness of the absorber foil.An interesting behavior is observed in the study ofevolution of the energy spectrum of the FF as theabsorber foil thickness is increased. The nature ofevolution of the energy distribution of fission frag-ments from
Cf with foil thickness is distinctlydifferent for Mylar and Aluminum though havingvery similar Z A ≈ .
5. The variation with increasingthickness of Mylar and Aluminum foils are shownin Figs. 5 and 6, respectively. To further investigatethe changing nature, we fitted both heavy and lightFF energy spectra by Gaussian functions and theratio of area under the light and the heavy frag-ment peaks have been estimated. It is observed thatthe ratio remains within a range of 10% relative tothe value obtained without any foil. This ensuresthat while estimating the spectrum parameters nocounts under the peaks have been missed.Three different spectrum shape parameters, viz.,the FWHM values of the fitted energy spectra of twoindividual FF groups and the parameter ∆S thatgives the width of the total energy spectrum esti-mated at the FWTM level, have been used to char-acterize the spectrum. The plots of FWHM and ∆Svs. foil thickness with Mylar and Aluminum foilsare shown in Figs. 5 and 6, respectively. The devia-tion from the TRIM-2013 simulated curve (dashedcarves) at higher foil thickness is clearly visible inthe figures. But semi-empirical description includ-ing dynamic effective charge better reproduce theexperimental features for both the absorber media.Interestingly, the FWHM of heavy fragment peakfalls off much more sharply compared to the TRIMprediction with increasing thickness of Mylar foil,
Mylar F W H M ( i n un i t s o f c hanne l / ) Expt.: Heavy FF Expt.: Light FF TRIM: Heavy FF TRIM: Light FF Eff. charge:Light FF Eff. charge:Heavy FF
Aluminium
Foil Thickness ( m)
Fig. 5.
Variation of FWHM of light- and heavy-fragmentenergy peaks with increasing thickness of absorber foil. while the FWHM of the light fragment peak de-creases slowly and matches with the TRIM predic-tion at larger foil thickness region. In case of Alu-minum absorber, the FWHM-s of light and heavyfragment peaks follow the trend yielded by TRIMsimulation. The parameter ∆S describing the overallwidth of the
Cf fission fragment energy spectrumin Mylar shows a much steeper fall relative to thesimulation data as the foil thickness increases. Onthe other hand in Aluminum medium, both the ex-tracted parameter ∆S and its simulated values showa very similar fall off with increasing foil thickness.
6. Conclusion
The observed behavior of the shape parametersin case of Mylar and Aluminum absorbers led us tolook for the dependence of the dynamical quantity γ , which indicates the evolution of effective Z valueof the particles as they pass through the absorbermedium (or as the velocity of the particles decrease),on the foil thickness. The resultant screening of theCoulomb field of the heavy charged nucleus of theprojectile strongly affects the energy loss behavior.Over the same thickness range, the neutralization ofthe heavy charged projectile is faster in case of or-ganic compound Mylar, although the free electron6ensity is lower in the Mylar medium compare tometallic Aluminum. Also in Mylar the rate of neu-tralization of heavier FF is quicker than the lighterFF. This is not the behavior in elemental Aluminumabsorbers. In Aluminum, the energy loss behaviorsof the two fragment groups are similar except for thisabsorber thicknesses. Thus energy loss mechanism ofheavier fragments is essentially through atom-atomcollision at low velocities in Mylar. Foil thickness ( m)
Expt. TRIM calculation Eff. charge S ( i n c hanne l un i t/ ) Mylar
Aluminium
Fig. 6.
Variation of FWTM or ∆ S of light- and heavy-frag-ments with increasing thickness of absorber foil.
Energy loss behavior of fission fragments in ele-mental Aluminum and in organic compound Mylarhas been investigated. It is observed that the mea-sured stopping cross section data is significantlyhigher compared to SRIM 2013 predictions in lighterorganic medium. The data in case of Al-absorber isquite well reproduced. The variation of the shapeparameters of the spectrum with increasing ab-sorber thickness has been compared with results ofTRIM simulation in SRIM 2013 code system. It isfound that the simulated dependence of the FWHMof energy spectrum, on absorber thickness for heavyFF in lighter absorber over predicts the data as thefoil thickness increases. However, for lighter FF thecalculation does reproduce the data in Mylar. Overprediction is also observed for FWTM data as afunction of foil thickness in Mylar. The data for Al- absorber is well reproduced by TRIM simulation. Itwould be interesting to extend the investigation ofenergy loss of fission fragments in elemental Beryl-lium foils with Z=4 for comparison with organiccompound Mylar having average Z=4.5.
Acknowledgment
We thank Prof. Maitreyee Saha Sarkar, NuclearPhysics Division, Saha Institute of Nuclear Physics,Kolkata for her useful suggestions and constant en-couragement in the work.
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