A realistic technique for selection of angular momenta from hot nuclei: A case study with 4He + 115In \to 119Sb at E_Lab = 35 MeV
Deepak Pandit, S. Mukhopadhyay, Srijit Bhattacharya, Surajit Pal, A. De, S. R. Banerjee
aa r X i v : . [ nu c l - e x ] S e p A realistic technique for selection of angularmomenta from hot nuclei: A case study with He + In → Sb ∗ at E Lab = 35 MeV
Deepak Pandit a , S. Mukhopadhyay a , Srijit Bhattacharya b ,Surajit Pal a , A. De c , S. R. Banerjee a , ∗ a Variable Energy Cyclotron Centre, 1/AF-Bidhannagar, Kolkata-700064, India b Department of Physics, Darjeeling Government College, Darjeeling-734101, India c Department of Physics, Raniganj Girls’ College, Raniganj - 713358, India
Abstract
A rather new approach employing Monte Carlo GEANT simulation for convertingthe experimentally measured fold distribution to angular momentum distributionhas been described. The technique has been successfully utilized to measure theangular momentum of the compound nucleus formed in the reaction He + In → Sb ∗ at E Lab = 35 MeV. A 50 element gamma multiplicity filter, fabricatedin-house, was used to measure experimentally the required fold distribution. Thepresent method has been compared with the other ones exiting in the literature andrelative merits have been discussed.
Key words:
Multiplicity filter, BaF scintillator, GEANT3 simulation PACS:
The emission of γ -rays from the decay of giant dipole resonance (GDR) in hotand fast rotating nuclei provides a unique tool to study the various kinds ofstructure (triaxial, prolate, oblate, spherical) that the nuclear system can as-sume at high temperature (T) and angular momentum J [1,2,3]. In heavy-ionfusion reaction, the compound nucleus is formed at well defined excitation en-ergy, but with a wide range of angular momenta. The hot compound nucleus ∗ Corresponding author.
Email address: [email protected] (S. R. Banerjee).
Preprint submitted to Elsevier 20 November 2018 oses most of the excitation energy via particle and gamma emissions abovethe yrast line. The remainder of the excitation energy and angular momentumis generally removed by the low energy yrast gamma emission [1]. The GDRparameters depend on both excitation energy and angular momentum and tounderstand the individual contribution of T and J, it is important to separatethe two effects. However, decoupling these two effects is a very difficult experi-mental task, the procedure adopted being the measurement of the high energyphoton spectrum in coincidence with the low energy gamma multiplicity. Aprecise measurement of this γ -multiplicity is very important since the num-ber of γ -rays emitted is directly related to the angular momentum populatedin the system. As per the usual techniques, the multiplicity gamma rays aremeasured with an array of many detectors placed closed to the target hav-ing high efficiency and granularity. The fold (number of multiplicity detectorsfired) distribution is recorded on an event-by-event basis in coincidence withthe high energy gamma rays. Finally, the angular momentum distribution isextracted from this fold distribution in offline analysis. However, there is nostraightforward procedure for mapping the fold distribution to angular mo-mentum distribution and quite a few methods have been adopted in literaturefor converting the folds to J distributions [4,5,6,7].In this paper, we present a rather new technique based on Monte CarloGEANT3 [8] simulation for converting the fold distribution to angular mo-mentum distribution. The approach has been tested for the reaction He + In → Sb ∗ at E Lab = 35 MeV, where the experimental fold distribution wasmeasured with our recently fabricated gamma multiplicity filter. The abovemethod has also been compared with other approaches adopted earlier.
Recently, a 50-element gamma-multiplicity filter made of BaF has been de-signed and developed at the Variable Energy Cyclotron Centre, Kolkata. Thesquare shaped crystals have a cross-section of 3.5 × and 5 cm in length.Standard procedures were followed for the fabrication of the detector from barebarium fluoride crystals [9]. Crystals were cleaned properly and then wrappedwith several layers of white teflon tape, aluminium foil and black electricaltape. Fast, UV sensitive photomultiplier tubes (29mm dia, Phillips XP2978)were coupled with the crystals using a highly viscous UV transmitting opticalgrease (Basylone, η ≈ C oun t s Energy (keV) Cs Na Co Fig. 1. Energy spectra from a single detector for different lab. standard gamma raysources.
Time (ns)
10 15 20 25 30 35 40 C oun t s FWHM = 450 ps16 ns
Fig. 2. Time resolution of an individual detector using Co γ -source. gamma ray sources. Typical experimental energy spectra for an individualdetector is shown in Fig. 1. The observed energy resolution is 7.2% at 1.17MeV. The time resolution between two BaF detectors was measured with the Co source. The source was placed in between two identical detectors, whichwere kept 180 ◦ apart. The energies and their relative times were measuredsimultaneously in event by event mode. The resulting energy gated (1.0-1.4MeV) time spectrum is shown in Fig. 2. The value obtained for time resolutionis 450 ps. 3 LAMBDA Multiplicity Filter Beam Pipe Scattering Chamber Beam Out
Fig. 3. Schematic view of the experimental setup.
The in-beam performance of the multiplicity filter was tested using alpha beamfrom the K-130 AVF cyclotron at VECC. A 1 mg/cm target of In wasbombarded with 35 MeV alpha beam producing
Sb at 36 MeV excitationenergy (L cr =16¯ h ). For the estimation of the angular momentum populated bythe compound nucleus, the 50-element filter was split into two blocks of 25detectors each and was placed on the top and the bottom of the scatteringchamber at a distance of 5 cm from the target center (covering 56% of 4 π )in castle geometry. The detectors of the multiplicity filter were gain matchedand equal threshold was applied to all. Along with the filter, a part of theLAMBDA spectrometer [9] (49 large BaF detectors arranged in 7 ×
7) wasalso used to measure the high energy gamma rays ( > ◦ to the beam direction and at a distance of 50 cm from thetarget. The schematic view of the experimental setup is shown in Fig. 3. Thedetectors of the multiplicity filter in castle geometry were staggered in orderto have equal solid angle for each detector in the array.A level-1 trigger (A) was generated from the multiplicity filter array whenany detector of the top block and any detector from the bottom block fired incoincidence above a threshold of 250 keV. Another trigger (B) was generatedwhen the signal in any of the detector elements of the LAMBDA spectrome-ter crossed a high threshold ( > ≥ Na (511, 12744 hreshold (keV)
200 250 300 350 C r o ss t a l k ( % )
662 keV1170 keV511 keV
Fig. 4. The crosstalk probabilities for three energies at different thresholds of themultiplicity filter. The symbols represent the experimental points while the linescorrespond to GEANT simulation. keV),
Cs (662 keV) and Co (1.17, 1.33 MeV) sources at different discrim-inator thresholds of the filter. The measured crosstalk probabilities are shownin Fig. 4(symbols). It is observed that the scattering probability is more athigher energies and it decreases with increasing the threshold of the multiplic-ity detectors.
In general, the multiplicity distribution method is widely used to convert theexperimentally measured fold distribution into angular momentum distribu-tion [4,5]. In this method, the low energy gamma multiplicity (M) is derivedfrom the measured fold (F) distribution where the M to F response functionof the multiplicity array is measured experimentally. The experimental proce-dure consists of placing a source at the target center emitting 2 gamma rays incascade (e.g Co) and recording the gamma rays in the multiplicity filter. Anexternal detector is used as a trigger, and the events are collected by selectingthe photo-peak of 1.33 MeV gamma rays in it from the Co source, ensuringthat exactly one gamma ray (1.17 MeV) is incident to the filter. With thiscondition, the events consisting of the analog signal proportional to the foldare stored in the list mode. Hence, the collected fold spectrum is the responseof the filter to the γ -ray multiplicity M=1 (at specific energy 1.17 MeV). Theresponse to the multiplicity M=k is generated, in offline analysis, by randomlyselecting k events from the previously stored data in list mode and summingup the amplitudes of the associated individual fold signals. The M distributionis assumed to have a gaussian or a triangular form and the corresponding F-distribution is calculated by folding it with the above response function. Theparameters of the M-distribution are varied until the best fit to the measuredF-distribution is obtained. After getting the full M-distribution, the constraint5 oun t s Fold C oun t s Energy = 511 keVM max = 7.5 d m = 1.4Energy = 1170 keVM max = 5.8 d m = 1.3 Fig. 5. The filled circles represent the experimentally measured fold distribution. Thesolid line represents the fold distribution obtained from the multiplicity distributionmethod while the dotted line corresponds to GEANT simulation.
Multiplicity C oun t s x Fig. 6. The continous line represents the triangular distribution obtained for 1.17MeV response funtion while the dashed line corresponds to the 511 keV responsefunction.
M-distributions are calculated for the different F-windows.In order to test the reliability of the method, the experimentally measured foldwas converted to the multiplicity M using the above formalism. To removethe contribution of non-fusion events, the final experimental fold spectrumwas generated, offline, by gating with high energy gamma rays ( >
10 MeV)[10]. Following the multiplicity distribution method, the response function ofthe multiplicity filter was created for 1.17 MeV using Co. Similarly, theresponse function for 511 keV was created using Na source. The multiplicitydistribution was assumed triangular as follows:- P ( M ) = 2 M + 11 + exp [( M − M max ) /δm ] (1)6here, M max is the maximum of this distribution and δ m is the diffuseness.The multiplicity distribution was folded with the response function to generatethe corresponding fold distribution. The parameters M max and δ m were variedin order to match the experimental fold distribution. The comparison betweenthe experimental fold distribution and those obtained using the multiplicitydistribution method is shown in Fig. 5. Interestingly, the M max and δ m valuesextracted using the two-response functions (for two different energies, 511 keVand 1.17 MeV) are quite different. For 511 keV the values of M max and δ m are7.5 and 1.4 respectively, whereas for 1.17 MeV, the corresponding values are5.8 and 1.3. The difference between the two triangular distributions is clearlyseen in Fig 6. This difference is due to the fact that the scattering probabilityand efficiency of the filter for the two energies is different (Fig 4). Consequently,the constraint M-distributions for different F-windows will be different for thetwo response functions. Moreover, the energy of the multiplicity gamma raysare not constant and depend on the initial and final J of a given transition.Therefore, generating the response function of the multiplicity filter at singleenergy will give incorrect values of average J for corresponding F windowsas both, efficiency and scattering probability, depends on the gamma energy.Ideally, the energy distribution of the emitted multiplicity gamma rays shouldbe measured experimentally and the response function should be created ac-cording to the measured energy distribution. However, calibrating the filterwith different energy is experimentally very difficult as the sources emittingtwo gamma rays in cascade are not available always. Moreover, selecting kevents from different response functions according to the energy distributionof the γ multiplicity will also be a very complicated job. As a result, for gener-ating a realistic response function of the multiplicity filter to incorporate theenergy dependence of efficiency and scattering probability, the only possibleprocedure is a Monte Carlo simulation.Another approach, the recursion method [5], has also been adopted in litera-ture to convert the fold to multiplicity distribution. In this method, the prob-ability P(F,M) of triggering F out of N detectors by a cascade of M γ -rays canbe calculated by using a simple recursive algorithm. The input parameters ofthe recursion are the total efficiency and scattering probability. This methodgives practically identical results as obtained from the multiplicity distributionmethod [5]. The above formalism also suffers from the same problem since theefficiency and the scattering probability depends on the γ energy. In this section, we describe an approach based on Monte Carlo GEANT3 [8]simulation for conversion of the experimental fold distribution to the angularmomentum distribution. In this simulation, the realistic experimental condi-7 nergy (keV) C oun t s Fig. 7. The experimentally measured energy distribution of the γ -multiplicity (sym-bol) fitted with Landau function as used in GEANT simulation. tions (including the detector threshold and trigger condition) are taken intoaccount. The consistency of our simulation was checked by generating the folddistribution for the energies of 1.17 MeV and 511 keV considering the sameparameters for incident gamma multiplicity as used earlier for multiplicity dis-tribution method. Two blocks of 25 detectors arranged in 5 × γ - rays were obtained by creating a randomnumber according to the multiplicity distribution P(M). Low energy gammarays, for each randomly generated multiplicity, were thrown isotropically fromthe target centre and the corresponding fold was recorded for that event. Twohundred thousand such events were triggered to record the final simulatedfold distribution considering single energy of the incident gamma rays (511keV and 1.17 MeV). The fold distribution obtained using GEANT simulationand those obtained from the multiplicity distribution method match quitewell with each other (dotted line in Fig 5). Earlier, the simulated scatteringprobability was also found to be in good agreement with the experimentalobservation (Fig 4).In order to have the correct energy distribution for simulation, the energiesof the gamma multiplicity were measured experimentally. The distribution isshown in Fig. 7 (filled circles). The angular momentum distribution for thisreaction was obtained from the statistical model code CASCADE [11]. Theconversion of the angular momentum distribution to multiplicity distributionis achieved using the relation J = 2M + C, where C is the free parameter whichtakes into account the angular momentum loss due to particle evaporationand emission of statistical γ -rays. The final simulated fold distribution wasgenerated using the multiplicity distribution along with its measured energydistribution. The incident energy distribution was parameterized by a Landau8 old C oun t s M max = 8.0 d m = 1.9 Fig. 8. Experimental fold spectrum (symbols) fitted with GEANT simulation (solidline). function (continous line in Fig. 7) given as L ( E γ ) = n s e − ( p + e − p ) π (2)where p=c · (E γ -b), n=5350, b=320 keV and c=0.0085. The parameters M max and δ m of the multiplicity distribution was obtained from the J-distribution byvarying the free parameter C until the best fit to the measured F-distributionwas achieved. The value of C was obtained as 0.5 and the parameters of theM-distribution were extracted as M max = 8.0 and δ m = 1.9 for best fit. Theextracted value of C seems to be reasonable as the angular momentum lossdue to particle emission will be negligible (since medium mass nuclei is pop-ulated at low excitation energy). Also, the experimental fold distribution wasgenerated by gating with high energy gamma rays ( >
10 MeV), which furtherreduces the average angular momentum loss. The simulated fold distributiongenerated using the above triangular distribution is shown by solid line inFig. 8. Next, the constraint multiplicity distributions for different folds weregenerated. The incident multiplicity distribution (dot-dashed line along withsymbol) and the multiplicity distributions for different fold windows are shownin Fig. 9. The continuous line, the dotted and the dashed lines indicate themultiplicity distributions gating on the events with folds 2, folds 3 and folds ≥ ∼ ultiplicity C oun t s x GEANT Simulation
Fig. 9. The incident multiplicity distribution used in GEANT simulation (symbolsalong with dot-dashed line). The multplicity distributions obtained for differentfolds are also shown in the figure. The solid line represents fold 2, the dotted linerepresents fold 3 and the dashed line, the multiplicity distribution for folds 4 andmore.
Multiplicity C oun t s x Multiplicity Distribution method
Fig. 10. The incident multiplicity distribution used in multiplicity distributionmethod using 511 keV response function(symbols along with dot-dashed line). Thesolid line represents fold 2, the dotted line represents fold 3 and the dashed line, themultiplicity distribution for folds 4 and more. tiplicity γ -rays is less than the single energy (511 keV) used in the multiplicitydistribution method. Thus, it seems to be important that the energy depen-dence of the efficiency and the cross talk probabilities of the filter should betaken into consideration while converting the measured fold distribution intocorresponding angular momentum distribution. An approach based on Monte Carlo GEANT3 simulation has been presentedfor the selection of angular momentum space from the experimentally mea-sured fold distribution. Drawback inherent in the existing approaches has beendiscussed and the present method has been applied to overcome the same. Ex-10 able 1Average angular momentum values corresponding to different folds as obtainedfrom GEANT simulation (present work) and from multiplicity distribution methodcalibrated at two different energies (511 keV & 1.17 MeV).Fold GEANT Simulation Multiplicity Distribution Multiplicity Distribution(511 keV) (1.17 MeV) h J i ¯ h h J i ¯ h h J i ¯ h ± ± ± ± ± ± ± ± ± perimental fold distribution was obtained employing our recently fabricated50-element BaF multiplicity filter in the reaction He + In → Sb ∗ at 35MeV beam energy. The present approach seems to have a significant impor-tance while selecting the angular momentum space properly. References [1] M. N. Harakeh and A. van der Woude, Giant Resonances, Fundamental High-frequency Modes of Nuclear Excitation, Clarendon Press, Oxford, 2001.[2] J.J. Gaardhoje, Ann. Rev. Nucl. Part. Sci. 42 (1992) 483.[3] K. Snover, Ann. Rev. Nucl. Part. Sci. 36 (1986) 545.[4] M. Mattiuzi et al., Nucl. Phys. A 612 (1997) 262.[5] A. Maj et al., Nucl. Phys. A 571 (1994) 185.[6] D.R. Chakrabarty Nucl. Instr. and Meth. 560 (2006) 546.[7] M. Jaaskelainen et al., Nucl. Instr. and Meth. 204 (1983) 385.[8] R. Brun et al., GEANT3, CERN-DD/EE/84-1 (1986).[9] S. Mukhopadhayay et al, Nucl. Instr. and Meth. A 582 603 (2007).[10] Srijit Bhattacharya et al, Phys. Rev. C 77 (2008) 024318.[11] F. Puhlhofer, Nucl. Phys. 280 (1977) 267.[1] M. N. Harakeh and A. van der Woude, Giant Resonances, Fundamental High-frequency Modes of Nuclear Excitation, Clarendon Press, Oxford, 2001.[2] J.J. Gaardhoje, Ann. Rev. Nucl. Part. Sci. 42 (1992) 483.[3] K. Snover, Ann. Rev. Nucl. Part. Sci. 36 (1986) 545.[4] M. Mattiuzi et al., Nucl. Phys. A 612 (1997) 262.[5] A. Maj et al., Nucl. Phys. A 571 (1994) 185.[6] D.R. Chakrabarty Nucl. Instr. and Meth. 560 (2006) 546.[7] M. Jaaskelainen et al., Nucl. Instr. and Meth. 204 (1983) 385.[8] R. Brun et al., GEANT3, CERN-DD/EE/84-1 (1986).[9] S. Mukhopadhayay et al, Nucl. Instr. and Meth. A 582 603 (2007).[10] Srijit Bhattacharya et al, Phys. Rev. C 77 (2008) 024318.[11] F. Puhlhofer, Nucl. Phys. 280 (1977) 267.