Nuclear level density of 69 Zn from gamma gated particle spectrum and its implication on 68 Zn(n, γ ) 69 Zn capture cross-section
Rajkumar Santra, Balaram Dey, Subinit Roy, Md. S. R. Laskard, R. Palit, H. Pai, S. Rajbanshi, Sajad Alia, Saikat Bhattacharjee, F. S. Babrad, Anjali Mukherjeec, S. Jadhavd, Balaji S Naidud, Abraham T. Vazhappillyd, Sanjoy Pald
aa r X i v : . [ nu c l - e x ] M a r Nuclear level density of Zn from gamma gated particle spectrum and its implication on Zn(n, γ ) Zn capture cross section
Rajkumar Santra a , Balaram Dey b , Subinit Roy c, ∗ , Md. S. R. Laskar d , R. Palit d , H. Pai c , S. Rajbanshi e , Sajad Ali a , SaikatBhattacharjee a , F. S. Babra d , Anjali Mukherjee c , S. Jadhav d , Balaji S Naidu d , Abraham T. Vazhappilly d , Sanjoy Pal d a Nuclear Physics Division, Saha Institute of Nuclear Physics, and Homi Bhabha National Institute, Kolkata-700064, India. b Department of Physics, Bankura University, Bankura-722155, India. c Nuclear Physics Division, Saha Institute of Nuclear Physics, Kolkata-700064, India. d Department of Nuclear and Atomic Physics, Tata Institute of Fundamental Research, Mumbai-400005, India. e Deptartment of Physics, Presidency University, Kolkata-700073, India.
Abstract
Evaporated α -spectra have been measured in coincidence with low energy discrete γ -rays from residual nucleus Zn populated inthe reaction Ni( Be, α n) Zn at E ( Be) =
30 MeV producing Ge compound nucleus. Low energy γ -gated α -particle spectra, forthe first time, have been used to extract the nuclear level density (NLD) for the intermediate Zn nucleus in the excitation energyrange of E ≈ Zn matches nicely with the slope determinedfrom RIPL estimates for NLD at low energies and the NLD from neutron resonance data. Extracted inverse NLD parameter (k = A / e a ) has been used to determine the nuclear level density parameter value a at neutron separation energy S n for Zn. Totalcross section of Zn(n, γ ) capture reaction as a function of neutron energy is then estimated employing the derived a ( S n ) in thereaction code TALYS. It is found that the estimated neutron capture cross section agrees well with the available experimental datawithout any normalization. The present result indicates that experimentally derived nuclear level density parameter can constrainthe statistical model description of astrophysical capture cross section and optimize the uncertainties associated with astrophysicalreaction rate. Keywords:
Compound nuclear reaction, nuclear level density, neutron capture cross sectionIn the domain of statistical model description of nuclear re-actions, level density as a function of excitation energy of thenucleus is one of the important quantities. A detailed knowl-edge of nuclear level density (NLD), especially in the regionaround the neutron separation of the nucleus, is crucial to under-stand various nuclear processes like nuclear fission [1], multi-fragmentation [2], spallation reaction [3] and capture reactionsin nuclear astrophysics [4, 5].In nuclear astrophysics, neutron capture reactions in s -and r -processes play a decisive role in the understanding of origin ofelements heavier than iron. The description of neutron capturereactions relies on statistical model calculations to determinethe astrophysical reaction rate. The Hauser-Feshbach model isused to calculate the reaction cross section. The model requiresthe optical model potentials (OMP) for particle transmission co-e ffi cients, nuclear level density (NLD) parameter and gammaray strength function for extraction of γ -ray transmission coef-ficients [6]. The parameters of the model, however, are ratherpoorly constrained. One of the main sources of uncertaintiesin the predicted n -capture reaction comes from lack of experi-mentally determined NLD or due to lack of reliable descriptionof NLD. An accurate description of NLD as a function of exci- ∗ Corresponding author at: Saha Institute of Nuclear Physics, Kolkata, India.
Email address: [email protected] (Subinit Roy) tation energy and angular momentum is, therefore, essential inestimating the relevant reaction cross sections.A number of approaches have been proposed to understandNLD theoretically as well as experimentally. Theoretically, theNLD has been characterized by phenomenological analyticalexpressions [7–9] as well as calculations based on di ff erent mi-croscopic approaches [10–13]. Experimentally, the NLD is es-timated from counting the levels at low excitation energy, fromneutron resonance studies [14], by Oslo technique [15], usingtwo-step cascade method [16], by β -Oslo method [17], from γ -ray calorimetry [18]. These experimental techniques can onlybe used to extract the NLD up to the particle threshold energyand can be extrapolated to higher energies using the functionalform of the Fermi gas (FG) model [7–9]. However, the func-tional form of NLD is not yet satisfactory due to the lack of atrend in experimental data at high excitation energy and spin.Therefore, it is very important to acquire the experimental leveldensity at low as well as high excitation energy E ∗ and spin J us-ing di ff erent techniques. The particle evaporation technique isanother approach to estimate the level density below as well asabove the particle threshold energy [19–23]. The validity of theparticle evaporation technique has been checked in Ref. [19],where it has been shown that particle spectra are most suitablefor NLD studies. It should be mentioned that although the parti-cle evaporation technique is model dependent, it can be used to Preprint submitted to Elsevier March 13, 2020 now the exact trend of experimental NLD as a function of E ∗ with a proper normalization based on the density of known dis-crete levels and the average neutron resonance spacing whichare generally well documented in literature [1, 24]. In addi-tion, the inverse level density parameter ( k = A / e a ), which is animportant ingredient in the functional form of FG model [7],should be measured experimentally as it varies strongly withtemperature (T) and spin (J) [25–27]. The potential problemwith the particle evaporation technique is that multistep and di-rect reactions may contribute. Recently, low-energy light-ionbeams (d, α ) have been used to extract the NLD from a partic-ular channel and the contribution from direct reaction has beenruled out by measuring the particle spectra at backward anglesand the angular distributions of the particles [19–23, 28].A new approach has been adopted for the first time in thepresent study. We have measured the particle evaporation spec-tra gated by low energy γ -rays decaying from states that can bepopulated predominantly through compound nuclear (CN) re-action process eliminating the possible contributions from mul-tistep and direct reactions in the outgoing particle spectra. Theselection of these particular de-excitation γ -rays of residual nu-cleus provides us the scope for extraction of the required NLDfor a particular nucleus after particle evaporation.In this work, γ -gated α -particle spectrum has been used toextract the inverse level density parameter k of FG model andthe NLD in the energy range of E ≈ Zn produced through α n decay channel in the reaction Be + Ni populating the compound nucleus Ge. The obtainedlevel density are normalized to the density of known levels inthe discrete energy region [29]as well as to the level densitiesat the neutron separation energy [30] in order to understand theexact trend of experimental Nods as a function of excitationenergy. Subsequently, the extracted k value has been used as aninput parameter in FF model prescription to calculate the crosssections of Zn(n, γ ) Zn capture reaction.The experiment was performed at NARC-RIFT Pellet LinaFacility in Mumbai, India. A self-supporting ≈
99 % enrichedmetallic Ni target of thickness about 500 µ g / cm thicknessfrom Oak Ridge National Laboratory, USA, was used for thepresent experiment. The target was bombarded by Be beam at30 MeV populating Ge at 41.8 MeV excitation energy. EightCsI(Tl) detectors, each of thickness 3 mm (size 15x15 mm ),were used to detect the outgoing charged particles. Two sets offour detectors each were placed symmetrically about the beamaxis at 5 cm from the target center. The detectors were put onboth sides of the beam line covering an angular region from 22 ◦ to 67 ◦ in the reaction plane. Tantalum absorbers of thickness 30mg / cm were used before the CsI(Tl) detectors to stop the elas-tically scattered particles from entering the detectors. CsI(Tl)detectors were calibrated using Th source. De-exciting γ -rays of residual nuclei were detected using the γ -detector setupconsisting of 14 Compton-suppressed Clover detectors placedat 40 ◦ , 90 ◦ , 140 ◦ , 115 ◦ and 157 ◦ with respect to the beam direc-tion. Data were recorded in list mode in a digital data acquisi-tion system (DDAQ) based on Pixie-16 modules of XIA-LLC,which provided both energy and timing information. Data weresorted using the Multiparameter time stamped based Coinci- E_gamma (keV)100 200 300 400 500 E _a l pha ( a r b i . un i t ) h1Entries 62229Mean x 298.4Mean y 648.4RMS x 138.5RMS y 361.4 h1Entries 62229Mean x 298.4Mean y 648.4RMS x 138.5RMS y 361.4 QDC1lo:E1*0.5 {CUTT}
Figure 1: (Color online) α - γ coincidence matrix extracted from raw particle- γ matrix. The events of interest are bounded by solid red boxes. dence Search program MARCOS [34] to generate the particle-gamma matrix file. Coincidence α - γ events are sorted into amatrix with the α -energy E α versus the γ energy E γ as shown inFig. 1. The projected γ -spectra of E α versus E γ matrix is shownin Fig. 2 and the various transitions of di ff erent α channels havebeen identified.While extracting the NLDs from particle evaporation spec-trum, it is to be ensured that the contributions from non-compound processes are negligibly small. Another necessarycondition for extracting the NLDs in this manner is that theparticle spectrum be from first-chance emission. These are thepre-requisites for the extraction of NLD parameter by particleevaporation technique. To select out purely compound events,the γ -decay (E γ =
332 and 152 keV of Zn) of lowest lyingnegative parity states 6 − and 8 − have been chosen to gate the α -spectrum. It should be mentioned that the level scheme of Zn(as shown in Fig. 3) from the γ - γ coincidence matrix of presentexperiment also conforms the level scheme reported earlier inRef. [35]. The nucleus Zn can be produced directly by α n decay of compound nucleus Ge or by n emission after incom-plete fusion / transfer of He fragment from Be to Ni. Again, Zn can also be produced by direct transfer of α -fragment of Be to the excited states of Zn. The CN decay can populatethe 6 − and 8 − states in Zn residue. Direct α (0 + ) transfer to Ni(0 + ) can not populate these even spin, odd parity states.In case of transfer of heavier He fragment having Q-value of + α from Be will have kinetic energyin the range of 36 to 39.44 MeV within the measured angulardomain of 22 ◦ to 67 ◦ . On the other hand, kinematically the en-ergy of break up α corresponding to incomplete fusion of Hewith Ni target will lie within 8 to 12 MeV. Thus, in the mea-sured γ -gated α -particle energy spectrum, the contributions ofdi ff erent reaction channels, other than the CN process, beyond12 MeV kinetic energy will be negligibly small. The γ -gated α -2
00 150 200 250 300 350 400100200300400500 k e V Zn Cu Zn Ni k e V k e V \ c ( X ) k e V k e V k e V k e V k e V C oun t s E (keV) k e V Figure 2: (Color Online) Projected gamma energy spectrum from Fig. 1. Sym-bol with γ -energy indicate γ -lines of di ff erent residual nuclei associated with α -emitting channels. Gamma energies of Cu [31], Zn [32] and Ni [33]are confirmed from γ − γ coincidence matrix. (8 ) (10 ) (12 ) Figure 3: (Color Online) Partial level scheme of Zn based on its populationin the present experiment. Transitions of interest and states shown in red andblue respectively. Figure 4: (Color online) Filled symbols represent the experimental γ -gated al-pha energy spectra. Lines represent the statistical model calculations with CAS-CADE code. Red continuous line represents spectrum of first chance α decayfrom compound nucleus Ge. Black dashed line represents the contribution of α emission following first step one neutron decay of Ge. energy spectra are shown in the upper and lower panels of Fig.4.The γ -gated alpha energy spectra are converted into the CMframe in order to compare them with the statistical model cal-culations and carried out to investigate the NLDs as a functionof excitation energy. The statistical model calculations (CAS-CADE) [36] have been carried out to fit the 152 and 332 keV γ -gated α spectra. The FG model [7] of nuclear level densityhas been used in CASCADE code and is given by ρ ( E ∗ , J ) = J + θ / √ a exp (2 √ aU ) U (1)where, U = E ∗ − J ( J + θ − S α − ∆ P, E ∗ being the excitation energy ofthe compound nucleus, θ = I ef f h , with I e f f , S α and ∆ P being thee ff ective rigid-body moment of inertia, α separation energy andpairing energy, respectively. Ignatyuk prescription [37] of leveldensity parameter a , which takes into account the shell e ff ectsas a function of excitation energy is adopted and it is expressedas a = ˜ a [1 + δ SU [1 − exp( − γ U )]] (2)where, ˜ a = A / k and k is inverse level density parameter. δ S is ground-state shell correction defined as the di ff erence ofthe experimental and theoretical (liquid drop) masses. γ − = . A / ˜ a is the rate at which the shell e ff ect is damped withthe increase in excitation energy. The optical model potentialparameters for alpha transmission coe ffi cient are taken fromRefs.[38]. The moment of inertia of the CN is taken as I e f f = ( E x ) E x (MeV) NLD from 152 keV- gated -spectrum NLD from 332 keV- gated-spectrum RIPL NLD at S n CT model Zn NLD @ 7.5 MeV Li Zn NLD @ 6 MeV Li Figure 5: (Color online) Nuclear level densities as a function of excitation en-ergy. Histogram represents the NLD taken from RIPL3, filled symbols repre-sent the present extracted NLD from γ -gated alpha spectra, filled square (green)denotes the NLD from neutron resonance data determined at neutron bindingenergy [30]. Data for Zn from present experiment is compared with the NLDof Zn nucleus [23] I (1 + δ J + δ J ), where I ( = MA / r ) is the moment of in-ertia of a spherical nucleus, δ ( = × − ) and δ ( = × − )are the deformability parameters, r is the radius parameter and J is the total spin of the nucleus. The e ff ect of the deforma-bility parameters δ and δ has been checked and found to beinsignificant. The shape of α energy spectra depends mostly onthe level density parameter and partly on the potential parame-ters. The normalized fits from statistical model calculation areshown in Fig.4 in comparison with the data. The solid curve isthe prediction for first chance α evaporation from the compoundnucleus with a subsequent n emission while the dashed line rep-resents the prediction for first chance n evaporation followedby α emission. Same normalization has been used for both thecurves. It is clear from the Fig.4 that ( n α ) decay has insignif-icant contribution compared to ( α n ) decay channel above 12MeV α energy. Thus the value of k has been extracted from thebest-fit statistical model calculations using a χ -minimizationin the energy range of E α ≈ α evaporation spectra also establishesthe fact that the contribution of pre-equilibrium α emission, ifany, in the higher energy region is insignificant and does not af-fect the extraction of inverse density parameter. The extractedvalues of inverse level density parameter ( k = A / ˜ a ) are 9.5 ± ± γ -gated α spectra, respectively.Finally, the experimental level density of residual nucleus hasbeen determined in terms of the measured and calculated yieldsof α emission following the prescription of Refs.[19, 21, 23, 39] ρ exp ( E X ) = ρ fit ( E X ) ( d σ/ dE ) exp ( d σ/ dE ) fit . (3)here, ( d σ/ dE ) exp and ( d σ/ dE ) fit are proportional to the exper-imental and the best-fit theoretical α energy spectra, respec-tively. E X = U − E CM α is the e ff ective excitation energy, where E CM α is the alpha energy in the center-of-mass frame. It shouldbe pointed out that the state with maximum angular momentum ( m b ) E n (MeV) DOVBENKO+74(total) GARG+82(total) TALYS web link(total) TALYS web link(total) TALYS FGM [a
Exp. (s n )=8.62+/- 0.22] TALYS FGM [a adopt (s n )=9.6] TALYS Micro. NLD [Goriely] Figure 6: (Color online) Zn(n, γ ) Zn capture cross-section as function ofneutron energy. Reported experimental data are compared with the resultsobtained from TALYS calculation using the present experimentally measuredlevel density parameter. in the level scheme of Zn is found to be 12 ~ in the presentreaction. Therefore, the angular momentum range of 152 keVand 332 keV γ -gated particle spectra are typically ≈ ~ and ≈ ~ , respectively. Here, the mean angular momenta (J = ± ± ~ for 152 keV and 332 keV γ -gated alphaspectra, respectively) have been considered in the calculationof level density. The level density of Zn residual nucleus asa function of excitation energy is shown in Fig.5. The uncer-tainty in the level density due to statistical model parametershas been checked and found to be ≈ et al. [30] stud-ied the systematic behaviour of nuclear level density parame-ters of 310 nuclei. In their systematic study, they reported thatthe NLDs for even-mass nuclei at neutron separation energy S n are much higher (few orders of magnitude) than their odd-massisotopes. To check this systematic behavior, we have shown inFig. 5 the available NLD data of Zn from Ref. [23] measuredusing neutron evaporation spectrum. The systematic behaviouris clearly seen for Zn isotopes.The importance of this extracted NLD lies in the mea-surement of inverse level density parameter ( k = ˜ a / A ) fromevaporated alpha energy spectra gated by the chosen low en-ergy discrete γ -rays. In addition, the extracted NLD havebeen compared with constant temperature (CT) formula ρ CT = T e ( E − E ) / T . The value of E and T are found to be -4.15 MeVand 1.77 MeV, respectively, which nicely explain the presentextracted NLD as shown in Fig. 5. It should be pointed outhere that the obtained E and T do not corroborate with thesystematic values reported in Ref.[40]. In extracting these pa-rameters the authors probably considered only the RIPL data.The present E and T values are obtained by taking into con-sideration the NLD at neutron separation energy from neutronresonance data [30], the low energy (up to 7 MeV excitation en-4rgy) data of present measurement and the RIPL data [29]. Thevalue of T resulted from CT model fit also corroborates withthe T = = q kUA [41] whereU = E ∗ -E rot - δ P -S α . The CT model fit describes the higher energydata upto 20 MeV within the error bar.Furthermore, the extracted inverse level density parameter k is used to calculate the nuclear level density parameter a at neutron separation energy S n from Eq.2 for Zn. Taking U ( S n ) = S n − ∆ = S n = ∆ = δ S = a ( S n ) = ± Zn(n, γ ) Zn capture cross-section.The Fermi gas modelof NLD [7] has been used in the TALYS code. The neutron cap-ture process is predominantly of E E a ( S n ). So in theTALYS calculation we could constrain both NLD and γ sF withthe use of a ( S n ) from the present maesurement. Global neutronoptical model potential valid over the energy region of 0.001MeV to 200 MeV for the mass range of 24 ≤ A ≤
209 as the neu-tron potential in the statistical model calculation [46]. In thecode, all other parameters are kept fixed except the nuclear leveldensity parameter, wwe have measured the particle evaporationspectra gated by low energy γ -rays decaying from states thatcan only be populated through compound nuclear (CN) reac-tion.hich is taken from the present measurement. Interestingly,it is observed that the reaction cross-sections obtained fromTALYS calculation using the measured NLD parameter explainthe available data quite nicely without any further normaliza-tion, as shown in Fig. 6. The estimation with the systematicvalue of NLD parameter (a( S n ) = γ =
152 and 332 keV) γ -gatedalpha emission spectra from the reaction Be + Ni have beenmeasured. The γ -gated alpha energy spectra is predominantlyfrom the compound nuclear events ensured by the even spin,odd parity (6 − or 8 − ) of the decaying states in Zn, the resid-ual nucleus from α n decay of compound nucleus Ge. Themeasured alpha energy spectra have been compared with thestatistical model calculations to extract the NLD parameter andutilized to extract the level density of Zn nucleus as a functionof excitation energy. The obtained NLD parameter evaluated atneutron separation has been used in TALYS code to calculatethe Zn(n, γ ) Zn capture cross-sections. Excellent agreementwith measured (n, γ ) cross section, does highlight the objec-tive of experimentally constraining the parameters of statisticalmodel for more accurate description of astrophysical reactions. Acknowledgements
Authors thank the BARC-TIFR PLF sta ff for uninterrupted,steady beam during the experiment. We would also like to thankProf. G. Gangopadhyay, Calcutta University and Dr. D. Pan-dit, VECC for their help and advice in this project. Author H.Pai is grateful for the supprot of the Ramanujan Fellowship Re- search Grant under SERB-DST (SB / S2 / RJN-031 / References [1] R. Capote et al., Nucl. Data Sheets 110, 3107 (2009).[2] J.P. Bondorf et al., Nucl. Phys. A 443, 321 (1985).[3] Davide Mancusi, Robert J. Charity and Joseph Cugnon, Phys. Rev. C 82,044610 (2010).[4] T. Rauscher and F. K. Thielemann, At. Data Nucl. Data Tables 75, 1(2000).[5] T. Rauscher, F. K. Thielemann, and K. L. Kratz, Phys.Rev. C 56, 1613(1997).[6] A. V. Voinov, S. M. Grimes, A. C. Larsen, C. R. Brune, M. Guttormsen, T.Massey, A. Schiller, S. Siem, and N. U. H. Syed, Phys. Rev. C , 034613(2008).[7] H. A. Bethe, Phys. Rev. 50, 332 (1936); Rev. Mod. Phys.9, 69 (1937)[8] A. V. Ignatyuk, K.K. Istekov, G.N. Smirenkin, Sov. J. Nucl. Phys. 29, 450(1979).[9] A. Gilbert and A. G. W. Cameron, Can. J. Phys. 43, 1446 (1965).[10] S. Goriely, S. Hilaire, and A. J. Koning, Phys. Rev. C 78, 064307 (2008).[11] S. M. Grimes, Phys. Rev. C 88, 024613 (2013).[12] C. Ozen, Y. Alhassid, and H. Nakada, Phys. Rev. Lett 110, 042502 (2013).[13] N. Quang Hung, N. Dinh Dang and L. T. Quynh Huong, Phys. Rev. Lett118, 022502 (2017).[14] J. R. Huizenga and L. G. Moretto, Ann. Rev. Nucl. Sci. 22 427 (1972).[15] A. Schiller et al., Nucl. Instrum. Methods Phys. Res. A 447, 498 (2000).[16] F. Becvar et al., Phys. Rev. C 46, 1276 (1992).[17] A. Spyrou et al., Phys. Rev. Lett 113, 232502 (2014).[18] J. L. Ullman et al., Phys. Rev. C 87, 044607 (2013).[19] A. V. Voinov et al., Phys. Rev. C 74, 014314 (2006).[20] Balaram Dey et al., Phys. Rev. C 96, 054326 (2017).[21] A. P. D. Ramirez, A. V. Voinov, S. M. Grimes, Y. Byun, C. R. Brune, T. N.Massey, S. Akhtar, S. Dhakal, and C. E. Parker., Phys. Rev. C 92, 014303(2015).[22] Y. Byun, A. P. D. Ramirez, S. M. Grimes, A. V. Voinov, C. R. Brune, andT. N. Massey., Phys. Rev. C 90, 044303 (2014).[23] A. P. D. Ramirez, A. V. Voinov, S. M. Grimes, A. Schiller, C. R. Brune,and T. N. Massey., Phys. Rev. C 88, 064324 (2013).[24] S. F. Mughabghab, Atlas of Neutron Resonances: Resonance Parametersand Thermal Cross Sections Z = // / RIPL-3 / .[30] Till von Egidy and Dorel Bururescu, Phys. Rev. C 72, 044311 (2005).[31] V K Tikku and S K Mukherjee, J. Phys. G: Nucl. Phys., Vol. 1, No. 4,(1975).[32] S. A. Wender and J. A. Cameron, Nuclear Physics A241, 332 (1975).[33] S. Cochavi and W. R. Kane, Phys. Rev. C 6, 1650 (1972).[34] R.Palit, et al., Nucl. Instrum. Methods A 680,90 (2012).[35] G. F. Neal, Z. P. Sawat, F. P. Venezia, P. R. Chagnon, Nucl. Phys. A280,161 (1977).[36] F. Puhlhofer et al. , Nucl. Phys. A , 267 (1976).[37] A. V. Ignatyuk, G. N. Smirenkin, and A. S. Tishin, Sov. J. Nucl. Phys. ,255 (1975).[38] Xin-Wu Su and Yin-Lu Han, International Journal of Modern PhysicsE24,12 1550092 (2015).[39] D. R. Chakrabarty et al. , Phys. Rev. C , 2942 (1995).[40] N. Iwamoto, Journal of Nuclear Science and Technology, 44, 1131 (2007)[41] A.V. Voinov, S.M. Grimes, U. Agvaanluvsan, E. Algin, et al. , Phys. Rev.C , 014314 (2006)[42] https: //