Energy Dependence of Exotic Nuclei Production Cross Sections by Photonuclear Reaction in the GDR Range

Home , Photofission

arXiv:1511.08149v1 [nucl-th] 24 Nov 2015 rs eto tGReeg for energy photofission GDR the at Although section 7]. cross [6, in photons fission directly induces bremsstrahlung or which generating [5] converter itself, (W) (U) target tungsten the a of in electrons (GDR). down incident resonance slowed dipole cover- of giant photons beam the energetic electron of The peak produce energetic entire to the of tool ing use promising the a is method, photofission the ex- found is important. where neutron-rich, actinides, tremely primarily of are fission fragments induced neu- mass [4] fission [1–3], of proton photon study and energy the [1] low context tron in this distribution In nuclei charge stability, studied. and be of to dynam- valley need and the ics structure from different away characteristically still far having are there However, e.g. decades. areas, several for studied been 8,weeasprodcigeeto IA ilpro- will LINAC electron superconducting construction a under where is IsotopE energetic [8], TRIUMF Rare Advanced at produce The (ARIEL) to range. 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(GDR) resonance dipole giant entire hhdMtniiHzaGv.Dge olg o oe,Taml Women, for College Degree Govt. Hazra Matangini Shahid htfiso fatndsi tde ntergo fnuclear of region the in studied is actinides of Photofission .INTRODUCTION I. § ∗ et fPyis nvriyo ahi,Hzabl Srinag Hazratbal, Kashmir, of University Physics, of Dept. aibeEeg ylto ete /FBda aa,Kolka Nagar, Bidhan 1/AF Centre, Cyclotron Energy Variable htncerratos htfiso;Ncerfissility; Nuclear Photofission; reactions; Photonuclear : 1 ∗ .A Khan A. F. , 238 ∼ saota order an about is U 05 e a be can MeV 10-50 238 htfiso.Teitgae il of yield integrated The photofission. U 2 §∗ Dtd uy2,2021) 26, July (Dated: eai Atta Debasis , nGRrange GDR in il ue2 e 0 Weba o htfiso (10 photofission for e-beam kW 100 MeV 25 duce oerahsa iha 2-3 as the high at as events reaches temperature explosive core the where during neu- explosions as Supernovae high like (such very environment, a flux in However, cap- tron neutron processes. rapid (r-process) and ture (s-process) capture neutron slow cen- photofission this for at accelerator up [11]. primary coming as be e-LINAC with will ter Beams) facility Isotope Unstable Rare a for and development, facility 20 National RIB (Advanced present MeV, ANURIB called the 25 of using extension by ALTO,an [10] at and Orsay [9] around IPN, Dubna of JINR, at phase.Yields achieved first perimentally the in 10 Uranium of sion/s) att siaetepouto rs eto fnrc nu- n-rich through of impor- produced section therefore, cross clei is is production the It question estimate the to key path. alter tant and A nuclei rates exotic reaction detail. of r-process properties in unusual region the this whether one study RIB to has Using hopes path experimentally. reaction inaccessible short-lived r-process been predicted through mostly The synthesis element nuclei. heavy exotic in role cial acltos h xsec fcnrbtosfo various quantitative from Without contributions of existence energies. the accelerator in calculations, two performed at was mass fragments [16] the photofission to of modes fission distribution various from contributions for the peak GDR the 9.09 of energies 11.5 of ener- excitation the of of region gies symmetric the by in the induced photofission photons of of bremsstrahlung behavior 13] [12, the modes of asymmetric and comparison a and ysis in reached be can path r-process laboratory. the the in nuclei many how 3 eto ihnce r eeal rdcdb both by produced generally are nuclei rich Neutron ntepeetwr,w efr iutnosanal- simultaneous a perform we work, present the In 11 25.Rm †∗ .N Basu N. D. , sinso rnu ypoosinhv enex- been have photofission by Uranium of fission/s e n t oei rdcn uliand nuclei producing in role its and ted − tbestaln nrisfo 11.5 from energies bremsstrahlung nt uin of butions 77MVwihcrepn oaeaephoton average to correspond which MeV 67.7 neeg f13.7 of energy on xiaineege htcvr the covers that energies excitation 238 D;Eoi nuclei. Exotic GDR; k etBna 2 4,India 649, 721 Bengal West uk, tteedon rmsrhugenergy bremsstrahlung endpoint the at U 0 e o1.0MV Among MeV. 15.90 to MeV .09 − r1006 ni and India 006, 190 ar 59 e 1 4 5 hc includes which 15] 14, [1, MeV 15.90 238 4 ∗ 238 sb htfiso reaction photofission by ns a7004 India 064, 700 ta 238 htfiso fragments photofission U n lkChakrabarti Alok and htfiso.Acluainof calculation A photofission. U 238 htfiso swell as photofission U htfiso n investigate and photofission U × ± 10 . e which MeV 0.3 9 o )rpoespa cru- a play r-process K) µ -em As e-beam. A 5 ∗ ∗ 13 fis- 2

500 Γi for i = 1, 2 extracted by fitting experimental data Hydrodynamic theory [20, 21] are provided in Ref.[22] for both photoabsorp- Talys calculation tion as well as photofission cross sections. It was found 400 Ratio method that for photoabsorption and photofission cross sections there are little changes in parameters Ei and Γi while σi decides the difference. Therefore, we find by fitting data of all the eight actinide nuclei that ratios R = (σ1)f and 300 1 (σ1)a

(mb) (σ2)f P σ R = for gamma absorption and subsequent fission h 2 (σ2) o a t o a scale as b s o 200 r p t i o n n io 2 s s Ri=1,2 = a2if + a1if + a0i (2) fi to o h 100 P where the fissility f = Z2/A with Z, A being the charge, mass numbers of the target nucleus. The scaling parameters obtained are a01 = 118.5486, a11 = −6.9389, 0 a21 = 0.1015, a02 = 175.5418, a12 = −10.2748 and 5 10 15 20 Eγ (MeV) a22 = 0.1504. In Fig.1, the measured photoabsorption and photofission cross sections (grey circles) for 238U as functions of incident photon energy are compared with FIG. 1: Comparison of the measured photoabsorption and photofission cross sections (grey circles) [20] for 238U as func- the predictions (solid lines) of the hydrodynamic theory tions of incident photon energy with predictions (solid lines) of photonuclear reactions for the giant dipole resonance of the hydrodynamic theory of photonuclear reactions for region that consists of Lorentz line shapes for spherical the giant dipole resonance region that consists of Lorentz nuclei. The dotted line represents photofission cross sec- line shapes for spherical nuclei. The dotted line represents tions obtained by using ratio method described above photofission cross sections obtained by using ratio method while the dashed line represents the calculations of the while the dashed line represents the calculations of the TALYS TALYS code [23] for the same. It is apparent from Fig.1 code for the same. that the Lorentz line shape fitting is quite accurate which reflects the fact that the uncertainties in the parameters [22] are quite small. The ratio method predictions for fission modes was highlighted in [17]. The results ob- photofission are almost as good upto the first GDR peak tained in this way are compared with the predictions of whereas it is off by about ten percent near the second the multimode-fission model for the dependence of in- GDR peak, but still provides much better predictions dividual fission modes on the excitation energy of the than that calculated by the TALYS code which under- fissioning nucleus. The integrated yield of 238U photofis- estimates as well as fails to reproduce the shape, or by sion and charge distribution of photofission products are the evaporation-fission process of the compound nucleus calculated. The role of photofission mass yield and its which although retains more or less the shape of the curve charge distribution in the production of neutron-rich nu- but overestimates [24] the photofission cross sections at clei are explored. these energies.

II. THEORETICAL FRAMEWORK OF III. CALCULATION OF MASS AND CHARGE PHOTONUCLEAR REACTION YIELDS IN PHOTOFISSION

The total photo absorption cross section are calculated In the multimode-fission model, the mass distribution with help of hydrodynamic theory of the interaction be- is interpreted as a sum of the contributions from the sym- tween photons and nuclei, where the shape of fundamen- metric and asymmetric fission modes. Each fission mode tal resonance in the absorption cross-section is given by corresponds to the passage through the fission barrier of [18, 19] specific shape. For each fission mode, the yield is described in the form of a Gaussian function. The shape GDR Σ2 σi σa (Eγ )= i=1 2 (1) of the mass distributions can be fitted approximately by (E2 −E ) 2 1+ γ i using five Gaussian functions (three fission modes) which h Eγ Γi i represent the characteristics of the shell structure of the 238 where σi, Ei and Γi are the peak cross section, reso- fissioning nuclei. For U fission, the symmetric fission nance energy and full width at half maximum, respec- mode (SM) is associated with the half of the mass of the tively. We find that like the photoabsorption cross sec- fissioning nucleus (A = 117 in the present case) and for tions, the photofission cross sections can also be described the asymmetric fission modes (ASMI,ASMII) in addi- quite well by Eq.(1). The list of parameters σi, Ei and tion to broad maxima at A = 138 and A = 96, the mass 3 distribution exhibits narrower maxima in mass-number ξ = 0 for stable nucleus and ξ = 1 for nucleus on neutron regions around A = 133 and A = 101. Thus the total drip line. The mass number Ad is obtained using mass yield of fragments whose mass number is A is given by table [27, 28]. The values of ASM , DASMI and DASMII the expression are 117, 21 and 16, respectively, whereas the other six parameter values for 13.7±0.3 MeV (that coincides with 238 GDR peak for U photofission) are CSM =0.49±0.25, Y (A)= YSM (A)+ YASMI (A)+ YASMII (A) σSM = 4.47±3.33, CASMI = 5.90 ± 0.28, σASMI = (A − A )2 5.96±0.28, CASMII =2.29±0.27, σASMII =1.62±0.39. = C exp − SM (3) SM h 2σ2 i Obviously, the fact that the uncertainties in the param- SM eters for the symmetric mode (single Gaussian) is large 2 (A − ASM − DASMI ) while those for asymmetric modes (double Gaussians) are +CASMI exp h − 2 i 2σASMI quite small, suggests that the importance of symmetric (A − A + D )2 mode is less in determining the mass distribution. The +C exp − SM ASMI ASMI h 2σ2 i Fig.6 shows the variations of six parameter values with ASMI the average photon energies ranging from 9.09 MeV to 2 (A − ASM − DASMII ) 15.90 MeV. The lines represent least square fits assum- +CASMII exp h − 2 i 2σASMII ing quadratic energy dependence of the parameters. 2 (A − ASM + DASMII ) The isobaric charge distribution of photofission prod- +CASMII exp h − 2 i. ucts can be well simulated by a Gaussian function as 2σASMII where the Gaussian function parameters 2 Y (A) (Z − Zs + ∆) CSM , CASMI , CASMII and σSM , σASMI , σASMII are Y (A, Z)= exp h − i (5) πC Cp the amplitudes and widths, respectively, of the one p p symmetric (SM) and two asymmetric (ASMI,ASMII) where Zs represents most stable isotope of fission frag- fission modes and ASM is the most probable mass value ment with mass number A while ∆ measures the depar- for the symmetric fission mode with ASM − DASMI ture of the most probable isobar from the stable one. and ASM + DASMI being the most probable masses of a light and the complementary heavy fragment in the The atomic number Zs for the most stable nucleus is calculated by is differentiating the liquid drop model mass ASMI asymmetric fission mode while ASM − DASMII formula while keeping mass number A constant and set- and ASM + DASMII being the most probable masses of a light and the complementary heavy fragment in the ting the term ∂Mnucleus(A, Z)/∂Z |A equal to zero [29]. ASMII asymmetric fission mode. The values of the parameter Cp which decides the dis- The recoiling nucleus after absorbing γ can be viewed persion and the shift parameter ∆ for the most probable as a compound nucleus having the same composition as isotope are extracted by fitting experimental data [14] to the target nucleus but with the excitation energy [25, 26] be 0.8 and 3.8, respectively [22]. In the present work the form of the charge distribution is assumed to be independent of average photon energy for the range considered ∗ ′ 2 2 2 2 1/2 here. E = m0c − m0c = m0c [(1 + 2Eγ/m0c ) − 1] 2 2 1/2 2 = [m0c (2Eγ + m0c )] − m0c (4) IV. RESULTS ′ where m0 and m0 are the rest masses of the target nucleus before and after the photon absorption, respectively. In GDR 2 The photofission cross sections σ are calculated the present case where m0c is very large compared to f incident photon energy Eγ , the excitation energy is al- using Lorentz line shape of Eq.(1) for gamma ab- most equal to the incident photon energy. In Figs.2- sorption while replacing σi by the ratio method de- 4, approximation by the above five Gaussian functions scribed in section-II. The production cross sections of 238 for the mass distribution Y (A) of fragments per 100 fis- individual fragments for U photofission induced by sion events originating from 238U photofission induced bremsstrahlung photons are obtained by multiplying fis- by bremsstrahlung photons which correspond to average sion cross section by charge distribution which means GDR photon energies of 9.09 MeV, 13.7 MeV and 15.9 MeV are σf (A, Z) = σf .Y (A, Z)/100. The endpoint energies plotted and compared with experimental data [1, 14, 15]. of 11.5−67.7 MeV (the energy of electrons which pro- In Fig.5, plots of the ratios of cross sections for average duce bremsstrahlung gammas when stopped by a W con- photon energies 9.09 MeV and 15.9 MeV to that for 13.7 verter) is so chosen because it corresponds to the average MeV are shown as a function of exoticity parameter ξ gamma energies of 9.09−15.9 MeV that covers the entire defined as A−As where A, A and A are, respectively, GDR range for 238U photofission. Ad−As s d the fragment mass number, mass number of stability line It is important to mention here that with increasing en- nucleus and mass number of neutron drip line nucleus ergy, amplitude increases, although not so appreciable in for the same charge number Z of the fragment so that the energy domain considered here. Furthermore, among 4

8 6 7

5 6

5 4

4 3

Y(A) Y(A) (per 100 fission) 2

1 1

0 0 80 100 120 140 160 80 100 120 140 160 A A

FIG. 2: Comparison of the measured mass yield distri- FIG. 4: Same as Fig.2 but for average photon energy of 15.9 bution (full circles) [1] for 238U photofission induced by MeV. bremsstrahlung photons having average photon energy of 9.09 MeV with the prediction (solid line) of the five Gaussian formula for yield Y (A) per 100 fission events. The dotted lines represent individual contributions of one symmetric Gaussian and two asymmetric double Gaussians.

the two asymmetric modes the peak of the ASMII Gaus- sian is higher than the ASMI and also with increasing energy the peak of the ASMI Gaussian decreases while the ASMII remains almost constant. The atomic numbers Zs used in Eq.(5) for the most stable nuclei are cal- 7 culated using values ac = 0.71 MeV and asym = 23.21 MeV [29].

6 In Fig.7, production of neutron rich nuclei by the photofission of 238U by bremsstrahlung gammas with average photon energies of 15.9 MeV, 13.7 MeV and 9.09 5 MeV are compared. It is evident from Fig.7 that for average photon energy of 13.7±0.3 MeV (which coincides 4 with GDR peak for 238U photofission) produces nuclei farthest from the stability line. The neutron rich species 3 produced with cross sections >100 fb at energies 9.09 MeV and 15.9 MeV are 743 and 765 respectively, while that at energy 13.7 MeV is 777, the maximum. In an Y(A) (per 100 Y(A) (per fission) 2 effort to investigate the production cross section of neutron rich nuclei by bremsstrahlung gammas, some iso- 1 topes with maximum cross sections (appearing at the two asymmetric peaks of the mass distributions), some with 0 little lower cross sections (appearing at the symmetric 80 100 120 140 160 mass distributions) are arranged in Table-I with average A photon energies of 15.9 MeV, 13.7 MeV and 9.09 MeV. It is evident from Table-I, that with increase of energy FIG. 3: Same as Fig.2 but for average photon energy of 13.7 from 9.09 MeV to 13.7 MeV the cross sections increase MeV. by about five times, whereas it decreases by a factor of two with about 2 MeV further increase in energy. More- 5 over, in Table-II the production cross sections of some 25 r-process nuclei are highlighted for average photon en- σ13.7 σ9.09 ergy of 13.7 MeV only where cross sections are found to Ce [ / ] σ13.7 σ15.9 lie in µb range: e.g. 80Zn and 134Sn, the waiting point 20 Ce [ / ] nuclei are produced with 2.6 µb and 0.18 µb. Comparing Zr [σ13.7/σ9.09] Table-I & II, one may notice that for A/Z almost equal Zr [σ13.7/σ15.9] to 2.55 ± 0.01, when Z − Zs = 4, the cross sections are 15 of the order of mb, while for A/Z almost equal to 2.66, when Z−Zs = 6 the cross sections reduces to µb order for fission of 238U which has A/Z nearly equal to 2.58. The 10 reduction of cross section is consistent since cross sections fall rapidly with increasing mass number because of the neutron richness which is obvious from Eq.(5). In the r- Ratio of cross sections process path neutron capture stops as neutron separation 5 energy falls approximately below 2 MeV. In our calculation, the production cross section of 162Ce is found to be 3.2×10−15 mb, where calculated value of last neutron 0 separation energy is 2.2 MeV according to mass table 0.0 0.2 0.4ξ 0.6 0.8 1.0 [27, 28]. It is worthwhile to mention here that at high energies [30] the projectile fragment separator type RIB FIG. 5: Plots of ratios of cross sections for different photon facilities, being developed in different laboratories, could energies as a function of exoticity parameter ξ. also provide the scope for producing many new exotic nuclei through fragmentation of high energy radioactive ion beams [31].

In Fig.5, it may be noticed that with increasing exoticity ξ, the energy dependence remains flat irrespective of the fact whether cross sections are five times more or less by a factor of two. However, for Zr the situation is re- markably different. The increase in ξ in the range 0.6-0.8 is found to be five times to twentythree times while with further increase in energy to 15.9 MeV the cross sections become half independent of ξ. 6

TABLE I: The the energy dependence of exotic nuclei production cross sections by photonuclear reaction in the GDR range. F F 9.09 13.7 15.9 Elements A/Z Zs As Zs − Z A − As σ (mb) σ (mb) σ (mb) 138Xe 2.55 58 132 4 6 8.182 × 10−1 3.893 × 100 2.184 × 100 133Te 2.56 56 128 4 5 9.147 × 10−1 3.715 × 100 1.875 × 100 101Zr 2.53 44 90 4 11 1.185 × 100 4.813 × 100 2.429 × 100 96Sr 2.53 42 88 4 8 9.194 × 10−1 4.375 × 100 2.454 × 100 80Ge 2.50 36 74 4 6 2.407 × 10−2 1.156 × 10−1 7.022 × 10−2 117Pd 2.54 50 106 4 9 1.631 × 10−2 3.280 × 10−1 2.489 × 10−1 122Cd 2.54 52 114 4 8 2.360 × 10−2 2.907 × 10−1 2.083 × 10−1 86Se 2.52 38 80 4 6 2.239 × 10−1 1.069 × 100 6.163 × 10−1 148Ba 2.55 62 138 4 10 2.326 × 10−1 1.111 × 100 6.403 × 10−1

8 80 * Nuclei (most n-rich >100fb) E γ=15.9 MeV * Nuclei (most n-rich >100fb) E γ=13.7 MeV * Nuclei (most n-rich >100fb) E γ=9.09 MeV Stable nuclei σ 6 ASMII CASMII 60 σ SM cess 4 -pro CASMI Z r

Parameters of Y(A) 40 σ 2 ASMI

C 0 SM 8 10 12 14 16 20 * E γ (MeV) 40 60N 80 100

FIG. 6: Variations of the parameters of symmetric Gaussian FIG. 7: Plots of atomic number Z versus neutron number and asymmetric double Gaussians with excitation energies. N for exotic nuclei produced by the photoﬁssion of 238U by bremsstrahlung γ’s with average photon energy of 15.9, 13.7 and 9.09 MeV.

TABLE II: The theoretical cross sections for production of V. SUMMARY AND CONCLUSION nuclei with same A/Z for average photon energy 13.7 MeV. F F Elements A/Z Zs As Zs − Z A − As σ(mb) In summary, we find that like the photoabsorption 80 × −3 Zn 2.66 36 64 6 16 2.6 10 cross sections, the photofission cross sections can also 96 −3 Kr 2.66 42 84 6 12 2.1 × 10 be described quite well by Lorentz line shapes. The ratio 106Zr 2.66 46 91 6 15 3.9 × 10−3 method predictions for photofission are almost as good as 133Sn 2.66 56 119 6 14 2.2 × 10−3 the Lorentz line shape fitting, whereas the evaporation- 143Xe 2.66 60 131 6 12 6.6 × 10−3 fission process of the compound nucleus overestimates 154Ce 2.66 64 140 6 14 2.2 × 10−3 the photofission cross sections. A detailed analysis of the production of each nuclear isobar via fission and the mass distributions of products originating from the 7 photofission induced by bremsstrahlung photons is pro- for products having cross sections in the mb range only. vided. The endpoint energy is chosen in the range However, for many of the r-process nuclei in intermediate 11.5−67.7 MeV, which includes of 29.1 MeV, that pro- mass range can be produced for three different energies duce bremsstrahlung gammas when slowed down by a that are very close and among them, the end point energy W converter. The average gamma energy of 13.7 MeV, of 29.1 MeV is the maximum. Therefore, so far march- which coincides with GDR peak for 238U photofission, ing away from β-stability towards neutron-rich nuclei is produces the maximum cross-section. concerned it appropriate to keep energy of the electron The present calculation indicates clearly that products within 50 MeV for e-LINAC construction. For producing having A/Z less than that of A/Z of fissioning nucleus neutron rich nuclei, in the higher mass range, more than are more probable than otherwise. In fact, products with A=140, one would need to go for nuclear process other neutron richnesss 8 ± 3 have cross sections in the mb than photonuclear reaction to produce them. range whereas it reduces to µb order for neutron richness in the range of 14 ± 2. Energy dependence is significant

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