Multi-nucleon transfer in the interaction of 977 MeV and 1143 MeV 204 Hg with 208 Pb
V. V. Desai, A. Pica, W. Loveland, J.S. Barrett, Department of Chemistry, Oregon State University, Corvallis, Oregon 97331 USA, E.A. McCutchan, National Nuclear Data Center, Brookhaven National Laboratory, Upton, New York 11973, S. Zhu, M. P. Carpenter, J.P. Greene, T. Lauritsen, Physics Division, Argonne National Laboratory, Argonne, Illinois 60439 USA, R.V.F. Janssens, Department of Physics, Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599 USA, Triangle Universities Nuclear Laboratory, Duke University, Durham, North Carolina 27708 USA, B. M. S. Amro, Dept. of Physics, University of Massachusetts Lowell, Lowell MA 01854 USA, W. B. Walters, Dept. of Chemistry, University of Maryland, College Park
aa r X i v : . [ nu c l - e x ] J u l Multi-nucleon transfer in the interaction of 977 MeV and1143 MeV
Hg with Pb V. V. Desai, A. Pica, W. Loveland, J.S. Barrett
Department of Chemistry, Oregon State University, Corvallis, Oregon 97331 USA
E.A. McCutchan
National Nuclear Data Center, BrookhavenNational Laboratory, Upton, New York 11973, USA
S. Zhu, ∗ A. D. Ayangeakaa, † and M. P. Carpenter, J.P. Greene, T. Lauritsen Physics Division, Argonne National Laboratory, Argonne, Illinois 60439 USA
R.V.F. Janssens
Department of Physics and Astronomy,University of North Carolina at Chapel Hill, Chapel Hill,North Carolina 27599 USA and Triangle Universities Nuclear Laboratory,Duke University, Durham, North Carolina 27708 USA
B. M. S. Amro
Dept. of Physics, University of Massachusetts Lowell, Lowell MA 01854 USA
W. B. Walters
Dept. of Chemistry, University of Maryland, College Park, MD (Dated: July 16, 2020) bstract A previous study of symmetric collisions of massive nuclei has shown that current modelsof multi-nucleon transfer (MNT) reactions do not adequately describe the transfer productyields. To gain further insight into this problem, we have measured the yields of MNTproducts in the interaction of 977 (E/A = 4.79 MeV) and 1143 MeV (E/A = 5.60 MeV)
Hg with
Pb. We find that the yield of multi-nucleon transfer products are similarin these two reactions and are substantially lower than those observed in the reactionof 1257 MeV (E/A = 6.16 MeV)
Hg +
Pt. We compare our measurements withthe predictions of the GRAZING-F, di-nuclear systems (DNS) and improved quantummolecular dynamics (ImQMD) models. For the observed isotopes of the elements Au, Hg,Tl, Pb and Bi, the measured values of the MNT cross sections are orders of magnitudelarger than the predicted values. Furthermore, the various models predict the formationof nuclides near the N=126 shell, which are not observed. ∗ Present address National Nuclear Data Center, Brookhaven National Laboratory, Upton, NewYork 11973, USA † Present address: United States Naval Academy, Annapolis, Maryland 21402 USA . INTRODUCTION Multi-nucleon transfer (MNT) reactions are thought to be useful paths for synthe-sizing new n-rich heavy nuclei [1, 2] and as possible paths for synthesizing nuclei nearthe N =126 shell closure (of interest to the studies of r-process nucleosynthesis [3]).Some of the most interesting of these reactions involve the near symmetric collisionsof massive nuclei, such as U +
Cm. In this regard, the recent result of Welsh etal. [4] is somewhat disturbing. Welsh et al. measured the yields of several nuclidesfrom the near symmetric reaction of 1257 MeV
Hg with
Pt. They found thatthe yields of the transfer products were significantly larger, even for small transfers,than those predicted by typical models for MNT reactions, such as GRAZING, theDNS model and the ImQMD model. While it is encouraging to see the larger thanexpected yields of the MNT products, it is vexing that we are unable to predictthese yields even for the smallest transfers, let alone the larger ones. Accordingly weundertook an investigation, reported in this paper, of the projectile-like fragments(PLFs) and target-like fragments (TLFs) yields in another symmetric reaction, thereaction of 977 and 1143 MeV
Hg with
Pb. By making this investigation, wehope to check whether there are some special features of near symmetric collisionsthat affect the MNT yields.
II. EXPERIMENTAL
The experimental method used was similar to that of Desai et al. [5]. Using theGammasphere facility of the Argonne National Laboratory, beams of
Hg strucktargets of
Pb. For the irradiation at 977 MeV, the effective target thickness was19.5 mg/cm and the total bombardment time was 1404 min. For the irradiation at1143 MeV, the effective target thickness was 28.0 mg/cm and the total bombardment3ime was 2632 min. (In the 977 MeV study the actual beam energy was 1360 MeV.The incident beam loses energy as it goes through the target and after traversing19.5 mg/cm of Pb, the beam energy drops below the interaction barrier of 586.7MeV. Thus the ‘effective’ target thickness was 19.5 mg/cm while the physical targetthickness was 48 mg/cm ) . In the higher energy irradiation (1143 MeV), the incidentbeam energy was 1700 MeV, the physical target thickness was 44 mg/cm , and theeffective target thickness was 27.7 mg/cm . The intensity of the beam was monitoredperiodically by inserting a suppressed Faraday cup in the beam line in front of thetarget. The beam intensities were 3.07 x 10 and 3.17 x 10 ions/min for thelower and higher energy irradiations, respectively. The lower energy irradiation wasperformed in May 2015, while the higher energy irradiation was performed in April,2016.At the end of each irradiation, the target was removed from Gammasphere and γ -ray spectroscopy of the target radioactivities was carried out using a well-calibratedGe detector in The Center for Accelerator Target Science (CATS) Counting Labora-tory. The total observation period for the lower energy was 5 days, during which 25measurements of target radioactivity were made. The total observation time for thehigher energy was 7 days during which 23 measurements of the sample were made.The analysis of these Ge γ -ray decay spectra was carried out using the FitzPeaks[6] software. The end of bombardment (EOB) activities of the nuclides were used tocalculate absolute production cross sections, taking into account the variable beamintensities using standard equations for the growth and decay of radionuclides duringirradiation [7]. These measured absolute nuclidic production cross sections are tabu-lated in Tables 1 and 2. These cross sections represent “cumulative” yields;, i.e., theyhave not been corrected for the effects of precursor beta decay. These cumulativeyields are the primary measured quantity in this experiment.To correct for precursor beta decay, we have assumed that the beta-decay cor-4ected independent yield cross sections for a given species, σ (Z,A), can be representedas a histogram that lies along a Gaussian curve σ ( Z, A ) = σ ( A ) (cid:2) πC Z ( A ) (cid:3) − / exp (cid:20) − ( Z − Z mp ) C Z ( A ) (cid:21) (1)where σ (A) is the total isobaric yield (the mass yield), C Z (A) is the Gaussian widthparameter for mass number A, and Z mp (A) is the most probable atomic number forthat A. Given this assumption, the beta-decay feeding correction factors for cumu-lative yield isobars can be calculated, once the centroid and width of the Gaussianfunction are known.To uniquely specify σ (A), C Z (A), and Z mp (A), one would need to measure threeindependent yield cross sections for each isobar. This is difficult and generally notfeasible for most isobars. Instead, one assumes that the value of σ (A) varies smoothlyand slowly as a function of mass number and is roughly constant within any Arange when determining C Z (A) and Z mp (A). The measured nuclidic formation crosssections are then placed in groups according to mass number. We assume that thecharge distributions of neighboring isobaric chains are similar and radionuclide yieldsfrom a limited mass region can be used to determine a single charge distributioncurve for that mass region. One can then use the laws of radioactive decay toiteratively correct the measured cumulative formation cross sections for precursordecay. These “independent yield” cross sections are also tabulated in Tables 1 and 2.The cumulative and independent yield cross sections are similar due to the fact that,without an external separation of the reaction products by Z or A, one most likelydetects only a single or a few nuclides for a given isobaric chain, and these nuclidesare located near the maximum of the Gaussian yield distribution. The uncertaintiesin the calculated “independent yield” cross sections deduced in this manner havebeen examined by Morrissey et al. [8] and they have found a systematic uncertaintyof ±
30 % associated with this procedure.5
II. RESULTS AND DISCUSSION
Due to the nearly symmetric character of the
Hg +
Pb reaction, separation ofthe products into projectile-like fragments (PLFs) and target-like fragments (TLFs)is not meaningful. While some models for these reactions classify fragments as PLFsand TLFs, we have summed all of the predicted yields to give “fragment yields”.
A. Comparison with phenomenological models
A well-known model for predicting the cross sections for transfer products isGRAZING, a semi-classical model due to Pollarolo and Winther [9, 10]. GRAZ-ING uses a semi-classical model of the reacting ions moving on classical trajectorieswith quantum calculations of the probability of excitation of collective states and ofnucleon transfer. This model describes few nucleon transfers [11] well. It has beenemployed to describe the production of projectile like fragments (PLFs) involvingtransfers of 45 nucleons in the asymmetric reaction of
Xe with
U, where thepredictions of this model agree well with measurements [12]. Yanez and Loveland [13]have published a variant of the GRAZING code, called GRAZING-F, which takesinto account the decay of the MNT primary fragments by both fission and neutronemission.The measured and predicted (GRAZING-F) values for selected nuclides areshown in Figures 1 -10.Another model for predicting the yields of MNT products is the dinuclear system(DNS) model which is described in [14, 15]. Unlike the GRAZING model, this modelfocuses on the more central collisions, in which there is considerable overlap betweenthe colliding nuclei. The GRAZING and DNS models are, thus, complementary. Thepredictions of the DNS model are compared to the measured data in Figures 1-10,as well. 6 third model for predicting MNT yields that has been quite successful [4, 5] is theImproved Quantum Molecular Dynamics (ImQMD) model [16, 17]. This model hasbeen shown to describe MNT yields in a wide variety of reactions. The predictionsof this model are also compared to the experimental data in Figures 1-10One’s first impression from Figures 1 -10 is that the increase in beam energy from977 to 1143 MeV has a small effect on the measured cross sections.In Figures 1-10, the observed MNT products are more neutron-deficient thanthose predicted by the models, with the exception of
Hg. The observed yields areorders of magnitude larger than those predicted by the various models. As the atomicnumber of the elements increases, the various models predict large yields for the nucleinear the N=126 shell– a prediction that is not consistent with the measurements.One can be encouraged or discouraged by this situation.The fact that the measuredcross sections are larger than the predicted cross sections is encouraging for usingMNT reactions to synthesize new n-rich nuclei, but the inability to see nuclei near theN=126 shell might indicate that these symmetric reactions are not a suitable path tothese very n-rich nuclei. For all the models there is an interesting ”odd-even” effectwith the atomic numbers of the MNT products. The even Z nuclides ( Hg and Pb)show higher yields than the odd Z nuclides (Au, Tl, Bi) but one must remember Hgand Pb were the projectile and target, respectively.If we compare the measured cross sections from this work (977 and 1143 MeV
Hg +
Pb) with the measurements of Welsh et al. [4] for (1257 MeV
Hg +
Pt)(Figure 11) we observe similar yield patterns except that the cross sections forthe higher energy reaction (1257 MeV
Hg +
Pt) are substantially greater.7
10 112 114 116 118 120 122 124 126 128 13010 -4 -3 -2 -1 ( m b ) NAu
FIG. 1. A comparison of the predicted (GRAZING-F, DNS and ImQMD) yields and themeasured yields of the Au isotopes formed in the reaction of 977 MeV
Hg with
Pb.The solid squares represent the experimental data, while the solid , dashed and the dash-dotlines represent the predictions of the GRAZING-F, DNS and ImQMD models, respectively.
10 112 114 116 118 120 122 124 126 128 13010 -4 -3 -2 -1 ( m b ) NHg
FIG. 2. A comparison of the predicted and measured yields of the Hg isotopes formed inthe reaction of 977 MeV
Hg with
Pb. See Figure 1 for the meaning of the symbols.
10 112 114 116 118 120 122 124 126 128 13010 -4 -3 -2 -1 ( m b ) NTl
FIG. 3. A comparison of the predicted and measured yields of the Tl isotopes formed inthe reaction of 977 MeV
Hg with
Pb. See Figure 1 for the meaning of the symbols.
10 112 114 116 118 120 122 124 126 128 13010 -4 -3 -2 -1 ( m b ) NPb
FIG. 4. A comparison of the predicted and measured yields of the Pb isotopes formed inthe reaction of 977 MeV
Hg with
Pb. See Figure 1 for the meaning of the symbols.
10 112 114 116 118 120 122 124 126 128 13010 -4 -3 -2 -1 ( m b ) NBi
FIG. 5. A comparison of the predicted and measured yields of the Bi isotopes formed inthe reaction of 977 MeV
Hg with
Pb. See Figure 1 for the meaning of the symbols.
10 112 114 116 118 120 122 124 126 128 13010 -4 -3 -2 -1 ( m b ) NAu
FIG. 6. A comparison of the predicted (GRAZING-F, DNS and ImQMD) yields and themeasured yields of the Au isotopes formed in the reaction of 1143 MeV
Hg with
Pb.The solid squares represent the experimental data, while the solid , dashed and the dash-dotlines represent the predictions of the GRAZING-F, DNS and ImQMD models, respectively.
10 112 114 116 118 120 122 124 126 128 13010 -4 -3 -2 -1 ( m b ) NHg
FIG. 7. A comparison of the predicted and measured yields of the Hg isotopes formed inthe reaction of 1143 MeV
Hg with
Pb. See Figure 6 for the meaning of the symbols.
10 112 114 116 118 120 122 124 126 128 13010 -4 -3 -2 -1 ( m b ) NTl
FIG. 8. A comparison of the predicted and measured yields of the Tl isotopes formed inthe reaction of 1143 MeV
Hg with
Pb. See Figure 6 for the meaning of the symbols.
10 112 114 116 118 120 122 124 126 128 13010 -4 -3 -2 -1 ( m b ) NPb
FIG. 9. A comparison of the predicted and measured yields of the Pb isotopes formed inthe reaction of 1143 MeV
Hg with
Pb. See Figure 6 for the meaning of the symbols.
10 112 114 116 118 120 122 124 126 128 13010 -4 -3 -2 -1 ( m b ) NBi
FIG. 10. A comparison of the predicted and measured yields of the Bi isotopes formed inthe reaction of 1143 MeV
Hg with
Pb. See Figure 6 for the meaning of the symbols.
10 112 114 116 118 120 122 124 126 128 13010 -4 -3 -2 -1
110 112 114 116 118 120 122 124 126 128 13010 -4 -3 -2 -1
110 112 114 116 118 120 122 124 126 128 13010 -4 -3 -2 -1
110 112 114 116 118 120 122 124 126 128 13010 -4 -3 -2 -1
110 112 114 116 118 120 122 124 126 128 13010 -4 -3 -2 -1 (( m b ) NAu ( m b ) NHg ( m b ) NTl ( m b ) NPb ( m b ) NBi
FIG. 11. A comparison of the yields of transfer products in the reaction of 997 MeV
Hg+
Pb (this work, black squares)), 1143 MeV
Hg +
Pb (this work, blue circles))and the reaction of 1257 MeV
Hg +
Pt [4] (red triangles) V. CONCLUSIONS
What have we learned from this experiment? We found that: (a) There is verylittle change in the yields of the MNT transfer products when the beam energy israised from 977 MeV to 1143 MeV. (E/A = 4.79 to 5.60 MeV/A)(b) Comparing ourresults to those of Welsh et al. [4], we find that raising the projectile from 977 or 1143MeV to 1267 MeV increases the MNT production cross sections by about two ordersof magnitude. (c) The frequently used models for MNT collisions (GRAZING-F,DNS and ImQMD) fail to describe these symmetric collisions, a situation similar tothat observed by Welsh et al. [4]. This is not a trivial observation as symmetricreactions like U + Cm, etc are frequently cited as pathways to n-rich heavy nuclei.
V. ACKNOWLEDGEMENTS
This material is based upon work supported in part by the U.S. Department ofEnergy, Office of Science, Office of Nuclear Physics under award numbers DE-FG06-97ER41026 (OSU), DE-FG02-97ER41041 (UNC), DE-FG02-97ER41033 (TUNL),DE-FG02-94ER40848 (UMassLowell) and contract numbers DE-AC02-06CH11357(ANL) and DE-AC02-98CH10886(BNL). This research used resources of ANL’s AT-LAS facility, which is a DOE Office of Science User facility.
TABLE I: Fragment cumulative and independent yields forthe reaction of
Hg +
Pb at E lab = 977 MeV.
Isotope σ CY (mb) σ IY (mb) Ga 0.078 ± ± Rb m ± ± Continued on next page ABLE I –
Continued from previous page
Isotope σ CY (mb) σ IY (mb) Kr 0.052 ± ± Sr 0.080 ± ± Sr 0.183 ± ± Zr 0.205 ± ± Nb 0.159 ± ± Mo 0.178 ± ± Tc 0.21 ± ± Tc 0.030 ± ± Ru 0.751 ± ± Ru 1.204 ± ± Ag 0.232 ± ± Cd 0.130 ± ± Sb 0.585 ± ± I 0.082 ± ± Xe 0.187 ± ± Xe 0.079 ± ± Ba 0.195 ± ± Ce 0.099 ± ± Sm 0.278 ± ± Tb 0.737 ± ± Ho 0.124 ± ± Lu 0.221 ± ± Continued on next page ABLE I –
Continued from previous page
Isotope σ CY (mb) σ IY (mb) Hf m ± ± Re 1.39 ± ± Re 1.883 ± ± Re 0.219 ± ± Os 0.594 ± ± Ir 0.192 ± ± Ir 0.137 ± ± Pt 0.918 ± ± Au 0.221 ± ± Au 0.430 ± ± Au 0.426 ± ± Au 1.652 ± ± Au 2.414 ± ± Au 3.25 ± ± Au m ± ± Hg m ± ± Hg 0.897 ± ± Hg 38.1 ± ± Tl 0.963 ± ± Tl 0.870 ± ± Tl 2.21 ± ± Tl 3.27 ± ± Continued on next page ABLE I –
Continued from previous page
Isotope σ CY (mb) σ IY (mb) Tl 3.14 ± ± Pb 0.388 ± ± Pb 0.962 ± ± Pb m ± ± Pb 5.42 ± ± Pb 1.95 ± ± Bi 0.412 ± ± Bi 0.577 ± ± Bi 0.786 ± ± Bi 1.87 ± ± Bi 1.53 ± ± Po 0.786 ± ± At 0.297 ± ± At 0.288 ± ± At 0.396 ± ± Rn 0.560 ± ± Hg +
Pb at E lab = 1143 MeV.
Isotope σ CY (mb) σ IY (mb) Zn 0.264 ± ± Zn 0.177 ± ± Continued on next page ABLE II –
Continued from previous page
Isotope σ CY (mb) σ IY (mb) Br 0.329 ± ± Y 0.083 ± ± Y 0.373 ± ± Sr 0.886 ± ± Nb 0.325 ± ± Tc 0.047 ± ± Tc 0.127 ± ± Zr 1.246 ± ± Ru 0.614 ± ± Mo 1.974 ± ± Rh 0.050 ± ± Ru 3.216 ± ± Ru 0.773 ± ± In 0.053 ± ± Cd 0.130 ± ± Sb 0.492 ± ± Sb m ± ± Sb 0.201 ± ± Sb 0.321 ± ± Cs 0.214 ± ± Ba m ± ± Ba 0.195 ± ± Continued on next page ABLE II –
Continued from previous page
Isotope σ CY (mb) σ IY (mb) Ce 0.210 ± ± Gd 0.118 ± ± Er 0.159 ± ± Tm 0.165 ± ± Lu 0.377 ± ± Lu 0.946 ± ± Hf 0.102 ± ± Hf 0.436 ± ± Hf m ± ± Ta 0.533 ± ± Ta 0.824 ± ± Ta 0.179 ± ± Ta 0.221 ± ± Re 0.555 ± ± Re 0.686 ± ± Re 0.716 ± ± Re 1.19 ± ± Os 0.196 ± ± Os 1.370 ± ± Ir 0.655 ± ± Ir 0.587 ± ± Ir 0.170 ± ± Continued on next page ABLE II –
Continued from previous page
Isotope σ CY (mb) σ IY (mb) Pt 0.748 ± ± Pt 1.76 ± ± Pt m ± ± Au 0.43 ± ± Au 0.430 ± ± Au 1.652 ± ± Au 2.414 ± ± Au 3.25 ± ± Au m ± ± Hg m ± ± Hg m ± ± Hg m ± ± Hg 1.75 ± ± Hg 19.0 ± ± Tl 1.53 ± ± Tl 1.51 ± ± Tl 2.92 ± ± Tl 4.70 ± ± Tl 2.73 ± ± Pb 0.39 ± ± Pb 0.962 ± ± Pb m ± ± Continued on next page ABLE II –
Continued from previous page
Isotope σ CY (mb) σ IY (mb) Pb 1.92 ± ± Bi 1.19 ± ± Bi 1.27 ± ± Bi 2.79 ± ± Bi 1.81 ± ± Po 1.00 ± ± Po 1.00 ± ± At 1.12 ± ± At 1.76 ± ± Rn 0.36 ± ± , 1 (2007)[2] V. I. Zagrebaev and W. Greiner, Phys. Rev. C , 044618 (2011)[3] V.I. Zagrebaev and W. Greiner, Phys. Rev. Lett. , 122701 (2008)[4] T. Welsh, et al., Phys. Lett. B , 119 (2017).[5] V.V. Desai, et al., Phys. Rev. C ,1783 (1980).[9] http://personalpages.to.infn.it/ nanni/grazing/.
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