Excited states of the odd-odd nucleus 158Eu from the (d,alpha) reaction
D. Bucurescu, S. Pascu, T. Faestermann, H-F. Wirth, C. Costache, A. Ionescu, R. Lica, R. Mihai, A. Turturica, R. Hertenberger
aa r X i v : . [ nu c l - e x ] A ug Excited states of the odd-odd nucleus
Eu from the (d, α ) reaction D. Bucurescu, S. Pascu, T. Faestermann, H-F. Wirth, C. Costache, A. Ionescu,
1, 4
R. Lic˘a, R. Mihai, A. Turturic˘a, and R. Hertenberger Horia Hulubei National Institute of Physics and Nuclear Engineering, P.O. Box MG-6, R-76900 Bucharest, Romania Physik Department, Technische Universit¨at M¨unchen, D-85748 Garching, Germany Fakult¨at f¨ur Physik, Ludwig Maximilians Universit¨at M¨unchen, Am Coulombwall 1, 85748 Garching, Germany Faculty of Physics, University of Bucharest, 405 Atomi¸stilor, Bucharest - M˘agurele, Romania (Dated: August 7, 2019)Excited states in the
Eu nucleus have been determined with the
Gd(d, α ) Eu reaction,studied at an incident energy of 18.0 MeV with the Munich tandem and Q3D spectrograph. Morethan 50 excited states have been determined up to 1.6 MeV excitation, some of them correspondingto states previously observed in the β − -decay of Sm. The number of levels found in this nucleusat low excitation energies follows the systematic trend of the level densities in the other isotopeswith mass 152–156.
I. INTRODUCTION
The study of nuclear structure in rare earth nuclei witha multitude of nuclear reactions has been rather inten-sive especially in the region near the neutron number N = 90 where the nuclear properties undergo a rapidchange, pinpointing one of the best examples of quan-tum shape phase transition. While the even-even nucleiand odd-mass nuclei are relatively well studied, the odd-odd nuclei in this region are less investigated. One ofthe possible study tools, making use of the many avail-able stable targets in this region, is the (d, α ) reaction.When performed on even-even targets, it leads to odd-odd nuclei, and the advantage is that the target has a0 + ground-state, which facilitates the determination ofthe spin and parity of the states in the odd-odd nu-cleus. Rather surprisingly, this powerful tool was practi-cally unused in the rare earth nuclei. With the exceptionof the reaction Sm(d, α ) Pm [and of two other reac-tions used for its energy calibration,
Ce(d, α ) La and
Nd(d, α ) Pr], which was used to determine the levelstructure of the practically unknown
Pm nucleus [1],this reaction was never performed on other targets in therare-earth region.We decided to use this reaction in order to determinethe level structure of the
Eu odd-odd nucleus. Forthis nucleus there are no adopted levels in the ENSDFdatabase [2], except for a ground state with a proposedspin-parity (1 − ) as expected from Nilsson configurations.The ENSDF evaluation mentions, however, determina-tions of excited levels of Eu in an unpublished studyof this nucleus by the β − -decay of Sm, which werealso used in a publication where an analysis of the totalabsorption γ -spectrum in the β -decay was performed [3].The study of the (d, α ) reaction on chains of even-eventargets, such as that of Nd, Sm, Gd, and Dy nuclei, wouldbe of considerable interest also because it may offer asystematic view of the structure evolution of the odd-odd nuclei, an aspect that will be exemplified at the endof this work. II. EXPERIMENT AND RESULTS
The experiment was performed at the Munich tandemaccelerator, using a deuteron beam of 18 MeV and a 0.5 µ A average intensity. The target was 125 µ g/cm Gd O Gd on 10 µ g/cm Carbon foil. Itsmain impurities were
Gd,
Gd, and
Gd, each lessthan 1%. The reaction products were analyzed in theQ3D spectrograph [4] and detected and identified in itsfocal plane detector, a multiwire proportional chamberwith readout of a cathode with microstrip foil structurefor ∆ E − E particle identification and position determi-nation [5].Spectra were recorded at an angle of 10 ◦ relative tothe beam direction, with an acceptance of the spectro-graph of 14.61 msr (21 . × . ). Figure 1 displaysa ∆ E − E plot for the reaction products that enter thefocal plane detector, showing the good separation of the α -particles. The other events from this plot very likelyrepresent tritons, deuterons, and He (from left to right),although a sure identification is difficult due to the differ-ent reaction Q -values, extended range of energies of theemergent particles, the rather compressed scale of therest energy axis, and the proximity to the threshold cut-off. With this identification of the alpha ’s the spectra ofthe ( d, α ) reaction were practically background-free. Thebeam current was integrated into a Faraday cup placedafter the target in order to determine the cross sections.Due to the small cross-sections of our reaction and theavailable beam intensity and measurement time, angulardistributions could not be measured. We concentratedon the measurement at just one angle, of 10 ◦ . Figure2(a) shows the 10 ◦ spectrum measured during a total of19 hours. The energy calibration of this spectrum hasbeen achieved by measuring, in the same conditions, thespectrum of the Cd(d, α ) Ag reaction, with a targetof 150 µ g/cm thickness, for which peaks correspondingto well-known levels of Ag [6] have been identified.This calibration spectrum is shown in Fig. 2(b).Both spectra in Fig. 2 have been processed with theGASPAN peak fitting program [7]. The FWHM energy
FIG. 1: (Color online) Graph of the energy loss versus the rest energy (both in arbitrary units) of the reaction products thatreach the focal plane detector, showing the good separation of the alpha particles. resolution was about 15 keV for the spectrum in Fig. 2(a)and 12 keV for that in Fig. 2(b), respectively. Peaks dueto the target impurities were not visible in the spectrumof Fig. 2(a). For the calibration spectrum in Fig. 2(b),an energy calibration curve for the excitation energy E x in Ag versus channel number was generated as a sec-ond degree polynomial. From the peak energy labels inFig. 2(b) one can see that this curve describes the excita-tion energies known with good precision [6] with an accu-racy of less than 1.5 keV. This calibration curve was thentransformed, by kinematics calculations, in a new cali-bration curve E abs versus channel number, where E abs is the absolute energy of the α -particles (of the order of27 MeV). This second calibration curve was used for thespectrum in Fig. 2(a) in order to determine the absolute α -particle energies of the peaks corresponding to statesin Eu, which were then transformed into excitationenergies by using kinematic calculations. This procedurewas necessary in order to take into account the ratherdifferent recoil energies of the residual nuclei in the tworeactions, due to the large mass difference between thetarget nuclei.
Q-value of the
Gd(d, α ) Eu reaction . A betterdetermination of this quantity resulted as a byprod-uct of the energy calibration described above. The Q -value of the calibration reaction (on the Cd target)is rather well known, Q ( d,α ) ( Cd) = 10178.0 ± Gd(d, α ) Eu the Q -value is given as Q ( d,α ) ( Gd)= 10024 ±
10 keV [8]. By using the Q -value of the Cdtarget, our measurement of the energy of the peak cor-responding to the ground state of
Eu (Fig. 2(a)) pro- vided a value of Q ( d,α ) ( Gd) = 10035.5 ± Excited states of the Eu nucleus . Table I shows theenergy levels found for Eu in the present experiment,In both Table I and Fig. 2 the errors given for the en-ergy values are the statistical errors, as resulted from thecalibration curve and the errors in the peak centroids.As one can see from Fig. 2, the calibration curve (sec-ond degree polynomial) deduced from the reaction on the
Cd target works well up to an excitation energy of 1.32MeV, corresponding to an excitation energy in
Eu ofabout 1.23 MeV. Beyond this excitation energy, up tothe highest excited state determined (about 1.6 MeV)the energies given in the table are based on the extrap-olation of the calibration curve. It is therefore expectedthat with increasing energy this procedure may provideincreasing deviations from the (unknown) real energies,that are larger than the specified statistical error. Also,to better see the basis of the peak assignments, Fig. 3shows details of the peak fitting with the GASPAN pro-gram. The peak shapes were fitted with a gaussian plus aleft side (lower α -particle energy) exponential tail whichis due to the energy loss of the alpha particles in the thintarget. A fixed tail fraction was chosen, which was foundby eliminating the tendency to fit the peaks as doublets,and by a good description of the shape of strong, betterseparated peaks. Figure 3 shows six panels correspond-ing to fits in the six adjacent regions of the total spec-trum shown in Fig. 2(a). Some weaker fits, e.g., thoseto the 95.5 keV and 228.6 keV peaks may be due to thefact that their shape did not reach stability yet due tothe weak statistics. Attempts to fit the 228.6 keV peak C oun t s Gd(d, α ) Eu / ( ) / . ( ) / . ( ) / . ( ) / . . . ( ) / . ( ) / ( ) / . ( ) / . ( ) / . ( ) . ( ) / . ( ) / . ( ) / . ( ) / . ( ) / . ( ) / . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) ( ) . ( ) ( ) ( ) . ( ) ? . ( ) . . . . . . . . . . . . . . . . . . . . . t o k e V . . ~ p ea k s i n r e g i on1213 . ( . ) . . . . . . . . . Cd(d, α ) Ag . . . . . . ( ) . ( . ) (a)(b) . . FIG. 2: (Color online) Spectra measured at 10 ◦ with the same magnetic settings of the spectrograph for (a) our reaction, and(b) the reaction used for energy calibration, Cd(d, α ) Ag. In spectrum (b) the peaks are labeled both with the ENSDFadopted energies [6] (in red italics) and those assigned with the calibration curve, respectively. In spectrum (a) the peaks arelabeled with the excitation energies of the states in
Eu, as found with the calibration curve (see text and Table I). Thespectrum in (a) was obtained in 19 h of measurement with a beam of about 0.5 µA . For comparison, the spectrum in (b) wasproduced in 100 min under similar conditions. by a doublet failed, while for the 95.5 keV peak sucha procedure was not justified due to the low number ofcounts. Tentative levels (shown within parentheses in Ta-ble I) correspond to rather small, less certain peaks foundthrough the peak decomposition procedure. Figure 3(e)corresponds to the region between 1015 and 1175 keVexcitation, where there are states with significant over-lap (average spacing comparable with the energy resolu-tion). The peak decomposition from this region shouldbe considered with some caution. The number of statesfound by GASPAN in this region depends somewhat onthe width allowed for the peaks; by imposing a FWHMvalue comparable to that in the adjacent regions (withbetter separated peaks) one finds a number of nine peaksin this region, two of them being tentative (see Table I).The other (stronger) peaks found in this region appear tobe relatively stable to reasonable variations allowed forthe widths of the peaks.As a result of the analysis of the (d, α ) spectrum of Fig.2(a), a number of 58 excited states have been assignedin the Eu nucleus (five of these being tentative) up to about 1.6 MeV excitation. In Table I they are comparedwith the 27 excited states proposed from the β − -decayof Sm in the same energy range [2, 3]. Fourteen ofthese states may coincide with states observed in the β -decay experiment. TABLE I: Energy levels of
Eu as observed in the present(d, α ) reaction experiment, compared to levels observed in the β − -decay study of Sm [2, 3]. When the energies of levelsfrom the two experiments differ by less than 3 keV, they areplaced on the same line and it is assumed that they may rep-resent the same excited state. Levels tentatively proposed inour experiment are given within parentheses (see also Fig. 3).The groups labeled by (a), (b), ... , (f) correspond to the sixgraphs in Fig. 3.Present experiment β -decay [2, 3]E x (keV) dσd Ω (10 ◦ ) [ µ b/sr] E x (keV)group (a)0 0.09 036.3(7) 0.37 38.9 . . . III. DISCUSSION AND CONCLUSIONS
As a result of the present experiment and of the un-published β -decay study [2, 3] a large number of excitedstates of Eu have been determined up to about 1.5MeV excitation (Table I). No spin and parity values wereassigned to any of these levels. In the β − decay of the 0 + ground state of Sm the populated states are expectedto have spin values 0, 1, and 2¯ h and many of these werepopulated in our reaction too. The spin window of thestates seen in the (d, α ) reaction is wider, states up tospin about 6 ¯ h may be populated (see, e.g., Ref. [9]),with higher spin states being favored due to the largeangular momentum mismatch of the reaction.Although without spin and parity value assignments,the knowledge available now on this odd-odd nucleus ex-tends the nuclear structure systematics of the odd-oddEu isotope chain, and allows a new, stimulating view ofthis interesting mass region.It was recently shown that the nuclear level density canbe employed as a useful indicator of the critical shapephase transitions (SPT) in nuclei [10]. The connectionbetween the evolution of the level density at low excita-tion energies and the phase transition phenomenon wasexamined in detail in the rare earths region, where thereis the well known first order SPT that takes place aroundthe critical point N ≈
90. This behavior is induced bythe variation of a non-thermal control parameter – thenumber of neutrons N . The SPT manifests itself by arapid evolution of the ground-state equilibrium deforma-tion around the critical point, which is reflected in dis-continuous variations of different so-called effective orderparameters (such as the two-neutron binding energy, nu-clear radii, etc.) as a function of N . The level densitywas shown to display a maximum value at the criticalpoint [10], which is also consistent with the phenomenonof phase coexistence in nuclei at, or close to, the criticalpoint.The critical shape phase transitions were less studiedin the odd-odd nuclei. Experimental determinations ofthe level density are rather scarce in such nuclei. Inparticular, the only isotopic chain for which systematicdata exist is that of the Europium [10]. Experimentallevel densities at low excitation energies were taken from ! " % & ’ ()*’(+*’ (,*’(-*’(.*’(/*’ ’ !2)$$-3’ ’ ’ : ’ ; ’ ;;< ’ ;:< ; ’ ;65 ’ ’ : ’ ’ : ’ ’ : ’ ’ ’ ’ ’ ’’’ ’ < ’ ’ ’ ’ ’ < ’ : ’ ’ : ’ ’ :;5 ’ :74 ’ ::4 ’ :60 ’ <46 ; ’ <;5 ; ’ <:6 ’ ’ ’ : ’ ’ ’ : ’ ’ : ’ ’’’’’’ ; ’ ’ ’ ; ’ ’ ’ ’ ; ’ ’ ’ ’ : ’ ; ’ ’ ’ ; ’ ’ :7’’70’’;7’’’’0’’ ’70’’’’’’ ’70’’’’’’0’800’’’’70’’’’’’0’ ’ ’70’’’’’0’8700’’’’’’’’’’’8500’’’’’’’’’’’8:00’’’’’’’’’’’8<00’’6<0’’’’’’’’’’’80<0’’’’’’’’’’’88<0’’’’’’’’’’8;<0’’ FIG. 3: The GASPAN program fits to the spectrum of Fig. 1(a). The peaks are labeled with the level energy in keV (see TableI). A residue spectrum with two standard deviations statistical limit is shown below each graph. The six graphs correspond tothe six groups of levels displayed in Table I.
Ref. [11], where the parameters of simple level densitymodels, such as the back-shifted Fermi gas (BSFG) orthe constant temperature (CT) models were determinedby fitting the experimental low-excitation complete levelschemes and the level density at the neutron binding en-ergy. In the BSFG model, the total level density is de-scribed as ρ ( E ) = e √ a ( E − E √ σa / ( E − E ) / , where E is the ex-citation energy, a and E are two empirical parametersand σ is the spin cutoff parameter [11]. The parameter a of the BSFG model may be taken as a measure of the leveldensity: for nuclei with comparable masses, the larger a ,the larger is the level density [10]. Figure 4 shows the evo-lution of the experimental a parameter known for threeodd-odd Eu isotopes: Eu,
Eu, and
Eu. For thesethree isotopes, the knowledge of the low-excitation levelscheme is considered complete within the following exci- tation energy/spin windows: (0–0.39 MeV)/(0 – 5¯ h ) for Eu, (0 – 0.49 MeV)/(1 – 5¯ h ) for Eu, and (0 – 0.35MeV)/(1 – 4¯ h ) for Eu, respectively [11]. In Fig. 4 itis seen that the experimental a has the largest value at N = 89, near the critical point of the control parameter N , and decreases with increasing N .Since Eu is far from the critical point of the phasetransition, we expect a relatively low level density in thisnucleus, compared to that of the isotopes of mass 152 to156. In order to examine the available data from a larger N region we adopt here a simplified procedure. For this,we will directly compare the number of levels known inthese nuclei up to an excitation energy of 0.35 MeV. Thisexcitation energy range was chosen because it is commonto the three nuclei in which complete level schemes exist( N = 89, 91, and 93). The number of states up to 0.35MeV is 83, 60, and 24 for N = 89, 91, and 93, respectively
84 86 88 90 92 94 96 N a [ M e V - ] . l n ( N . / . ) [ M e V - ] FIG. 4: (Color online) The experimental a parameter of theBSFG model level densities [11] (black triangles) and the sim-plified level density of levels up to 0.35 MeV excitation (circlesand dotted line). [12].For N = 95 ( Eu) we count a number of 13 lev-els up to 0.35 MeV excitation (Table I). Given the spinvalues covered by the two experiments , it is likely thatthis level scheme is well known up to this energy, closeto completeness (within the same spin range as that ofthe three lighter isotopes). Actually, a few missing levelswould not significantly alter our conclusions. For N = 87( Eu), we have a similar situation, with a number ofabout 13 levels [12]. In Fig. 4 we represent also a roughlevel density determined as the number of levels per MeV, N . /0.35 (where N . is the number of levels counted up to an excitation energy of 0.35 MeV), arbitrarily nor-malized such as its logarithm approximately scales as the a parameter. This approximate low-energy level densityshows the same pattern as that of the experimental a parameter. Eu (at N = 95) continues the decreasingtrend of the level density with increasing N . On the otherside of N = 89, Eu also displays a rather low value.With the points added now at N = 87 and N = 95 onecan see that the low-energy level density of Eu odd-oddnuclei displays a well defined maximum at N = 89.In conclusion, a large number of excited states,close to 60, have been determined up to about 1.5MeV excitation for the odd-odd nucleus Eu, froma spectrum of the
Gd(d, α ) Eu reaction measuredat 10 ◦ . Although the experiment was limited to thismeasurement and could not provide spin/parity valueassignments, it allowed an examination of the low-energynumber of levels in the Eu isotopes with N from 87 to95. The low-energy level density determined for Eusmoothly continues the decreasing trend of the lighterisotopes.Partial support for this work within the TE67/2018project with the UEFISCDI Romanian research fundingAgency is aknowledged. The authors thank the techni-cal staff of the Tandem accelerator for the good qualitybeam. This was the last transfer reaction experiment(of the Romanian authors) with the Q3D spectrographof the tandem accelerator laboratory in Garching – Mu-nich, which will be closed at the end of 2019. [1] D. Bucurescu, E. Dr˘agulescu, S. Pascu, H-F. Wirth, D.Filipescu, G. C˘ata-Danil, I. C˘ata-Danil, D. Deleanu, K.Eppinger, T. Faestermann, D.G. Ghit¸˘a, T. Glodariu, R.Hertenberger, M. Iva¸scu, R. Kruecken, N. M˘arginean,R. M˘arginean, C. Mihai, A. Negret, T. Sava. L. Stroe,K. Wimmer, and N.V. Zamfir, Phys. Rev.
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